Modal Interferometers Based on a Tapered Special Photonic Crystal Fiber for Highly Sensitive Detection

*Vladimir (or Uladzimir) P. Minkovich, Joel Villatoro and Pavel V. Minkovich*

## **Abstract**

The use of a tapered special photonic crystal fiber (PCF) with collapsed air holes in the waist (the thinnest part of a taper) for highly sensitive detection of strain, high temperature, and fast detection of hydrogen with concentrations between 1.2 and 5.6 vol.% and biosensing is demonstrated. In the tapered PCF, a fundamental core mode couples to a few modes of the solid taper waist. Owing to the beating between the waist modes, the transmission spectra of the tapered PCF exhibit several interference peaks, which are sensitive to refractive index changes of a medium that surrounds the taper and also to changes of a taper length. The changes can be visualized as a shift of the peaks in the output spectrum pattern.

**Keywords:** modal interferometer, optical fiber devices, optical fiber sensors, interferometry, photonic crystal fiber

## **1. Introduction**

Photonic crystal fibers (PCFs), also known as microstructured or holey optical fibers [1–4], consist of a waveguiding core surrounded by a system of air channels in glass cladding that run along the length of the fiber and arranged in a hexagonal structure around the core. The structure of PCFs enables new possibilities for optical sensing in comparison with standard optical fibers. The most common approach consists of making a sample to interact with the evanescent fields of the PCF guided modes [5–7]. To do so one has to fill the holes with the sample, a gas or liquid, for example, and then the analysis or detection is carried out. In some situation such a process may be inconvenient or impractical. Mach-Zehnder modal interferometers (MZMIs) based on no adiabatic tapered silica PCFs, first fabricated in our facilities [8–10], are attractive for sensing application because of their intrinsic advantages, such as simplicity of fabrication and practical using, high sensitivity, small size, and immunity to electromagnetic interference and their aptitude for remote measurements. Initially, our MZMIs were used for high-resolution refractive index sensing of liquids with indices ranging from 1.41 to 1.45 [8]. In this work, it is presented

fabrication such MZMIs and also their application for detection (with a very high sensitivity) of strain, high temperature, and fast detection of hydrogen with concentrations between 1.2 and 5.6 vol.% or for biosensing.

## **2. PCF taper fabrication and operating mechanism**

To fabricate tapers we employed a homemade quasi-single-mode large-modearea PCF consisting of a solid core surrounded by four rings of air holes in a cladding arranged in a hexagonal pattern [11]. A micrograph of a cleaved end face of our PCF before the tapering is shown in **Figure 1** (left). The parameters of our PCF are outer diameter of 125 μm, core diameter of 11 μm, average hole diameter of 2.7 μm, and average hole spacing (pitch) of 5.45 μm. To reduce the PCF diameter, the fiber is heated with an oscillating high-temperature flame torch and slowly stretched ("slow-and-hot" method). A Vytran GPX3400 glass-processing machine also can be used. At such a no adiabatic tapering process, a waist of the PCF (the thinnest part of a taper) can be reduced until the air holes collapse, obtaining a piece of a solid fiber with the diameter *ρW* ~ <33 μm, which can support multiple modes (waist modes). In the first transition zone, see **Figure 1** (right), some energy from the PCF fundamental mode passes to a few waist modes.

The beating of these modes inside the solid waist section is sensitive to an external environment, since the propagation constants of the waist modes depend on it. In the final transition zone, the waist modes are again transformed into the PCF fundamental mode, which intensity is determined by the phase difference between the waist modes [9]. The resulting mode carries the interference information generated at the tapered zone to a detector. If, for the simplicity, we consider only two waist modes for the interference with effective refractive indices *n1* and *n2*, then, intensity output is

$$I\_t = I\_1 + I\_2 + 2\sqrt{I\_1 I\_2} \cos(\Delta \theta),\tag{1}$$

where *I*1 and *I*2 are the intensities of the interactive waist modes, respectively, and *Δθ* is the phase difference between them. This phase difference creates the output pattern and depends on the difference between the effective waist mode refractive indices (*Δn*) and the length of the waist *L*0:

$$
\Delta\theta = \frac{2\pi}{\lambda} (\Delta n) \, L\_0,\tag{2}
$$

**73**

**Figure 2.**

*Modal Interferometers Based on a Tapered Special Photonic Crystal Fiber for Highly Sensitive…*

There are a number of applications in which the monitoring of straininduced changes is important. Some designs based on standard optical fibers have been reported in the literature. For example, strain sensors based on in-fiber gratings [12] and Brillouin scattering [13] are commercially available. The main shortage of these strain sensors is their high thermal sensitivity [14]. In this case, one needs to simultaneously and independently measure strain and temperature [12, 13]. So, the complexity of the sensor is increased. It is necessary to mention that a few attempts to sense strain with PCFs have been reported in the literature at the beginning of our study. They include the use of Brillouin frequency shift [15], long-period grating [16], and fiber Bragg grating [17, 18]. However, these sensors also exhibit an undesirable cross sensitivity to temperature. The application of our tapered PCFs with collapsed air holes for temperature-independent strain sensing is described in this section [19, 20]. Using the fiber, and the tapering process as described in a previous section, a silica PCF taper with waist diameter *ρW* = 28 μm and *L*0 = 5 mm was fabricated. **Figure 2** shows the normalized transmission spectra of the used PCF before (dotted line) and after (continuous line) a no adiabatic tapering process.

*Image of the cross section of an untapered PCF (left) used to fabricate our tapers and illustration of a uniform-waist tapered PCF (right).* L0 *is the length of the uniform waist, and* ρW *is the taper waist diameter.*

The measurements were carried out in a measuring setup consisting of an LED, with peak emission at 1540 and 40 nm of spectral width, and an optical spectrum

*Normalized transmission spectra of the PCF before (dotted curve) and after (continuous curve) tapering. The* 

*taper waist diameter is 28 μm (reprinted with permission from Ref. [19], OSA).*

*DOI: http://dx.doi.org/10.5772/intechopen.82458*

**3. Strain detection**

**Figure 1.**

where *λ* is the center wavelength of the light source used. The interferometer transmittance maxima will be at *2πΔnL*0/*λ* = 2*πm*, where *m* is an integer. Peaks in the output spectrum pattern will be appeared at wavelengths given by *λ<sup>m</sup>* ≈ *ΔnL*0/*m*, and the spacing between consecutive peaks (period) is provided by *P* ≈ *λ* 2 /*ΔnL*0. When the refractive index of the surrounding medium is changed, *Δn* is changed too (keeping *L*0 fixed), and a change of phase is generated. This change can be visualized as a peak shift in the output spectrum pattern. The shift in the output spectrum pattern is also happened, when *L*0 is changed [9]. It should be pointed out that additional losses, because of PCF tapering, were found to be typically below 3 dB. To test our sensors, we implemented a simple light transmission measuring setup consisting of a low-power light-emitting diode (LED) with peak emission at 1280 nm (or 1550 nm) and about 40–80 nm of spectral width and an optical spectrum analyzer (OSA), Ando AQ-6315E. The tapered PCFs (with a PCF full length of approximately 30 cm) were fusion spliced between standard fibers (SMF-28), and the tapered section was held straight and secured in a mount in all the experiments.

*Modal Interferometers Based on a Tapered Special Photonic Crystal Fiber for Highly Sensitive… DOI: http://dx.doi.org/10.5772/intechopen.82458*

**Figure 1.**

*Interferometry - Recent Developments and Contemporary Applications*

concentrations between 1.2 and 5.6 vol.% or for biosensing.

**2. PCF taper fabrication and operating mechanism**

from the PCF fundamental mode passes to a few waist modes.

*It* = *I*<sup>1</sup> + *I*<sup>2</sup> + 2√

Δ*θ* = \_\_\_ <sup>2</sup>*<sup>π</sup>*

refractive indices (*Δn*) and the length of the waist *L*0:

fabrication such MZMIs and also their application for detection (with a very high sensitivity) of strain, high temperature, and fast detection of hydrogen with

To fabricate tapers we employed a homemade quasi-single-mode large-modearea PCF consisting of a solid core surrounded by four rings of air holes in a cladding arranged in a hexagonal pattern [11]. A micrograph of a cleaved end face of our PCF before the tapering is shown in **Figure 1** (left). The parameters of our PCF are outer diameter of 125 μm, core diameter of 11 μm, average hole diameter of 2.7 μm, and average hole spacing (pitch) of 5.45 μm. To reduce the PCF diameter, the fiber is heated with an oscillating high-temperature flame torch and slowly stretched ("slow-and-hot" method). A Vytran GPX3400 glass-processing machine also can be used. At such a no adiabatic tapering process, a waist of the PCF (the thinnest part of a taper) can be reduced until the air holes collapse, obtaining a piece of a solid fiber with the diameter *ρW* ~ <33 μm, which can support multiple modes (waist modes). In the first transition zone, see **Figure 1** (right), some energy

The beating of these modes inside the solid waist section is sensitive to an external environment, since the propagation constants of the waist modes depend on it. In the final transition zone, the waist modes are again transformed into the PCF fundamental mode, which intensity is determined by the phase difference between the waist modes [9]. The resulting mode carries the interference information generated at the tapered zone to a detector. If, for the simplicity, we consider only two waist modes for the interference with effective refractive indices *n1* and *n2*, then, intensity output is

\_\_\_\_

where *I*1 and *I*2 are the intensities of the interactive waist modes, respectively, and *Δθ* is the phase difference between them. This phase difference creates the output pattern and depends on the difference between the effective waist mode

where *λ* is the center wavelength of the light source used. The interferometer transmittance maxima will be at *2πΔnL*0/*λ* = 2*πm*, where *m* is an integer. Peaks in the output spectrum pattern will be appeared at wavelengths given by *λ<sup>m</sup>* ≈ *ΔnL*0/*m*,

When the refractive index of the surrounding medium is changed, *Δn* is changed too (keeping *L*0 fixed), and a change of phase is generated. This change can be visualized as a peak shift in the output spectrum pattern. The shift in the output spectrum pattern is also happened, when *L*0 is changed [9]. It should be pointed out that additional losses, because of PCF tapering, were found to be typically below 3 dB. To test our sensors, we implemented a simple light transmission measuring setup consisting of a low-power light-emitting diode (LED) with peak emission at 1280 nm (or 1550 nm) and about 40–80 nm of spectral width and an optical spectrum analyzer (OSA), Ando AQ-6315E. The tapered PCFs (with a PCF full length of approximately 30 cm) were fusion spliced between standard fibers (SMF-28), and the tapered section was held straight and secured in a mount in all the experiments.

and the spacing between consecutive peaks (period) is provided by *P* ≈ *λ*

*I*<sup>1</sup> *I*<sup>2</sup> cos(*Δθ*), (1)

<sup>λ</sup> (Δ*n*)*L*0, (2)

2 /*ΔnL*0.

**72**

*Image of the cross section of an untapered PCF (left) used to fabricate our tapers and illustration of a uniform-waist tapered PCF (right).* L0 *is the length of the uniform waist, and* ρW *is the taper waist diameter.*

## **3. Strain detection**

There are a number of applications in which the monitoring of straininduced changes is important. Some designs based on standard optical fibers have been reported in the literature. For example, strain sensors based on in-fiber gratings [12] and Brillouin scattering [13] are commercially available. The main shortage of these strain sensors is their high thermal sensitivity [14]. In this case, one needs to simultaneously and independently measure strain and temperature [12, 13]. So, the complexity of the sensor is increased. It is necessary to mention that a few attempts to sense strain with PCFs have been reported in the literature at the beginning of our study. They include the use of Brillouin frequency shift [15], long-period grating [16], and fiber Bragg grating [17, 18]. However, these sensors also exhibit an undesirable cross sensitivity to temperature. The application of our tapered PCFs with collapsed air holes for temperature-independent strain sensing is described in this section [19, 20]. Using the fiber, and the tapering process as described in a previous section, a silica PCF taper with waist diameter *ρW* = 28 μm and *L*0 = 5 mm was fabricated. **Figure 2** shows the normalized transmission spectra of the used PCF before (dotted line) and after (continuous line) a no adiabatic tapering process.

The measurements were carried out in a measuring setup consisting of an LED, with peak emission at 1540 and 40 nm of spectral width, and an optical spectrum

#### **Figure 2.**

*Normalized transmission spectra of the PCF before (dotted curve) and after (continuous curve) tapering. The taper waist diameter is 28 μm (reprinted with permission from Ref. [19], OSA).*

analyzer with a resolution of 0.1 nm. It is possible to note that the transmission of our untapered PCF is basically the output spectrum of the LED used. However, the spectrum of the 28-μm-thick taper exhibits a series of peaks, two of which are higher than the others. For this taper we investigated the shift of the interference peaks caused by longitudinal strain. The PCF was fixed between two displacement mechanical mounts, with the tapered section in the middle. Then the fiber was stretched using the calibrated micrometer screws of the mounts. **Figure 3(a)** shows the normalized spectra, measured at 1540 nm, of the taper, when it has been subjected to 0 (continuous curve), 1100 (dashed curve), and 2200 (dotted curve) με. In this figure we can see shift of the initial spectrum to shorter wavelengths, when the strain is increased. When the strain was removed from the sensor, all the peaks returned to their baselines. At this point, we exchanged the LED for another with peak emission at 1300 nm and repeated the experiments. **Figure 3(b)** shows the normalized spectra, measured at 1300 nm, of the taper, when it also subjected to three applied strains: 0 (continuous curve), 1100 (dashed curve), and 2200 (dotted curve) με. It is possible to see in this figure that the transmission spectrum of the device also exhibits interference peaks near 1300 nm and that such peaks also shift to shorter wavelengths. Note from **Figure 3** that the height of some peaks increases and that of others decreases. All the peaks, however, maintain almost the same shape. The influence of temperature on the peaks was also investigated. The taper subjected to 0 με was exposed to different temperatures between 0 and 180°C. In that range of temperatures the interference peaks did not suffer any shift, but, at higher temperatures, the peaks shifted to longer wavelength. We did not carry out measurements below 0°C because of technical limitations. Hence, a no adiabatic tapered silica PCF with collapsed air holes can be used for temperature-independent strain sensing.

The advantage of the sensor is that one can monitor one or all the peaks. In addition, different wavelengths can be used to interrogate the sensor. **Figure 4** shows the peak shift as a function of the applied strain, when the initial peaks are centered around 1520 and 1250 nm, see **Figure 3(a)** and **(b)**, respectively. It is possible to

#### **Figure 3.**

*Normalized transmission spectra of a 28-μm-thick tapered PCF under three applied strains measured at (a) 1550 and (b) 1330 nm. In both figures the continuous curves represent 0 με, the dashed curves 1100 με, and dotted curves 2200 με (reprinted with permission from Ref. [19], OSA).*

**75**

*Modal Interferometers Based on a Tapered Special Photonic Crystal Fiber for Highly Sensitive…*

note from the figure that the shift of both peaks has a linear behavior and the slope of both lines is basically the same. The observed shift of the other peaks shown in **Figure 3** was also linear, and their slope was similar to that of the peaks shown in **Figure 4**. The experiments were carried out several times. It was observed that in all

*Typical shift of the peaks as a function of the applied strain (reprinted with permission from Ref. [19], OSA).*

It is important to point out that optical fiber interferometric strain sensors are useful devices, because they can provide important information or solutions in a number of applications of practical interest. These sensors, incorporated into civil aircraft and spacecraft structures, smart materials, active devices and components, etc., permit the monitoring of strain-induced changes suffered by such structures, materials, or components. In all these applications, temperature-independent, intrinsic, and wavelength-encoded strain sensors with high resolution are desirable.

It is known variety of standard fiber-based temperature sensors, for both point and distributed detection. The sensing mechanisms include [21] fluorescence and time decay effects in active materials and doped fibers, remote blackbody radiation, Raman and Brillouin scattering, interferometry, and Bragg or long-period grating technology. The large majority of reported so far fiber temperature sensors have been designed to operate in a range from −20 to 200°C. However, there are some applications in which high-temperature sensing is necessary, for example, for monitoring furnace operation or volcanic events, or in fire alarm systems, etc. [22]. Most of the techniques mentioned in this chapter before are not suitable for high-temperature sensing. Materials traditionally used for fluorescence-based fiber thermometers have an inferior fluorescence intensity emission at temperatures above 600°C [23, 24]. Some interferometric temperature sensors can be designed for measurement of temperatures higher than 1600°C [25, 26]. However, their construction is complicated and a sensing element is external to the fiber. Important advances have been made to fabricate fiber Bragg grating devices for measurement of high temperatures [23], but these devices require a complicated fabrication process or a long and controlled temperature treatment [27–29]. A long-period grating

cases the sensor was reversible in the 0–8000 με range.

**4. High-temperature detection**

**Figure 4.**

*DOI: http://dx.doi.org/10.5772/intechopen.82458*

*Modal Interferometers Based on a Tapered Special Photonic Crystal Fiber for Highly Sensitive… DOI: http://dx.doi.org/10.5772/intechopen.82458*

#### **Figure 4.**

*Interferometry - Recent Developments and Contemporary Applications*

analyzer with a resolution of 0.1 nm. It is possible to note that the transmission of our untapered PCF is basically the output spectrum of the LED used. However, the spectrum of the 28-μm-thick taper exhibits a series of peaks, two of which are higher than the others. For this taper we investigated the shift of the interference peaks caused by longitudinal strain. The PCF was fixed between two displacement mechanical mounts, with the tapered section in the middle. Then the fiber was stretched using the calibrated micrometer screws of the mounts. **Figure 3(a)** shows the normalized spectra, measured at 1540 nm, of the taper, when it has been subjected to 0 (continuous curve), 1100 (dashed curve), and 2200 (dotted curve) με. In this figure we can see shift of the initial spectrum to shorter wavelengths, when the strain is increased. When the strain was removed from the sensor, all the peaks returned to their baselines. At this point, we exchanged the LED for another with peak emission at 1300 nm and repeated the experiments. **Figure 3(b)** shows the normalized spectra, measured at 1300 nm, of the taper, when it also subjected to three applied strains: 0 (continuous curve), 1100 (dashed curve), and 2200 (dotted curve) με. It is possible to see in this figure that the transmission spectrum of the device also exhibits interference peaks near 1300 nm and that such peaks also shift to shorter wavelengths. Note from **Figure 3** that the height of some peaks increases and that of others decreases. All the peaks, however, maintain almost the same shape. The influence of temperature on the peaks was also investigated. The taper subjected to 0 με was exposed to different temperatures between 0 and 180°C. In that range of temperatures the interference peaks did not suffer any shift, but, at higher temperatures, the peaks shifted to longer wavelength. We did not carry out measurements below 0°C because of technical limitations. Hence, a no adiabatic tapered silica PCF with collapsed air holes can be used for temperature-independent strain sensing. The advantage of the sensor is that one can monitor one or all the peaks. In addition, different wavelengths can be used to interrogate the sensor. **Figure 4** shows the peak shift as a function of the applied strain, when the initial peaks are centered around 1520 and 1250 nm, see **Figure 3(a)** and **(b)**, respectively. It is possible to

*Normalized transmission spectra of a 28-μm-thick tapered PCF under three applied strains measured at (a) 1550 and (b) 1330 nm. In both figures the continuous curves represent 0 με, the dashed curves 1100 με, and* 

*dotted curves 2200 με (reprinted with permission from Ref. [19], OSA).*

**74**

**Figure 3.**

*Typical shift of the peaks as a function of the applied strain (reprinted with permission from Ref. [19], OSA).*

note from the figure that the shift of both peaks has a linear behavior and the slope of both lines is basically the same. The observed shift of the other peaks shown in **Figure 3** was also linear, and their slope was similar to that of the peaks shown in **Figure 4**. The experiments were carried out several times. It was observed that in all cases the sensor was reversible in the 0–8000 με range.

It is important to point out that optical fiber interferometric strain sensors are useful devices, because they can provide important information or solutions in a number of applications of practical interest. These sensors, incorporated into civil aircraft and spacecraft structures, smart materials, active devices and components, etc., permit the monitoring of strain-induced changes suffered by such structures, materials, or components. In all these applications, temperature-independent, intrinsic, and wavelength-encoded strain sensors with high resolution are desirable.

## **4. High-temperature detection**

It is known variety of standard fiber-based temperature sensors, for both point and distributed detection. The sensing mechanisms include [21] fluorescence and time decay effects in active materials and doped fibers, remote blackbody radiation, Raman and Brillouin scattering, interferometry, and Bragg or long-period grating technology. The large majority of reported so far fiber temperature sensors have been designed to operate in a range from −20 to 200°C. However, there are some applications in which high-temperature sensing is necessary, for example, for monitoring furnace operation or volcanic events, or in fire alarm systems, etc. [22]. Most of the techniques mentioned in this chapter before are not suitable for high-temperature sensing. Materials traditionally used for fluorescence-based fiber thermometers have an inferior fluorescence intensity emission at temperatures above 600°C [23, 24]. Some interferometric temperature sensors can be designed for measurement of temperatures higher than 1600°C [25, 26]. However, their construction is complicated and a sensing element is external to the fiber. Important advances have been made to fabricate fiber Bragg grating devices for measurement of high temperatures [23], but these devices require a complicated fabrication process or a long and controlled temperature treatment [27–29]. A long-period grating

inscribed with a pulsed CO2 laser in a PCF [30] or a very small stub of indexguiding PCF fusion spliced between two standard single-mode fibers [31] can be also used for high-temperature measurements. We have proposed a novel hightemperature sensor based on the developed PCF taper with collapsed air holes in the waist [32, 33]. The PCF taper with *ρw* = 31 μm and *L*0 = 5 mm (see **Figure 1**) was used for high-temperature measurements. Before the tapering, a few centimeters of the referred PCF were inserted between two standard single-mode fibers (SMF-28) by fusion splicing. Then the PCF was slowly stretched, while a section of length *L*<sup>0</sup> was heated at a high temperature (at about 1000°C). It is important to point out that the PCF can also be tapered without the need of splicing it with conventional optical fibers. The fabricated taper was placed within a pure silica capillary tube, in order to have the taper straight during experiments (bending affects the sensor response). Then, the whole set was placed into a temperature chamber. To interrogate the device, light was injected from an LED with a peak emission at 1290

#### **Figure 5.**

*(a) Normalized transmission spectrum of a taper with* ρw *= 31 μm and* L0 *= 5 mm, at different temperatures. (b) Position of the highest peak of the spectrum (a) versus temperature. The filled triangles (heating) and the hollow circles (cooling) are experimental values. The solid line is a linear fit to the data in the 200–1000°C range (reprinted with permission from Ref. [32], IEEE).*

**77**

*Modal Interferometers Based on a Tapered Special Photonic Crystal Fiber for Highly Sensitive…*

and with 80 nm of spectral width. The output spectrum was monitored with an optical spectrum analyzer (OSA) with a resolution of 0.1 nm. We also realized our experiments using an LED, with a center wavelength at 1520 nm and with 40 nm of spectral width. The heating or cooling of the taper in the furnace was conducted in steps of 50°C. In each step of heating or cooling, one waited for about 30 min before collecting any data. With this procedure a homogeneous temperature inside the chamber was ensured. The exhibited around 1300 nm transmission spectra of the referred taper at temperatures of 200°C (solid line), 600°C (dashed line), and 1000°C (dotted line) are shown in **Figure 5(a)**. Measurements for temperatures above 1000°C were not possible for limitations of our furnace. In the plots of **Figure 5(a)**, we can see that the interference peaks shift toward longer wavelengths as the temperature increases. We have also found that the shift of the peaks shown in **Figure 5(a)** using the LED centered at 1290 nm and the shift of the peaks using the LED centered at 1520 nm (is not shown) are similar. This means that the central peak of the LED is not important. One also can see that the peaks are not deformed, when the device is exposed to a temperature higher than 1000°C. This is so, because the fiber was made of pure silica and the taper was fabricated, when the PCF was exposed to a high-temperature flame (of approximately 1000°C). The experiments were repeated several times in a period of 4 weeks, and it was observed the same behavior of the sensor. The position of the highest peak maximum for the spectrum

*DOI: http://dx.doi.org/10.5772/intechopen.82458*

of **Figure 5(a)** versus temperature is shown in **Figure 5(b)**.

bine them with a fitting algorithm.

**5. Gas detection**

One can see that the peaks are insensitive to temperature in the 0–180°C range; but they shift linearly to longer wavelengths in the 200–1000°C range. The slope of the curve in such a range is 12 pm/°C. Deviations from this line were, in our opinion, due to errors in the readings of the furnace temperature and also in the definition of the peak maxima position. The resolution of the sensor can be improved using thinner tapers, which exhibit sharper peaks that are easier to monitor.

