4. Low coherence, off-axis DHM for in vitro sandwiched biological samples investigation

In digital holographic microscopy (DHM), optical sources with long coherent lengths such as He-Ne laser have been widely used to feature the sample. Because of the high degree of coherence of the He-Ne laser light, harmful coherent noise often arises. This noise affects the quality of the holograms and hence leads to error in phase measurement. The larger the phase noise is, the lower the measurement precision will be. The harmful coherent noise is mainly classified into two types. The first is the random diffraction patterns (speckle noise) due to scattered light. The second is the formation of unwanted interference fringes (spurious noise) due to stray light. The spurious noise is formed when light reflected or scattered from various surfaces in the optical path is coherent with the main beam. The amplitude of the scattered light as adds vectorially to the amplitude of the main beam, resulting in a phase error Δφ as illustrated in Figure 8(a). Some practical solutions such as introducing a wedged beam splitter, a rotating diffuser, and antireflection coating to the optical surfaces, in the optical system setup, were proposed to minimize the unwanted coherent noise. Although these practical solutions are effective and may circumvent to suppress the coherent noise to some amount, they have some drawbacks in terms of blurring the fringe visibility and hindering the fringe formation in DHM, which require perfect alignment. Optical sources with short coherent lengths such as LEDs were proposed in order to avoid the harmful coherent noise. However, the limited coherence length of LED and its insufficient brightness hinder its application in an off-axis DHM, since just a limited number of interference fringes with poor visibility appear in the field of view (FOV). In Section 4, we present an off-axis DHM configuration using bright femtosecond pulse light with ultrashort coherent length, which makes possible to feature sandwiched biological samples with no coherent noise (speckle and spurious) in the reconstructed object wave [9].

A typical configuration of the sandwiched biological sample is shown in Figure 8(b), where the specimen is mounted in between two thin glass plates to avoid dehydration. Investigating such biological samples using conventional DHM with long coherent He-Ne laser light is challenging because of existence of the harmful coherent noise. Photograph of the investigated sample taken by the proposed DHM system (see Figure 9) with blocking the reference arm is shown in Figure 8(c). The DHM experimental setup is schematically shown in Figure 9. The configuration is comprised of two parts: generation of femtosecond pulse light in near-infrared region and a Mach-Zehnder interferometer in transmission. A mode-locked Er-doped fiber laser light (center wavelength λ<sup>c</sup> = 1550 nm, spectral bandwidth Δλ = 73 nm, pulse duration Δτ = 100 fs, mean power Pmean = 380 mW, and repetition frequency frep = 250 MHz) was focused on a periodically poled lithium niobate (PPLN) crystal to convert the wavelength by second

displaced as shown in Figure 7(a) at position 2 (slightly imperfect collimation), the beams converge toward the reference and the object. The convergent beams would then be canceled out and subsequently have no impact on the height variations. However, it is hard to achieve ideal mounting mechanically. Thus we expect that the effect of nonideal mounting as shown in

Figure 7. The effect of design of mounting and the adjustment of the collimation lens on the very small height variations:

Figure 6. Line height profiles of the tested step surface at perfect (1) and imperfect (2–8) collimations produced at (a)

d = 0.0 mm (imaging scheme) and (b) d = − 500.0 mm (Fresnel transform).

280 Holographic Materials and Optical Systems

In digital holographic microscopy (DHM), optical sources with long coherent lengths such as He-Ne laser have been widely used to feature the sample. Because of the high degree of

Figure 7(b) may be the reason of small height variations as shown in Figure 7(b).

4. Low coherence, off-axis DHM for in vitro sandwiched biological

samples investigation

(a) ideal mounting, (b) nonideal mounting.

