Preface

The aim of this book is to provide a broad range of topics on interferometry. The topics include some modern techniques, recent approaches to solve issues with a technique, applicability of interferometry in novel scenarios, as well as analytical treatments needed to pursue in-depth exploration.

In recent times, the application of interferometry has broadened. With that in mind, an overview of updates and recent contributions is provided in Chapter 1, the introductory chapter. It is intended to highlight the significance of recent works as well, with emphasis on connections between other scientific areas of research that have been key to the relevance of the technique. In Chapter 2, radial shearing interferometer is discussed. Chapter 3 describes a detailed method to differentiate superposition principle from measurable superposition effects. Fiber-optic ring resonator is discussed in Chapter 4. Chapter 5 highlights modal interferometers based on a tapered special photonics crystal fiber for highly sensitive detection. Finally, in Chapter 6, application of interferometry in biological systems is addressed through dynamic speckle interferometry technique.

It was an exciting journey for us to work on this project. We would like to thank all the contributors for sharing their expertise on the topic and for their commitment to academic integrity. We want to acknowledge our author service manager, Ms. Sara Debeuc, and other staff of IntechOpen for their untiring support and patience, which made the book possible.

Finally, we would like to thank the readers; we sincerely hope this book achieves its goals by contributing positively to the research community.

> **Mithun Bhowmick** School of Chemical Sciences, University of Illinois, Urbana, USA

Department of Mathematical and Physical Sciences Miami University, Ohio, USA

> **Bruno Ullrich** Ullrich Photonics LLC, Ohio, USA

**1**

**Chapter 1**

**1. Introduction**

mental conditions [2].

technique will be discussed.

Introductory Chapter:

*Mithun Bhowmick and Bruno Ullrich*

Interferometry has been a very effective tool for science and industry for many years. From optics to astronomy, from materials science to mechanical engineering, interferometry has been instrumental in pushing the boundaries of technological progress. The field has come a long way since one of its earliest mention in the news section of *Nature* in 1920 [1]. At one time optical interferometry relied heavily on on monochromators, limiting the potential applications. Nowadays, the electromagnetic source used in generating fringes is far advanced, owing to the advent of lasers with unprecedented bandwidths and intensities. However, the techniques associated to interference of electromagnetic waves is no longer limited to all optical methods. Incoherent sources can now be made to interfere under certain experi-

The power of interferometry has made it an obvious tool to explore interdisciplinary research in modern times and has expanded to topics related to chemistry, mechanical engineering and material science related topics such as shock spectroscopy, surface profiling, and microfluidics [3–5]. In the recent gravitational wave discovery, it was an interferometer called "LIGO" that made it possible. In this chapter, a brief discussion will be presented on how the field has evolved in different research directions with time along with some examples from the recent literature which has helped the expansion. A brief overview of issues of interferometry technique in general will also be provided where artifacts inherent with the

Interferometry represents a set of techniques where, in its most common form, electromagnetic waves superimpose thereby forming interference fringes. The phenomenon involving interference occurs all around us. For example, a drop of oil on water or a soap bubble generates coloration because of naturally occurring interference. In interference, small changes in optical path cause significant and precisely measurable changes in intensity pattern. Using this property, a wide variety of experiments is designed where precise length measurements are necessary. In mechanochemistry, shock science, and detonation studies, measuring free surface velocity is very important. Optical interferometry with the highest time resolution has enabled such measurements. These techniques fall under the umbrella of "laser velocity interferometry" and consist of well-known and established methods such as VISAR, ORVIS, several Quartz-based stress gauges and so on [6]. A similar technique, termed as photon Doppler velocimetry (PDV) has been very useful to probe explosive chemistry in the short length scale with nanosecond time resolution [3]. These interferometric techniques can also accurately investigate shock response in solids. In this technique, typically a single mode laser beam is split into two. One of them is focused onto a moving, flat surface. The surface is usually polished; hence a strong reflection of the beam is generated. The reflected beam combines with the

Interferometry

## **Chapter 1**

## Introductory Chapter: Interferometry

*Mithun Bhowmick and Bruno Ullrich*

## **1. Introduction**

Interferometry has been a very effective tool for science and industry for many years. From optics to astronomy, from materials science to mechanical engineering, interferometry has been instrumental in pushing the boundaries of technological progress. The field has come a long way since one of its earliest mention in the news section of *Nature* in 1920 [1]. At one time optical interferometry relied heavily on on monochromators, limiting the potential applications. Nowadays, the electromagnetic source used in generating fringes is far advanced, owing to the advent of lasers with unprecedented bandwidths and intensities. However, the techniques associated to interference of electromagnetic waves is no longer limited to all optical methods. Incoherent sources can now be made to interfere under certain experimental conditions [2].

The power of interferometry has made it an obvious tool to explore interdisciplinary research in modern times and has expanded to topics related to chemistry, mechanical engineering and material science related topics such as shock spectroscopy, surface profiling, and microfluidics [3–5]. In the recent gravitational wave discovery, it was an interferometer called "LIGO" that made it possible. In this chapter, a brief discussion will be presented on how the field has evolved in different research directions with time along with some examples from the recent literature which has helped the expansion. A brief overview of issues of interferometry technique in general will also be provided where artifacts inherent with the technique will be discussed.