Unfortunately, thinner tapers are more difficult to work with. Another possibility to improve the sensor resolution is to monitor all the interference peaks and to com-

To the beginning of our study, several sensors that exploit the direct interaction of evanescent fields of PCF guided modes with the target gas within the holes of unmodified PCFs have been proposed and demonstrated [5, 34–37]. The walls of the PCF air holes can also be covered with thin layers for a selective detection of specific gases [38]. Unfortunately, the filling of the air holes with a target gas is not convenient enough, since it takes a long time. Theoretical and experimental studies have shown that the time for a gas to diffuse into the very small holes of a PCF takes about tens of seconds to several minutes and depends on the fiber length [34]. To the time needed for a gas to diffuse into the holes of a PCF, one has to add the time needed to detect, analyze, and process the signal. Leaving the microscopic holes open in a PCF is also not convenient, since they can be filled with undesirable microparticles or moisture that can block the holes or change an output signal. In some potentially explosive or flammable environment, for example, in hydrogen environments, fast gas detection is necessary, and a rapid response of the sensor is desirable [39]. It is necessary also to remind that even existent this time hydrogen sensors have the response time not fast enough [40, 41]. We proposed the use of developed tapered PCFs, coated with thin layers, which can absorb the sensing gas or chemicals, for faster detection. In the taper waist (see **Figure 1**), the external medium plays the role of cladding, and the solid waist section plays the role of core. Therefore, a thin layer deposited on a waist region will attenuate or absorb the

## *Modal Interferometers Based on a Tapered Special Photonic Crystal Fiber for Highly Sensitive… DOI: http://dx.doi.org/10.5772/intechopen.82458*

and with 80 nm of spectral width. The output spectrum was monitored with an optical spectrum analyzer (OSA) with a resolution of 0.1 nm. We also realized our experiments using an LED, with a center wavelength at 1520 nm and with 40 nm of spectral width. The heating or cooling of the taper in the furnace was conducted in steps of 50°C. In each step of heating or cooling, one waited for about 30 min before collecting any data. With this procedure a homogeneous temperature inside the chamber was ensured. The exhibited around 1300 nm transmission spectra of the referred taper at temperatures of 200°C (solid line), 600°C (dashed line), and 1000°C (dotted line) are shown in **Figure 5(a)**. Measurements for temperatures above 1000°C were not possible for limitations of our furnace. In the plots of **Figure 5(a)**, we can see that the interference peaks shift toward longer wavelengths as the temperature increases. We have also found that the shift of the peaks shown in **Figure 5(a)** using the LED centered at 1290 nm and the shift of the peaks using the LED centered at 1520 nm (is not shown) are similar. This means that the central peak of the LED is not important. One also can see that the peaks are not deformed, when the device is exposed to a temperature higher than 1000°C. This is so, because the fiber was made of pure silica and the taper was fabricated, when the PCF was exposed to a high-temperature flame (of approximately 1000°C). The experiments were repeated several times in a period of 4 weeks, and it was observed the same behavior of the sensor. The position of the highest peak maximum for the spectrum of **Figure 5(a)** versus temperature is shown in **Figure 5(b)**.

One can see that the peaks are insensitive to temperature in the 0–180°C range; but they shift linearly to longer wavelengths in the 200–1000°C range. The slope of the curve in such a range is 12 pm/°C. Deviations from this line were, in our opinion, due to errors in the readings of the furnace temperature and also in the definition of the peak maxima position. The resolution of the sensor can be improved using thinner tapers, which exhibit sharper peaks that are easier to monitor. Unfortunately, thinner tapers are more difficult to work with. Another possibility to improve the sensor resolution is to monitor all the interference peaks and to combine them with a fitting algorithm.

## **5. Gas detection**

*Interferometry - Recent Developments and Contemporary Applications*

inscribed with a pulsed CO2 laser in a PCF [30] or a very small stub of indexguiding PCF fusion spliced between two standard single-mode fibers [31] can be also used for high-temperature measurements. We have proposed a novel hightemperature sensor based on the developed PCF taper with collapsed air holes in the waist [32, 33]. The PCF taper with *ρw* = 31 μm and *L*0 = 5 mm (see **Figure 1**) was used for high-temperature measurements. Before the tapering, a few centimeters of the referred PCF were inserted between two standard single-mode fibers (SMF-28) by fusion splicing. Then the PCF was slowly stretched, while a section of length *L*<sup>0</sup> was heated at a high temperature (at about 1000°C). It is important to point out that the PCF can also be tapered without the need of splicing it with conventional optical fibers. The fabricated taper was placed within a pure silica capillary tube, in order to have the taper straight during experiments (bending affects the sensor response). Then, the whole set was placed into a temperature chamber. To interrogate the device, light was injected from an LED with a peak emission at 1290

*(a) Normalized transmission spectrum of a taper with* ρw *= 31 μm and* L0 *= 5 mm, at different temperatures. (b) Position of the highest peak of the spectrum (a) versus temperature. The filled triangles (heating) and the hollow circles (cooling) are experimental values. The solid line is a linear fit to the data in the 200–1000°C* 

**76**

**Figure 5.**

*range (reprinted with permission from Ref. [32], IEEE).*

To the beginning of our study, several sensors that exploit the direct interaction of evanescent fields of PCF guided modes with the target gas within the holes of unmodified PCFs have been proposed and demonstrated [5, 34–37]. The walls of the PCF air holes can also be covered with thin layers for a selective detection of specific gases [38]. Unfortunately, the filling of the air holes with a target gas is not convenient enough, since it takes a long time. Theoretical and experimental studies have shown that the time for a gas to diffuse into the very small holes of a PCF takes about tens of seconds to several minutes and depends on the fiber length [34]. To the time needed for a gas to diffuse into the holes of a PCF, one has to add the time needed to detect, analyze, and process the signal. Leaving the microscopic holes open in a PCF is also not convenient, since they can be filled with undesirable microparticles or moisture that can block the holes or change an output signal. In some potentially explosive or flammable environment, for example, in hydrogen environments, fast gas detection is necessary, and a rapid response of the sensor is desirable [39]. It is necessary also to remind that even existent this time hydrogen sensors have the response time not fast enough [40, 41]. We proposed the use of developed tapered PCFs, coated with thin layers, which can absorb the sensing gas or chemicals, for faster detection. In the taper waist (see **Figure 1**), the external medium plays the role of cladding, and the solid waist section plays the role of core. Therefore, a thin layer deposited on a waist region will attenuate or absorb the

evanescent fields of different propagating waist modes. As a result, the output pattern of the tapered fiber will be also modified. Thus, the sensing of different gases or any other chemicals is observable. To confirm of the principle, we demonstrated the sensing of hydrogen [42, 43]. Hydrogen is one of the cleanest energy sources. It can be used in many chemical processes and in various fields, for example, as propellant in aerospace rockets, fuel for fuel cells, or engines in automotive devices. However, hydrogen is extremely flammable and can be explosive in air at room temperature and pressure even at concentrations of 4 vol.% and of course at more ones [39]. Therefore, fast detection of hydrogen at low concentrations is necessary. To do so, an ultrathin palladium layer was deposited on a solid section of a tapered PCF. It is well known that a thin palladium (or palladium alloy or composite) film can selectively and reversibly absorb hydrogen [39, 44–51]. When a Pd or Pd-alloy film is exposed to hydrogen, it is converted to PdH. The hydration of the thin film makes the real and imaginary part of the film dielectric constants to decrease [45, 49]. Such changes in the Pd film are possible to monitor with optical methods [39, 44–51].

Using the same fiber, and the same tapering process as in previous sections, a silica PCF taper with waist diameter *ρ*w = 28 μm and *L*0 = 10 mm was fabricated. An 8-nm-thin film was deposited on the waist of the tapered PCF over a length of 10 mm. The palladium film was deposited in a high-vacuum chamber by thermal evaporation. The sensor was tested (at normal conditions) in a gas chamber, which had an inlet and outlet to allow the hydrogen or the hydrogen/ carrier mixture to flow in and out. Nitrogen was used as a carrier gas. The flow of nitrogen and hydrogen was controlled individually with mass flow controllers. The sensor is tested in a transmission measurement setup consisting of a low-power LED with peak emission at 1290 and 80 nm of spectral width and an OSA. The spectra of the device were recorded and analyzed at different concentrations of hydrogen. Before measurements, about 30 cm of the PCF was fusion spliced between two standard single-mode fibers to decrease the sensor cost, and then the tapered section was held straight in a mechanical mount during all the experiments. Results of our experiments are presented in **Figure 6**. The top side plots in **Figure 6** show the spectra that were received, when the sensor was exposed to hydrogen concentrations between 1.2 and 5.6%. Four peaks of the spectra are numbered for convenience. Intensity of the peaks 1–4 as a function of hydrogen concentrations is presented in the bottom side of **Figure 6**. One can see that the intensity of the peaks increases in a nonlinear manner with the increase of the hydrogen concentration. For hydrogen concentrations, more than 6% the sensor exhibited spectra similar to that at 5.6%, which indicated the saturation of the 8-nm-thick palladium film. The reason of increase of the obtained peak intensity is because the index of the thin palladium film decreases, when it is exposed to hydrogen [45, 47, 49]. Such a decrement of the index causes the absorption of the evanescent fields to decrease. The remarkable increment of the peak intensity demonstrates the high sensitivity of the sensor. The sensor response time (the time required for the sensor to reach 90% of transmission change) was approximately 10 s. In **Figure 6** one can see that the intensity changes are more in the peaks or maxima than in the valleys or minima. One can also note that the intensity changes at longer wavelengths, see peaks 3 and 4, are more pronounced than at shorter wavelengths, see peaks 1 and 2. This is due to the fact that the attenuation of the palladium film increases, when the wavelength augments, according to the increase of the evanescent fields [47].

The interferometric hydrogen sensor reported here is more compact, simpler, and also faster than other interferometer-based hydrogen sensors reported in the literature [39, 44–46, 50].

**79**

**Figure 6.**

**6. Highly sensitive biosensing**

*Modal Interferometers Based on a Tapered Special Photonic Crystal Fiber for Highly Sensitive…*

Previous experimental studies of modal interferometers, for the biosensing refractive index (RI) range (1.33–1.34), have informed about sensitivities of 320 nm/ RIU for a sensing length of PCF (~3.0 mm) [52] and sensitivities of 1629 nm/RIU for a longer sensing length (~24 mm) [53]. PCF MZMIs based on no adiabatic tapered fibers are attractive for biosensing applications, because they can have a very small sensing length [8, 10]. Unfortunately, PCF MZMI RI sensors for biosensing applications usually can only be used to detect a solution with one analyte and when the RI dependence of an analyte at different concentrations is known. To obtain a specific sensitivity for a chosen analyte in some complex solutions, we coated the sensing surface (tapered PCF) of our RI sensor with a layer of an active biological component (an immobilization method), characterized by having a high affinity with the chosen analyte. The usual immobilization method, for glass substrates, is

*Transmission spectra of a tapered PCF coated with an 8-nm-thick Pd film at different hydrogen concentrations (top) and relative increment of the peaks 1–4 as a function of hydrogen concentration (bottom). Parameters of* 

*the sensor:* ρw *= 28 μm,* L0 *= 10 mm (reprinted with permission from Ref. [42], OSA).*

*DOI: http://dx.doi.org/10.5772/intechopen.82458*

*Modal Interferometers Based on a Tapered Special Photonic Crystal Fiber for Highly Sensitive… DOI: http://dx.doi.org/10.5772/intechopen.82458*

**Figure 6.**

*Interferometry - Recent Developments and Contemporary Applications*

monitor with optical methods [39, 44–51].

evanescent fields of different propagating waist modes. As a result, the output pattern of the tapered fiber will be also modified. Thus, the sensing of different gases or any other chemicals is observable. To confirm of the principle, we demonstrated the sensing of hydrogen [42, 43]. Hydrogen is one of the cleanest energy sources. It can be used in many chemical processes and in various fields, for example, as propellant in aerospace rockets, fuel for fuel cells, or engines in automotive devices. However, hydrogen is extremely flammable and can be explosive in air at room temperature and pressure even at concentrations of 4 vol.% and of course at more ones [39]. Therefore, fast detection of hydrogen at low concentrations is necessary. To do so, an ultrathin palladium layer was deposited on a solid section of a tapered PCF. It is well known that a thin palladium (or palladium alloy or composite) film can selectively and reversibly absorb hydrogen [39, 44–51]. When a Pd or Pd-alloy film is exposed to hydrogen, it is converted to PdH. The hydration of the thin film makes the real and imaginary part of the film dielectric constants to decrease [45, 49]. Such changes in the Pd film are possible to

Using the same fiber, and the same tapering process as in previous sections, a silica PCF taper with waist diameter *ρ*w = 28 μm and *L*0 = 10 mm was fabricated. An 8-nm-thin film was deposited on the waist of the tapered PCF over a length of 10 mm. The palladium film was deposited in a high-vacuum chamber by thermal evaporation. The sensor was tested (at normal conditions) in a gas chamber, which had an inlet and outlet to allow the hydrogen or the hydrogen/ carrier mixture to flow in and out. Nitrogen was used as a carrier gas. The flow of nitrogen and hydrogen was controlled individually with mass flow controllers. The sensor is tested in a transmission measurement setup consisting of a low-power LED with peak emission at 1290 and 80 nm of spectral width and an OSA. The spectra of the device were recorded and analyzed at different concentrations of hydrogen. Before measurements, about 30 cm of the PCF was fusion spliced between two standard single-mode fibers to decrease the sensor cost, and then the tapered section was held straight in a mechanical mount during all the experiments. Results of our experiments are presented in **Figure 6**. The top side plots in **Figure 6** show the spectra that were received, when the sensor was exposed to hydrogen concentrations between 1.2 and 5.6%. Four peaks of the spectra are numbered for convenience. Intensity of the peaks 1–4 as a function of hydrogen concentrations is presented in the bottom side of **Figure 6**. One can see that the intensity of the peaks increases in a nonlinear manner with the increase of the hydrogen concentration. For hydrogen concentrations, more than 6% the sensor exhibited spectra similar to that at 5.6%, which indicated the saturation of the 8-nm-thick palladium film. The reason of increase of the obtained peak intensity is because the index of the thin palladium film decreases, when it is exposed to hydrogen [45, 47, 49]. Such a decrement of the index causes the absorption of the evanescent fields to decrease. The remarkable increment of the peak intensity demonstrates the high sensitivity of the sensor. The sensor response time (the time required for the sensor to reach 90% of transmission change) was approximately 10 s. In **Figure 6** one can see that the intensity changes are more in the peaks or maxima than in the valleys or minima. One can also note that the intensity changes at longer wavelengths, see peaks 3 and 4, are more pronounced than at shorter wavelengths, see peaks 1 and 2. This is due to the fact that the attenuation of the palladium film increases, when the wavelength augments, according to the increase of the evanescent fields [47].

The interferometric hydrogen sensor reported here is more compact, simpler, and also faster than other interferometer-based hydrogen sensors reported in the

**78**

literature [39, 44–46, 50].

*Transmission spectra of a tapered PCF coated with an 8-nm-thick Pd film at different hydrogen concentrations (top) and relative increment of the peaks 1–4 as a function of hydrogen concentration (bottom). Parameters of the sensor:* ρw *= 28 μm,* L0 *= 10 mm (reprinted with permission from Ref. [42], OSA).*

## **6. Highly sensitive biosensing**

Previous experimental studies of modal interferometers, for the biosensing refractive index (RI) range (1.33–1.34), have informed about sensitivities of 320 nm/ RIU for a sensing length of PCF (~3.0 mm) [52] and sensitivities of 1629 nm/RIU for a longer sensing length (~24 mm) [53]. PCF MZMIs based on no adiabatic tapered fibers are attractive for biosensing applications, because they can have a very small sensing length [8, 10]. Unfortunately, PCF MZMI RI sensors for biosensing applications usually can only be used to detect a solution with one analyte and when the RI dependence of an analyte at different concentrations is known. To obtain a specific sensitivity for a chosen analyte in some complex solutions, we coated the sensing surface (tapered PCF) of our RI sensor with a layer of an active biological component (an immobilization method), characterized by having a high affinity with the chosen analyte. The usual immobilization method, for glass substrates, is

through the process of silanization, followed by the covalent bonding of an antigen or antibody [52, 54]. In [52], a detection limit of 10 μg/ml was demonstrated for streptavidin using a modal interferometer based on a short piece of PCF (~3.0 mm) spliced between two standard single-mode fibers, while in [55], a modal interferometer based on a thin-core fiber spliced between two standard single-mode fibers was used, and a detection limit of 1.1 ng/ml was achieved. In this paragraph, we inform about a MZMI based on a no adiabatic tapered special silica PCF acting as a highly sensitive biosensor. We also demonstrated that as a refractometer, it has good sensitivity in the RI range of interest for biological solutions and a record detection limit of 125 pg/ml of a protein concentration as a biosensor [56, 57]. In our experiments we used a homemade large-mode-area photonic crystal fiber. A cross section of the untapered fiber is shown in **Figure 7(a)**. The used fiber has an average hole spacing (pitch) *Λ* of 5.45 μm, an average hole diameter *d* of 2.7 μm, and an external diameter of 125 μm. The modal properties of the fiber are explained in [11]. To reduce our sensor cost, we spliced about 30 cm of the PCF between two standard SMF-28 single-mode fibers. The difficulty in splicing the PCF with the used standard SMF is that each one requires different temperatures to reach the needed fusion conditions. A commercial splicing machine, Sumitomo Type-46S, was used in the process. The splicing configuration is shown in **Figure 7(b)**. We used a Vytran GPX3400 glassprocessing machine to make the no adiabatic tapering. The tapered fiber for our sensor was fabricated with both transition regions (down taper and up taper) being symmetrical with a length of 5 mm, a waist length of 10 mm, and a waist diameter of 18.1 μm, like the one presented as an example in [58] on a base of a standard fiber. The pulling speed of the fiber holding blocks was kept at a rate of 1 mm/s, while the heat was set at 90 W. We used an LED source with a center wavelength of 1550 nm and an optical spectrum analyzer (OSA), Ando AQ-6315E, which has a resolution of up to 0.05 nm, to make the SM-PC-SM fiber transmission spectrum measurements, as shown in **Figure 8(a)**. To make it easier to measure aqueous solutions with the fiber sensor, a work cell, shown in **Figure 8(b)**, was designed.

The cell was fabricated with a working volume of 50 μl and a cavity length of 13 mm. To test a sensitivity of our device for biosensing RI range, solutions of sodium chloride (NaCl) diluted in distilled water were prepared in the following concentrations, 0.0, 0.2, 0.4, 0.6, 0.8, and 1 M, with corresponding refractive indices at 1550 nm of 1.30864, 1.31104, 1.31339, 1.31569, 1.31794, and 1.32014 [59]. An antigen-antibody test was proposed to evaluate the performance of the device for a biosensor application. We chose the bovine serum albumin (BSA) antigen because of its low cost, ease of handling, availability, and immobilization (covalent binding between the molecule and the transducer surface), which has been widely studied. The immobilization process was conducted like the

**Figure 7.**

*(a) PCF untapered cross section, (b) SM-PCF splicing configuration (reprinted with permission from Ref. [56], IEEE/OSA).*

**81**

**Figure 9.**

*IEEE/OSA).*

the anti-BSA concentration.

*Modal Interferometers Based on a Tapered Special Photonic Crystal Fiber for Highly Sensitive…*

one presented in [54]. Preliminary, the activation of the taper surface with an aminosilane APTES was made, and then the BSA antigen was covalent coupled to the taper surface. After the antigen-immobilization process, the performance tests were conducted by passing the respective antibody (anti-BSA) diluted in phosphate-buffered saline (PBS) buffer at different concentrations (125, 12.5, 1.25, and 0.125 ng/ml) over the sensitive sensor's surface. All tests were carried out at room temperature, at about 25°C. The protocol used for the tests was as follows. Step 1: Apply tris(hydroxymethyl)aminomethane (TRIS) buffer for 3 min to clean and break previous bonds. Step 2: Remove the TRIS buffer, apply the PBS, and make a measurement of the optical spectrum that corresponds to the baseline. Step 3: Remove the PBS buffer, apply the desired antibody-PBS sample, and take measures for 10 min. Previous experiments have demonstrated that after 6 min of interaction, the variation of the signal can be neglected for practical measurements. For each sample, repeat the protocol. The difference in wavelength between a peak on the baseline and the same peak, measured after 8 min of sample interaction, is the biosensor response, which is directly related to the sample concentration. **Figure 9(a)** shows that as the refractive indices of the NaCl solutions increase, the peaks shift to longer wavelengths. Peaks with similar morphologies were selected for the analysis of the peak shifts. **Figure 9(b)** corresponds to the linear fit built by taking the wavelength of the peak maxima (between 1538 and 1548 nm) and correlating them with the respective RI. A sensitivity of 722.3 nm/RIU was achieved (with a linearity of 0.9965), which can be compared with other sensors reported. **Figure 10** shows the results of the biosensor application, where the magnitude of the response is directly proportional to

*(a) Transmission spectra of the sensor at different concentrations of NaCl, (b) linear fit of the sensor response for concentrations of NaCl with RI between 1.30864 and 1.32014 (reprinted with permission from Ref. [56],* 

*(a) Experimental setup, (b) work cell (reprinted with permission from Ref. [56], IEEE/OSA).*

*DOI: http://dx.doi.org/10.5772/intechopen.82458*

**Figure 8.**

*Modal Interferometers Based on a Tapered Special Photonic Crystal Fiber for Highly Sensitive… DOI: http://dx.doi.org/10.5772/intechopen.82458*

**Figure 8.** *(a) Experimental setup, (b) work cell (reprinted with permission from Ref. [56], IEEE/OSA).*

one presented in [54]. Preliminary, the activation of the taper surface with an aminosilane APTES was made, and then the BSA antigen was covalent coupled to the taper surface. After the antigen-immobilization process, the performance tests were conducted by passing the respective antibody (anti-BSA) diluted in phosphate-buffered saline (PBS) buffer at different concentrations (125, 12.5, 1.25, and 0.125 ng/ml) over the sensitive sensor's surface. All tests were carried out at room temperature, at about 25°C. The protocol used for the tests was as follows. Step 1: Apply tris(hydroxymethyl)aminomethane (TRIS) buffer for 3 min to clean and break previous bonds. Step 2: Remove the TRIS buffer, apply the PBS, and make a measurement of the optical spectrum that corresponds to the baseline. Step 3: Remove the PBS buffer, apply the desired antibody-PBS sample, and take measures for 10 min. Previous experiments have demonstrated that after 6 min of interaction, the variation of the signal can be neglected for practical measurements. For each sample, repeat the protocol. The difference in wavelength between a peak on the baseline and the same peak, measured after 8 min of sample interaction, is the biosensor response, which is directly related to the sample concentration. **Figure 9(a)** shows that as the refractive indices of the NaCl solutions increase, the peaks shift to longer wavelengths. Peaks with similar morphologies were selected for the analysis of the peak shifts. **Figure 9(b)** corresponds to the linear fit built by taking the wavelength of the peak maxima (between 1538 and 1548 nm) and correlating them with the respective RI. A sensitivity of 722.3 nm/RIU was achieved (with a linearity of 0.9965), which can be compared with other sensors reported. **Figure 10** shows the results of the biosensor application, where the magnitude of the response is directly proportional to the anti-BSA concentration.

#### **Figure 9.**

*(a) Transmission spectra of the sensor at different concentrations of NaCl, (b) linear fit of the sensor response for concentrations of NaCl with RI between 1.30864 and 1.32014 (reprinted with permission from Ref. [56], IEEE/OSA).*

*Interferometry - Recent Developments and Contemporary Applications*

fiber sensor, a work cell, shown in **Figure 8(b)**, was designed.

The cell was fabricated with a working volume of 50 μl and a cavity length of 13 mm. To test a sensitivity of our device for biosensing RI range, solutions of sodium chloride (NaCl) diluted in distilled water were prepared in the following concentrations, 0.0, 0.2, 0.4, 0.6, 0.8, and 1 M, with corresponding refractive indices at 1550 nm of 1.30864, 1.31104, 1.31339, 1.31569, 1.31794, and 1.32014 [59]. An antigen-antibody test was proposed to evaluate the performance of the device for a biosensor application. We chose the bovine serum albumin (BSA) antigen because of its low cost, ease of handling, availability, and immobilization (covalent binding between the molecule and the transducer surface), which has been widely studied. The immobilization process was conducted like the

*(a) PCF untapered cross section, (b) SM-PCF splicing configuration (reprinted with permission from* 

through the process of silanization, followed by the covalent bonding of an antigen or antibody [52, 54]. In [52], a detection limit of 10 μg/ml was demonstrated for streptavidin using a modal interferometer based on a short piece of PCF (~3.0 mm) spliced between two standard single-mode fibers, while in [55], a modal interferometer based on a thin-core fiber spliced between two standard single-mode fibers was used, and a detection limit of 1.1 ng/ml was achieved. In this paragraph, we inform about a MZMI based on a no adiabatic tapered special silica PCF acting as a highly sensitive biosensor. We also demonstrated that as a refractometer, it has good sensitivity in the RI range of interest for biological solutions and a record detection limit of 125 pg/ml of a protein concentration as a biosensor [56, 57]. In our experiments we used a homemade large-mode-area photonic crystal fiber. A cross section of the untapered fiber is shown in **Figure 7(a)**. The used fiber has an average hole spacing (pitch) *Λ* of 5.45 μm, an average hole diameter *d* of 2.7 μm, and an external diameter of 125 μm. The modal properties of the fiber are explained in [11]. To reduce our sensor cost, we spliced about 30 cm of the PCF between two standard SMF-28 single-mode fibers. The difficulty in splicing the PCF with the used standard SMF is that each one requires different temperatures to reach the needed fusion conditions. A commercial splicing machine, Sumitomo Type-46S, was used in the process. The splicing configuration is shown in **Figure 7(b)**. We used a Vytran GPX3400 glassprocessing machine to make the no adiabatic tapering. The tapered fiber for our sensor was fabricated with both transition regions (down taper and up taper) being symmetrical with a length of 5 mm, a waist length of 10 mm, and a waist diameter of 18.1 μm, like the one presented as an example in [58] on a base of a standard fiber. The pulling speed of the fiber holding blocks was kept at a rate of 1 mm/s, while the heat was set at 90 W. We used an LED source with a center wavelength of 1550 nm and an optical spectrum analyzer (OSA), Ando AQ-6315E, which has a resolution of up to 0.05 nm, to make the SM-PC-SM fiber transmission spectrum measurements, as shown in **Figure 8(a)**. To make it easier to measure aqueous solutions with the

**80**

**Figure 7.**

*Ref. [56], IEEE/OSA).*

**Figure 10.**

*Sensor response for concentrations of anti-BSA between 0.125 and 125 ng/ml (reprinted with permission from Ref. [56], IEEE/OSA).*

We can see in **Figure 10** that the sensor can take measurements of concentrations as low as 125 pg/ml; this means that our detection limit is lower than the one reported in [58]. Another fact to highlight is that our sensor is capable to detect a specific protein inside a complex sample (with different proteins diluted) that is not possible for the sensor proposed in [58]. The increased sensitivity in our case is possible, when compared with that in [58], because in [58] the detection of protein concentrations was done by reading a change in the refractive index of the bulk solution; therefore, higher concentrations were needed to produce a change big enough to be detected by the sensor. In our case, the antigen of the target molecule was immobilized onto the transducer surface, making it possible to detect the antigen-antibody interaction with higher sensitivity. The changes in refractive index near the surface are mostly affected by the coupling of the specific protein and not by other proteins in the sample. In addition, the area near the surface of the fiber has exponentially higher sensitivity than areas that are farther away. The developed sensor also has a lower detection limit when compared with those reported in [52, 55], with detection limits of 10 and 1.1 ng/ml, respectively, outperforming the former in three orders of magnitude and the latter in one order of magnitude. It is also necessary to point out that the estimated maximum resolution of our sensor was found to be around 1 × 10<sup>−</sup><sup>2</sup> ng/ml, considering that the resolution of the spectrum analyzer used was 0.05 nm. The higher resolution of our measurements is possible at using an OSA with higher resolution. More precise localization of interference fringes by performing a Fourier transformation will be also helpful [60]. As can be also seen in **Figure 10**, we did not have any saturation in a sensor response for concentrations of anti-BSA between 0.125 and 125 ng/ml, although the spectral shift had highly nonlinear dependence on the anti-BSA concentration. Comparing with **Figure 10**, where we had a linear dependence of our sensor response and did not have any chemical binding between NaCl solutions and the taper surface, one can conclude that the antibody-antigen binding process has a great impact on our sensor response. A definition of the impact requires further investigations.