Figure 8. (a) Phase error Δφ produced by scattered long coherent light as, (b) sliced biological specimen mounted in between two thin glass plates to avoid dehydration, and (c) photograph of the investigated sarcomere sample taken by the proposed setup with blocking the reference arm.

harmonic generation (SHG) into the operating wavelength region of a charge-coupled device (CCD) camera used. To extract the SHG light, we used a narrow band-pass optical filter (F, passband wavelength = 775 ± 5 nm). The extracted SHG light has λ<sup>c</sup> of 777.8 nm, Δλ of 10 nm, Δτ of 120 fs, and Pmean of 14 mW (left inset of Figure 9).

The output power was sufficient to illuminate the sample and produce off-axis holograms with high contrast in the entire field of the CCD camera. The coherence length of the SHG pulse light was 30 μm. The SHG beam was expanded to a diameter of 20 mm by a telescope system. In the Mach-Zehnder off-axis setup in transmission, a pair of non-polarized beam splitters (NPBS1 and NPBS2) was used to separate the two SHG beams into reference (R) and object (O) beams and combine them again. Difference of optical path length in the two arms was precisely adjusted within the coherence length of 30 μm by a scanning mirror, equipped with a mechanical translation stage, in the reference arm. The interfering object beam and the reference beam were tilted at small angle with respect to each other to produce off-axis hologram at the plane of the beam splitter NPBS2. The off-axis hologram was transferred via a microscope lens MO3 (20 +, NA = 0.1) to a black-and-white CCD camera (640 pixels by 480 pixels, pixel size = 4.3 μm). We conducted the experiment on microstructured sarcomere sample, which was isolated fibers dissected from rabbit muscle and mounted in between two thin glass plates to avoid dehydration (gap distance t = 15 μm) as shown in Figure 8(c). The off-axis hologram was recorded by making the reference wave (instead of the object wave) subtending the offaxis angle with the optical axis. Such arrangement is not only easier to align but also makes the image plane parallel to the sensor surface.

Figure 9. Experimental setup: PPLN is periodically poled lithium niobate (PPLN) crystal; F is a band bass filter at 775 nm; M is mirror; NF is neutral density filter; NPBS1 and NPBS2 are nonpolarizing beam splitters; MO1, MO2, and MO3 are microscope objectives with (50 +, NA = 0.45), (20 +, NA = 0.45), and (20 +, NA = 0.1), respectively.

The off-axis digital hologram recorded by the CCD camera was reconstructed using convolution-based Fresnel method. Three spectra were obtained when 2D-FFT was implemented to the off-axis hologram as shown in Figure 10. Only one filtered spectrum from the three spectra in 2D-FFT is used. The inverse 2D-FFT was applied after filtering out the spectrum, and the calculation result gives a complex object wave (amplitude and phase). The obtained complex amplitude was multiplied by the digital reference wave RD(m,n) to generate the final amplitudes and phases. An amplitude-contrast image and a phase-contrast image can be obtained by using the following intensity [Re(Г) <sup>2</sup> + Im(Г) 2 ] and the argument arctan[Re(Г)/Im(Г)], respectively. The digital reference wave RD(m,n) can be calculated as RD(m,n) = AR exp[i(2π/λ) (kxmΔx+kynΔy)], where AR is the amplitude, λ is the wavelength of the light source(777.8 nm for the femtosecond pulse light), and kx and ky are the two components of the wave vectors, which are adjusted such that the propagation direction of RD(m,n) matches as closely as possible with that of the experimental reference wave. The reconstructed amplitude and phase were recorded by selecting the appropriate values of the two components of the wave vector kx = 0.02145 mm−<sup>1</sup> and ky = −0.51570 mm−<sup>1</sup> . In order to see the effectiveness of our method compared to the conventional DHM, the femtosecond pulse light and PPLN crystal were replaced by long coherent He-Ne laser light source (λ = 632.8 nm).

harmonic generation (SHG) into the operating wavelength region of a charge-coupled device (CCD) camera used. To extract the SHG light, we used a narrow band-pass optical filter (F, passband wavelength = 775 ± 5 nm). The extracted SHG light has λ<sup>c</sup> of 777.8 nm, Δλ of