Interferometry represents a set of techniques where, in its most common form, electromagnetic waves superimpose thereby forming interference fringes. The phenomenon involving interference occurs all around us. For example, a drop of oil on water or a soap bubble generates coloration because of naturally occurring interference. In interference, small changes in optical path cause significant and precisely measurable changes in intensity pattern. Using this property, a wide variety of experiments is designed where precise length measurements are necessary. In mechanochemistry, shock science, and detonation studies, measuring free surface velocity is very important. Optical interferometry with the highest time resolution has enabled such measurements. These techniques fall under the umbrella of "laser velocity interferometry" and consist of well-known and established methods such as VISAR, ORVIS, several Quartz-based stress gauges and so on [6]. A similar technique, termed as photon Doppler velocimetry (PDV) has been very useful to probe explosive chemistry in the short length scale with nanosecond time resolution [3]. These interferometric techniques can also accurately investigate shock response in solids. In this technique, typically a single mode laser beam is split into two. One of them is focused onto a moving, flat surface. The surface is usually polished; hence a strong reflection of the beam is generated. The reflected beam combines with the

remaining beam, which has gone through a delay line meanwhile, to generate beats. The beats are counted using suitable algorithm to make a velocity history of the surface (i.e., the reflector). The same experiment can be performed in two different geometries, the most common being one where we can record a velocity history for an incoming object. In shocked systems, one can thus obtain information regarding pressure and density evolutions with high time resolution [3, 6]. In another geometry, a thin layer of reflective surface (typically a metal) is deposited at one side of the substrate being shocked, and the substrate is exposed to shock in such a way that the shock emerges through the reflective surface. This is a very powerful technique to generate shock break out profiles and is also used in generating Hugoniot points in materials. A Hugoniot is a collection of data points obtained from single shot shock experiments. Each data point in a Hugoniot curve gives us a shock velocity (Us) corresponding to a mass particle velocity (Up). Using this information, one can distinguish between shock loading and unloading mechanisms in solids. In a recent study, the researchers have shown that shock break out experiments in explosives are significantly affected on solid properties if the solids are different in crystallinity [7]. Thus, a highly crystalline sample such as sapphire or calcium fluoride would show different shock break out traces compared to polymer or glassy substances [7]. Gauge experiments are also reputed for accurately generating Hugoniot points. A series of such experiments performed LASL data center is currently being used by the shock community for impedance matching in designing experiments [8].

Interdisciplinary research has seen a great deal of hybrid techniques where two powerful spectroscopic methods are simultaneously used to extract unique information from a system. Fluorescence interferometry (FI) is one such example. There are various configurations of FI. In one variant, the self-reference interferometer consists of lenses that gather light from two sides of the sample simultaneously after the main beam is split using suitable optics [9]. The two beams are used as excitation and probe [9]. In another version, a Fourier transformed signal is used to generate a time domain information [9]. In general, fluorescence interferometry is very powerful as it complements the traditional fluorescence experiments by extracting the phase information. Such experiments have already provided with high resolution single shot images in biological specimens with marking capability [9]. Several ongoing and future research efforts are focused on getting a reliable, detailed 3D image using selective markers with the help of quantum dots. In summary, more advanced techniques such as optical nanoscopy is where FI is going to be very useful.

Another established area of research that benefitted greatly is materials science laboratories where optical materials are characterized using either white-lightinterferometry or where interferometry is used for surface profiling [10, 11]. Both two- and three-dimensional optical profilers use interferometry to accurately map surface roughness. In the most common set up, an optical profiler uses the optical path difference to generate interference fringes between two signals coming from a reference surface and a "signal" surface. The "signal" surface is basically the surface under investigation. Many commercial optical profilers (for example, Zygo) are in operation in modern characterization laboratories [11]. Surface profiling is very crucial for understanding stress models in solids. There is a huge demand of modeling solids under stress. A lot of efforts are being made currently in those directions, where one would be able to numerically simulate response of solids [12]. To do that, the model should be robust enough to successfully simulate existing experimental data. There are open questions related to chemical kinetics and initiation of energetic materials which could be answered once the models can accurately simulate current high-resolution interferometry data [13]. One such example is the reactive and flow model "ALE3D," developed at Lawrence Livermore National Laboratory [14].

**3**

*Introductory Chapter: Interferometry*

*DOI: http://dx.doi.org/10.5772/intechopen.84371*

including optical frequency comb [20].

In fields such as industrial sensing and space engineering, measuring distances with high precision is important, where a traditional form of single-wavelength interferometry has been used in the past [15]. To get the distance, a fringe counting algorithm is used in single-wavelength interferometry, which sometimes can cause errors in position measurements [16]. However, a relatively new technique called multiple-wavelength interferometry has been in practice recently which avoids fringe counting [17]. The technique has lots of advantage such as capability of measuring very small distances, flexibility, etc., with one small disadvantage; it requires several synthetic wavelengths for increasing the experiment range of the system, thereby increasing complexity of the technique. To solve this problem, researchers have started to use a frequency comb, which emits equally spaced ultra-short pulses [17]. These pulses are spread over a broad spectrum with discrete and uniform modes. The modes are also spaced equally, with very narrow lines [17]. This resembles an ultra-accurate ruler, with deviation in the order of 70 nm for a measurement of 100 mm length [19]. Frequency combs are generated in different ways such as 4-wave mixing or using a mode locked laser, or even by electro-optic modulation. In 2005, Theodor W. Hänsch and John L. Hall shared half of the Nobel prize in Physics for the discovery of a group of precision spectroscopy techniques,