## **7. Conclusions**

In this chapter, a special homemade quasi-single-mode PCF was used for fabrication of no adiabatic tapered fibers with a solid waist. The fabrication of tapers is simple and takes only few minutes. It is also possible to control the process of tapering at all times. It has been found that in PCF tapers with waist diameters small

**83**

provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

1 Division of Photonics, Centro de Investigaciones en Optica, Leon, GTO, Mexico

2 Department of Communications Engineering, University of the Basque Country,

3 Ikerbasque-Basque Foundation for Science, Bilbao, Spain

4 Mogilev State Medical College, Mogilev, Belarus

\*Address all correspondence to: vladimir@cio.mx

*Modal Interferometers Based on a Tapered Special Photonic Crystal Fiber for Highly Sensitive…*

enough (thinner than 33 μm), the air holes of a PCF cladding were collapsed. A waist of such tapers consists of a solid multimode fiber supporting multiple modes. The interference between such modes gives series of peaks in an output spectrum pattern. The peaks are sensitive to a medium that surrounds the taper and also to the length of the waist, since the propagation constants of the interfering modes depend on them. Any changes in a surrounding medium or in the length of the taper are visualized as a shift of peaks in the output spectrum pattern. The tapers were used for fabrication of very sensitive interferometric devices with selective transmission for temperature-insensitive detection (in the 0–180°C range) of microstrain, for sensing of high temperature in the 200–1000°C range, and for fast detection of hydrogen concentrations between 1.2 and 5.6 vol.%. Moreover, the developed interferometers can be used for detection of interaction between a BSA antigen and an anti-BSA antibody with a record detection limit of 125 pg/ml of antibody concentration. The parameters that are necessary to measure by using the interferometers are transformed into the shift of peaks in the output spectrum pattern. It is not difficult by using an optical spectrum analyzer to monitor the shift. Detection is fast and takes approximately 10 s. It is necessary also to note that the output spectrum patterns are stable and immune to possible fluctuations of a light source power.

The authors of the chapter would like to thank their colleagues and co-authors of joint publications Monzon-Hernandez D, Kir'yanov AV, Calixto S, Sotsky AB, Sotskaya LI, Badenes G, Betancur-Ochoa JE, and Montagut-Ferizzola YJ for long-

\*, Joel Villatoro2,3 and Pavel V. Minkovich4

*DOI: http://dx.doi.org/10.5772/intechopen.82458*

**Acknowledgements**

**Author details**

Bilbao, Spain

term and productive scientific cooperation.

Vladimir (or Uladzimir) P. Minkovich1

*Modal Interferometers Based on a Tapered Special Photonic Crystal Fiber for Highly Sensitive… DOI: http://dx.doi.org/10.5772/intechopen.82458*

enough (thinner than 33 μm), the air holes of a PCF cladding were collapsed. A waist of such tapers consists of a solid multimode fiber supporting multiple modes. The interference between such modes gives series of peaks in an output spectrum pattern. The peaks are sensitive to a medium that surrounds the taper and also to the length of the waist, since the propagation constants of the interfering modes depend on them. Any changes in a surrounding medium or in the length of the taper are visualized as a shift of peaks in the output spectrum pattern. The tapers were used for fabrication of very sensitive interferometric devices with selective transmission for temperature-insensitive detection (in the 0–180°C range) of microstrain, for sensing of high temperature in the 200–1000°C range, and for fast detection of hydrogen concentrations between 1.2 and 5.6 vol.%. Moreover, the developed interferometers can be used for detection of interaction between a BSA antigen and an anti-BSA antibody with a record detection limit of 125 pg/ml of antibody concentration. The parameters that are necessary to measure by using the interferometers are transformed into the shift of peaks in the output spectrum pattern. It is not difficult by using an optical spectrum analyzer to monitor the shift. Detection is fast and takes approximately 10 s. It is necessary also to note that the output spectrum patterns are stable and immune to possible fluctuations of a light source power.

## **Acknowledgements**

*Interferometry - Recent Developments and Contemporary Applications*

We can see in **Figure 10** that the sensor can take measurements of concentrations as low as 125 pg/ml; this means that our detection limit is lower than the one reported in [58]. Another fact to highlight is that our sensor is capable to detect a specific protein inside a complex sample (with different proteins diluted) that is not possible for the sensor proposed in [58]. The increased sensitivity in our case is possible, when compared with that in [58], because in [58] the detection of protein concentrations was done by reading a change in the refractive index of the bulk solution; therefore, higher concentrations were needed to produce a change big enough to be detected by the sensor. In our case, the antigen of the target molecule was immobilized onto the transducer surface, making it possible to detect the antigen-antibody interaction with higher sensitivity. The changes in refractive index near the surface are mostly affected by the coupling of the specific protein and not by other proteins in the sample. In addition, the area near the surface of the fiber has exponentially higher sensitivity than areas that are farther away. The developed sensor also has a lower detection limit when compared with those reported in [52, 55], with detection limits of 10 and 1.1 ng/ml, respectively, outperforming the former in three orders of magnitude and the latter in one order of magnitude. It is also necessary to point out that the estimated maximum resolution of our sensor was found to be around 1 × 10<sup>−</sup><sup>2</sup> ng/ml, considering that the resolution of the spectrum analyzer used was 0.05 nm. The higher resolution of our measurements is possible at using an OSA with higher resolution. More precise localization of interference fringes by performing a Fourier transformation will be also helpful [60]. As can be also seen in **Figure 10**, we did not have any saturation in a sensor response for concentrations of anti-BSA between 0.125 and 125 ng/ml, although the spectral shift had highly nonlinear dependence on the anti-BSA concentration. Comparing with **Figure 10**, where we had a linear dependence of our sensor response and did not have any chemical binding between NaCl solutions and the taper surface, one can conclude that the antibody-antigen binding process has a great impact on our sensor response. A definition of the impact

*Sensor response for concentrations of anti-BSA between 0.125 and 125 ng/ml (reprinted with permission from* 

In this chapter, a special homemade quasi-single-mode PCF was used for fabrication of no adiabatic tapered fibers with a solid waist. The fabrication of tapers is simple and takes only few minutes. It is also possible to control the process of tapering at all times. It has been found that in PCF tapers with waist diameters small

**82**

requires further investigations.

**7. Conclusions**

**Figure 10.**

*Ref. [56], IEEE/OSA).*

The authors of the chapter would like to thank their colleagues and co-authors of joint publications Monzon-Hernandez D, Kir'yanov AV, Calixto S, Sotsky AB, Sotskaya LI, Badenes G, Betancur-Ochoa JE, and Montagut-Ferizzola YJ for longterm and productive scientific cooperation.

## **Author details**

Vladimir (or Uladzimir) P. Minkovich1 \*, Joel Villatoro2,3 and Pavel V. Minkovich4

1 Division of Photonics, Centro de Investigaciones en Optica, Leon, GTO, Mexico

2 Department of Communications Engineering, University of the Basque Country, Bilbao, Spain

3 Ikerbasque-Basque Foundation for Science, Bilbao, Spain

4 Mogilev State Medical College, Mogilev, Belarus

\*Address all correspondence to: vladimir@cio.mx

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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[18] Frazão O, Carvalho JP, Ferreira LA, Araujo FM, Santos JL. Discrimination of strain and temperature using Bragg gratings in microstructured and standard optical fibers. Measurement Science and Technology. 2005;**16**:2109- 2113. DOI: 10.1088/0957-0233/16/10/028

[19] Villatoro J, Minkovich VP, Monzon-Hernandez D. Temperatureindependent strain sensor made of tapered holey optical fiber. Optics Letters. 2006;**31**:305-307. DOI: 10.1364/ OL.31.000305

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[26] Xiao H, Deng J, Pickrell G, May RG, Wang A. Single-crystal sapphire fiber-based strain sensor for hightemperature applications. Journal of Lightwave Technology. 2003;**21**:2276- 2283. DOI: 10.1109/JLT.2003.816882

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*Interferometry - Recent Developments and Contemporary Applications*

Modeling of holey fiber tapers with selective transmission for sensor application. Journal of Lightwave Technology. 2006;**24**:4319-4326. DOI:

10.1109/JLT.2006.884207

LPT.2006.875520

JOSAB.21.001161

10.1109/50.618377

[10] Villatoro J, Minkovich VP, Monzon-Hernandez D. Compact modal interferometer built with tapered microstructured optical fiber. IEEE Photonics Technology Letters. 2006;**18**:1258-1260. DOI: 10.1109/

[11] Minkovich VP, Kir'yanov AV, Sotsky AB, Sotskaya LI. Largemode-area holey fibers with a few air channels in cladding: Modeling and experimental investigation of the modal properties. Journal of the Optical Society of America B: Optical Physics. 2004;**21**:1161-1169. DOI: 10.1364/

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[14] Villatoro J, Finazzi V, Minkovich VP, Pruneri V, Badenes G. Temperature-

[15] Zou L, Bao X, Afshar S, Chen L. Dependence of the Brillouin frequency shift on strain and temperature in a photonic crystal fiber. Optics Letters. 2004;**29**:1485-1487. DOI: 10.1364/

DOI: 10.1006/ofte.2000.0344

insensitive photonic crystal fiber interferometer for absolute strain sensing. Applied Physics Letters. 2007;**91**:AD091109. DOI:

10.1063/1.2775326

OL.29.001485

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10.1126/science.1079280

298 p. ISBN: 1-4020-7610-X

10.1088/0957-0233/12/7/318

Photonic-crystal fiber as a

Chemical Society Reviews. 2013;**42**:8629-8648. DOI: 10.1039/

OPEX.13.003454

C3CS60128E

JLT.2006.885258

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[2] Russell P. Photonic crystal fibers. Science. 2003;**299**:358-362. DOI:

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hydrogen sensors. The Review of Scientific Instruments. 1999;**70**: 4370-4376. DOI: 10.1063/1.1150082

*Interferometry - Recent Developments and Contemporary Applications*

palladium-based fiber-optic sensors for molecular hydrogen detection. IEEE Sensors Journal. 2012;**12**:93-102. DOI:

[40] Huang P-C, Chen Y-P, Zhang G, Song H, Liu Y. Note: Durability analysis of optical fiber hydrogen sensor based on Pd-Y alloy film. The Review of Scientific Instruments. 2016;**87**:026104.

[41] Zhang Y-N, Wu Q, Peng H, Zhao Y.

interferometer with Pd/WO3 coating for real-time monitoring of dissolved hydrogen concentration in transformer

[43] Minkovich VP, Villatoro J, Sotsky AB. Tapered photonic crystal fibers coated with ultra-thin films for highly sensitive bio-chemical sensing. In: Proceedings of the European Optical Society Biennal Meeting (EOSAM); 8-12 October 2018. Netherlands: Delft; 2018.

[44] Butler MA. Optical fiber hydrogen sensor. Applied Physics Letters. 1984;**45**:1007-1009. DOI:

[45] Bearzotti A, Caliendo C, Verona E, D'Amico A. Integrated optic sensor for the detection of H2 concentrations. Sensors and Actuators B: Chemical. 1992;**7**:685-688. DOI: 10.1016/0925-4005(92)80386-C

[46] Wang C, Mandelis A, Garcia JA. Detectivity comparison between thin-film Pd/PVDF photopyroelectric interferometric and optical reflectance

10.1109/JSEN.2011.2138130

DOI: 10.1063/1.4941749

Photonic crystal fiber modal

oil. The Review of Scientific Instruments. 2016;**87**:125002. DOI:

[42] Minkovich VP, Monzon-Hernandez D, Villatoro J, Badenes G. Microstructured optical fiber coated with thin films for gas and chemical sensing. Optics Express. 2006;**14**:8413- 8418. DOI: 10.1364/OE.14.008413

10.1063/1.4971321

pp. 1-2

10.1063/1.95060

[31] Coviello G, Finazzi V, Villatoro J, Pruneri V. Thermally stabilized PCF-based sensor for temperature measurements up to 1000°C. Optics Express. 2009;**17**:21531-21559. DOI:

[32] Monzon-Hernandez D, Minkovich VP, Villatoro J. High-temperature sensing with tapers made of microstructured optical fibers. IEEE Photonics Technology Letters. 2006;**18**:511-513. DOI: 10.1109/

[33] Minkovich U. Special Photonic Crystal Fibers. Saarbrücken: Lambert Academic Publishing; 2011. 74 p. ISBN:

[34] Hoo YL, Jin W, Shi C, Ho HL, Wang DN, Ruan SC. Design and modeling of a photonic crystal fiber gas sensor. Applied Optics. 2003;**42**:3509-3515.

[35] Ritari T, Tuominen J, Ludvigsen H, Petersen JC, Sorensen T, Hansen TP, et al. Gas sensing using air-guiding photonic bandgap fibers. Optics Express. 2004;**12**:4080-4087. DOI:

10.1364/OE.17.021551

LPT.2005.863173

978-3-8465-3622-3

DOI: 10.1364/AO.42.003509

10.1364/OPEX.12.004080

OL.29.001476

msec.2005.10.43

[36] Pickrell G, Peng W, Wang A. Random-hole optical fiber evanescentwave gas sensing. Optics Letters. 2004;**29**:1476-1478. DOI: 10.1364/

[37] Fini JM. Microstructure fibres for optical sensing in gases and liquids. Measurement Science and Technology. 2004;**15**:1120-1128. DOI:

[38] Matejec V, Mrazek J, Hayer M, Kask I, Peterka P, Kanka J, et al.

[39] Silva SF, Coelho L, Frazão O, Santos JL, Malcata FX. A review of

Microstructure fibers for gas detection. Materials Science and Engineering: C. 2006;**26**:317-321. DOI: 10.1016/J.

10.1088/0957-0233/15/6/011

**86**

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[51] Xu T, Zach MP, Xiao ZL, Rosenmann D, Welp U, Kwok WK, et al. Self-assembled monolayerenhanced hydrogen sensing with ultrathin palladium films. Applied Physics Letters. 2005;**86**:203104. DOI: 10.1063/1.1929075

[52] Juan Hu DJ, Lim JL, Park MK, Kao LT-H, Wang Y, Wei H, et al. Photonic crystal fiber-based interferometric biosensor for streptavidin and biotin detection. IEEE Journal of Selected Topics in Quantum Electronics. 2012;**18**:1293-1297. DOI: 10.1109/ JSTQE.2011.2169492

[53] Li C, Qiu S-J, Chen Y, Xu F, Lu Y-Q. Ultra-sensitive refractive index sensor with slightly tapered photonic crystal fiber. IEEE Photonics Technology Letters. 2012;**24**:1771-1774. DOI: 10.1109/LPT.2012.2214379

[54] Nagel T, Ehrentreich-Forster E, Singh M, Shmitt K, Brandenburg A, Berka A, et al. Direct detection of tuberculosis infection in blood serum using three optical label-free approaches. Sensors and Actuators B: Chemical. 2008;**129**:934-940. DOI: 10.1016/j.snb.2007.10.009

[55] Yu W, Lang T, Bian J, Kong W. Labelfree fiber optic biosensor based on thincore modal interferometer. Sensors and Actuators B: Chemical. 2016;**228**:322-329. DOI: 10.1016/j.snb.2016.01.029

[56] Betancur-Ochoa JE, Minkovich VP, Montagut-Ferizzola YJ. Special photonic crystal modal interferometer for highly sensitive biosensing. Journal of Lightwave Technology. 2017;**35**:4747- 4751. DOI: 10.1109/JLT.2017.2761738

[57] Betancur-Ochoa JE, Minkovich VP, Montagut-Ferizzola YJ, Minkovich PV. Highly sensitive biosensing based on a photonic crystal fiber modal interferometer. In: Proceedings of OSA International Conference on Optical Fiber Sensors (OFS 26); 24-28 September 2018; Lausanne: OSA; 2018. p. WF58(1-4)

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Chapter 6

Abstract

Alexander Vladimirov

with the virus are demonstrated.

processes can occur simultaneously.

1. Introduction

89

estimation of time to failure, crack nucleation

Dynamic Speckle Interferometry

of Technical and Biological Objects

The theory of speckle dynamics in the image plane of a reflecting and thin transparent object is considered. It was assumed that the optical paths of the reflected and probing transparent object waves vary due to (1) translational motion, (2) oscillations with a period T, and (3) random relative displacements of pairs of scattering centers Δu (reflecting object) and random changes in the refractive index Δn (transparent object). The formulas relating the mean value, dispersion, and relaxation time of Δu and Δn values with the time-averaged radiation intensity at the observation point and the time autocorrelation function of this intensity are obtained. It is shown that at the averaging time multiple of T, the technique in real time allows to determine plastic deformations of the order of 10<sup>3</sup> on bases of the order of 10 microns, which is suitable for the control of elastic deformations on bases of the order of 100 microns. The possibilities of the method of averaged speckle images for the study of (1) features of the nucleation, start, and movement of the fatigue crack, and (2) the activity of living cells infected and not infected

Keywords: theory, experiment, high cycle fatigue, live cell, speckle dynamics,

If a rough object is illuminated by coherent radiation, macroscopically homogeneous but microscopically inhomogeneous distribution of scattered radiation intensity emerges at some distance from the object and behind the lens that forms the object image. As the surface microrelief heights are random, the waves reflected from various microscopic areas of the surface have random amplitudes and phases. Mutual interference of these waves results in spotted or "speckle" structure of scattered radiation. When the object surface varies for some reason, the amplitudes and phases of the reflected waves change, so the speckle pattern also varies. Variation of wave amplitudes and phases can be caused by displacement of the object or its rigid rotation or by small variations in the distances between the area elements due to elastic or plastic strains of the surface. The reason may be a small or strong surface microrelief variation due to corrosion or loosening of the material with ionizing radiation, material fatigue, etc. The specified macroscopic or microscopic

It is noteworthy that the speckle pattern can be formed when studying objects with a mirror surface by lighting them via mat glass. Phenomena occurring inside

## Chapter 6

## Dynamic Speckle Interferometry of Technical and Biological Objects

Alexander Vladimirov

## Abstract

The theory of speckle dynamics in the image plane of a reflecting and thin transparent object is considered. It was assumed that the optical paths of the reflected and probing transparent object waves vary due to (1) translational motion, (2) oscillations with a period T, and (3) random relative displacements of pairs of scattering centers Δu (reflecting object) and random changes in the refractive index Δn (transparent object). The formulas relating the mean value, dispersion, and relaxation time of Δu and Δn values with the time-averaged radiation intensity at the observation point and the time autocorrelation function of this intensity are obtained. It is shown that at the averaging time multiple of T, the technique in real time allows to determine plastic deformations of the order of 10<sup>3</sup> on bases of the order of 10 microns, which is suitable for the control of elastic deformations on bases of the order of 100 microns. The possibilities of the method of averaged speckle images for the study of (1) features of the nucleation, start, and movement of the fatigue crack, and (2) the activity of living cells infected and not infected with the virus are demonstrated.

Keywords: theory, experiment, high cycle fatigue, live cell, speckle dynamics, estimation of time to failure, crack nucleation

## 1. Introduction

If a rough object is illuminated by coherent radiation, macroscopically homogeneous but microscopically inhomogeneous distribution of scattered radiation intensity emerges at some distance from the object and behind the lens that forms the object image. As the surface microrelief heights are random, the waves reflected from various microscopic areas of the surface have random amplitudes and phases. Mutual interference of these waves results in spotted or "speckle" structure of scattered radiation. When the object surface varies for some reason, the amplitudes and phases of the reflected waves change, so the speckle pattern also varies. Variation of wave amplitudes and phases can be caused by displacement of the object or its rigid rotation or by small variations in the distances between the area elements due to elastic or plastic strains of the surface. The reason may be a small or strong surface microrelief variation due to corrosion or loosening of the material with ionizing radiation, material fatigue, etc. The specified macroscopic or microscopic processes can occur simultaneously.

It is noteworthy that the speckle pattern can be formed when studying objects with a mirror surface by lighting them via mat glass. Phenomena occurring inside transparent objects can be studied in a similar way. Such objects are live cells cultured or precipitated on a transparent substrate. If there is an empty space, the cells can alter their shape and the intracellular processes randomly change the phases of the waves that have passed via the cell. So, by the character of the speckle pattern change, one can study and monitor the phenomena occurring on the surface or near the surface of reflecting objects or inside transparent media.

deformations of the objects normally appear. That is why conventional approaches developed for devices exploited under the conditions of quasi-static loading are

The situation with high-cycle as well as giga-cycle fatigue is different. According to various literature sources, from 50 to 80% of equipment is destroyed due to highcycle fatigue [10–12]. Despite research history [13–16] and a great number of publications [17, 18], at present, there are no techniques for assessment and estimation of the remaining life of construction elements in their high-cycle fatigue that would meet the requirements of the engineering practice [11, 18]. According to [11, 18, 19], the situation has arisen due to absence of physical models of high-cycle fatigue. In the author's opinion, this circumstance is in turn related to absence of physical monitoring techniques that would permit to record the features of local fatigue damage accumulation without interruption of exploitation or fatigue testing of various objects. Analysis of studies [20–25] devoted to development of such methods shows that their practical application implies methodological issues. Immediately after the creation of lasers and detection of spotted or speckle structure of scattered radiation, speckles were used to study fatigue phenomena [26–28]. However, because of high manpower effort and no monotone character of

applicable for monitoring and estimating of the remaining object life.

Dynamic Speckle Interferometry of Technical and Biological Objects

DOI: http://dx.doi.org/10.5772/intechopen.81389

the recorded signal variation, the technique was not put to wide use.

static deformation of specimens up to their fracture [29, 30].

cycle fatigue conducted using this technique.

3. Theory

shown in Figure 1.

91

The author learnt the difficulties of fatigue phenomena studies using conventional nondestructive testing techniques at first hand. Early in our research aimed at the study of high-cycle material fatigue, we used various modifications of optical, X-ray, magnetic, electric, and acoustic techniques (13 in all). The results obtained using these techniques were negative. The parameters of the signals either did not vary or the variations were at the same level as the hardware noise. As in high-cycle fatigue localization of fatigue damage takes place [11], it was supposed that the obtained negative result is related to a large base (averaging region) of the applied techniques. Hence, for measurements on a small base, we upgraded a speckle technique that was previously successfully used to monitor the damage in quasi-

Section 3 presents the results of the theoretical studies aimed at developing an optical technique intended to study the irreversible processes emerging while testing specimens for high-cycle fatigue. Section 4 discusses the experiments with high-

This section discusses the results of theoretical underpinning of speckle techniques permitting the study of fatigue accumulation in periodical deformations of the objects. Sections 3.1 and 3.2 discuss the regularities of speckle dynamics observed while capturing the frames of the speckle image on fixed position of the object oscillations. Section 3.3 is dedicated to the theory of time-averaged speckle images.

3.1 Dynamic speckle interferometry of microscopic processes: reflecting object

A thin lens with focal distance f and diaphragm diameter D located in plane (ηх,ηz) forms the object image in plane (qх,qу). We regard all the waves at hand as linearly polarized in the same direction. We accept that phase φ<sup>j</sup> of complex amplitude а<sup>j</sup> of a wave scattered by the j-th center is random, and that the waves from all the scattering

! illu-

Let the source of coherent radiation with wavelength λ located at point s

minate the point scattering centers located in some region S in plane (x,y), as is

At present, one is familiar with application of variations, displacements, and interferences of speckle fields for the study of macroscopic phenomena, namely, for determination of transition, motion velocity, rotations, elastic or plastic strains of objects, gas, and fluid flows [1–7]. At the same time, the logic of speckle optics development and practical needs sets the task to analyze not only macroscopic but also microscopic processes occurring at the structural level. For example, a task like that appears in studies of the phenomena accompanying crack initiation in high-cycle fatigue of metallic materials as well as during the analysis of the processes occurring in the membranes and inside the cells of live systems. The rationale for such studies is related to development of a technique for assessing the remaining life of construction elements, and in case of biological objects, to individualized drug selection for a patient.

As the properties of materials are random at the structural level, the amplitudes and phases of the waves reflected from the object or that have passed through the object randomly vary in time and space. In the general case, the solution to the problem of establishing a relation between the parameters of wave phase dynamics and speckle dynamics is far from simple. Nevertheless, lately certain advances in solving such problems have been observed.

The objective of this publication is to familiarize the readers with the author's recent developments in the theory and application of dynamic speckle interferometry. They were aimed at study of the processes occurring in technical materials in their high-cycle fatigue and also in live cells subject to some external effects. The rationale for the specified studies, for the theory of the techniques proposed, the conducted experiments and their practical prospects are discussed in brief. The advantage of the techniques under discussion over the conventional speckle holographic techniques is the possibility for real-time study of reversible and irreversible processes. Most part of this chapter is devoted to dynamic speckle interferometry of high-cycle fatigue. When high-cycle fatigue is studied, the technique permits determination of the limiting local microrelief and surface shapes variations (deformations) with high sensitivity. When the variation rate of the named values is monitored, the time to the fatigue crack start can be determined. When the reaction of cells to viruses and bacteria is studied, an opportunity for timely development of procedures preventing and blocking their development progress appears.

## 2. High-cycle fatigue: the problems and the rationale for the studies

When technical objects are exploited, their various elements are affected by alternate forces. As load cycle number N in the materials increases, their properties change irreversibly resulting in fracture of the construction elements. In the literature, this phenomenon was called material fatigue. Depending on number Na, of the cycles preceding the fracture, we distinguish low-cycle, high-cycle, and giga-cycle fatigue. Their borders are rather blurred. It is usually supposed that a part was destroyed in low-cycle fatigue if Na < 104 . If a part is exploited at 10<sup>5</sup> < N < 10<sup>7</sup> , then high-cycle fatigue is supposed, and at N > 10<sup>8</sup> , the part is supposed to be exploited in giga-cycle fatigue.

At present, various features of low-cycle fatigue are fairly well characterized [8, 9]. It is explained by the fact that in low-cycle fatigue, sufficient plastic

## Dynamic Speckle Interferometry of Technical and Biological Objects DOI: http://dx.doi.org/10.5772/intechopen.81389

deformations of the objects normally appear. That is why conventional approaches developed for devices exploited under the conditions of quasi-static loading are applicable for monitoring and estimating of the remaining object life.

The situation with high-cycle as well as giga-cycle fatigue is different. According to various literature sources, from 50 to 80% of equipment is destroyed due to highcycle fatigue [10–12]. Despite research history [13–16] and a great number of publications [17, 18], at present, there are no techniques for assessment and estimation of the remaining life of construction elements in their high-cycle fatigue that would meet the requirements of the engineering practice [11, 18]. According to [11, 18, 19], the situation has arisen due to absence of physical models of high-cycle fatigue. In the author's opinion, this circumstance is in turn related to absence of physical monitoring techniques that would permit to record the features of local fatigue damage accumulation without interruption of exploitation or fatigue testing of various objects. Analysis of studies [20–25] devoted to development of such methods shows that their practical application implies methodological issues.

Immediately after the creation of lasers and detection of spotted or speckle structure of scattered radiation, speckles were used to study fatigue phenomena [26–28]. However, because of high manpower effort and no monotone character of the recorded signal variation, the technique was not put to wide use.

The author learnt the difficulties of fatigue phenomena studies using conventional nondestructive testing techniques at first hand. Early in our research aimed at the study of high-cycle material fatigue, we used various modifications of optical, X-ray, magnetic, electric, and acoustic techniques (13 in all). The results obtained using these techniques were negative. The parameters of the signals either did not vary or the variations were at the same level as the hardware noise. As in high-cycle fatigue localization of fatigue damage takes place [11], it was supposed that the obtained negative result is related to a large base (averaging region) of the applied techniques. Hence, for measurements on a small base, we upgraded a speckle technique that was previously successfully used to monitor the damage in quasistatic deformation of specimens up to their fracture [29, 30].

Section 3 presents the results of the theoretical studies aimed at developing an optical technique intended to study the irreversible processes emerging while testing specimens for high-cycle fatigue. Section 4 discusses the experiments with highcycle fatigue conducted using this technique.

## 3. Theory

transparent objects can be studied in a similar way. Such objects are live cells cultured or precipitated on a transparent substrate. If there is an empty space, the cells can alter their shape and the intracellular processes randomly change the phases of the waves that have passed via the cell. So, by the character of the speckle pattern change, one can study and monitor the phenomena occurring on the surface

At present, one is familiar with application of variations, displacements, and interferences of speckle fields for the study of macroscopic phenomena, namely, for determination of transition, motion velocity, rotations, elastic or plastic strains of objects, gas, and fluid flows [1–7]. At the same time, the logic of speckle optics development and practical needs sets the task to analyze not only macroscopic but also microscopic processes occurring at the structural level. For example, a task like that appears in studies of the phenomena accompanying crack initiation in high-cycle fatigue of metallic materials as well as during the analysis of the processes occurring in the membranes and inside the cells of live systems. The rationale for such studies is related to development of a technique for assessing the remaining life of construction elements, and in case of biological objects, to individualized drug selection for a patient. As the properties of materials are random at the structural level, the amplitudes and phases of the waves reflected from the object or that have passed through the object randomly vary in time and space. In the general case, the solution to the problem of establishing a relation between the parameters of wave phase dynamics and speckle dynamics is far from simple. Nevertheless, lately certain advances in

The objective of this publication is to familiarize the readers with the author's recent developments in the theory and application of dynamic speckle interferometry. They were aimed at study of the processes occurring in technical materials in their high-cycle fatigue and also in live cells subject to some external effects. The rationale for the specified studies, for the theory of the techniques proposed, the conducted experiments and their practical prospects are discussed in brief. The advantage of the techniques under discussion over the conventional speckle holographic techniques is the possibility for real-time study of reversible and irreversible processes. Most part of this chapter is devoted to dynamic speckle interferometry of high-cycle fatigue. When high-cycle fatigue is studied, the technique permits determination of the limiting local microrelief and surface shapes variations (deformations) with high sensitivity. When the variation rate of the named values is

monitored, the time to the fatigue crack start can be determined. When the reaction of cells to viruses and bacteria is studied, an opportunity for timely development of

2. High-cycle fatigue: the problems and the rationale for the studies

When technical objects are exploited, their various elements are affected by alternate forces. As load cycle number N in the materials increases, their properties change irreversibly resulting in fracture of the construction elements. In the literature, this phenomenon was called material fatigue. Depending on number Na, of the cycles preceding the fracture, we distinguish low-cycle, high-cycle, and giga-cycle fatigue. Their borders are rather blurred. It is usually supposed that a part was

At present, various features of low-cycle fatigue are fairly well characterized

[8, 9]. It is explained by the fact that in low-cycle fatigue, sufficient plastic

. If a part is exploited at 10<sup>5</sup> < N < 10<sup>7</sup>

, the part is supposed to be

,

procedures preventing and blocking their development progress appears.

or near the surface of reflecting objects or inside transparent media.

Interferometry - Recent Developments and Contemporary Applications

solving such problems have been observed.

destroyed in low-cycle fatigue if Na < 104

exploited in giga-cycle fatigue.

90

then high-cycle fatigue is supposed, and at N > 10<sup>8</sup>

This section discusses the results of theoretical underpinning of speckle techniques permitting the study of fatigue accumulation in periodical deformations of the objects. Sections 3.1 and 3.2 discuss the regularities of speckle dynamics observed while capturing the frames of the speckle image on fixed position of the object oscillations. Section 3.3 is dedicated to the theory of time-averaged speckle images.

### 3.1 Dynamic speckle interferometry of microscopic processes: reflecting object

Let the source of coherent radiation with wavelength λ located at point s ! illuminate the point scattering centers located in some region S in plane (x,y), as is shown in Figure 1.

A thin lens with focal distance f and diaphragm diameter D located in plane (ηх,ηz) forms the object image in plane (qх,qу). We regard all the waves at hand as linearly polarized in the same direction. We accept that phase φ<sup>j</sup> of complex amplitude а<sup>j</sup> of a wave scattered by the j-th center is random, and that the waves from all the scattering

Figure 1. Optical system for reflecting objects and designations.

centers come to an arbitrary point of plane (ηх,ηу). First, let us obtain an expression for radiation intensity I q!� � at some point <sup>q</sup> ! of the object image plane. For total complex amplitude A η !� � at arbitrary point <sup>η</sup> ! of plane (ηх,ηу), we have:

$$A\left(\overrightarrow{\eta}\right) = \sum\_{j=1}^{N} a\_j,\tag{1}$$

Let us take arbitrary point q

DOI: http://dx.doi.org/10.5772/intechopen.81389

� �

series in a small neighborhood of point r

� in the vicinity of points <sup>η</sup>

I q!� � <sup>¼</sup> A q!� � � <sup>A</sup><sup>∗</sup> <sup>q</sup>

lsx; lsy; lsz � � and l

function of radiation intensity η1, <sup>2</sup>ð Þ t1; t<sup>2</sup> at point q

the summation sign; Δϕκ ¼ kΔu<sup>κ</sup> ¼ kΔu<sup>κ</sup>

<sup>þ</sup> <sup>φ</sup>j, complex amplitude ffiffiffiffiffiffi

� in the vicinity of points <sup>r</sup>

A q!� � <sup>¼</sup> ffiffiffiffiffiffi

<sup>I</sup><sup>01</sup> <sup>p</sup> <sup>e</sup>

! ¼ l !

⇀

a diaphragm with diameter D and the center at point qr

Dynamic Speckle Interferometry of Technical and Biological Objects

!. Now, let N be the number of such centers.

wave going from point r

point qr

Ls !� � � � � � <sup>¼</sup> Ls ! r ! <sup>þ</sup> <sup>u</sup> ! � � � �

Lη ! r ! <sup>þ</sup> <sup>u</sup> ! � � � �

Lη ! q ! � � � � �

�

�

� �

A q!� � and I q!� �:

where ls ! ¼ ls !

N Nð Þ � 1 =2.

time points t<sup>1</sup> and t2.

point r ⇀

krj ! ls ! þ l � �!

93

� �

of the pattern equals 1, 22λL<sup>0</sup>

! <sup>¼</sup> qr

<sup>0</sup>=D, where L<sup>0</sup>

(qx,qy). Region with radius а<sup>s</sup> = bs/m, where m is the magnification of the lens, corresponds to regions with radius bs in plane (х,у). It is known that 85% of the energy of the wave that passed via the lens falls on the central spot of the Airy pattern. We will neglect the energy that falls on the sections beyond the region with radius bs. This in turn means that we suggest that the waves from the scattering centers located only in the region with radius а<sup>s</sup> with the center at point r

Let us further assume that the region with radius аs, values D, and u

derivatives to the first-order inclusive. Let us similarly expand expression

well as that from the lens to the image plane. Regarding expression

� as continuous function <sup>r</sup>

compared to the distances from the object to the radiation source and to the lens as

! ¼ r ⇀ <sup>q</sup>, u

! <sup>¼</sup> rq !, η

with the results in specified expansions in [31, 32]. Taking the obtained expansion, as well as formulas (3) and (2) into account, we in [31] obtained an expression for

! ¼ 0 and q

<sup>i</sup>ψ<sup>j</sup> ∑ N j¼1 e i kuj ! ls ! þ l � � � �!

!� � <sup>¼</sup> <sup>I</sup>01<sup>N</sup> <sup>þ</sup> <sup>2</sup>I<sup>01</sup> <sup>∑</sup>

lx; ly; lz

<sup>I</sup><sup>01</sup> <sup>p</sup> <sup>e</sup>

! ls ! þl � �, <sup>Δ</sup>u<sup>κ</sup>

vector of the κ-th pair of scattering centers; and Δθκ ¼ θ<sup>j</sup> � θm, j 6¼ m, κ = 1, 2…К, К =

Then, let us assume that process Δuκ(t) is random, and for а fixed κ, there is correlation of values Δu<sup>κ</sup> in time. Assuming that all the random values are independent, in [31], we obtained an expression for temporal normalized autocorrelation

where h i x<sup>1</sup> and h i x<sup>2</sup> are values Δϕκ average by the ensemble of objects at time points t<sup>1</sup> and t2, respectively, k<sup>11</sup> and k<sup>22</sup> are variances of values Δϕκ at time points t<sup>1</sup> and t2, respectively, and k<sup>12</sup> is the correlation coefficient of phase differences Δϕκ at

η1, <sup>2</sup>ð Þ¼ t1; t<sup>2</sup> cos½ �� h i x<sup>2</sup> � h i x<sup>1</sup> e

<sup>q</sup> to the radiation source and to the observer, respectively; θ<sup>j</sup> ¼

! and u

! <sup>¼</sup> qr

! ¼ 0, and u

� �

K κ¼1

!:

�1 2 <sup>k</sup>11�<sup>1</sup> 2

þ θ<sup>j</sup>

� � are unit vectors targeted from

<sup>i</sup>ψ<sup>j</sup> determines the expression preceding

! and its conjugated point r

<sup>q</sup> forms an Airy pattern as the result of light diffraction on

⇀

<sup>0</sup> is the distance from the lens to plane

<sup>q</sup>. It is known that a

⇀

! � � � � � �

!, let us expand it in a Taylor

! = 0, and expression

, (4)

cos½ � Δϕκ þ Δθκ , (5)

! is the relative displacement

<sup>k</sup>22þk<sup>12</sup> , (6)

! = 0, taking into account the

!. One can familiarize oneself

<sup>q</sup> come to

is small

!. The radius of central spot bs

where N is the number of scattering centers. We will get the complex amplitude of light A q!� � at point <sup>q</sup> ! adding up the amplitudes of the waves that came from the points of plane (ηх,ηу) to point q !, considering amplitude P η !� � and phase exp i η � �!� � 2 =ð Þ 2f h i transmission of the lens [3]:

$$A\left(\overrightarrow{q}\right) = \int\_{-\infty}^{+\infty} \int P\left(\overrightarrow{\eta}\right) e^{\frac{i\left|\overrightarrow{\eta}\right|^2}{\overleftarrow{q}}} e^{ik\left|\overrightarrow{L\_{q}}\left(\overrightarrow{\eta}\right)\right|} \sum\_{j=1}^{N} a\_{j} \, d\eta\_{x} d\eta\_{y},\tag{2}$$

where i is an imaginary unit and Lq ! η !� � is a vector targeted from point <sup>η</sup> ! to point q !.

Let us take the relation between complex amplitude of light in proximity of point rj ! and at point η ! in the same form as in [3]:

$$a\_{\vec{\eta}}\left(\overrightarrow{\eta}\right) = \sqrt{I\_0\left(\overrightarrow{r\_{\vec{\eta}}}\right)}\xi\left(\overrightarrow{r\_{\vec{\eta}}}\right)e^{i\left\{k\left[\left|\overrightarrow{L}\_{\eta}\left(\overrightarrow{r\_{\vec{\eta}}} + \overrightarrow{u\_{\vec{\eta}}}\right)\right| + \left|\overrightarrow{L}\_{\eta}\left(\overrightarrow{r\_{\vec{\eta}}} + \overrightarrow{u\_{\vec{\eta}}}\right)\right|\right] + \phi\_{\vec{\eta}}\right\}}\tag{3}$$

where I<sup>0</sup> ¼ I<sup>0</sup> r !� � is the distribution intensity of the illuminating radiation, ξ ¼ ξ r !� � in the general case is the complex reflection coefficient that takes into account the proportion of the radiation going from point r ! to point η !, Ls ! r !� � is the vector targeted from point r ! to point s !, L<sup>η</sup> ! r !� � is the vector targeted from point <sup>r</sup> ! to point η !, uj ! is the vector of small displacement of the j-th center.

Let us take arbitrary point q ! <sup>¼</sup> qr ! and its conjugated point r ⇀ <sup>q</sup>. It is known that a wave going from point r ⇀ <sup>q</sup> forms an Airy pattern as the result of light diffraction on a diaphragm with diameter D and the center at point qr !. The radius of central spot bs of the pattern equals 1, 22λL<sup>0</sup> <sup>0</sup>=D, where L<sup>0</sup> <sup>0</sup> is the distance from the lens to plane (qx,qy). Region with radius а<sup>s</sup> = bs/m, where m is the magnification of the lens, corresponds to regions with radius bs in plane (х,у). It is known that 85% of the energy of the wave that passed via the lens falls on the central spot of the Airy pattern. We will neglect the energy that falls on the sections beyond the region with radius bs. This in turn means that we suggest that the waves from the scattering centers located only in the region with radius а<sup>s</sup> with the center at point r ⇀ <sup>q</sup> come to point qr !. Now, let N be the number of such centers.

Let us further assume that the region with radius аs, values D, and u ! � � � � � � is small compared to the distances from the object to the radiation source and to the lens as well as that from the lens to the image plane. Regarding expression Ls !� � � � � � <sup>¼</sup> Ls ! r ! <sup>þ</sup> <sup>u</sup> ! � � � � � � � � as continuous function <sup>r</sup> ! and u !, let us expand it in a Taylor series in a small neighborhood of point r ! ¼ r ⇀ <sup>q</sup>, u ! = 0, taking into account the derivatives to the first-order inclusive. Let us similarly expand expression Lη ! r ! <sup>þ</sup> <sup>u</sup> ! � � � � � � � � in the vicinity of points <sup>r</sup> ! <sup>¼</sup> rq !, η ! ¼ 0, and u ! = 0, and expression Lη ! q ! � � � � � � � � in the vicinity of points <sup>η</sup> ! ¼ 0 and q ! <sup>¼</sup> qr !. One can familiarize oneself with the results in specified expansions in [31, 32]. Taking the obtained expansion, as well as formulas (3) and (2) into account, we in [31] obtained an expression for A q!� � and I q!� �:

$$A\left(\overrightarrow{q}\right) = \sqrt{I\_{01}}e^{i\varphi\_j} \sum\_{j=1}^{N} e^{i\left\{k\left[\overrightarrow{u\_j}\left(\overrightarrow{l\_i} + \overrightarrow{l}\right)\right] + \theta\_j\right\}},\tag{4}$$

$$I\left(\overrightarrow{q}\right) = A\left(\overrightarrow{q}\right) \times A^\*\left(\overrightarrow{q}\right) = I\_{01}N + 2I\_{01}\sum\_{\kappa=1}^{K} \cos\left[\Delta\phi\_{\kappa} + \Delta\theta\_{\kappa}\right],\tag{5}$$

where ls ! ¼ ls ! lsx; lsy; lsz � � and l ! ¼ l ! lx; ly; lz � � are unit vectors targeted from point r ⇀ <sup>q</sup> to the radiation source and to the observer, respectively; θ<sup>j</sup> ¼ krj ! ls ! þ l � �! <sup>þ</sup> <sup>φ</sup>j, complex amplitude ffiffiffiffiffiffi <sup>I</sup><sup>01</sup> <sup>p</sup> <sup>e</sup> <sup>i</sup>ψ<sup>j</sup> determines the expression preceding the summation sign; Δϕκ ¼ kΔu<sup>κ</sup> ¼ kΔu<sup>κ</sup> ! ls ! þl � �, <sup>Δ</sup>u<sup>κ</sup> ! is the relative displacement vector of the κ-th pair of scattering centers; and Δθκ ¼ θ<sup>j</sup> � θm, j 6¼ m, κ = 1, 2…К, К = N Nð Þ � 1 =2.

Then, let us assume that process Δuκ(t) is random, and for а fixed κ, there is correlation of values Δu<sup>κ</sup> in time. Assuming that all the random values are independent, in [31], we obtained an expression for temporal normalized autocorrelation function of radiation intensity η1, <sup>2</sup>ð Þ t1; t<sup>2</sup> at point q !:

$$\eta\_{1,2}(t\_1, t\_2) = \cos\left[\langle \mathbf{x}\_2 \rangle - \langle \mathbf{x}\_1 \rangle \right] \times e^{-\frac{1}{2}k\_{11} - \frac{1}{2}k\_{22} + k\_{12}},\tag{6}$$

where h i x<sup>1</sup> and h i x<sup>2</sup> are values Δϕκ average by the ensemble of objects at time points t<sup>1</sup> and t2, respectively, k<sup>11</sup> and k<sup>22</sup> are variances of values Δϕκ at time points t<sup>1</sup> and t2, respectively, and k<sup>12</sup> is the correlation coefficient of phase differences Δϕκ at time points t<sup>1</sup> and t2.

centers come to an arbitrary point of plane (ηх,ηу). First, let us obtain an expression

¼ ∑ N j¼1

where N is the number of scattering centers. We will get the complex amplitude

! adding up the amplitudes of the waves that came from

!, considering amplitude P η

! of the object image plane. For total

aj, (1)

!� �

is a vector targeted from point η

! to point η

is the vector targeted from point r

!, Ls ! r !� �

�<sup>þ</sup> <sup>L</sup><sup>η</sup> ! rj !þuj ! ð Þ � � � � � �þϕ<sup>j</sup> � �

is the distribution intensity of the illuminating radiation,

in the general case is the complex reflection coefficient that takes into

!, L<sup>η</sup> ! r !� �

! is the vector of small displacement of the j-th center.

and phase

! to

, (3)

is the

!

aj dηxdηy, (2)

! of plane (ηх,ηу), we have:

at some point q

Interferometry - Recent Developments and Contemporary Applications

at arbitrary point η

А η !� �

transmission of the lens [3]:

ð P η !� � e i η ! j j2 <sup>2</sup><sup>f</sup> e ik Lq ! η ! ð Þ � � � � ∑ N j¼1

> ! η !� �

! in the same form as in [3]:

ξ rj !� � e ik Ls ! rj !þuj ! ð Þ � � �

Let us take the relation between complex amplitude of light in proximity of

for radiation intensity I q!� �

!� �

Optical system for reflecting objects and designations.

at point q

A q!� �

where i is an imaginary unit and Lq

! and at point η

where I<sup>0</sup> ¼ I<sup>0</sup> r

!, uj

vector targeted from point r

aj η !� � ¼

!� �

¼ þ ð∞

�∞

ffiffiffiffiffiffiffiffiffiffiffiffiffi I<sup>0</sup> rj ! r � �

account the proportion of the radiation going from point r

! to point s

the points of plane (ηх,ηу) to point q

complex amplitude A η

of light A q!� �

exp i η � �!� � 2 =ð Þ 2f h i

Figure 1.

point q !.

point rj

ξ ¼ ξ r !� �

to point η

92

If process Δuκð Þt is stationary, then h i x<sup>1</sup> = h i x<sup>2</sup> and k<sup>11</sup> = k22, and instead of (6), we have:

$$\eta(\mathfrak{r}) = \mathfrak{e}^{-k\_{11} + k\_{11}\rho\_{12}(\mathfrak{r})},\tag{7}$$

we can obtain an expression for radiation intensity I q!� � at point 7, and also for

formula (6), but the value Δu<sup>κ</sup> is determined by a different formula:

Dynamic Speckle Interferometry of Technical and Biological Objects

DOI: http://dx.doi.org/10.5772/intechopen.81389

½ � n lðÞ� n<sup>0</sup> dl, um ¼

where κ is the wave pair number again, and

lj

3.3 Theory of time averaging method for speckle images

uj ¼ ð

gΔ<sup>u</sup>ð Þ ω remain valid.

simplified.

95

normalized autocorrelation function ηð Þ t1; t<sup>2</sup> of this intensity. Such calculations were performed in [33]. It was obtained that the expression for ηð Þ t1; t<sup>2</sup> is precisely

ð

lm

are the optical path lengths of the j-th and m-th sounding waves, respectively; lj and lm are the paths of the corresponding waves, and n lð Þ is the distribution of the refraction index along the wave path. The above features of functions ηð Þ t1; t<sup>2</sup> and

The results of the theory discussed above in Sections 3.1 and 3.2 were used in studies of irreversible processes arising in metals with their high-cycle fatigue [31, 34] and in live cells [35]. In the cases when spatially homogeneous and temporally stationary random variation of optical wave paths occurred at the structural level, good coincidence between the theory and the experiment was observed. However, the drawback of the theories discussed in Sections 3.1 and 3.2 is the difficulty of application in the cases when random variations of the wave phases

For example, in high-cycle metal fatigue, the phase of the wave reflected from part of the surface can vary as a result of translational motion of the object, its elastic or plastic deformation, phase transformation, and formation of microcracks. When a live cell is studied, the wave phase can vary due to diffusion of the substances through the membrane, endocytosis (capture of large particles due to

To overcome the drawback named in [32, 36, 37], the theory was upgraded. The idea consisted in application of the time averaging procedure to speckle dynamics. If the characteristic time τ<sup>0</sup> of wave phase variation corresponding to the fastest process is known, then the averaging time Т<sup>1</sup> of the recorded optical signals can be taken larger than τ0. In this case, speckle dynamics will be formed due to occurrence of slower processes; moreover, interpretation of the experimental data can get

Let us discuss the results of the theoretical studies, first for a reflecting object, and then for a transparent object. In [32], from the model of scattering reflecting object discussed in Section 3.1, a problem concerning speckle dynamics in the image plane of a flat surface performs a complex motion. It was supposed that the scattering centers located in plane (хоу) (Figure 1) simultaneously (1) move at a low rate toward ох axis, (2) perform periodic motions with the same period and amplitude toward ох axis, and (3) randomly move in space. It was supposed that the

after another cycle of the object oscillation. The averaging time must be equal to the

occur due to various simultaneous processes occurring at different rates.

local cell shape variation), and protein synthesis as well as cell motion.

difference of irreversible random center displacements Δu<sup>κ</sup> ¼ Δu<sup>κ</sup>

Δu<sup>κ</sup> ¼ uj � um (8)

½ � n lðÞ� n<sup>0</sup> dl, (9)

! ls ! þ l � �!

appear

where ρ12ð Þτ is a normalized autocorrelation function of relative displacements, τ = t<sup>2</sup> � t1. From (7), it follows that if τ exceeds correlation time τ<sup>0</sup> of values Δuκ, function η τð Þ levels off to <sup>η</sup><sup>∗</sup> = exp ð Þ �k<sup>11</sup> . In our experiments discussed below, this circumstance was used to determine value k<sup>11</sup> as the parameter of fatigue damage to the specimens.

At values Δu<sup>κ</sup> that are small compared with λ, it is convenient to exclude the permanent part of <sup>η</sup> <sup>¼</sup> <sup>η</sup><sup>∗</sup>, proceeding to a new normalized autocorrelation function η0 ð Þ¼ <sup>τ</sup> η τð Þ� <sup>η</sup><sup>∗</sup> ½ �<sup>=</sup> <sup>η</sup>ð Þ� <sup>0</sup> <sup>η</sup><sup>∗</sup> ½ �. It is easy to show that at <sup>Δ</sup>u<sup>κ</sup> << <sup>λ</sup>, we have η0 ð Þffi τ ρ12ð Þτ . Therefore, the corresponding normalized spectral functions gI ð Þ ω of intensity fluctuation and relative displacements gΔ<sup>u</sup>ð Þ ω are equal. The correlation (relaxation) times τ<sup>0</sup> of values Δu<sup>κ</sup> and fluctuations of radiation intensity τ<sup>κ</sup> in the conjugated region are also equal.