There are several applications of precision interferometric methods in metrology, materials science, satellite technology, and a myriad of similar fields where optoelectronic and photonic properties are utilized. As mentioned earlier while briefly discussing white light interferometry (WLI), a series of novel quantum optical techniques employed for reducing noise in a superposition signal, to avoid third-order dispersion, and thrive on interferometric equalization [21]. The resulting variant of WLI is called quantum-WLI (or Q-WLI). Q-WLI is a fast, all-optical

Despite its versatility and impact, there are some areas where optical interferometric effects make spectroscopy very difficult to perform. One such example is a coherent artifact occurs in ultrafast degenerate pump-probe experiment with femtosecond pulses, where the strong signal at temporal overlap of the two beams screens the actual rise time of the "true signal" [21]. A degenerate pump-probe experiment (DPP) is the case where both the pump and probe are of same wavelengths [22]. DPPs are heavily used in probing novel materials to extract signatures of many-body effects in electron/spin scattering mechanisms [21, 22]. By varying the relative intensities of two beams, or by adjusting the polarization angle that effect can be corrected [23, 24]. Interference patterns generated by unwanted resonance can thus affect optical measurements. There are various experimental scenarios of light-matter interaction where signal to noise ratio needs to be very high. Raman scattering measurements, photoluminescence and fluorescence experiments, quantum confinement studies, spin injection and manipulation studies, absorption spectroscopy, and many such complex and delicate probing techniques rely on efficient collection of photons. It is important to understand the limitations in those collection processes as the measurement is designed, since interference of signals can obscure the data one is looking for. For example, while measuring transmission spectra from a thin film, or a layered material, interference effects are observed as oscillations in the spectra [25]. Sometimes, the effect is welcome when the film thickness is unknown and needs to be measured [26, 27]. At other times the interference effect makes it difficult to efficiently fit the spectra to get important band parameters in solids [28]. In photoluminescence measurements, such effects can change the linewidth and the analysis based on broadening of the signal gets affected [29, 30]. In micro and nano-fabrication techniques, and various laser based thin-film deposition systems, interference effects are also visible [30]. A

technique for investigating material properties with high precision [10].

### *Introductory Chapter: Interferometry DOI: http://dx.doi.org/10.5772/intechopen.84371*

*Interferometry - Recent Developments and Contemporary Applications*

remaining beam, which has gone through a delay line meanwhile, to generate beats. The beats are counted using suitable algorithm to make a velocity history of the surface (i.e., the reflector). The same experiment can be performed in two different geometries, the most common being one where we can record a velocity history for an incoming object. In shocked systems, one can thus obtain information regarding pressure and density evolutions with high time resolution [3, 6]. In another geometry, a thin layer of reflective surface (typically a metal) is deposited at one side of the substrate being shocked, and the substrate is exposed to shock in such a way that the shock emerges through the reflective surface. This is a very powerful technique to generate shock break out profiles and is also used in generating Hugoniot points in materials. A Hugoniot is a collection of data points obtained from single shot shock experiments. Each data point in a Hugoniot curve gives us a shock velocity (Us) corresponding to a mass particle velocity (Up). Using this information, one can distinguish between shock loading and unloading mechanisms in solids. In a recent study, the researchers have shown that shock break out experiments in explosives are significantly affected on solid properties if the solids are different in crystallinity [7]. Thus, a highly crystalline sample such as sapphire or calcium fluoride would show different shock break out traces compared to polymer or glassy substances [7]. Gauge experiments are also reputed for accurately generating Hugoniot points. A series of such experiments performed LASL data center is currently being used by the shock community for impedance matching in designing experiments [8].

Interdisciplinary research has seen a great deal of hybrid techniques where two powerful spectroscopic methods are simultaneously used to extract unique information from a system. Fluorescence interferometry (FI) is one such example. There are various configurations of FI. In one variant, the self-reference interferometer consists of lenses that gather light from two sides of the sample simultaneously after the main beam is split using suitable optics [9]. The two beams are used as excitation and probe [9]. In another version, a Fourier transformed signal is used to generate a time domain information [9]. In general, fluorescence interferometry is very powerful as it complements the traditional fluorescence experiments by extracting the phase information. Such experiments have already provided with high resolution single shot images in biological specimens with marking capability [9]. Several ongoing and future research efforts are focused on getting a reliable, detailed 3D image using selective markers with the help of quantum dots. In summary, more advanced techniques such as optical nanoscopy is where FI is going to

Another established area of research that benefitted greatly is materials science

laboratories where optical materials are characterized using either white-lightinterferometry or where interferometry is used for surface profiling [10, 11]. Both two- and three-dimensional optical profilers use interferometry to accurately map surface roughness. In the most common set up, an optical profiler uses the optical path difference to generate interference fringes between two signals coming from a reference surface and a "signal" surface. The "signal" surface is basically the surface under investigation. Many commercial optical profilers (for example, Zygo) are in operation in modern characterization laboratories [11]. Surface profiling is very crucial for understanding stress models in solids. There is a huge demand of modeling solids under stress. A lot of efforts are being made currently in those directions, where one would be able to numerically simulate response of solids [12]. To do that, the model should be robust enough to successfully simulate existing experimental data. There are open questions related to chemical kinetics and initiation of energetic materials which could be answered once the models can accurately simulate current high-resolution interferometry data [13]. One such example is the reactive and flow model "ALE3D," developed at Lawrence Livermore National Laboratory [14].

**2**

be very useful.