At Δu<sup>κ</sup> ≥λ, establishing a relation between gΔ<sup>u</sup>ð Þ ω and gI ð Þ ω is not a simple task. In [33], it was done for the case when function ρ12ð Þτ is a Gaussian function. It was shown that in this case, gΔ<sup>u</sup>ð Þ ω and gIð Þ ω are also Gaussian functions, with the function range gIð Þ ω at level 1/е is k<sup>11</sup> times as wide as that of function gΔ<sup>u</sup>ð Þ ω .

#### 3.2 Theory of speckle dynamics of microscopic processes: transparent object

Let us discuss an optical system (Figure 2) that forms an image of a thin transparent (phase) object. Let the source of coherent light 1 illuminate thin diffuser 2 consisting of point stationary diffusers chaotically located near plane (x,y). The waves spreading from point centers first pass through various sections of thin transparent object 3 and then via lens with diagram 4. Planes (x,y) and ðqx,qyÞ are conjugated. Let us accept that the sum of the diffuser thickness, the distance from the diffuser to the object, and the object thickness are less than the longitudinal resolution of the lens. To simplify the calculations, let us suggest that the refraction indexes of the medium inside and outside the diffuser are same and equal 1. Let us assume that the optical paths of the sounding waves in the object 3 randomly change, in time, and let us neglect the refraction of waves within the object. Let us take the conjugated points 6 and 7. Reasoning the same way as we did in Section 3.1,

#### Figure 2.

Optical system for a transparent object: 1—light source, 2—diffuser, 3—transparent object, 4—lens with diaphragm, 5—image plane, and 6 and 7—conjugated points.

we can obtain an expression for radiation intensity I q!� � at point 7, and also for normalized autocorrelation function ηð Þ t1; t<sup>2</sup> of this intensity. Such calculations were performed in [33]. It was obtained that the expression for ηð Þ t1; t<sup>2</sup> is precisely formula (6), but the value Δu<sup>κ</sup> is determined by a different formula:

$$
\Delta u\_{\kappa} = u\_{j} - u\_{m} \tag{8}
$$

where κ is the wave pair number again, and

If process Δuκð Þt is stationary, then h i x<sup>1</sup> = h i x<sup>2</sup> and k<sup>11</sup> = k22, and instead of (6),

where ρ12ð Þτ is a normalized autocorrelation function of relative displacements, τ = t<sup>2</sup> � t1. From (7), it follows that if τ exceeds correlation time τ<sup>0</sup> of values Δuκ, function η τð Þ levels off to <sup>η</sup><sup>∗</sup> = exp ð Þ �k<sup>11</sup> . In our experiments discussed below, this circumstance was used to determine value k<sup>11</sup> as the parameter of fatigue damage to

At values Δu<sup>κ</sup> that are small compared with λ, it is convenient to exclude the permanent part of <sup>η</sup> <sup>¼</sup> <sup>η</sup><sup>∗</sup>, proceeding to a new normalized autocorrelation function

ð Þ¼ <sup>τ</sup> η τð Þ� <sup>η</sup><sup>∗</sup> ½ �<sup>=</sup> <sup>η</sup>ð Þ� <sup>0</sup> <sup>η</sup><sup>∗</sup> ½ �. It is easy to show that at <sup>Δ</sup>u<sup>κ</sup> << <sup>λ</sup>, we have

At Δu<sup>κ</sup> ≥λ, establishing a relation between gΔ<sup>u</sup>ð Þ ω and gI

ð Þffi τ ρ12ð Þτ . Therefore, the corresponding normalized spectral functions gI

intensity fluctuation and relative displacements gΔ<sup>u</sup>ð Þ ω are equal. The correlation (relaxation) times τ<sup>0</sup> of values Δu<sup>κ</sup> and fluctuations of radiation intensity τ<sup>κ</sup> in the

In [33], it was done for the case when function ρ12ð Þτ is a Gaussian function. It was shown that in this case, gΔ<sup>u</sup>ð Þ ω and gIð Þ ω are also Gaussian functions, with the function range gIð Þ ω at level 1/е is k<sup>11</sup> times as wide as that of function gΔ<sup>u</sup>ð Þ ω .

3.2 Theory of speckle dynamics of microscopic processes: transparent object

Let us discuss an optical system (Figure 2) that forms an image of a thin transparent (phase) object. Let the source of coherent light 1 illuminate thin diffuser 2 consisting of point stationary diffusers chaotically located near plane (x,y). The waves spreading from point centers first pass through various sections of thin transparent object 3 and then via lens with diagram 4. Planes (x,y) and ðqx,qyÞ are conjugated. Let us accept that the sum of the diffuser thickness, the distance from the diffuser to the object, and the object thickness are less than the longitudinal resolution of the lens. To simplify the calculations, let us suggest that the refraction indexes of the medium inside and outside the diffuser are same and equal 1. Let us assume that the optical paths of the sounding waves in the object 3 randomly change, in time, and let us neglect the refraction of waves within the object. Let us take the conjugated points 6 and 7. Reasoning the same way as we did in Section 3.1,

Optical system for a transparent object: 1—light source, 2—diffuser, 3—transparent object, 4—lens with

diaphragm, 5—image plane, and 6 and 7—conjugated points.

�k11þk11ρ12ð Þ<sup>τ</sup> , (7)

ð Þ ω of

ð Þ ω is not a simple task.

η τð Þ¼ e

Interferometry - Recent Developments and Contemporary Applications

we have:

the specimens.

conjugated region are also equal.

η0

η0

Figure 2.

94

$$\mu\_j = \int\_j [n(l) - n\_0] dl, \mu\_m = \int\_{l\_m} [n(l) - n\_0] dl,\tag{9}$$

are the optical path lengths of the j-th and m-th sounding waves, respectively; lj and lm are the paths of the corresponding waves, and n lð Þ is the distribution of the refraction index along the wave path. The above features of functions ηð Þ t1; t<sup>2</sup> and gΔ<sup>u</sup>ð Þ ω remain valid.

### 3.3 Theory of time averaging method for speckle images

The results of the theory discussed above in Sections 3.1 and 3.2 were used in studies of irreversible processes arising in metals with their high-cycle fatigue [31, 34] and in live cells [35]. In the cases when spatially homogeneous and temporally stationary random variation of optical wave paths occurred at the structural level, good coincidence between the theory and the experiment was observed.

However, the drawback of the theories discussed in Sections 3.1 and 3.2 is the difficulty of application in the cases when random variations of the wave phases occur due to various simultaneous processes occurring at different rates.

For example, in high-cycle metal fatigue, the phase of the wave reflected from part of the surface can vary as a result of translational motion of the object, its elastic or plastic deformation, phase transformation, and formation of microcracks.

When a live cell is studied, the wave phase can vary due to diffusion of the substances through the membrane, endocytosis (capture of large particles due to local cell shape variation), and protein synthesis as well as cell motion.

To overcome the drawback named in [32, 36, 37], the theory was upgraded. The idea consisted in application of the time averaging procedure to speckle dynamics. If the characteristic time τ<sup>0</sup> of wave phase variation corresponding to the fastest process is known, then the averaging time Т<sup>1</sup> of the recorded optical signals can be taken larger than τ0. In this case, speckle dynamics will be formed due to occurrence of slower processes; moreover, interpretation of the experimental data can get simplified.

Let us discuss the results of the theoretical studies, first for a reflecting object, and then for a transparent object. In [32], from the model of scattering reflecting object discussed in Section 3.1, a problem concerning speckle dynamics in the image plane of a flat surface performs a complex motion. It was supposed that the scattering centers located in plane (хоу) (Figure 1) simultaneously (1) move at a low rate toward ох axis, (2) perform periodic motions with the same period and amplitude toward ох axis, and (3) randomly move in space. It was supposed that the difference of irreversible random center displacements Δu<sup>κ</sup> ¼ Δu<sup>κ</sup> ! ls ! þ l � �! appear after another cycle of the object oscillation. The averaging time must be equal to the oscillation period or be divisible by it. For the time-average radiation intensity <sup>~</sup>I q! at arbitrary point q ! and for normalized temporal autocorrelation function <sup>η</sup>ð Þ <sup>t</sup>1; <sup>t</sup><sup>2</sup> of this intensity, the following was obtained:

$$\tilde{I} = I\_1 + I\_2 e^{-\sigma^2/2} \cos \left( \mathfrak{x} + a \right), \tag{10}$$

3.4 Discussion of theoretical results

DOI: http://dx.doi.org/10.5772/intechopen.81389

Dynamic Speckle Interferometry of Technical and Biological Objects

"stationary" object will vary.

object illumination or observation.

4. Experiment

97

displacement difference of surface points Δu ¼ Δ u

potentiality to determine the components of vector Δ u

ensemble. Measurement of η was determined by formula:

Therefore, if translational motion of a reflecting or transparent object is absent, the averaging time is divisible by the cyclic loading period, and there are no irreversible deformations in the object, then, according to Eqs. (9)–(11), the observer in the image plane will see a pattern of averaged speckles invariable in time. If irreversible processes that alter the optical paths of the waves emerge in a small region of the object at some phase of oscillation, then the speckle pattern in the conjugated region will change. As the formulas for normalized autocorrelation functions (6) and (11) at ηð Þ¼ ux 1 coincide, the pattern of averaged speckles can be regarded as a speckle pattern of some stationary object. In case of the emergence of irreversible processes that alter the shape of the reflecting object at the structural and/or macroscopic level, or the density of the transparent object, the speckle pattern of such a

For the reflecting object, value х in the cosine input is proportional to the

acteristic (mean) distance Δх. If the deformation variance is small (k11, k<sup>22</sup> ! 0), then values ~I and η in the above formulas will depend on Δu by the law of cosines. Thus, the formulas go into the ratios known in the shear variants of holographic, correlation, and dynamic speckle interferometry. Let us note that there emerges a

procession of speckle images recorded simultaneously at different directions of the

4.1 Dynamic speckle interferometry of flat specimens in periodic bending

In our first experiment, the results of theoretical analysis presented in Section 3.1 were applied to study fatigue phenomena emerging in high-cycle fatigue of medium-carbon steel 50 [34]. The scheme of specimen loading is presented in Figure 3; the dimensions and shapes of the specimen as well as the speckle image of the control area are shown in Figure 4. Before testing, the sample was subjected to fine grinding and annealing. A 2 mm thick flat specimen was loaded with 50 Hz frequency; the number of cycles reached 1,200,000; and maximum cycle amplitude σmax varied from 0.2 to 0.82 σ02, where σ<sup>02</sup> is the flow limit of steel 50. The surface area near the maximum stresses was illuminated by a laser module with wavelength λ = 655 nm and 20-mW power. Speckle images with magnification m = 0.1 were captured at a certain phase of the object oscillation and entered into a computer with a frequency about 10 Hz. The minimum speckle size 2b<sup>s</sup> in the object image plane equaled 40 μm. Films of 20- to 60-s duration were recorded at various stages of specimen testing. To determine value η that is involved in formula (7), we took digital values of intensity at one point (pixel), but at different time points t<sup>1</sup> and t<sup>1</sup> + τ. The digital value of intensity I1(t1) corresponded to the beginning of the film, and I2(t<sup>1</sup> + τ) corresponded to a frame at time point (t<sup>1</sup> + τ). A part of the surface size 2a<sup>s</sup> = 2bs/m was regarded as one "object" of the object ensemble. It was supposed that this "object" was located in the vicinity of a point conjugated to the pixel we are discussing. The array of the areas'size 2a<sup>s</sup> located in surface area size 1 � 4 mm (1 and 4 mm along axes x and y, respectively) was regarded as an object

! ls ! þ l !

located at some char-

! by means of recording and

$$\eta(t\_1, t\_2) = \eta(\mathfrak{u}\_{\mathfrak{x}}) \times e^{-k\_{11}/2 - k\_{22}/2 + k\_{12}(t\_1, t\_2)} \times \cos\left(\langle \mathfrak{x}\_1 \rangle - \langle \mathfrak{x}\_2 \rangle\right),\tag{11}$$

where I1, I2, α are constants, х and σ<sup>2</sup> are the mean value and variance of Δu<sup>κ</sup>, respectively, obtained by averaging over the time Т<sup>1</sup> and over the region with a radius Δx ¼ 2as. This area is located in the vicinity of the point that conjugates the point q !. Function <sup>η</sup>ð Þ ux is a normalized temporal autocorrelation function corresponding to a translational displacement of object toward ох axis; ux is value of displacement. Values k11, k22, k12, xh i<sup>1</sup> , xh i<sup>2</sup> have the same meaning as in formula (6). However, now they are parameters characterizing random wave pair phase differences averaged by time Т1.

A similar problem concerning speckle dynamics in the image plane of a transparent object was solved in [37]. An optical system presented in Figure 2 was discussed. It was supposed that object 3, located near thin diffuser 2, is a thin transparent plate whose lateral surfaces are parallel to plane (х,у). As in the previous case, the discussion was about the complex motion of the plate consisting of (1) its translational lowrate motion along ох axis, (2) its periodic motion toward ох axis, and (3) random small variation of the optical thickness of the plate. The formula for time-average intensity coincided with formula (10), and the formula for the temporal autocorrelation function of this intensity was determined by the expression:

$$\eta(\mathbf{t}\_1, \mathbf{t}\_2) = \left[ e^{-k\_{\rm{11}}/2 - k\_{\rm{22}}/2 + k\_{\rm{12}}(\mathbf{t}\_1, \mathbf{t}\_2)} \times e^{-\tilde{k}\_{\rm{11}}/2 - \tilde{k}\_{\rm{22}}/2 + \tilde{k}\_{\rm{12}}(\mathbf{t}\_1, \mathbf{t}\_2)} \right] \times \cos\left( \left< \mathbf{x}\_1 \right> - \left< \mathbf{x}\_2 \right> + \left< \tilde{\mathbf{x}}\_1 \right> - \left< \tilde{\mathbf{x}}\_2 \right> \right) . \tag{12}$$

Now, in formula (12), the value х is a wave pair phase difference averaged by time and region with diameter Δх, whose changes are determined by variations of the optical thickness of the plate using formula (9). Parameters k11, k22, k12, xh i<sup>1</sup> , xh i<sup>2</sup> in formulas (11) and (12) have the same meaning. Parameters ~ <sup>k</sup>11, <sup>~</sup> <sup>k</sup>22, <sup>~</sup> <sup>k</sup>12, <sup>x</sup>~1i, <sup>x</sup>~2<sup>i</sup> are similar to values k11, k22, k12, xh i<sup>1</sup> , xh i<sup>2</sup> , but they are the parameters of the speckle dynamics emerging due to the roughness of the plate performing a translational motion.

If the roughness is homogeneous, i.e., ~ <sup>k</sup><sup>11</sup> <sup>¼</sup> <sup>~</sup> <sup>k</sup>22, <sup>x</sup>~1i ¼ <sup>x</sup>~2<sup>i</sup> , then instead of (12), we have:

$$\eta(t\_1, t\_2) = \eta(u\_{\mathbf{x}}) \times e^{-k\_{11}/2 - k\_{12}/2 + k\_{12}(t\_1, t\_2)} \times \cos\left(\langle \mathbf{x}\_1 \rangle - \langle \mathbf{x}\_2 \rangle\right),\tag{13}$$

where

$$\eta(u\_x) = \mathfrak{e}^{-\tilde{k}\_{11} + \tilde{k}\_{11}\rho\_{12}(u\_x)}\tag{14}$$

is a normalized temporal autocorrelation function of radiation intensity corresponding to the translational motion of the plate, and ρ12ð Þ ux is a normalized temporal autocorrelation function of phase difference of wave pairs changing in time as a result of movement of a rough transparent plate.

Let us note that the theory of dynamics of time-averaged speckles in the image plane of a thin transparent object in the absence of its displacement and oscillation was discussed in [36].

## 3.4 Discussion of theoretical results

oscillation period or be divisible by it. For the time-average radiation intensity <sup>~</sup>I q!

where I1, I2, α are constants, х and σ<sup>2</sup> are the mean value and variance of Δu<sup>κ</sup>, respectively, obtained by averaging over the time Т<sup>1</sup> and over the region with a radius Δx ¼ 2as. This area is located in the vicinity of the point that conjugates the

A similar problem concerning speckle dynamics in the image plane of a transparent object was solved in [37]. An optical system presented in Figure 2 was discussed. It was supposed that object 3, located near thin diffuser 2, is a thin transparent plate whose lateral surfaces are parallel to plane (х,у). As in the previous case, the discussion was about the complex motion of the plate consisting of (1) its translational lowrate motion along ох axis, (2) its periodic motion toward ох axis, and (3) random small variation of the optical thickness of the plate. The formula for time-average intensity coincided with formula (10), and the formula for the temporal autocorrela-

<sup>k</sup>22=2þ<sup>~</sup>

values k11, k22, k12, xh i<sup>1</sup> , xh i<sup>2</sup> , but they are the parameters of the speckle dynamics emerging due to the roughness of the plate performing a translational motion.

ηð Þ¼ ux e

time as a result of movement of a rough transparent plate.

�~ <sup>k</sup>11þ<sup>~</sup>

Let us note that the theory of dynamics of time-averaged speckles in the image plane of a thin transparent object in the absence of its displacement and oscillation

is a normalized temporal autocorrelation function of radiation intensity corresponding to the translational motion of the plate, and ρ12ð Þ ux is a normalized temporal autocorrelation function of phase difference of wave pairs changing in

Now, in formula (12), the value х is a wave pair phase difference averaged by time and region with diameter Δх, whose changes are determined by variations of the optical thickness of the plate using formula (9). Parameters k11, k22, k12, xh i<sup>1</sup> , xh i<sup>2</sup> in formulas

<sup>k</sup><sup>11</sup> <sup>¼</sup> <sup>~</sup>

<sup>k</sup>11, <sup>~</sup> <sup>k</sup>22, <sup>~</sup>

!. Function <sup>η</sup>ð Þ ux is a normalized temporal autocorrelation function corresponding to a translational displacement of object toward ох axis; ux is value of displacement. Values k11, k22, k12, xh i<sup>1</sup> , xh i<sup>2</sup> have the same meaning as in formula (6). However, now they are parameters characterizing random wave pair phase differ-

<sup>~</sup><sup>I</sup> <sup>¼</sup> <sup>I</sup><sup>1</sup> <sup>þ</sup> <sup>I</sup>2<sup>e</sup>

Interferometry - Recent Developments and Contemporary Applications

tion function of this intensity was determined by the expression:

�~ <sup>k</sup>11=2�<sup>~</sup>

�k11=2�k22=2þk12ð Þ <sup>t</sup>1;t<sup>2</sup> � <sup>e</sup>

(11) and (12) have the same meaning. Parameters ~

If the roughness is homogeneous, i.e., ~

ηð Þ¼ t1; t<sup>2</sup> ηð Þ� ux e

! and for normalized temporal autocorrelation function <sup>η</sup>ð Þ <sup>t</sup>1; <sup>t</sup><sup>2</sup> of

�σ2=<sup>2</sup> cosð Þ <sup>x</sup> <sup>þ</sup> <sup>α</sup> , (10)

�k11=2�k22=2þk12ð Þ <sup>t</sup>1;t<sup>2</sup> � cosð Þ h i <sup>x</sup><sup>1</sup> � h i <sup>x</sup><sup>2</sup> , (11)

<sup>k</sup>12ð Þ <sup>t</sup>1;t<sup>2</sup> � � cos h i� <sup>x</sup><sup>1</sup> h iþ <sup>x</sup><sup>2</sup> <sup>x</sup>~<sup>1</sup>

�k11=2�k22=2þk12ð Þ <sup>t</sup>1;t<sup>2</sup> � cosð Þ h i <sup>x</sup><sup>1</sup> � h i <sup>x</sup><sup>2</sup> , (13)

� <sup>x</sup>~<sup>2</sup>

(12)

:

<sup>k</sup>12, <sup>x</sup>~1i, <sup>x</sup>~2<sup>i</sup> are similar to

<sup>k</sup>22, <sup>x</sup>~1i ¼ <sup>x</sup>~2<sup>i</sup> , then instead of (12),

<sup>k</sup>11ρ12ð Þ ux (14)

at arbitrary point q

ences averaged by time Т1.

point q

ηð Þ¼½ t1; t<sup>2</sup> e

we have:

where

was discussed in [36].

96

this intensity, the following was obtained:

ηð Þ¼ t1; t<sup>2</sup> ηð Þ� ux e

Therefore, if translational motion of a reflecting or transparent object is absent, the averaging time is divisible by the cyclic loading period, and there are no irreversible deformations in the object, then, according to Eqs. (9)–(11), the observer in the image plane will see a pattern of averaged speckles invariable in time. If irreversible processes that alter the optical paths of the waves emerge in a small region of the object at some phase of oscillation, then the speckle pattern in the conjugated region will change. As the formulas for normalized autocorrelation functions (6) and (11) at ηð Þ¼ ux 1 coincide, the pattern of averaged speckles can be regarded as a speckle pattern of some stationary object. In case of the emergence of irreversible processes that alter the shape of the reflecting object at the structural and/or macroscopic level, or the density of the transparent object, the speckle pattern of such a "stationary" object will vary.

For the reflecting object, value х in the cosine input is proportional to the displacement difference of surface points Δu ¼ Δ u ! ls ! þ l ! located at some characteristic (mean) distance Δх. If the deformation variance is small (k11, k<sup>22</sup> ! 0), then values ~I and η in the above formulas will depend on Δu by the law of cosines. Thus, the formulas go into the ratios known in the shear variants of holographic, correlation, and dynamic speckle interferometry. Let us note that there emerges a potentiality to determine the components of vector Δ u ! by means of recording and procession of speckle images recorded simultaneously at different directions of the object illumination or observation.

## 4. Experiment

## 4.1 Dynamic speckle interferometry of flat specimens in periodic bending

In our first experiment, the results of theoretical analysis presented in Section 3.1 were applied to study fatigue phenomena emerging in high-cycle fatigue of medium-carbon steel 50 [34]. The scheme of specimen loading is presented in Figure 3; the dimensions and shapes of the specimen as well as the speckle image of the control area are shown in Figure 4. Before testing, the sample was subjected to fine grinding and annealing. A 2 mm thick flat specimen was loaded with 50 Hz frequency; the number of cycles reached 1,200,000; and maximum cycle amplitude σmax varied from 0.2 to 0.82 σ02, where σ<sup>02</sup> is the flow limit of steel 50. The surface area near the maximum stresses was illuminated by a laser module with wavelength λ = 655 nm and 20-mW power. Speckle images with magnification m = 0.1 were captured at a certain phase of the object oscillation and entered into a computer with a frequency about 10 Hz. The minimum speckle size 2b<sup>s</sup> in the object image plane equaled 40 μm. Films of 20- to 60-s duration were recorded at various stages of specimen testing. To determine value η that is involved in formula (7), we took digital values of intensity at one point (pixel), but at different time points t<sup>1</sup> and t<sup>1</sup> + τ. The digital value of intensity I1(t1) corresponded to the beginning of the film, and I2(t<sup>1</sup> + τ) corresponded to a frame at time point (t<sup>1</sup> + τ). A part of the surface size 2a<sup>s</sup> = 2bs/m was regarded as one "object" of the object ensemble. It was supposed that this "object" was located in the vicinity of a point conjugated to the pixel we are discussing. The array of the areas'size 2a<sup>s</sup> located in surface area size 1 � 4 mm (1 and 4 mm along axes x and y, respectively) was regarded as an object ensemble. Measurement of η was determined by formula:

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η τð Þ¼ h i ½ � <sup>I</sup>1ð Þ� <sup>t</sup><sup>1</sup> h i <sup>I</sup>1ð Þ <sup>t</sup><sup>1</sup> ½ � <sup>I</sup><sup>2</sup> � h i <sup>I</sup>2ð Þ <sup>t</sup><sup>1</sup> <sup>þ</sup> <sup>τ</sup> σ<sup>1</sup> � σ<sup>2</sup>

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DOI: http://dx.doi.org/10.5772/intechopen.81389

where the angle brackets denote arithmetic mean values in the named object ensemble, and σ<sup>1</sup> and σ<sup>2</sup> are standard deviations of values I1(t1) and I2(t<sup>1</sup> + τ). Figure 5 presents a typical dependencies η = η(τ) obtained early in the fatigue testing experiment at σmax = 0.4σ02. The dark spots denote the experiment; and the dashed line denotes a Gaussian autocorrelation function. The deviation of the experimental data from the theory is in the 5% range. As is seen from the graphs, the autocorrelation function declines from 1 to the fixed level <sup>η</sup><sup>∗</sup> <sup>¼</sup> <sup>0</sup>:83. According to our theory, the decline of value η and leveling-off are the indicators of homogeneity and stationarity of random process Δu ¼ Δu tð Þ discussed in Section 3.1. As the

directions of illumination and observation are close to the surface normal,

4σ<sup>2</sup> Δuz

normal. Using the surface decline on 1/е to level η<sup>∗</sup>, we obtain that the intensity fluctuation correlation time is 7 s. One can accept that this time rivals with relaxation time τ<sup>0</sup> of random value Δuz, or difference of the displacement of two surface points toward the normal. These points are located in a 400-μm area. From formula

ffi 2Δuz, where Δuz is the projection of vector Δu

Analysis of the experimental data obtained in the sections of stationary surface relief variations showed the following. When σmax varies from 0.2σ<sup>02</sup> to 0.82 σ02, correlation time τ<sup>0</sup> of relative displacements Δu<sup>z</sup> varies from 60 s to values of the


In many cases, we recorded very complex dependences η = η(τ). Their analysis enabled us to suppose that they corresponded to several processes occurring simultaneously and altering the phases of scattered waves at different rates. Because of difficulties in the interpretation of such data, the technique was upgraded. A theory of time-averaged speckles discussed in Section 3.3 was proposed. Applications of

Temporary autocorrelation function of intensity fluctuations due to metal fatigue: •—experiment and

h i, we obtain that standard deviation <sup>σ</sup>Δuz of

Δu ¼ Δ u

10�<sup>1</sup>

Figure 5.


99

! ls ! þ l � �!

<sup>η</sup><sup>∗</sup> <sup>¼</sup> exp ½ �¼ �k<sup>11</sup> exp �ð Þ <sup>2</sup>π=<sup>λ</sup> <sup>2</sup>

lunges of σΔuz from 10 to 20 nm were observed.

the results of this theory are discussed in the next section.

values Δu<sup>z</sup> equals to 23 nm.

(15)

! on the surface

Scheme of periodic bending: 1—laser module, 2—TV camera, 3—control zone, 4—specimen, and 5—electromagnet.

#### Figure 4.

Dimensions and shape of the specimen (top) and speckle pattern (bottom): 1—control zone, 2—clamp line, and 3—maximum stress spot.

Dynamic Speckle Interferometry of Technical and Biological Objects DOI: http://dx.doi.org/10.5772/intechopen.81389

$$\eta(\tau) = \frac{\langle [I\_1(t\_1) - \langle I\_1(t\_1) \rangle][I\_2 - \langle I\_2(t\_1 + \tau) \rangle] \rangle}{\sigma\_1 \times \sigma\_2} \tag{15}$$

where the angle brackets denote arithmetic mean values in the named object ensemble, and σ<sup>1</sup> and σ<sup>2</sup> are standard deviations of values I1(t1) and I2(t<sup>1</sup> + τ).

Figure 5 presents a typical dependencies η = η(τ) obtained early in the fatigue testing experiment at σmax = 0.4σ02. The dark spots denote the experiment; and the dashed line denotes a Gaussian autocorrelation function. The deviation of the experimental data from the theory is in the 5% range. As is seen from the graphs, the autocorrelation function declines from 1 to the fixed level <sup>η</sup><sup>∗</sup> <sup>¼</sup> <sup>0</sup>:83. According to our theory, the decline of value η and leveling-off are the indicators of homogeneity and stationarity of random process Δu ¼ Δu tð Þ discussed in Section 3.1. As the directions of illumination and observation are close to the surface normal, ! � �!

Δu ¼ Δ u ! ls þ l ffi 2Δuz, where Δuz is the projection of vector Δu ! on the surface normal. Using the surface decline on 1/е to level η<sup>∗</sup>, we obtain that the intensity fluctuation correlation time is 7 s. One can accept that this time rivals with relaxation time τ<sup>0</sup> of random value Δuz, or difference of the displacement of two surface points toward the normal. These points are located in a 400-μm area. From formula <sup>η</sup><sup>∗</sup> <sup>¼</sup> exp ½ �¼ �k<sup>11</sup> exp �ð Þ <sup>2</sup>π=<sup>λ</sup> <sup>2</sup> 4σ<sup>2</sup> Δuz h i, we obtain that standard deviation <sup>σ</sup>Δuz of values Δu<sup>z</sup> equals to 23 nm.

Analysis of the experimental data obtained in the sections of stationary surface relief variations showed the following. When σmax varies from 0.2σ<sup>02</sup> to 0.82 σ02, correlation time τ<sup>0</sup> of relative displacements Δu<sup>z</sup> varies from 60 s to values of the 10�<sup>1</sup> -s order. At the same time, when σmax varied in the named range, value σΔuz stayed practically invariable, at the 5-nm level on the average. Rare measurement lunges of σΔuz from 10 to 20 nm were observed.

In many cases, we recorded very complex dependences η = η(τ). Their analysis enabled us to suppose that they corresponded to several processes occurring simultaneously and altering the phases of scattered waves at different rates. Because of difficulties in the interpretation of such data, the technique was upgraded. A theory of time-averaged speckles discussed in Section 3.3 was proposed. Applications of the results of this theory are discussed in the next section.

Figure 5.

Temporary autocorrelation function of intensity fluctuations due to metal fatigue: •—experiment and - - - - theory.

Figure 3.

Figure 4.

98

and 3—maximum stress spot.

5—electromagnet.

Scheme of periodic bending: 1—laser module, 2—TV camera, 3—control zone, 4—specimen, and

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Dimensions and shape of the specimen (top) and speckle pattern (bottom): 1—control zone, 2—clamp line,

## 4.2 Application of time-averaged speckles

We used the technique of time-averaged speckles to study the micro- and macro-variations of the surface shape in high-cycle fatigue of constructive and model materials. The main objective of the conducted research work was to clear up the matter of what happens in the material during crack initiation.

Beams made from pipe steel 09Г2С loaded by three-point bending were used in the experiment. The shape and dimensions of the specimens as well as the position of the bumps are presented in Figure 6. A Charpy notch was made in the beam to localize the crack initiation spot. The surface of the beams was subject to fine grinding, and then they were annealed in vacuum. After annealing, the surface of some specimens was polished. After polishing, roughness parameter R<sup>a</sup> was in the 1- to 50-nm range. Let us note that for both polished and unpolished specimens, we observed the same results in a qualitative sense.

The specimens were tested in a resonance-type machine of MIKROTRON (RUMUL) type with near-100 Hz frequency and a 0.1 load ratio. The value of the maximum force exerted (1.1 kN) was selected experimentally from the condition of emergence of a 0.1-mm long crack after hundreds of thousands of loading cycles. Variation of resonance frequency by 10% usually preceded the emergence of a crack of this length.

The scheme of the optical setup applied for recording of the average speckle images is presented in Figure 7. The optical setup was located on the platform of the testing machine. Object 4 was illuminated by beam 2 from laser module 1 of a KLM-H650-40-5 type with the wavelength of 0.65 μm and 40-mW power. As speckles do not emerge when a mirror surface is illuminated, mat glass 3 was put into the lighting beam to form speckle fields when specimens with the polished surface were tested. The speckle image was recorded in the specimen image plane. The magnification of the optical system equaled 0.7. The diaphragm size of lens 5 was selected so that the minimum speckle size slightly exceeded that of a photocell in the photocell array of the TV camera 6. A monochrome VIDEOSCAN-415M-USB TV camera with an array containing 782 582 photocells of 8.3 8.3 μm size was used in the experiments. Averaging time T<sup>1</sup> equaled 50 oscillation periods. We supposed that in the most damaged surface area, this time exceeded the correlation time of wave pair phase difference τ<sup>0</sup> which is equal to 0.1 s.

Figure 8 presents distribution of correlation coefficient η found by two 8-bit digital speckle images of the specimen.

The first image was obtained at loading cycle number N<sup>1</sup> equal to 57,000, and the second image was obtained at cycle number N<sup>2</sup> = 92,000. Speckle field variations started at N<sup>2</sup> equal to 72,000 cycles. Value η was found using formula (15). Figure 9 presents three-dimensional surface profiles near the notch at N<sup>1</sup> = 57,000 and N<sup>2</sup> = 92,000. The profiles were recorded using an optical profilometer WYKO NT-1100 with a 3-nm height measuring error.

Scheme of the optical setup. 1—laser module, 2—illuminating radiation, 3—mat glass, 4—specimen,

5—lens with diaphragm, and 6—photosensor array of the TV camera.

Dynamic Speckle Interferometry of Technical and Biological Objects

DOI: http://dx.doi.org/10.5772/intechopen.81389

Distribution of correlation coefficients η found in a 4 4-pixel section.

Figure 7.

Figure 8.

101

As it is seen from Figure 9, at 92,000 cycles, two zones emerged in front of the notch. The first zone is a pitch about 0.5 μm deep with the diameter of 500 μm. The pitch center was at the distance of about 250 μm from the notch tip. Besides, a second small zone of about 50 100-μm size where a fatigue crack initiated

Figure 6. Shape and dimensions of the specimen.

Dynamic Speckle Interferometry of Technical and Biological Objects DOI: http://dx.doi.org/10.5772/intechopen.81389

#### Figure 7.

4.2 Application of time-averaged speckles

observed the same results in a qualitative sense.

wave pair phase difference τ<sup>0</sup> which is equal to 0.1 s.

digital speckle images of the specimen.

of this length.

Figure 6.

100

Shape and dimensions of the specimen.

We used the technique of time-averaged speckles to study the micro- and macro-variations of the surface shape in high-cycle fatigue of constructive and model materials. The main objective of the conducted research work was to clear up

The specimens were tested in a resonance-type machine of MIKROTRON (RUMUL) type with near-100 Hz frequency and a 0.1 load ratio. The value of the maximum force exerted (1.1 kN) was selected experimentally from the condition of emergence of a 0.1-mm long crack after hundreds of thousands of loading cycles. Variation of resonance frequency by 10% usually preceded the emergence of a crack

The scheme of the optical setup applied for recording of the average speckle images is presented in Figure 7. The optical setup was located on the platform of the testing machine. Object 4 was illuminated by beam 2 from laser module 1 of a KLM-H650-40-5 type with the wavelength of 0.65 μm and 40-mW power. As speckles do not emerge when a mirror surface is illuminated, mat glass 3 was put into the lighting beam to form speckle fields when specimens with the polished surface were tested. The speckle image was recorded in the specimen image plane. The magnification of the optical system equaled 0.7. The diaphragm size of lens 5 was selected so that the minimum speckle size slightly exceeded that of a photocell in the photocell array of the TV camera 6. A monochrome VIDEOSCAN-415M-USB TV camera with an array containing 782 582 photocells of 8.3 8.3 μm size was used in the experiments. Averaging time T<sup>1</sup> equaled 50 oscillation periods. We supposed that in the most damaged surface area, this time exceeded the correlation time of

Figure 8 presents distribution of correlation coefficient η found by two 8-bit

Beams made from pipe steel 09Г2С loaded by three-point bending were used in the experiment. The shape and dimensions of the specimens as well as the position of the bumps are presented in Figure 6. A Charpy notch was made in the beam to localize the crack initiation spot. The surface of the beams was subject to fine grinding, and then they were annealed in vacuum. After annealing, the surface of some specimens was polished. After polishing, roughness parameter R<sup>a</sup> was in the 1- to 50-nm range. Let us note that for both polished and unpolished specimens, we

the matter of what happens in the material during crack initiation.

Interferometry - Recent Developments and Contemporary Applications

Scheme of the optical setup. 1—laser module, 2—illuminating radiation, 3—mat glass, 4—specimen, 5—lens with diaphragm, and 6—photosensor array of the TV camera.

#### Figure 8.

Distribution of correlation coefficients η found in a 4 4-pixel section.

The first image was obtained at loading cycle number N<sup>1</sup> equal to 57,000, and the second image was obtained at cycle number N<sup>2</sup> = 92,000. Speckle field variations started at N<sup>2</sup> equal to 72,000 cycles. Value η was found using formula (15).

Figure 9 presents three-dimensional surface profiles near the notch at N<sup>1</sup> = 57,000 and N<sup>2</sup> = 92,000. The profiles were recorded using an optical profilometer WYKO NT-1100 with a 3-nm height measuring error.

As it is seen from Figure 9, at 92,000 cycles, two zones emerged in front of the notch. The first zone is a pitch about 0.5 μm deep with the diameter of 500 μm. The pitch center was at the distance of about 250 μm from the notch tip. Besides, a second small zone of about 50 100-μm size where a fatigue crack initiated

Figure 9. Surface profiles: (a) at 57,000 cycles and (b) at 92,000 cycles.

emerged immediately at the notch tip. This area is shown by an arrow in Figure 9b. This zone consisted of irregularities of 5- to 1-μm transverse size and the height of scores of nanometers.

Figure 10 presents joint graphs showing altered relief heights Δh and correlation coefficient variation η in the pitch image plane along ох axis.

maximum measurement of the surface profile slope ratio γ. The latter value was found by the surface profile in the graph. The dotted line corresponded to formula (11), in which it was accepted that h i x<sup>1</sup> ¼ 0 and ηð Þ¼ ux 1; the exponent was substituted by 1 and the cosine argument was 4ð Þ π=λ γ2xs, where 2xs is the size of the surface area equal to the linear resolution of the lens (12 μm). As seen from Figure 11, we have fairly good coincidence of the theory and experiment.

As seen from Figure 9, about half of the crack formation region lies within the pit, and the other half is beyond the pit. For the latter section, the measurement of η equaled 0.8. Suppose in (11) if the cosine equals 1, ηð Þ¼ ux 1, and k11, k<sup>12</sup> = 0, we

The measurement of <sup>R</sup><sup>a</sup> was determined by the equation Ra ffi <sup>0</sup>:8<sup>λ</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2π l ½ � ð Þ sz þ lz , which is fair if the relief heights are distributed by the Gaussian law.

According to the profilometer data, variation of value R<sup>a</sup> in the segment equaled

Figure 12 presents typical dependences of η(N) that correspond to five surface sections of another specimen. The graph numbers coincide with the section numbers. The fatigue test conditions for this specimen did not differ from those for the previous one; the test was stopped only after the crack initiation and a small

Analysis of three-dimensional profiles of the surfaces of two specimens showed that they were the same in the qualitative sense. The surface spots for plotting of dependences η(N) in Figure 12 were selected so that they could clear up the emergence order of the two above zones at the notch tip. This information can be beneficial for creation of crack initiation physical models. Section 1 was selected beyond the contraction; sections 2 and 3 were selected on the path of the motion of the plasticity zones in front of the crack. Section 4 was located at the very notch tip, and section 5 was taken on the contraction edge on the line approximately passing through its center parallel to the specimen axis. The decrease of value η from 1 to 0.95–0.97 for section 1 at the end of the experiment is caused by the hardware noises and partially by slight translational motion due to degradation of the material. The centers of sections 2 and 3 rivaled, but their size differed. Section 2 of 22 � 22-μm size consisted of four regions of Δх = 11-μm size, and in section 3, there were 16 such regions. It is evident that dependences η (N) for these two sections

! and l ! �2 ln <sup>η</sup> <sup>p</sup> <sup>=</sup>

on axis z, respectively,

obtain that the roughness parameter R<sup>a</sup> variation equals 20 nm.

Here, lsz and lz are the projections of unit vectors ls

Theoretical (—) and experimental (•) dependences η(γ).

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and lsz ¼ lz ¼ 0, 98.

increase in its length.

25 nm.

103

Figure 11.

The scan line of the profilometer passed through the pit center, and value η was determined using formula (15) by scanning of a 4 � 4 pixel-size section. It is seen from the picture that the maximum variations of value η fall on the steepest surface slopes in the pit. Minimum variations of value η correspond to the sections beyond the pit and at its bottom.

Comparison of surface shape variation within the pit with variations of value η in the conjugated region showed that these variations agree with formula (11). The mean value of the scattering center displacement difference at the bottom of the pit can be accepted as zero. In this case, in formula (11), variation of value η will be determined by the parameters contained in the exponent. Values ½ � <sup>λ</sup>=ð Þ <sup>4</sup><sup>π</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi � ln ð Þ<sup>η</sup> <sup>p</sup> corresponding to the bottom of the pitch equaled several nanometers which corresponded to the profilometer data. In Figure 11, for five scan lines, black dots show dependence of value η that falls on the steepest slopes of the surface, from the

Figure 10. Joint dependences (1) Δh(x) and (2) η(x).

Dynamic Speckle Interferometry of Technical and Biological Objects DOI: http://dx.doi.org/10.5772/intechopen.81389

Figure 11. Theoretical (—) and experimental (•) dependences η(γ).

emerged immediately at the notch tip. This area is shown by an arrow in Figure 9b. This zone consisted of irregularities of 5- to 1-μm transverse size and the height of

Figure 10 presents joint graphs showing altered relief heights Δh and correlation

The scan line of the profilometer passed through the pit center, and value η was determined using formula (15) by scanning of a 4 � 4 pixel-size section. It is seen from the picture that the maximum variations of value η fall on the steepest surface slopes in the pit. Minimum variations of value η correspond to the sections beyond

Comparison of surface shape variation within the pit with variations of value η in the conjugated region showed that these variations agree with formula (11). The mean value of the scattering center displacement difference at the bottom of the pit can be accepted as zero. In this case, in formula (11), variation of value η will be determined by the parameters contained in the exponent. Values ½ � <sup>λ</sup>=ð Þ <sup>4</sup><sup>π</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

corresponding to the bottom of the pitch equaled several nanometers which corresponded to the profilometer data. In Figure 11, for five scan lines, black dots show dependence of value η that falls on the steepest slopes of the surface, from the

� ln ð Þ<sup>η</sup> <sup>p</sup>

coefficient variation η in the pitch image plane along ох axis.

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Surface profiles: (a) at 57,000 cycles and (b) at 92,000 cycles.

scores of nanometers.

Figure 9.

Figure 10.

102

Joint dependences (1) Δh(x) and (2) η(x).

the pit and at its bottom.

maximum measurement of the surface profile slope ratio γ. The latter value was found by the surface profile in the graph. The dotted line corresponded to formula (11), in which it was accepted that h i x<sup>1</sup> ¼ 0 and ηð Þ¼ ux 1; the exponent was substituted by 1 and the cosine argument was 4ð Þ π=λ γ2xs, where 2xs is the size of the surface area equal to the linear resolution of the lens (12 μm). As seen from Figure 11, we have fairly good coincidence of the theory and experiment.

As seen from Figure 9, about half of the crack formation region lies within the pit, and the other half is beyond the pit. For the latter section, the measurement of η equaled 0.8. Suppose in (11) if the cosine equals 1, ηð Þ¼ ux 1, and k11, k<sup>12</sup> = 0, we obtain that the roughness parameter R<sup>a</sup> variation equals 20 nm.

The measurement of <sup>R</sup><sup>a</sup> was determined by the equation Ra ffi <sup>0</sup>:8<sup>λ</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffi �2 ln <sup>η</sup> <sup>p</sup> <sup>=</sup> 2π l ½ � ð Þ sz þ lz , which is fair if the relief heights are distributed by the Gaussian law. Here, lsz and lz are the projections of unit vectors ls ! and l ! on axis z, respectively, and lsz ¼ lz ¼ 0, 98.

According to the profilometer data, variation of value R<sup>a</sup> in the segment equaled 25 nm.

Figure 12 presents typical dependences of η(N) that correspond to five surface sections of another specimen. The graph numbers coincide with the section numbers. The fatigue test conditions for this specimen did not differ from those for the previous one; the test was stopped only after the crack initiation and a small increase in its length.

Analysis of three-dimensional profiles of the surfaces of two specimens showed that they were the same in the qualitative sense. The surface spots for plotting of dependences η(N) in Figure 12 were selected so that they could clear up the emergence order of the two above zones at the notch tip. This information can be beneficial for creation of crack initiation physical models. Section 1 was selected beyond the contraction; sections 2 and 3 were selected on the path of the motion of the plasticity zones in front of the crack. Section 4 was located at the very notch tip, and section 5 was taken on the contraction edge on the line approximately passing through its center parallel to the specimen axis. The decrease of value η from 1 to 0.95–0.97 for section 1 at the end of the experiment is caused by the hardware noises and partially by slight translational motion due to degradation of the material. The centers of sections 2 and 3 rivaled, but their size differed. Section 2 of 22 � 22-μm size consisted of four regions of Δх = 11-μm size, and in section 3, there were 16 such regions. It is evident that dependences η (N) for these two sections

fatigue test. The equipment shown in Figure 7 was used to record the speckle images. The specimen was illuminated through mat glass, the sounding waves passed through the specimen. The observation direction was selected either along the normal or at the angle of 30° to the normal. In the latter case, irreversible processes in the depth of the specimen could be controlled by distribution of value η. The three-point bending test under the condition of high-cycle fatigue was run on the machine discussed in the previous section. By now, an article has been prepared on the basis of the obtained data, which is now being reviewed by the editors of an optical magazine. As agreed with the magazine editors, the results of the conducted experiments will be available after publishing. We will only note that we were for the first time able to view in detail the process of transition of originally continuous three-dimensional medium into a destroyed state. Using the formulas in Section 3.3, we evaluated the limiting variations of the refraction index and density prior to fatigue destruction of Plexiglas. The crack initiation processes in steel and Plexiglas were very similar, even coinciding in some details. The difference consists in the fact that metals have the mechanism of energy dissipation connected to dislocation motion. That is why during local plastic deformation, variation of the object shape (emergence of a contraction) can take place. An amorphous material like Plexiglas does not have such a mechanism. That is why plastic deformations come into effect

Dynamic Speckle Interferometry of Technical and Biological Objects

DOI: http://dx.doi.org/10.5772/intechopen.81389

4.4 Dynamic speckle interferometry of intracellular processes

In our early experiments studying the processes occurring inside live cells, we

36 0.1°С. A transparent cuvette with two glass supporters in a horizontal position in the nutrient solution was fixed on a small table near the mat glass. The first supporter contained a monolayer of cultured cells; the second one was cell-free. Speckle images of the supporters are shown in Figure 14. The light lines in the picture show the typical sections selected for determination of value η using

Photograph of the optical device: 1—laser module with micro-objective, 2—mat glass, 3—lock of the object on

the platform of the motorized translator, and 4—camera with lens.

used the formulas discussed in Section 3.2 of the theory. The main long-term objective of the undertaken studies was search of approaches that would permit creation of an optical technique and a device studying the processes in the live cell membranes. The first objective of the experiments was search of cell metabolism parameters. We used an optical setup whose scheme corresponded to the optical scheme discussed in the theory (Figure 2). The photo of the setup is shown in Figure 13. A semi-conductor laser module with the wavelength λ = 532 nm and 20-mW power as well as the TV camera discussed above in Section 4.2 were used. The setup was placed into a thermostat that maintained the temperature of

as volume/density variations.

Figure 13.

105

#### Figure 12.

Dependences η(N) corresponding to five sections of the surface: 1—section of 44 � 44-μm size at the distance of 640 μm from the notch tip. 2—section of 22 � 22 μm size at the distance of 180 μm, 3—section of 44 � 44-μm size at the distance of 180 μm, 4—section at the notch tip of 44 � 44-μm size, 5—section of 44 � 44-μm size on the slope of the contraction.

twice arrive at zero nearly simultaneously; however, their minimum measurements differ. For section 2, value а η nearly reaches �1, and for section 3 the minimum measurement equals �0.62. From the viewpoint of our theory, in compliance with formula (11) reaching �1 by value η means its dependence on h i Δuz by the law of cosines with amplitude expð Þ �k<sup>22</sup> equaling 1 (k<sup>22</sup> = 0), and values k � 1:96 � Δγ � Δx=λ in every small region of 11-μm size reach value π/2. Let us take value Δγ that characterizes a rigid surface rotation for the measure of plastic deformation on the 11-μm base. Then it follows from our analysis that at η = �1, a homogeneous plastic surface deformation equaling 7.5 � <sup>10</sup>�<sup>3</sup> occurs in section 2. For section 3 amplitude, exp ð Þ �k<sup>22</sup> equals 0.62. Thus, we get that the plastic deformations in section 3 of 44 � 44-μm size are inhomogeneous, and the standard deviation of values <sup>Δ</sup><sup>γ</sup> from 7.5 � <sup>10</sup>�<sup>3</sup> equals 3.3 � <sup>10</sup>�<sup>3</sup> .

It is seen in Figure 12 that notable deviations of dependences 4 and 5 from the horizontal line start practically simultaneously at 70,000–80,000 cycles. This suggests that the formation of irregularities in the small zone and the contractions probably start simultaneously. Above, it was shown that a decline of value η from 1 to about 0.8 in the conjugated region corresponds to crack initiation at the notch tip. For section 4, such a decline occurred at about 280,000–300,000 thousand cycles. Then, dependence 4 levels off at N ≈ 400,000. This suggests cessation of irreversible process in section 4 after the crack start and the increase in the crack length. A decrease of value η to 0.45 at 330,000 cycles approximately in linear fashion is characteristic for to section 5. Then dependence η(N) also goes to the horizontal section which speaks for the completion of contraction formation.

## 4.3 Studying fatigue of Plexiglas

The experiments conducted with Plexiglas of "ACRUMA" brand aimed at studying the peculiarities of fatigue damage accumulation in the volume of the specimen shown in Figure 6. The specimens were made from a plate 5-mm thick. The protective film preserving the polished surfaces was taken off before the

## Dynamic Speckle Interferometry of Technical and Biological Objects DOI: http://dx.doi.org/10.5772/intechopen.81389

fatigue test. The equipment shown in Figure 7 was used to record the speckle images. The specimen was illuminated through mat glass, the sounding waves passed through the specimen. The observation direction was selected either along the normal or at the angle of 30° to the normal. In the latter case, irreversible processes in the depth of the specimen could be controlled by distribution of value η. The three-point bending test under the condition of high-cycle fatigue was run on the machine discussed in the previous section. By now, an article has been prepared on the basis of the obtained data, which is now being reviewed by the editors of an optical magazine. As agreed with the magazine editors, the results of the conducted experiments will be available after publishing. We will only note that we were for the first time able to view in detail the process of transition of originally continuous three-dimensional medium into a destroyed state. Using the formulas in Section 3.3, we evaluated the limiting variations of the refraction index and density prior to fatigue destruction of Plexiglas. The crack initiation processes in steel and Plexiglas were very similar, even coinciding in some details. The difference consists in the fact that metals have the mechanism of energy dissipation connected to dislocation motion. That is why during local plastic deformation, variation of the object shape (emergence of a contraction) can take place. An amorphous material like Plexiglas does not have such a mechanism. That is why plastic deformations come into effect as volume/density variations.