In fields such as industrial sensing and space engineering, measuring distances with high precision is important, where a traditional form of single-wavelength interferometry has been used in the past [15]. To get the distance, a fringe counting algorithm is used in single-wavelength interferometry, which sometimes can cause errors in position measurements [16]. However, a relatively new technique called multiple-wavelength interferometry has been in practice recently which avoids fringe counting [17]. The technique has lots of advantage such as capability of measuring very small distances, flexibility, etc., with one small disadvantage; it requires several synthetic wavelengths for increasing the experiment range of the system, thereby increasing complexity of the technique. To solve this problem, researchers have started to use a frequency comb, which emits equally spaced ultra-short pulses [17]. These pulses are spread over a broad spectrum with discrete and uniform modes. The modes are also spaced equally, with very narrow lines [17]. This resembles an ultra-accurate ruler, with deviation in the order of 70 nm for a measurement of 100 mm length [19]. Frequency combs are generated in different ways such as 4-wave mixing or using a mode locked laser, or even by electro-optic modulation. In 2005, Theodor W. Hänsch and John L. Hall shared half of the Nobel prize in Physics for the discovery of a group of precision spectroscopy techniques, including optical frequency comb [20].

There are several applications of precision interferometric methods in metrology, materials science, satellite technology, and a myriad of similar fields where optoelectronic and photonic properties are utilized. As mentioned earlier while briefly discussing white light interferometry (WLI), a series of novel quantum optical techniques employed for reducing noise in a superposition signal, to avoid third-order dispersion, and thrive on interferometric equalization [21]. The resulting variant of WLI is called quantum-WLI (or Q-WLI). Q-WLI is a fast, all-optical technique for investigating material properties with high precision [10].

Despite its versatility and impact, there are some areas where optical interferometric effects make spectroscopy very difficult to perform. One such example is a coherent artifact occurs in ultrafast degenerate pump-probe experiment with femtosecond pulses, where the strong signal at temporal overlap of the two beams screens the actual rise time of the "true signal" [21]. A degenerate pump-probe experiment (DPP) is the case where both the pump and probe are of same wavelengths [22]. DPPs are heavily used in probing novel materials to extract signatures of many-body effects in electron/spin scattering mechanisms [21, 22]. By varying the relative intensities of two beams, or by adjusting the polarization angle that effect can be corrected [23, 24]. Interference patterns generated by unwanted resonance can thus affect optical measurements. There are various experimental scenarios of light-matter interaction where signal to noise ratio needs to be very high. Raman scattering measurements, photoluminescence and fluorescence experiments, quantum confinement studies, spin injection and manipulation studies, absorption spectroscopy, and many such complex and delicate probing techniques rely on efficient collection of photons. It is important to understand the limitations in those collection processes as the measurement is designed, since interference of signals can obscure the data one is looking for. For example, while measuring transmission spectra from a thin film, or a layered material, interference effects are observed as oscillations in the spectra [25]. Sometimes, the effect is welcome when the film thickness is unknown and needs to be measured [26, 27]. At other times the interference effect makes it difficult to efficiently fit the spectra to get important band parameters in solids [28]. In photoluminescence measurements, such effects can change the linewidth and the analysis based on broadening of the signal gets affected [29, 30]. In micro and nano-fabrication techniques, and various laser based thin-film deposition systems, interference effects are also visible [30]. A recent paper attempted to analyze intrinsic photoluminescence stoke shift in pulsed laser deposited thin film of CdS to interpret physical meaning of a phenomenological parameter used in Urbach model [30]. The same paper also tried to look at the Raman peaks and probed the phonon population by calculating Huang-Rhys factor [30]. Raman lines are particularly susceptible of background noise, and there are many techniques developed for enhancing Raman signal. A recent study concluded that interference effects are crucial in the micro-Raman spectroscopy of graphene and must be included in analysis when extracting various material information from the spectra [31]. As we move into ternary and quaternary alloys and magnetically doped novel materials for ambient operable devices that successfully exploit charge and spin mobility, experimenters have come to avoid any such effects in the measurement scheme [32].

On February 11, 2016, observation of gravitational waves was announced from the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) [33]. It has become one of the most significant scientific landmarks of recent times, prompting a Nobel prize in 2017 to Rainer Weiss, Kip Thorne and Barry Barish for their contribution towards this discovery [34, 35]. A detailed description of LIGO is out of the scope of this chapter. In short, the apparatus is a Michelson interferometer built at a massive scale [35]. Just like the Michelson-Morley experiment made a conclusive discovery in 1887 to disprove "Luminiferous Aether," LIGOinterferometer measurements have conclusively detected presence of a gravitation waves. It is clear from the updates presented above, how interferometry is one of the most advanced and precision techniques presently being pursued. The development in the field of laser technology has made the progress rapid. Very high time resolutions are being increasingly attained using attosecond laser pulses [36]. This is another huge improvement in understanding reaction mechanisms and will enable scientists to understand processes involved in solar cells by watching in real time the detailed step-by-step energy flow/conversion [36].

To summarize, interferometry is undoubtedly one of the most thriving and rapidly progressing experimental techniques. With applications in so many different fields, interferometers are going to be employed with increasing fashion. The versatility makes the technique almost indispensable in high precision spectroscopy and novel materials. The small and large-scale applicability made it an automatic choice as a consistent and transferable tool. The fact that two of the historic discoveries were made in the field of Physics on interferometer vouches for its power and significance. With increasing finesse in laser engineering, ultra-short laser-pulse based interferometers are going to resolve fundamental mechanisms of physical and life sciences with even greater detail, and this will impact a few of the most urgent technological needs modern society face today: renewable energy/energy harvesting, incorporating devices in biomaterials, and scarcity of resources.