## 4.4 Dynamic speckle interferometry of intracellular processes

In our early experiments studying the processes occurring inside live cells, we used the formulas discussed in Section 3.2 of the theory. The main long-term objective of the undertaken studies was search of approaches that would permit creation of an optical technique and a device studying the processes in the live cell membranes. The first objective of the experiments was search of cell metabolism parameters. We used an optical setup whose scheme corresponded to the optical scheme discussed in the theory (Figure 2). The photo of the setup is shown in Figure 13. A semi-conductor laser module with the wavelength λ = 532 nm and 20-mW power as well as the TV camera discussed above in Section 4.2 were used. The setup was placed into a thermostat that maintained the temperature of 36 0.1°С. A transparent cuvette with two glass supporters in a horizontal position in the nutrient solution was fixed on a small table near the mat glass. The first supporter contained a monolayer of cultured cells; the second one was cell-free. Speckle images of the supporters are shown in Figure 14. The light lines in the picture show the typical sections selected for determination of value η using

#### Figure 13.

Photograph of the optical device: 1—laser module with micro-objective, 2—mat glass, 3—lock of the object on the platform of the motorized translator, and 4—camera with lens.

twice arrive at zero nearly simultaneously; however, their minimum measurements differ. For section 2, value а η nearly reaches �1, and for section 3 the minimum measurement equals �0.62. From the viewpoint of our theory, in compliance with formula (11) reaching �1 by value η means its dependence on h i Δuz by the law of

Dependences η(N) corresponding to five sections of the surface: 1—section of 44 � 44-μm size at the distance of 640 μm from the notch tip. 2—section of 22 � 22 μm size at the distance of 180 μm, 3—section of 44 � 44-μm size at the distance of 180 μm, 4—section at the notch tip of 44 � 44-μm size, 5—section of 44 � 44-μm

k � 1:96 � Δγ � Δx=λ in every small region of 11-μm size reach value π/2. Let us take value Δγ that characterizes a rigid surface rotation for the measure of plastic deformation on the 11-μm base. Then it follows from our analysis that at η = �1, a homogeneous plastic surface deformation equaling 7.5 � <sup>10</sup>�<sup>3</sup> occurs in section 2. For section 3 amplitude, exp ð Þ �k<sup>22</sup> equals 0.62. Thus, we get that the plastic deformations in section 3 of 44 � 44-μm size are inhomogeneous, and the standard

It is seen in Figure 12 that notable deviations of dependences 4 and 5 from the horizontal line start practically simultaneously at 70,000–80,000 cycles. This suggests that the formation of irregularities in the small zone and the contractions probably start simultaneously. Above, it was shown that a decline of value η from 1 to about 0.8 in the conjugated region corresponds to crack initiation at the notch tip. For section 4, such a decline occurred at about 280,000–300,000 thousand cycles. Then, dependence 4 levels off at N ≈ 400,000. This suggests cessation of irreversible process in section 4 after the crack start and the increase in the crack length. A decrease of value η to 0.45 at 330,000 cycles approximately in linear fashion is characteristic for to section 5. Then dependence η(N) also goes to the horizontal

.

cosines with amplitude expð Þ �k<sup>22</sup> equaling 1 (k<sup>22</sup> = 0), and values

Interferometry - Recent Developments and Contemporary Applications

section which speaks for the completion of contraction formation.

The experiments conducted with Plexiglas of "ACRUMA" brand aimed at studying the peculiarities of fatigue damage accumulation in the volume of the specimen shown in Figure 6. The specimens were made from a plate 5-mm thick. The protective film preserving the polished surfaces was taken off before the

4.3 Studying fatigue of Plexiglas

104

Figure 12.

size on the slope of the contraction.

deviation of values <sup>Δ</sup><sup>γ</sup> from 7.5 � <sup>10</sup>�<sup>3</sup> equals 3.3 � <sup>10</sup>�<sup>3</sup>

#### Figure 14.

Speckle images of supports in a transparent cuvette with nutrient solution.

formula (15). The measurements of η were determined using the films recorded during 20–40 s. Figure 15 presents dependences η(t) corresponding to the nutrient solution (top), to the cells in the nutrient solution (middle), and to the herpes simplex-infected cells (bottom). It is seen from the graphs that in all the cases dependence η(t) levels off in several seconds. According to the theory, the presence of a constant level speaks for the fact that random radiation intensity variations in the selected image fragment and variations in difference Δu of the optical wave paths in time in the conjugated region are stationary processes. By the measurements of the fixed levels, we determined variances σ<sup>2</sup> <sup>Δ</sup><sup>u</sup> of values Δu. In the assumption that random values Δu corresponding to the cells and the nutrient solution are uncorrelated variables, we determined values σ<sup>2</sup> <sup>Δ</sup><sup>u</sup> corresponding to the cells.

the presence of several processes altering the phases of the sounding waves at different rates. In this regard, we used a time-averaged speckle technique discussed in Section 3.3. Application of this technique enabled us to obtain well-reproducible data. Figure 16 presents typical dependences of the time-averaged digital value of intensity ~I corresponding to the nutrient solution, to a cell in the nutrient solution and to a herpes simplex virus-infected cell in the solution. The dependences are taken from our paper [38]. Analysis of the dependences belonging to the latter type showed that variation features of value ~I well corresponds to the stages of virus development in cells. Figure 17 presents typical dependences ηð Þt corresponding to the nutrient solution, to the cells in the nutrient solution, and to the herpes simplex

Dependence of time-averaged intensity ~I on time for the pixels corresponding to: 1—nutrient solution, 2—cell,

The shown dependences were well-reproducible when a monolayer of cultured

Figure 18 presents joint dependences of σΔ<sup>u</sup>ð Þt and temperature T on time for L-41 cell line [39]. For the linear correlation coefficient of two arrays σΔ<sup>u</sup> and T, we obtained a value equal to 0.88. Figure 14 shows dependence of σΔ<sup>u</sup> on Т from our

As the metabolic processes are manifested more distinctly when the temperature rises, the above data presented in [38] were used to substantiate application of value

virus-infected cells in the nutrient medium.

Figure 16.

Figure 17.

107

and 3—herpes simplex virus in a cell.

cells of various cell lines was infected with herpes virus.

Dynamic Speckle Interferometry of Technical and Biological Objects

DOI: http://dx.doi.org/10.5772/intechopen.81389

early work [35]. L-41 cell line was also used in the experiment.

σΔ<sup>u</sup> as the parameter that characterizes the activity of cultured cells.

Typical dependence ηð Þt for Vero line: 1—nutrient solution, 2—virus-free cells, and 3—cells with virus.

While processing the films of 20- to 40-s duration recorded for several hours, we detected various types of dependences ηð Þt . Along with the graphs similar to those presented in Figure 15, we obtained dependences that did not level off as well as graphs that had rather a composite view. All-day graphs of dependences σΔ<sup>u</sup>ð Þt at a 0.5-h pitch were reproducible in about 50% of the cases. Analysis of obtained dependences ηð Þt showed that their complicated character is probably connected to

#### Figure 15.

Dependence η(t) corresponding to: 1—nutrient solution, 2—cells in the nutrient solution, and 3—infected cells in the nutrient solution.

Dynamic Speckle Interferometry of Technical and Biological Objects DOI: http://dx.doi.org/10.5772/intechopen.81389

Figure 16.

formula (15). The measurements of η were determined using the films recorded during 20–40 s. Figure 15 presents dependences η(t) corresponding to the nutrient solution (top), to the cells in the nutrient solution (middle), and to the herpes simplex-infected cells (bottom). It is seen from the graphs that in all the cases dependence η(t) levels off in several seconds. According to the theory, the presence of a constant level speaks for the fact that random radiation intensity variations in the selected image fragment and variations in difference Δu of the optical wave paths in time in the conjugated region are stationary processes. By the measure-

assumption that random values Δu corresponding to the cells and the nutrient

Dependence η(t) corresponding to: 1—nutrient solution, 2—cells in the nutrient solution, and 3—infected

While processing the films of 20- to 40-s duration recorded for several hours, we detected various types of dependences ηð Þt . Along with the graphs similar to those presented in Figure 15, we obtained dependences that did not level off as well as graphs that had rather a composite view. All-day graphs of dependences σΔ<sup>u</sup>ð Þt at a 0.5-h pitch were reproducible in about 50% of the cases. Analysis of obtained dependences ηð Þt showed that their complicated character is probably connected to

<sup>Δ</sup><sup>u</sup> of values Δu. In the

<sup>Δ</sup><sup>u</sup> corresponding to the

ments of the fixed levels, we determined variances σ<sup>2</sup>

Speckle images of supports in a transparent cuvette with nutrient solution.

Interferometry - Recent Developments and Contemporary Applications

cells.

Figure 15.

106

cells in the nutrient solution.

Figure 14.

solution are uncorrelated variables, we determined values σ<sup>2</sup>

Dependence of time-averaged intensity ~I on time for the pixels corresponding to: 1—nutrient solution, 2—cell, and 3—herpes simplex virus in a cell.

the presence of several processes altering the phases of the sounding waves at different rates. In this regard, we used a time-averaged speckle technique discussed in Section 3.3. Application of this technique enabled us to obtain well-reproducible data. Figure 16 presents typical dependences of the time-averaged digital value of intensity ~I corresponding to the nutrient solution, to a cell in the nutrient solution and to a herpes simplex virus-infected cell in the solution. The dependences are taken from our paper [38]. Analysis of the dependences belonging to the latter type showed that variation features of value ~I well corresponds to the stages of virus development in cells. Figure 17 presents typical dependences ηð Þt corresponding to the nutrient solution, to the cells in the nutrient solution, and to the herpes simplex virus-infected cells in the nutrient medium.

The shown dependences were well-reproducible when a monolayer of cultured cells of various cell lines was infected with herpes virus.

Figure 18 presents joint dependences of σΔ<sup>u</sup>ð Þt and temperature T on time for L-41 cell line [39]. For the linear correlation coefficient of two arrays σΔ<sup>u</sup> and T, we obtained a value equal to 0.88. Figure 14 shows dependence of σΔ<sup>u</sup> on Т from our early work [35]. L-41 cell line was also used in the experiment.

As the metabolic processes are manifested more distinctly when the temperature rises, the above data presented in [38] were used to substantiate application of value σΔ<sup>u</sup> as the parameter that characterizes the activity of cultured cells.

values ~I multiplied by 10�<sup>2</sup>

mean measurement in the image fragment.

DOI: http://dx.doi.org/10.5772/intechopen.81389

Dynamic Speckle Interferometry of Technical and Biological Objects

sity variation on the background of this value.

109

limiting roughness parameter variation ΔRa, of value Δu ¼ Δu

The conducted experiments showed the possibility in principle to determine the

reflecting object and the refraction index of a transparent object corresponding to the crack start. By monitoring the variation rate of these parameters on the bases of the 10–100 μm order, one can assess the approximate time to macro-fracture. It is noteworthy that in practice, not always is there an opportunity to illuminate the object under control with laser radiation, and the conventional nondestructive testing techniques are poorly adapted for measurement on such bases. The

! ls ! þ l !

for the


meaning of the sign was determined by the difference of ~I in a pixel and by the

High sensitivity of the speckle technique to deformations is based on the phenomenon of multiple-wave interference with the same initial phases. Speckles emerge as the result of multiple-wave interference with random initial phases. So the emergence of multiple-ray interference is in many ways similar to wave interference in a diffraction grid is not evident. This question was briefly discussed in [34, 40]. Because of the significance of the matter, let us dwell upon it. Let there be a great number of point diffusers on the surface in a region of ΔX diameter with the center at point А, and let value ΔX equal the linear resolution of the lens. For certainty, let the surface be illuminated and observed along the normal. The waves with random initial phases going from the scattering centers form random intensity value ~I at conjugated point A<sup>0</sup> of image plane. Now let us imagine that a slight plastic rotation around an axis parallel to oy axis. Let the rotation axis be located at the edge of a region with ΔX diameter. Now let us discuss the scattering centers with the following properties: (1) the waves scattered by these centers have the same amplitudes and initial phases, (2) y-coordinates of the centers are random, (3) along ox axis they are located at the same Δx distance. We suppose that such centers will always be found if their number is large. Let Δuz be the maximum displacement along the normal in the region, and M = ΔX/Δx. In [34], we showed that at point A<sup>0</sup> the radiation intensity will vary in a quasi-periodic mode proportionally to value sin <sup>2</sup>ð Þ <sup>2</sup><sup>π</sup> � <sup>Δ</sup>uz0M=<sup>λ</sup> <sup>=</sup> sin <sup>2</sup>ð Þ <sup>2</sup><sup>π</sup> � <sup>Δ</sup>uz0=<sup>λ</sup> , where <sup>Δ</sup>uz<sup>0</sup> <sup>=</sup> <sup>Δ</sup>uz=M. Analysis of the obtained expression showed that in deformation of the materials used in practice, the periodicity corresponding to the denominator is difficult to implement. From the numerator period, we obtain that Δuz<sup>0</sup> � M ¼ Δuz ¼ λN=2, where N is the interference period (period of value ~I). The latter ratio is also implied by formulas (6), (10), (11), if in these formulas we accept that <sup>σ</sup><sup>2</sup> <sup>¼</sup> 0, h i <sup>x</sup><sup>1</sup> <sup>¼</sup> 0, and <sup>k</sup>11, k<sup>22</sup> <sup>¼</sup> 0. Therefore, the multiple-wave interference that we have discussed is equivalent to interference of two waves spreading from the centers located at the opposite edges of the region with ΔX diameter. Expression Δuz<sup>0</sup> � M ¼ λN=2 may be interpreted in a different way. Having accepted that N = 1, we have: Δuz<sup>0</sup> ¼ ð Þ <sup>1</sup>=<sup>2</sup> <sup>λ</sup>=<sup>M</sup> <sup>¼</sup> ð Þ <sup>1</sup>=<sup>2</sup> <sup>λ</sup>0. We obtain that variation of value <sup>~</sup><sup>I</sup> per period may also be interpreted as the variation result of the interference period of two coherent waves with wave length λ<sup>0</sup> ¼ λ=M. This variation appears in a relative displacement of two scattering centers located at distance Δx by value Δuz0. Let us accept the limiting sensitivity Δuz<sup>0</sup> of the technique, the 1-nm order is theoretically evaluated above and experimentally confirmed in [41]. Then, formally we obtain that value λ<sup>0</sup> is in the X-ray wave range. This way, if the region with ΔX diameter is so small that the macroscopic deformations in it are homogeneous, then the reflected waves with random initial phases form some random hardly variable speckle brightness value, and the waves with the same initial phases are responsible for quasi-periodic inten-

Figure 18. Joint dependence of σΔ<sup>u</sup> and temperature on time at small heating rates.

Figure 19. Dependence of σΔ<sup>u</sup> on the temperature.

## 5. Discussion of results and prospects for further studies

### 5.1 Studying high-cycle fatigue of metals

The conducted theoretical and experimental research showed that the dynamic variant of speckle interferometry can be used for quantitative evaluation of irreversible displacements and deformations occurring in metals with high-cycle fatigue on the 10-μm order bases. The peculiarity of this evaluation is that application of time-average speckles makes it can be conducted in real time, i.e., without interruption of cyclic deformations (Figure 19).

The technique is fairly simple, because it does not require any synchronization of the load value applied to the object and the frame capture moment. It is characterized by high accuracy and sensitivity.

In [32], it was shown that when a 10 10-pixel fragment is selected at the variation of η from 0.3 to 0.99, the ratio error of its determination does not exceed 1%. It was shown that a small error in determination of value η by formula (15) is related to the features of radiation intensity ~I distribution in the speckle pattern. The record error of value η was found to equal the sum of determination errors of

values ~I multiplied by 10�<sup>2</sup> -order coefficients with different signs. The random meaning of the sign was determined by the difference of ~I in a pixel and by the mean measurement in the image fragment.

High sensitivity of the speckle technique to deformations is based on the phenomenon of multiple-wave interference with the same initial phases. Speckles emerge as the result of multiple-wave interference with random initial phases. So the emergence of multiple-ray interference is in many ways similar to wave interference in a diffraction grid is not evident. This question was briefly discussed in [34, 40]. Because of the significance of the matter, let us dwell upon it. Let there be a great number of point diffusers on the surface in a region of ΔX diameter with the center at point А, and let value ΔX equal the linear resolution of the lens. For certainty, let the surface be illuminated and observed along the normal. The waves with random initial phases going from the scattering centers form random intensity value ~I at conjugated point A<sup>0</sup> of image plane. Now let us imagine that a slight plastic rotation around an axis parallel to oy axis. Let the rotation axis be located at the edge of a region with ΔX diameter. Now let us discuss the scattering centers with the following properties: (1) the waves scattered by these centers have the same amplitudes and initial phases, (2) y-coordinates of the centers are random, (3) along ox axis they are located at the same Δx distance. We suppose that such centers will always be found if their number is large. Let Δuz be the maximum displacement along the normal in the region, and M = ΔX/Δx. In [34], we showed that at point A<sup>0</sup> the radiation intensity will vary in a quasi-periodic mode proportionally to value sin <sup>2</sup>ð Þ <sup>2</sup><sup>π</sup> � <sup>Δ</sup>uz0M=<sup>λ</sup> <sup>=</sup> sin <sup>2</sup>ð Þ <sup>2</sup><sup>π</sup> � <sup>Δ</sup>uz0=<sup>λ</sup> , where <sup>Δ</sup>uz<sup>0</sup> <sup>=</sup> <sup>Δ</sup>uz=M. Analysis of the obtained expression showed that in deformation of the materials used in practice, the periodicity corresponding to the denominator is difficult to implement. From the numerator period, we obtain that Δuz<sup>0</sup> � M ¼ Δuz ¼ λN=2, where N is the interference period (period of value ~I). The latter ratio is also implied by formulas (6), (10), (11), if in these formulas we accept that <sup>σ</sup><sup>2</sup> <sup>¼</sup> 0, h i <sup>x</sup><sup>1</sup> <sup>¼</sup> 0, and <sup>k</sup>11, k<sup>22</sup> <sup>¼</sup> 0. Therefore, the multiple-wave interference that we have discussed is equivalent to interference of two waves spreading from the centers located at the opposite edges of the region with ΔX diameter. Expression Δuz<sup>0</sup> � M ¼ λN=2 may be interpreted in a different way. Having accepted that N = 1, we have: Δuz<sup>0</sup> ¼ ð Þ <sup>1</sup>=<sup>2</sup> <sup>λ</sup>=<sup>M</sup> <sup>¼</sup> ð Þ <sup>1</sup>=<sup>2</sup> <sup>λ</sup>0. We obtain that variation of value <sup>~</sup><sup>I</sup> per period may also be interpreted as the variation result of the interference period of two coherent waves with wave length λ<sup>0</sup> ¼ λ=M. This variation appears in a relative displacement of two scattering centers located at distance Δx by value Δuz0. Let us accept the limiting sensitivity Δuz<sup>0</sup> of the technique, the 1-nm order is theoretically evaluated above and experimentally confirmed in [41]. Then, formally we obtain that value λ<sup>0</sup> is in the X-ray wave range. This way, if the region with ΔX diameter is so small that the macroscopic deformations in it are homogeneous, then the reflected waves with random initial phases form some random hardly variable speckle brightness value, and the waves with the same initial phases are responsible for quasi-periodic intensity variation on the background of this value.

The conducted experiments showed the possibility in principle to determine the limiting roughness parameter variation ΔRa, of value Δu ¼ Δu ! ls ! þ l ! for the reflecting object and the refraction index of a transparent object corresponding to the crack start. By monitoring the variation rate of these parameters on the bases of the 10–100 μm order, one can assess the approximate time to macro-fracture. It is noteworthy that in practice, not always is there an opportunity to illuminate the object under control with laser radiation, and the conventional nondestructive testing techniques are poorly adapted for measurement on such bases. The

5. Discussion of results and prospects for further studies

Joint dependence of σΔ<sup>u</sup> and temperature on time at small heating rates.

Interferometry - Recent Developments and Contemporary Applications

The conducted theoretical and experimental research showed that the dynamic variant of speckle interferometry can be used for quantitative evaluation of irreversible displacements and deformations occurring in metals with high-cycle fatigue on the 10-μm order bases. The peculiarity of this evaluation is that application of time-average speckles makes it can be conducted in real time, i.e., without

The technique is fairly simple, because it does not require any synchronization of the load value applied to the object and the frame capture moment. It is charac-

In [32], it was shown that when a 10 10-pixel fragment is selected at the variation of η from 0.3 to 0.99, the ratio error of its determination does not exceed 1%. It was shown that a small error in determination of value η by formula (15) is related to the features of radiation intensity ~I distribution in the speckle pattern. The record error of value η was found to equal the sum of determination errors of

5.1 Studying high-cycle fatigue of metals

Dependence of σΔ<sup>u</sup> on the temperature.

Figure 18.

Figure 19.

108

interruption of cyclic deformations (Figure 19).

terized by high accuracy and sensitivity.

discussed speckle method could be used as the tool for upgrading of the conventional testing techniques. The technique is convenient for target detection in search of local irreversible deformations and calibration of other techniques.

The dependence of value η both on the mean value of x<sup>2</sup> ¼ kΔu and on its variance k<sup>22</sup> is the peculiarity of this technique. We managed to obtain numerical values of x<sup>2</sup> and k<sup>22</sup> for cases k<sup>22</sup> = 0 and x<sup>2</sup> = 0, respectively. In [32], it was proposed to obtain the values of h i x<sup>2</sup> and k<sup>22</sup> by simultaneous recording of two speckle images obtained using two lasers. Development of such a technique can be

Dynamic Speckle Interferometry of Technical and Biological Objects

In the conducted fatigue experiments, we used an optical system that permits determination mean values, variance, and relaxation time of Δuz-component of

!. However, the measurements of the above values for other components

! are of practical interest. Development of such a technique is the

The matters of the accuracy and sensitivity of the technique, the peculiarities of speckle image variations, contribution assessment for values h i x<sup>2</sup> and k<sup>22</sup> to variation of value η discussed in the previous section are fully applied to dynamic speckle

<sup>Δ</sup><sup>u</sup> and to what extent. The study of this problem is the subject of our further

Obtaining data by averaging by the cell thickness is a drawback of this technique. Still, the logic of the technique development and the practical needs set the task of determining the mean value, variance, and relaxation time of the medium refraction index in every small section of the cell. The author reported about the ways to solve this problem at two conferences [44, 45]. Theoretical and experimental underpinning of a speckle tomography for the live cell that would permit a

This work discussed theoretical and experimental underpinning of an interference technique that permits studying irreversible processes occurring near the surface of reflecting objects and inside thin transparent objects by variation of speckle images. The author's scientific interests lie in the sphere of studying longevity of living and nonliving matter. So, the research targets were specimens made from constructive materials tested for high-cycle fatigue as well as cultured live

The theoretically obtained formulas established the relationship among the parameters characterizing variation of optical wave paths in small sections of an object and the parameters characterizing variation of speckles in the conjugated region. Such parameters for a reflecting object were the mean value, variance, the relaxation time of difference Δu in displacement of scattering centers (points of the surface), time-averaged radiation intensity ~I, and correlation coefficient η for the speckle image fragment taken at the reference and at the current time points. Similar ratios were obtained for a transparent object sounded by multiple waves with random initial phases. The difference consisted of the fact that value Δu was

the difference in the optical path of the waves sounding the object.

<sup>Δ</sup><sup>u</sup>, or variance of the

We underpinned and approved a cell activity parameter σ<sup>2</sup>

solution to this problem is the subject of our further research.

difference in the optical path of the cell-sounding waves is such a parameter. However, it is not yet clear what constituents of metabolism affect variation of

the subject for further research.

DOI: http://dx.doi.org/10.5772/intechopen.81389

subject of our further research.

interferometry of live cells.

5.2 Study of the processes inside live cells

vector Δu

value σ<sup>2</sup>

research.

6. Conclusion

cells.

111

of vector Δu

Fatigue experiments improved understanding of the processes occurring in high-cycle fatigue of materials. For example, the pins that we observed at the notch tip (shown by the arrow in Figure 9b) turned out to be pieces of iron carbide. We managed to identify them using Raman scattering [42]. This fact speaks for the significance of heat generation accounting in high-cycle fatigue. The experiments also showed that irreversible processes in the small region close to the notch emerge at the early stages of the fatigue. If inconsistent local deformations emerge at the stage of loading increase, then in arbitrary unloading residual compressive stress must inevitably appear. Thus, the stress and deformation fields at the notch tip will vary considerably with progress of the fatigue. In this context, analysis of not only local plastic, but also of periodically varying elastic deformations is important.

The opportunity for application of the elastic deformation control technique that we have discussed was substantiated in [32]. Deformation <sup>ε</sup> <sup>¼</sup> <sup>Δ</sup>u=Δ<sup>X</sup> of the 10�<sup>3</sup> order corresponds to values Δu of the 1-nm order and ΔX of the 10-μm order. Plastic deformations 10�<sup>3</sup> up are more characteristic for most of the conventional constructive materials. If we increase the measurement base by an order, we will proceed into the range of elastic deformations of the 10�<sup>4</sup> order. It is deformations of this order that emerge in constructions during exploitation. In [43], we conducted a successful pilot model experiment recording values ~I and η in a specimen under elastic strain. Figure 20 presents dependences of ~I and η on the time taken from that paper. The graphs were obtained in periodic deflection of a steel beam. The data correspond to a single oscillation period; the observation and illumination directions selected were not on the surface normal, measurement base ΔX equaled 670 μm. Thus, the approaches that we have discussed are in principle applicable for simultaneous monitoring of both macroscopic elastic deformations on relatively large bases and of local plastic deformations. Development of such techniques can be the subject for further research.

Figure 20. Dependence of ~I and η on time in elastic deflection of a steel beam.

Dynamic Speckle Interferometry of Technical and Biological Objects DOI: http://dx.doi.org/10.5772/intechopen.81389

The dependence of value η both on the mean value of x<sup>2</sup> ¼ kΔu and on its variance k<sup>22</sup> is the peculiarity of this technique. We managed to obtain numerical values of x<sup>2</sup> and k<sup>22</sup> for cases k<sup>22</sup> = 0 and x<sup>2</sup> = 0, respectively. In [32], it was proposed to obtain the values of h i x<sup>2</sup> and k<sup>22</sup> by simultaneous recording of two speckle images obtained using two lasers. Development of such a technique can be the subject for further research.

In the conducted fatigue experiments, we used an optical system that permits determination mean values, variance, and relaxation time of Δuz-component of vector Δu !. However, the measurements of the above values for other components of vector Δu ! are of practical interest. Development of such a technique is the subject of our further research.

### 5.2 Study of the processes inside live cells

The matters of the accuracy and sensitivity of the technique, the peculiarities of speckle image variations, contribution assessment for values h i x<sup>2</sup> and k<sup>22</sup> to variation of value η discussed in the previous section are fully applied to dynamic speckle interferometry of live cells.