**5**

**Author details**

provided the original work is properly cited.

Mithun Bhowmick1,3\* and Bruno Ullrich2

2 Ullrich Photonics LLC, Wayne, Ohio, USA

\*Address all correspondence to: bhowmick@illinois.edu

1 School of Chemical Sciences, University of Illinois, Urbana, USA

*Introductory Chapter: Interferometry*

*DOI: http://dx.doi.org/10.5772/intechopen.84371*

© 2019 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,

3 Department of Mathematical and Physical Sciences, Miami University, Ohio, USA

*Introductory Chapter: Interferometry DOI: http://dx.doi.org/10.5772/intechopen.84371*

*Interferometry - Recent Developments and Contemporary Applications*

measurement scheme [32].

detailed step-by-step energy flow/conversion [36].

recent paper attempted to analyze intrinsic photoluminescence stoke shift in pulsed laser deposited thin film of CdS to interpret physical meaning of a phenomenological parameter used in Urbach model [30]. The same paper also tried to look at the Raman peaks and probed the phonon population by calculating Huang-Rhys factor [30]. Raman lines are particularly susceptible of background noise, and there are many techniques developed for enhancing Raman signal. A recent study concluded that interference effects are crucial in the micro-Raman spectroscopy of graphene and must be included in analysis when extracting various material information from the spectra [31]. As we move into ternary and quaternary alloys and magnetically doped novel materials for ambient operable devices that successfully exploit charge and spin mobility, experimenters have come to avoid any such effects in the

On February 11, 2016, observation of gravitational waves was announced from the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) [33]. It has become one of the most significant scientific landmarks of recent times, prompting a Nobel prize in 2017 to Rainer Weiss, Kip Thorne and Barry Barish for their contribution towards this discovery [34, 35]. A detailed description of LIGO is out of the scope of this chapter. In short, the apparatus is a Michelson interferometer built at a massive scale [35]. Just like the Michelson-Morley experiment made a conclusive discovery in 1887 to disprove "Luminiferous Aether," LIGOinterferometer measurements have conclusively detected presence of a gravitation waves. It is clear from the updates presented above, how interferometry is one of the most advanced and precision techniques presently being pursued. The development in the field of laser technology has made the progress rapid. Very high time resolutions are being increasingly attained using attosecond laser pulses [36]. This is another huge improvement in understanding reaction mechanisms and will enable scientists to understand processes involved in solar cells by watching in real time the

To summarize, interferometry is undoubtedly one of the most thriving and rapidly progressing experimental techniques. With applications in so many different fields, interferometers are going to be employed with increasing fashion. The versatility makes the technique almost indispensable in high precision spectroscopy and novel materials. The small and large-scale applicability made it an automatic choice as a consistent and transferable tool. The fact that two of the historic discoveries were made in the field of Physics on interferometer vouches for its power and significance. With increasing finesse in laser engineering, ultra-short laser-pulse based interferometers are going to resolve fundamental mechanisms of physical and life sciences with even greater detail, and this will impact a few of the most urgent technological needs modern society face today: renewable energy/energy harvest-

ing, incorporating devices in biomaterials, and scarcity of resources.

**4**

## **Author details**

Mithun Bhowmick1,3\* and Bruno Ullrich2

1 School of Chemical Sciences, University of Illinois, Urbana, USA

2 Ullrich Photonics LLC, Wayne, Ohio, USA

3 Department of Mathematical and Physical Sciences, Miami University, Ohio, USA

\*Address all correspondence to: bhowmick@illinois.edu

© 2019 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.

## **References**

[1] Applications of interferometry. Nature. 1920;**104**:677. Available from: https://www.nature.com/ articles/104677b0

[2] Patel R, Achamfuo-Yeboah S, Light R, Clark M. Widefield two laser interferometry. Optics Express. 2014;**22**:27094-27101. DOI: 10.1364/ OE.22.027094

[3] Bhowmick M, Nissen EJ, Dlott DD. Detonation on a tabletop: Nitromethane with high time and space resolution. Journal of Applied Physics. 2018;**124**:075901. DOI: 10.1063/1.5043540

[4] Chen LC, Nguyen XL. Measurement science and technology. 2010;**21**(5)

[5] Domachuk P, Grillet C, Ta'eed V, Mägi E, Bolger J, Eggleton BJ, et al. Microfluidic interferometer. Applied Physics Letters. 2005;**86**:024103. DOI: 10.1063/1.1849415

[6] Forbes JW. Shock Wave Compression of Condensed Matter: A Primer. New York: Springer; 2012. DOI: 10.1007/978-3-642-32535-9

[7] Bhowmick M, Basset WP, Matveev S, Salvati L III, Dlott DD. Optical windows as high-speed shock wave detectors. AIP Advances. 2018;**8**:125123. DOI: 10.1063/1.5055676

[8] Marsh SP, editor. LASL Shock Hugoniot Data. University of California Press; 1980

[9] Bilenca A, Cao J, Colice M, Ozcan A, Bouma B, Raftery L, et al. Fluorescence interferometry: Principles and applications in biology. Annals of the New York Academy of Sciences. 2008;**1130**:68-77. DOI: 10.1196/ annals.1430.038

[10] Kaiser F et al. Quantum enhancement of accuracy and precision in optical interferometry. Light: Science & Applications. 2018;**7**:17163. DOI: 10.1038/lsa.2017.163

[11] https://www.zygo.com/?/met/ profilers/surfaceprofiling.htm

[12] Stekovic S, Nissen EJ, Bhowmick M, Stewart DS, Dlott DD. Numerical predictions of shock propagation through unreactive and reactive liquids with experimental validation. AIP Conference Proceedings. 2018;**1979**(1):100039. DOI: 10.1063/1.5044911

[13] Bhowmick M, Nissen EJ, Matveev SM, Dlott DD. Studies in shocked nitromethane through high dynamic range spectroscopy. AIP Conference Proceedings. 2018;**1979**(1):100004. DOI: 10.1063/1.5044876

[14] Nichols AL III et al. ALE3D v4.14 Manual Volume 2, Material and Chemical models. Livermore, CA: Lawrence Livermore National Laboratory; 2011

[15] Bender PL, Hall JL, Ye J, Klipstein WM. Satellite-satellite laser links for future gravity missions. Space Science Reviews. 2003;**108**:377-384. DOI: 10.1023/A:1026195913558

[16] Falaggis K, Towers DP, Towers CE. Multiwavelength interferometry: Extended range metrology. Optics Letters. 2009;**34**:950-952. DOI: 10.1364/ OL.34.000950

[17] Dandliker R, Salvade Y, Zimmermann E. Distance measurement by multiple-wavelength interferometry. Journal of Optics-Nouvelle Revue D Optique. 1998;**29**:105-114. DOI: 10.1088/0150-536X/29/3/002

**7**

*Introductory Chapter: Interferometry*

*DOI: http://dx.doi.org/10.5772/intechopen.84371*

[27] Ullrich B, Singh AK, Barik P, Xi H, Bhowmick M. Inherent

DOI: 10.1364/OL.40.002580

10.1063/1.4980142

DOI: 10.1063/1.4897383

tsf.2014.02.047

PhysRevB.80.125422

DOI: 10.1063/1.4808346

2019]

[30] Ullrich B, Ariza-Flores D, Bhowmick M. Intrinsic

photoluminescence Stokes shift in semiconductors demonstrated by thin-film CdS formed with pulsedlaser deposition. Thin Solid Films. 2014;**558**:24-26. DOI: 10.1016/j.

[31] Yoon D, Moon H, Soon Y, Choi JS, Park BH, Cha YH, et al. Interference effect on Raman spectrum of graphene SiO2/Si. Physical Review B. 2009;**80**:125422. DOI: 10.1103/

[32] Meeker MA, Magill BA, Merritt TR, Bhowmick M, McCutcheon K. Dynamics of photoexcited carriers and spins in InAsP ternary alloys. Applied Physics Letters. 2013;**102**(22):222102.

[33] Castelvecchi D, Witze A. Einstein's Gravitational Waves Found at Last. Nature/News [Internet]. February 11, 2016. Available from: https:// www.nature.com/news/einsteins-gravitational-waves-found-atlast-1.19361 [Accessed: January 12,

[34] Overbye D. Gravitational Waves Detected, Confirming Einstein's Theory. New York Times [Internet]. February

[28] Ullrich B, Bhowmick M, Xi H. Relation between Debye temperature and energy band gap of semiconductors. AIP Advances. 2017;**7**(4):045109. DOI:

[29] Ullrich B, Singh AK, Bhowmick M, Barik P, Ariza-Flores D, Xi H, et al. Photoluminescence lineshape of ZnO. AIP Advances. 2014;**4**(12):123001.

photoluminescence Stokes shift in GaAs. Optics Letters. 2015;**40**(11):2580-2583.

[19] Wu G, Liao L, Xiong S, Li G, Zhu Z. Synthetic wavelength interferometry of an optical frequency comb for absolute distance measurement. Scientific Reports. 2018;**8**:4362. DOI: 10.1038/s41598-018-22838-0DO

[20] https://en.wikipedia.org/wiki/ Frequency\_comb#Applications

[21] Bhowmick M, Khodaparast GA, Mishima TD, Santos MB, Saha D, Sanders G, et al. Interband and intraband relaxation dynamics in InSb based quantum wells. Journal of Applied Physics. 2016;**120**(23):235702.

DOI: 10.1063/1.4971347

[22] Bhowmick M, Merritt TR,

10.1103/PhysRevB.85.125313

[24] Lebedev MV, Misochko OV, Dekorsy T, Georgiev N. On the nature of "coherent artifact". Journal of Experimental and Theoretical Physics. 2005;**100**(2):272-282. DOI:

[25] Heavens OS. Optical Properties of Thin Solid Films. New York: Dover

[26] Ullrich B, Antillón A, Bhowmick M, Wang JS, Xi H. Atomic transition region at the crossover between quantum dots to molecules. Physica Scripta. 2014;**89**(2):025801. DOI: 10.1088/0031-8949/89/02/025801

10.1134/1.1884668

Publications; 1954

Khodaparast GA, Wessels BW, McGill SA, Saha D, et al. Time-resolved differential transmission in MOVPEgrown ferromagnetic InMnAs. Physical Review B. 2012;**85**(12):125313. DOI:

[23] Hui L, Hang Z, Jin-Hai S, Li-He Y, Fengand C, Xun H. Elimination of the coherent effect in a pumpprobe experiment by directly detecting the background-free diffraction signal. Chinese Physics Letters. 2011;**28**(8). DOI: 10.1088/0256-307X/28/8/086602

[18] Kim SW. Combs rule. Nature Photonics. 2009;**3**:313-314. DOI: 10.1038/nphoton.2009.86