We underpinned and approved a cell activity parameter σ<sup>2</sup> <sup>Δ</sup><sup>u</sup>, or variance of the difference in the optical path of the cell-sounding waves is such a parameter. However, it is not yet clear what constituents of metabolism affect variation of value σ<sup>2</sup> <sup>Δ</sup><sup>u</sup> and to what extent. The study of this problem is the subject of our further research.

Obtaining data by averaging by the cell thickness is a drawback of this technique. Still, the logic of the technique development and the practical needs set the task of determining the mean value, variance, and relaxation time of the medium refraction index in every small section of the cell. The author reported about the ways to solve this problem at two conferences [44, 45]. Theoretical and experimental underpinning of a speckle tomography for the live cell that would permit a solution to this problem is the subject of our further research.

## 6. Conclusion

discussed speckle method could be used as the tool for upgrading of the conventional testing techniques. The technique is convenient for target detection in search

Fatigue experiments improved understanding of the processes occurring in high-cycle fatigue of materials. For example, the pins that we observed at the notch tip (shown by the arrow in Figure 9b) turned out to be pieces of iron carbide. We managed to identify them using Raman scattering [42]. This fact speaks for the significance of heat generation accounting in high-cycle fatigue. The experiments also showed that irreversible processes in the small region close to the notch emerge at the early stages of the fatigue. If inconsistent local deformations emerge at the stage of loading increase, then in arbitrary unloading residual compressive stress must inevitably appear. Thus, the stress and deformation fields at the notch tip will vary considerably with progress of the fatigue. In this context, analysis of not only local plastic, but also of periodically varying elastic deformations is important.

The opportunity for application of the elastic deformation control technique that we have discussed was substantiated in [32]. Deformation <sup>ε</sup> <sup>¼</sup> <sup>Δ</sup>u=Δ<sup>X</sup> of the 10�<sup>3</sup> order corresponds to values Δu of the 1-nm order and ΔX of the 10-μm order. Plastic deformations 10�<sup>3</sup> up are more characteristic for most of the conventional constructive materials. If we increase the measurement base by an order, we will proceed into the range of elastic deformations of the 10�<sup>4</sup> order. It is deformations

of this order that emerge in constructions during exploitation. In [43], we

niques can be the subject for further research.

Dependence of ~I and η on time in elastic deflection of a steel beam.

Figure 20.

110

conducted a successful pilot model experiment recording values ~I and η in a specimen under elastic strain. Figure 20 presents dependences of ~I and η on the time taken from that paper. The graphs were obtained in periodic deflection of a steel beam. The data correspond to a single oscillation period; the observation and illumination directions selected were not on the surface normal, measurement base ΔX equaled 670 μm. Thus, the approaches that we have discussed are in principle applicable for simultaneous monitoring of both macroscopic elastic deformations on relatively large bases and of local plastic deformations. Development of such tech-

of local irreversible deformations and calibration of other techniques.

Interferometry - Recent Developments and Contemporary Applications

This work discussed theoretical and experimental underpinning of an interference technique that permits studying irreversible processes occurring near the surface of reflecting objects and inside thin transparent objects by variation of speckle images. The author's scientific interests lie in the sphere of studying longevity of living and nonliving matter. So, the research targets were specimens made from constructive materials tested for high-cycle fatigue as well as cultured live cells.

The theoretically obtained formulas established the relationship among the parameters characterizing variation of optical wave paths in small sections of an object and the parameters characterizing variation of speckles in the conjugated region. Such parameters for a reflecting object were the mean value, variance, the relaxation time of difference Δu in displacement of scattering centers (points of the surface), time-averaged radiation intensity ~I, and correlation coefficient η for the speckle image fragment taken at the reference and at the current time points. Similar ratios were obtained for a transparent object sounded by multiple waves with random initial phases. The difference consisted of the fact that value Δu was the difference in the optical path of the waves sounding the object.

For the variant, when variation of Δu in time is a random stationary process, we obtained a relation between the normalized spectrum of value Δu and the normalized fluctuation spectrum of ~I.

References

1032-1054

1359-1376

258-265

[1] Anisimov VI, Kozel SM, Lokshin GR. Space-time statistical properties of the coherent radiation scattered by a moving diffuse reflector. Optics and Spectroscopy. 1969;27(3):483-491

DOI: http://dx.doi.org/10.5772/intechopen.81389

Dynamic Speckle Interferometry of Technical and Biological Objects

Netherlands: University of Groningen;

Materialov [Physical Mechanics of Real Materials]. Мoscow: Nauka; 2004. 328p;

[12] Lasar J, Hola M, Cip O. Differential

measurement in high cycle fatigue metal

Conference on PhotoMechanics 2015. 25–27 May 2015. Delft, Netherlands.

[13] Gough HJ. Fatigue of Metals.

[14] Ustalost metallov. Sbornik statei pod red, G.V. Uzhika [Metal fatigue. Collected papers ed. By G.V. Uzhik]. Moscow: Izd-vo inostr.lit. – Мoscow,

[15] Ivanova VS, Terentiev VF. Priroda Ustalosti Materialov [The Nature of Metal Fatigue]. Мoscow: Metallurgija;

[16] Taylor D. The Theory of Critical Distances. Amsterdam: Elsevier; 2007.

[17] Manson SS. Fatigue: A complex subject—Some simple approximations. The William M. Murray Lecture. Experimental Mechanics. 1965;5(7):

[18] Schijve J. Fatigue of structures and materials in the 20th century and the state of art. International Journal of Fatigue. 2003;25(8):679-702

Metallicheskih Materialov [Fatigue of Metallic Materials]. Мoscow: Nauka;

[19] Terentiev VF. Ustalost

2002. 248p; (rus)

[11] Novikov II, Yermishin VA. Fizicheskaia Mehanika Realnyh

interferometry for real-time

testing. Book of abstracts. In:

2005

(rus)

pp. 64-65

London: Benn; 1926

1961. 378 p. (rus)

1975. 456p; (rus)

307p

193-226

[2] Yoshimura T. Statistical properties of dynamic speckles. JOSA. 1986;A3(7):

[3] Yamaguchi I. Speckle displacement and decorrelation in the diffraction and

[4] Aleksandrov EB, Bonch-Bruevich AM. Investigation of surface strains by

the hologram technique. Soviet Physics-Technical Papers. 1967;12:

[5] Leendertz JA. Interferometric displacement measurement on scattering surfaces utilizing speckle effect. Journal of Physics E: Scientific

Instruments. 1970;3:214-218

SPIE. 1999;3726:38-43

1988. 282p; (rus)

113

Springer-Verlag; 1998. 219p

[8] Romanov AN. Razrushenie pri Malotsiklovom Nagruzhenii [Fracture in Low-Cycle Loading]. Мoscow: Nauka;

[9] Ellyin F. Fatigue damage, crack growth life prediction. London: Chapman and Hall; 1997. 483p

[10] Brinckmann S. On the role of dislocations in fatigue crack initiation [Dissertation]. Groningen, The

[6] Vladimirov AP, Mikushin VI. Interferometric determination of vector components of relative displacements: Theory and experiment. Proceedings of

[7] Fomin NA. Speckle Photography for Fluid Mechanics Measurements. Berlin:

image fields for small object deformation. Optica Acta. 1991;28:

In experiments set up for testing of the theory, speckle dynamics was created by displacement of a rough transparent plate, by variation of shape, roughness, and the refraction index of metal and Plexiglas specimens in their high-cycle fatigue. Good quantitative coincidence of the theory and the experiment was shown.

It was shown that by way of speckle time-averaging the technique permits realtime determination of the 1-nm-order measurements of Δu on the 10-μm order on bases ΔX, which corresponds to local plastic deformation ε = Δu/ΔX of the 10�<sup>3</sup> order.

It was demonstrated that with increasing base ΔX by an order, the technique allows to monitor the variation of elastic macroscopic deformations. So, the possibility, in principle, to use the same technique for monitoring both the deformation field of a part and accumulation of local plastic deformations in an object under periodic strain appears.

It was also shown that using this technique, one can determine the limiting variations of roughness parameter Ra, value ε and refraction index n that correspond to the crack start. Therefore, knowing the limiting measurements of these parameters and monitoring their variation rate while exploiting the part, one could in principle assess the time to its macroscopic fracture. Development of such a technique can be the subject of further research.

When the technique was applied for studying live cells, it was shown that the variance of value Δu can be used as a live cell activity parameter. It was also shown that dependences <sup>~</sup>I tð Þ and <sup>η</sup>(t) for virus-infected and virus-free cells differ considerably. Modification of this technique for determination of the average measurement, variance, and relaxation time of the refraction index in small areas of the live cell can be the line of further research.

## Acknowledgements

The author would like to thank the young colleagues and students I. Kamantsev, N. Drukarenko, Yu. Mikhailova, and K. Myznov for their help in conducting experiments.

## Author details

Alexander Vladimirov Ural Federal University, Yekaterinburg Institute of Virus Infections, Yekaterinburg, Russia

\*Address all correspondence to: vap52@bk.ru

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Dynamic Speckle Interferometry of Technical and Biological Objects DOI: http://dx.doi.org/10.5772/intechopen.81389

## References

For the variant, when variation of Δu in time is a random stationary process, we obtained a relation between the normalized spectrum of value Δu and the normal-

In experiments set up for testing of the theory, speckle dynamics was created by displacement of a rough transparent plate, by variation of shape, roughness, and the refraction index of metal and Plexiglas specimens in their high-cycle fatigue. Good

It was shown that by way of speckle time-averaging the technique permits realtime determination of the 1-nm-order measurements of Δu on the 10-μm order on bases ΔX, which corresponds to local plastic deformation ε = Δu/ΔX of the 10�<sup>3</sup>

It was demonstrated that with increasing base ΔX by an order, the technique allows to monitor the variation of elastic macroscopic deformations. So, the possibility, in principle, to use the same technique for monitoring both the deformation field of a part and accumulation of local plastic deformations in an object under

It was also shown that using this technique, one can determine the limiting variations of roughness parameter Ra, value ε and refraction index n that correspond to the crack start. Therefore, knowing the limiting measurements of these parameters and monitoring their variation rate while exploiting the part, one could in principle assess the time to its macroscopic fracture. Development of such a

When the technique was applied for studying live cells, it was shown that the variance of value Δu can be used as a live cell activity parameter. It was also shown that dependences <sup>~</sup>I tð Þ and <sup>η</sup>(t) for virus-infected and virus-free cells differ considerably. Modification of this technique for determination of the average measurement, variance, and relaxation time of the refraction index in small areas of the live

The author would like to thank the young colleagues and students I. Kamantsev,

Ural Federal University, Yekaterinburg Institute of Virus Infections, Yekaterinburg,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

N. Drukarenko, Yu. Mikhailova, and K. Myznov for their help in conducting

quantitative coincidence of the theory and the experiment was shown.

Interferometry - Recent Developments and Contemporary Applications

ized fluctuation spectrum of ~I.

periodic strain appears.

Acknowledgements

experiments.

Author details

Russia

112

Alexander Vladimirov

technique can be the subject of further research.

cell can be the line of further research.

\*Address all correspondence to: vap52@bk.ru

provided the original work is properly cited.

order.

[1] Anisimov VI, Kozel SM, Lokshin GR. Space-time statistical properties of the coherent radiation scattered by a moving diffuse reflector. Optics and Spectroscopy. 1969;27(3):483-491

[2] Yoshimura T. Statistical properties of dynamic speckles. JOSA. 1986;A3(7): 1032-1054

[3] Yamaguchi I. Speckle displacement and decorrelation in the diffraction and image fields for small object deformation. Optica Acta. 1991;28: 1359-1376

[4] Aleksandrov EB, Bonch-Bruevich AM. Investigation of surface strains by the hologram technique. Soviet Physics-Technical Papers. 1967;12: 258-265

[5] Leendertz JA. Interferometric displacement measurement on scattering surfaces utilizing speckle effect. Journal of Physics E: Scientific Instruments. 1970;3:214-218

[6] Vladimirov AP, Mikushin VI. Interferometric determination of vector components of relative displacements: Theory and experiment. Proceedings of SPIE. 1999;3726:38-43

[7] Fomin NA. Speckle Photography for Fluid Mechanics Measurements. Berlin: Springer-Verlag; 1998. 219p

[8] Romanov AN. Razrushenie pri Malotsiklovom Nagruzhenii [Fracture in Low-Cycle Loading]. Мoscow: Nauka; 1988. 282p; (rus)

[9] Ellyin F. Fatigue damage, crack growth life prediction. London: Chapman and Hall; 1997. 483p

[10] Brinckmann S. On the role of dislocations in fatigue crack initiation [Dissertation]. Groningen, The

Netherlands: University of Groningen; 2005

[11] Novikov II, Yermishin VA. Fizicheskaia Mehanika Realnyh Materialov [Physical Mechanics of Real Materials]. Мoscow: Nauka; 2004. 328p; (rus)

[12] Lasar J, Hola M, Cip O. Differential interferometry for real-time measurement in high cycle fatigue metal testing. Book of abstracts. In: Conference on PhotoMechanics 2015. 25–27 May 2015. Delft, Netherlands. pp. 64-65

[13] Gough HJ. Fatigue of Metals. London: Benn; 1926

[14] Ustalost metallov. Sbornik statei pod red, G.V. Uzhika [Metal fatigue. Collected papers ed. By G.V. Uzhik]. Moscow: Izd-vo inostr.lit. – Мoscow, 1961. 378 p. (rus)

[15] Ivanova VS, Terentiev VF. Priroda Ustalosti Materialov [The Nature of Metal Fatigue]. Мoscow: Metallurgija; 1975. 456p; (rus)

[16] Taylor D. The Theory of Critical Distances. Amsterdam: Elsevier; 2007. 307p

[17] Manson SS. Fatigue: A complex subject—Some simple approximations. The William M. Murray Lecture. Experimental Mechanics. 1965;5(7): 193-226

[18] Schijve J. Fatigue of structures and materials in the 20th century and the state of art. International Journal of Fatigue. 2003;25(8):679-702

[19] Terentiev VF. Ustalost Metallicheskih Materialov [Fatigue of Metallic Materials]. Мoscow: Nauka; 2002. 248p; (rus)

[20] Gilanyi A, Morishita K, Sukegawa T, Uesaka M, Miya K. Magnetic nondestructive evaluation of fatigue damage of ferromagnetic steels for nuclear fusion energy systems. Fusion Engineering and Design. 1998;42:485-491

[21] Gorkunov ES, Savray RА, Makarov АV, Zadvorkin SМ. Magnetic techniques for estimating elastic and plastic strains in steels under cyclic loading. Diagnostics, Resource and Mechanics of Materials and Structures. 2015;2:6-15

[22] Tupikin DA. Thermoelectric method of fatigue phenomena control. Control Diagnostika. 2003;11:53-61. (rus)

[23] Ignatovich VN, Shmarov SS, Yutskevich SR. Features of formation of deformation relief on the surface of the alloy D16AT fatigue. Aviatsionno-Kosmicheslaiia Tehnika i Tehnologiia. 2009;67(10):132-135. (rus)

[24] Yermishkin VA, Murat DP, Podbelskiy VV. Application of photometric analysis of structural images to assess fatigue resistance. Avtomatizatsija i Sovremennije Tehnologii. 2008;2:11-21. (rus)

[25] Plehov ОА, Panteleiev IA, Leontiev VA. Features of heat release and generation of acoustic emission signals during cyclic deformation of Armcoiron. Fizicheskaija Mezomehanika. 2009;12(5):37-43. (rus)

[26] Marom E. Holographic Correlation. In: Erf PK, editor. Holographic Nondestructive Testing. New York: Academic Press; 1974. p. 149-180

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[28] Kozubenko VP, Potichenko VA, Borodin YS. Study of metal fatigue by speckle-correlation method. Problemy Prochnosti. 1989;7:103-107. (rus)

[37] Vladimirov AP. Dynamic speckle interferometry of high-cycle material fatigue: Theory and some experiments. AIP Conf. Proc. 2016;1740:040004.

DOI: http://dx.doi.org/10.5772/intechopen.81389

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[42] Tihonova IN, Men'shchikova AA, Vladimirov AP, Ponosov YS, Kamantsev IS, Drukarenko NA, Ishchenko AV. Kompleksnoie izuchenie mnogotsiklovoi ustalosti stali metodami dinamiki speklov, opticheskoi profilometrii, konfokal'noi, skaniruiiushei, magnitnoi I

ramanovskoi mikroscopii, ХХХ

Mezhdunarodnaia shkola-simposium po golographii, kogerentnoi optike I fotonike: Materialy shkoly-simposiuma.

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978-953-51-2956-1

[29] Vladimirov AP. Dinamika speklov v ploskosti izobrazhenija plasticheski deformiruiemogo ob'ekta. Diss… cand. fiz.-mat. nauk [Speckle dynamics in the image plane of the deformed object] [Dissert. Cand. Sci]. Sverdlovsk; 1986. 106p; (rus)

[30] Vladimirov AP. Dinamicheskaia spekl-interferometrija deformiruiemyh ob'iektov. Diss… dokt. tehn. nauk [Dynamic speckle interferometry of deformed objects] [Dissert. Doc. Eng. Sci.] Yekaterinburg; 2002. 393p; (rus)

[31] Vladimirov AP. Dynamic speckle interferometry of the microscopic processes. Proceedings of SPIE. 2012; 8413:841305; 1-6

[32] Vladimirov AP. Speckle metrology of dynamic macro- and micro-processes in deformable media. Optical Engineering. 2016;55(12):121727; 1-10. DOI: 10.1117/1.OE.55.12.121727

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[34] Vladimirov AP. Dynamic speckle – Interferometry of micro-displacements. AIP Conference Proceedings. 2012;1457: 459-468

[35] Malygin AS, Bebenina NV, Vladimirov AP, Mikitas' KN, Bakharev AA. A speckle\_interferometric device for studying the cell biological activity. Instruments and Experimental Techniques. 2012;55(3):415-418

[36] Vladimirov AP. Dynamic speckle interferometry of microscopic processes in thin biological objects. Radiophysics and Quantum Electronics. 2015;57(8): 564-576

Dynamic Speckle Interferometry of Technical and Biological Objects DOI: http://dx.doi.org/10.5772/intechopen.81389

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[20] Gilanyi A, Morishita K, Sukegawa T, Uesaka M, Miya K. Magnetic nondestructive evaluation of fatigue damage of ferromagnetic steels for nuclear fusion energy systems. Fusion Engineering and

Interferometry - Recent Developments and Contemporary Applications

speckle-correlation method. Problemy Prochnosti. 1989;7:103-107. (rus)

[29] Vladimirov AP. Dinamika speklov v ploskosti izobrazhenija plasticheski deformiruiemogo ob'ekta. Diss… cand. fiz.-mat. nauk [Speckle dynamics in the image plane of the deformed object] [Dissert. Cand. Sci]. Sverdlovsk; 1986.

[30] Vladimirov AP. Dinamicheskaia spekl-interferometrija deformiruiemyh ob'iektov. Diss… dokt. tehn. nauk [Dynamic speckle interferometry of deformed objects] [Dissert. Doc. Eng. Sci.] Yekaterinburg; 2002. 393p; (rus)

[31] Vladimirov AP. Dynamic speckle interferometry of the microscopic processes. Proceedings of SPIE. 2012;

[32] Vladimirov AP. Speckle metrology of dynamic macro- and micro-processes

Engineering. 2016;55(12):121727; 1-10.

in deformable media. Optical

DOI: 10.1117/1.OE.55.12.121727

[33] Vladimirov AP, Druzhinin AV, Malygin AS, Mikitas' КN. Theory and calibration of speckle dynamics of phase object. SPIE Proceedings. 2012;8337:

[34] Vladimirov AP. Dynamic speckle – Interferometry of micro-displacements. AIP Conference Proceedings. 2012;1457:

Vladimirov AP, Mikitas' KN, Bakharev AA. A speckle\_interferometric device for studying the cell biological activity.

[36] Vladimirov AP. Dynamic speckle interferometry of microscopic processes in thin biological objects. Radiophysics and Quantum Electronics. 2015;57(8):

[35] Malygin AS, Bebenina NV,

Instruments and Experimental Techniques. 2012;55(3):415-418

106p; (rus)

8413:841305; 1-6

8337ОС; 1-15

459-468

564-576

[21] Gorkunov ES, Savray RА, Makarov

Design. 1998;42:485-491

2015;2:6-15

(rus)

АV, Zadvorkin SМ. Magnetic techniques for estimating elastic and plastic strains in steels under cyclic loading. Diagnostics, Resource and Mechanics of Materials and Structures.

[22] Tupikin DA. Thermoelectric method of fatigue phenomena control. Control Diagnostika. 2003;11:53-61.

[23] Ignatovich VN, Shmarov SS,

2009;67(10):132-135. (rus)

2009;12(5):37-43. (rus)

[24] Yermishkin VA, Murat DP, Podbelskiy VV. Application of photometric analysis of structural images to assess fatigue resistance. Avtomatizatsija i Sovremennije Tehnologii. 2008;2:11-21. (rus)

Yutskevich SR. Features of formation of deformation relief on the surface of the alloy D16AT fatigue. Aviatsionno-Kosmicheslaiia Tehnika i Tehnologiia.

[25] Plehov ОА, Panteleiev IA, Leontiev VA. Features of heat release and generation of acoustic emission signals during cyclic deformation of Armcoiron. Fizicheskaija Mezomehanika.

[26] Marom E. Holographic Correlation.

In: Erf PK, editor. Holographic Nondestructive Testing. New York: Academic Press; 1974. p. 149-180

[27] Marom E, Muller RK. Optical correlation for impending fatigue failure detection. International Journal of Nondestructive Testing. 1971;3:171-187

[28] Kozubenko VP, Potichenko VA, Borodin YS. Study of metal fatigue by

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[38] Vladimirov AP, Bakharev AA. Dynamic speckle interferometry of thin biological objects: Theory, experiments and practical perspectives. In: Banishev AA, Bhowmick M, Wang J, editors. Optical Interferometry. Rijeka, Croatia: InTech; 2017. pp. 103-141. Print ISBN: 978-953-51-2955-4; Online ISBN: 978-953-51-2956-1

[39] Mikhailova YA, Vladimirov AP, Bakharev AA, Sergeev AG, Novoselova IA, Yakin DI. Study of cell culture reaction to temperature change by dynamic speckle interferometry [Electronic resource]. Rossijskij Zhurnal Biomehaniki. 2017;21(1):64-73

[40] Vladimirov AP, Kamantsev IS, Veselova VE, Gorkunov ES, Gladkovskii SV. Use of dynamic speckle interferometry for contactless diagnostics of fatigue crack initiation and determining its growth rate. Technical Physics. 2016;61(4): 563-568

[41] Vladimirov AP, Kamantsev IS, Ishchenko AV, Gorkunov ES, Gladkovskii SV, Zadvorkin SM. The study of the process of nucleation of fatigue cracks by changing the surface topography of the sample and its speckle images. Deformatsija i Razrushenije Materialov. 2015;1:21-26

[42] Tihonova IN, Men'shchikova AA, Vladimirov AP, Ponosov YS, Kamantsev IS, Drukarenko NA, Ishchenko AV. Kompleksnoie izuchenie mnogotsiklovoi ustalosti stali metodami dinamiki speklov, opticheskoi profilometrii, konfokal'noi, skaniruiiushei, magnitnoi I ramanovskoi mikroscopii, ХХХ Mezhdunarodnaia shkola-simposium po golographii, kogerentnoi optike I fotonike: Materialy shkoly-simposiuma.

Pod red. kand. fiz.-mat. nauk I.V. Alekseienko [In-depth study of highcycle fatigue of steel using speckle dynamics, optical profilometry, confocal, scanning, magnetic and Raman microscopy. In: XXX International symposium school in holography, coherent optics and photonics: Proceedings of symposium school. Ed. by Cand. Sci. I.V. Alekseienko]. Kaliningrad: BFU; 2017. pp. 122-123

[43] Vladimirov AP, Korovin BB, Chervoniuk VV. K razrabotke sredstv kontrolia vibratsiy rabochih lopatok GTD s ispolzovaniiem metoda dinamicheskogo specklinterferometricheskogo opredeleniia deformatsii. Perspectivy razvitiia aviatsionnyh kompleksov gosudarstvennoi aviatsii i ih silovyh ustanovok. Sbornik nauchnyh statei po materialam V Mezhdunarodnoi nauchno-practicheskoi konferentsii "Zhukovskiie akademicheskiie chteniia" [On developing facilities for monitoring the vibrations of GTE blades using speckle interferometry for strain determination/Development prospects of state aircraft systems and their power units. Collected papers based on Proceedings of V International Applied Science Conference "Zhukovsky Academic readings"]; 22–23 Nov. 2017. Voronezh; 2018. pp. 79-84

[44] Vladimirov AP. Chetyrehmernaiia spekl-tomografiia zhivyh I tehnicheskih tonkih ob'iektov: Teoreticheskaia baza, eksperimenty, dostizheniia i problemy. ХХХ Mezhdunarodnaia shkolasimposium po golographii, kogerentnoi optike I fotonike: Materialy shkolysimposiuma . Pod red. kand. fiz.-mat. nauk I.V. Alekseienko [Fourdimensional speckle tomography of live and technical thin objects: Theoretical underpinning, experiments, advances and problems. In: XXX International symposium school in holography, coherent optics and photonics: Proceedings of symposium school. Ed.

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by Cand. Sci. I.V. Alekseienko]. Kaliningrad: BFU; 2017. pp. 48-49

on Microscopy & Spectroscopy (INTERM 2018). Oludeniz, Turkey.

April 24–30. 2018; p. 36

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Interferometry - Recent Developments and Contemporary Applications

## *Edited by Mithun Bhowmick and Bruno Ullrich*

The authors provide an overview of recent developments in the field of interferometry. To achieve this aim, a broad range of topics is presented by experts who have summarized recent results drawn from theory and experiments. The simplicity and versatility of interferometry technique can be easily seen in the broad range of problems discussed in the text. This important book project presents recent, unique updates on interferometry.

Published in London, UK © 2019 IntechOpen © sakkmesterke / iStock

Interferometry - Recent Developments and Contemporary Applications

Interferometry

Recent Developments

and Contemporary Applications

*Edited by Mithun Bhowmick and Bruno Ullrich*