## *Introductory Chapter: Interferometry DOI: http://dx.doi.org/10.5772/intechopen.84371*

[19] Wu G, Liao L, Xiong S, Li G, Zhu Z. Synthetic wavelength interferometry of an optical frequency comb for absolute distance measurement. Scientific Reports. 2018;**8**:4362. DOI: 10.1038/s41598-018-22838-0DO

[20] https://en.wikipedia.org/wiki/ Frequency\_comb#Applications

[21] Bhowmick M, Khodaparast GA, Mishima TD, Santos MB, Saha D, Sanders G, et al. Interband and intraband relaxation dynamics in InSb based quantum wells. Journal of Applied Physics. 2016;**120**(23):235702. DOI: 10.1063/1.4971347

[22] Bhowmick M, Merritt TR, Khodaparast GA, Wessels BW, McGill SA, Saha D, et al. Time-resolved differential transmission in MOVPEgrown ferromagnetic InMnAs. Physical Review B. 2012;**85**(12):125313. DOI: 10.1103/PhysRevB.85.125313

[23] Hui L, Hang Z, Jin-Hai S, Li-He Y, Fengand C, Xun H. Elimination of the coherent effect in a pumpprobe experiment by directly detecting the background-free diffraction signal. Chinese Physics Letters. 2011;**28**(8). DOI: 10.1088/0256-307X/28/8/086602

[24] Lebedev MV, Misochko OV, Dekorsy T, Georgiev N. On the nature of "coherent artifact". Journal of Experimental and Theoretical Physics. 2005;**100**(2):272-282. DOI: 10.1134/1.1884668

[25] Heavens OS. Optical Properties of Thin Solid Films. New York: Dover Publications; 1954

[26] Ullrich B, Antillón A, Bhowmick M, Wang JS, Xi H. Atomic transition region at the crossover between quantum dots to molecules. Physica Scripta. 2014;**89**(2):025801. DOI: 10.1088/0031-8949/89/02/025801

[27] Ullrich B, Singh AK, Barik P, Xi H, Bhowmick M. Inherent photoluminescence Stokes shift in GaAs. Optics Letters. 2015;**40**(11):2580-2583. DOI: 10.1364/OL.40.002580

[28] Ullrich B, Bhowmick M, Xi H. Relation between Debye temperature and energy band gap of semiconductors. AIP Advances. 2017;**7**(4):045109. DOI: 10.1063/1.4980142

[29] Ullrich B, Singh AK, Bhowmick M, Barik P, Ariza-Flores D, Xi H, et al. Photoluminescence lineshape of ZnO. AIP Advances. 2014;**4**(12):123001. DOI: 10.1063/1.4897383

[30] Ullrich B, Ariza-Flores D, Bhowmick M. Intrinsic photoluminescence Stokes shift in semiconductors demonstrated by thin-film CdS formed with pulsedlaser deposition. Thin Solid Films. 2014;**558**:24-26. DOI: 10.1016/j. tsf.2014.02.047

[31] Yoon D, Moon H, Soon Y, Choi JS, Park BH, Cha YH, et al. Interference effect on Raman spectrum of graphene SiO2/Si. Physical Review B. 2009;**80**:125422. DOI: 10.1103/ PhysRevB.80.125422

[32] Meeker MA, Magill BA, Merritt TR, Bhowmick M, McCutcheon K. Dynamics of photoexcited carriers and spins in InAsP ternary alloys. Applied Physics Letters. 2013;**102**(22):222102. DOI: 10.1063/1.4808346

[33] Castelvecchi D, Witze A. Einstein's Gravitational Waves Found at Last. Nature/News [Internet]. February 11, 2016. Available from: https:// www.nature.com/news/einsteins-gravitational-waves-found-atlast-1.19361 [Accessed: January 12, 2019]

[34] Overbye D. Gravitational Waves Detected, Confirming Einstein's Theory. New York Times [Internet]. February

**6**

*Interferometry - Recent Developments and Contemporary Applications*

in optical interferometry. Light: Science & Applications. 2018;**7**:17163. DOI:

[11] https://www.zygo.com/?/met/ profilers/surfaceprofiling.htm

[12] Stekovic S, Nissen EJ, Bhowmick M, Stewart DS, Dlott DD. Numerical predictions of shock propagation through unreactive and reactive liquids with experimental validation.

[13] Bhowmick M, Nissen EJ, Matveev SM, Dlott DD. Studies in shocked nitromethane through high dynamic range spectroscopy. AIP Conference Proceedings. 2018;**1979**(1):100004.

AIP Conference Proceedings. 2018;**1979**(1):100039. DOI:

10.1063/1.5044911

DOI: 10.1063/1.5044876

10.1023/A:1026195913558

[17] Dandliker R, Salvade Y,

[18] Kim SW. Combs rule. Nature Photonics. 2009;**3**:313-314. DOI: 10.1038/nphoton.2009.86

Laboratory; 2011

OL.34.000950

[14] Nichols AL III et al. ALE3D v4.14 Manual Volume 2, Material and Chemical models. Livermore, CA: Lawrence Livermore National

[15] Bender PL, Hall JL, Ye J, Klipstein WM. Satellite-satellite laser links for future gravity missions. Space Science Reviews. 2003;**108**:377-384. DOI:

[16] Falaggis K, Towers DP, Towers CE. Multiwavelength interferometry: Extended range metrology. Optics Letters. 2009;**34**:950-952. DOI: 10.1364/

Zimmermann E. Distance measurement by multiple-wavelength interferometry. Journal of Optics-Nouvelle Revue D Optique. 1998;**29**:105-114. DOI: 10.1088/0150-536X/29/3/002

10.1038/lsa.2017.163

**References**

articles/104677b0

OE.22.027094

10.1063/1.5043540

10.1063/1.1849415

10.1063/1.5055676

Press; 1980

annals.1430.038

[1] Applications of interferometry. Nature. 1920;**104**:677. Available from: https://www.nature.com/

[2] Patel R, Achamfuo-Yeboah S, Light R, Clark M. Widefield two laser interferometry. Optics Express. 2014;**22**:27094-27101. DOI: 10.1364/

[3] Bhowmick M, Nissen EJ, Dlott DD. Detonation on a tabletop: Nitromethane with high time and space resolution. Journal of Applied Physics. 2018;**124**:075901. DOI:

[4] Chen LC, Nguyen XL. Measurement science and technology. 2010;**21**(5)

[6] Forbes JW. Shock Wave Compression

[7] Bhowmick M, Basset WP, Matveev S, Salvati L III, Dlott DD. Optical windows as high-speed shock wave detectors. AIP Advances. 2018;**8**:125123. DOI:

of Condensed Matter: A Primer. New York: Springer; 2012. DOI: 10.1007/978-3-642-32535-9

[8] Marsh SP, editor. LASL Shock Hugoniot Data. University of California

[9] Bilenca A, Cao J, Colice M, Ozcan A, Bouma B, Raftery L, et al. Fluorescence interferometry: Principles and applications in biology. Annals of the New York Academy of Sciences. 2008;**1130**:68-77. DOI: 10.1196/

[10] Kaiser F et al. Quantum

enhancement of accuracy and precision

[5] Domachuk P, Grillet C, Ta'eed V, Mägi E, Bolger J, Eggleton BJ, et al. Microfluidic interferometer. Applied Physics Letters. 2005;**86**:024103. DOI:

Chapter 2

Abstract

Naiting Gu and Qun Luo

compact RSI based micro-optics technique.

1. Introduction

9

vibration insensitive, modal wavefront reconstruction

Radial Shearing Interferometer

Radial shearing interferometer (RSI) is one of the most powerful tools in many domains, especially in optical testing. RSI has compact size and good vibration immunity, which is adaptive to various environments, due to its common-path configuration. Moreover, it is very convenient application because no plane referencing wavefront is needed. The disadvantages of the conventional RSIs are that the distorted wavefront is hard to extract quickly and accurately from one radial shearography due to the phase extract algorithm is complex. Fortunately, the new RSIs can receive benefits from the accuracy of the methods of phase-shifting interferometry, and phase-shifting shearography is more sensitive than simple digital shearography. There are two mainly trend to the RSIs based on phase-shifting technique, i.e. instantaneous phase-shifting and compact size. In this chapter, a development process of RSI will be introduced briefly firstly, and then the some new RSIs based phase-shifting techniques in our work will be described in following parts, including initial RSI by using four-step polarization phase-shifting, modal wavefront reconstruction method for RSI with lateral shear and a new kind of

Keywords: radial shearing interferometer, phase-shifting technique, instantaneous,

Radial shearing interferometer (RSI) was proposed firstly in 1961 [1]. After development of many years, the RSI has been used widely in optical testing [2–4], corneal topographic inspection [5–7], wavefront sensing [8–11] and laser beam characterization [12–14]. Radial shear can be introduced by some classical optical components [15, 16] and the other different ways [17–21] including optical gratings [17, 18], zone plate [19], speckle interference [20, 21] and the other applications. It is very convenient application because no plane referencing wavefront is needed [24], especially comparing to the point diffraction interferometer (PDI) [22, 23]. RSI has compact size and good vibration immunity, which is adaptive to various environments, due to its common-path configuration. Recently, RSI has been becoming one of the most important tools for diagnosing the wavefront of laser beams and the other applications. The disadvantages of the conventional RSIs are that the distorted wavefront is hard to extract from only one radial shearography due to the complexity of the phase extract algorithm. However, fortunately, many of these applications can receive benefits from the high accuracy of phase-shifting interference methods, and phase-shifting shearography is more sensitive than simple radial shearography [25]. Thus some authors [8, 26–28] have proposed several kinds of RSIs by using temporal or spatial phase-shifting

11, 2016. Available from: https://www. nytimes.com/2017/10/03/science/nobelprize-physics.html [Accessed: January 12, 2019]

[35] LIGO's Interferometer [Internet]. Available from: https://www.ligo. caltech.edu/page/ligos-ifo [Accessed: January 12, 2019]

[36] Schnabi J. The World's Shortest Laser Pulse. Physics.org [Internet]. October 27, 2017. Available from: https:// phys.org/news/2017-10-world-shortestlaser-pulse.html [Accessed: January 12, 2019]

## Chapter 2

*Interferometry - Recent Developments and Contemporary Applications*

11, 2016. Available from: https://www. nytimes.com/2017/10/03/science/nobelprize-physics.html [Accessed: January

[35] LIGO's Interferometer [Internet]. Available from: https://www.ligo. caltech.edu/page/ligos-ifo [Accessed:

[36] Schnabi J. The World's Shortest Laser Pulse. Physics.org [Internet]. October 27, 2017. Available from: https:// phys.org/news/2017-10-world-shortestlaser-pulse.html [Accessed: January 12,

12, 2019]

2019]

January 12, 2019]

**8**