The output power was sufficient to illuminate the sample and produce off-axis holograms with high contrast in the entire field of the CCD camera. The coherence length of the SHG pulse light was 30 μm. The SHG beam was expanded to a diameter of 20 mm by a telescope system. In the Mach-Zehnder off-axis setup in transmission, a pair of non-polarized beam splitters (NPBS1 and NPBS2) was used to separate the two SHG beams into reference (R) and object (O) beams and combine them again. Difference of optical path length in the two arms was precisely adjusted within the coherence length of 30 μm by a scanning mirror, equipped with a mechanical translation stage, in the reference arm. The interfering object beam and the reference beam were tilted at small angle with respect to each other to produce off-axis hologram at the plane of the beam splitter NPBS2. The off-axis hologram was transferred via a microscope

size = 4.3 μm). We conducted the experiment on microstructured sarcomere sample, which was isolated fibers dissected from rabbit muscle and mounted in between two thin glass plates to avoid dehydration (gap distance t = 15 μm) as shown in Figure 8(c). The off-axis hologram was recorded by making the reference wave (instead of the object wave) subtending the offaxis angle with the optical axis. Such arrangement is not only easier to align but also makes the

Figure 9. Experimental setup: PPLN is periodically poled lithium niobate (PPLN) crystal; F is a band bass filter at 775 nm; M is mirror; NF is neutral density filter; NPBS1 and NPBS2 are nonpolarizing beam splitters; MO1, MO2, and MO3 are

, NA = 0.45), and (20

+

, NA = 0.1), respectively.

, NA = 0.1) to a black-and-white CCD camera (640 pixels by 480 pixels, pixel

10 nm, Δτ of 120 fs, and Pmean of 14 mW (left inset of Figure 9).

lens MO3 (20

+

282 Holographic Materials and Optical Systems

microscope objectives with (50

+

, NA = 0.45), (20

+

image plane parallel to the sensor surface.

The obtained off-axis hologram was reconstructed with the same procedure of Figure 10 and the final amplitude and phase obtained at kx = 0.00999 mm−<sup>1</sup> and ky = −0.5239 mm−<sup>1</sup> . Figure 11 (a) and (d) shows the off-axis holograms of the sarcomere sample obtained by a He-Ne laser light and femtosecond pulse light, respectively. A layered structure of around 15 sarcomeres

Figure 10. Sequential reconstruction steps (a) off-axis hologram, (b) Fourier transformed spatial frequency domain data, (c) filtered one spectrum, (d) and (e) reconstructed amplitude and phase before removing the fringes in the observation plane, (f) digital reference wave, and (g) and (h) final amplitude and phase maps.

Figure 11. Off-axis holograms of layered structure of sarcomeres taken by (a) He-Ne laser light and (d) femtosecond pulse light. (b) and (e) are filtered 2D-FFT spectrum of (a) and (b), respectively. (c) and (f) are 3D pseudocolor reconstructed phase-contrast image of stripy sarcomere with He-Ne laser light and femtosecond pulse light, respectively.

was captured at nearly same region of FOV. Comparison of these images indicated that the image brightness of DHM with the femtosecond pulse light was higher than that of the He-Ne laser light due to temporally localized energy of the femtosecond pulse light. Figure 11(b) and (e) shows one filtered spectrum from the three spectra in frequency domain when two-dimensional fast Fourier transform (2D-FFT) has been used for the off-axis interferogram as shown in Figure 11(a) and (d), respectively. Note that the three spectra appearing in the filtered one spectrum are due to the off-axis fringes of the sarcomere sample itself. Figure 11(b) shows the appearance of both spurious and speckle noises, while such noise was totally disappearing by using our setup as shown in Figure 11(e). In order to see the effectiveness of our setup compared to the conventional DHM with He-Ne laser light, we have not applied any of the numerous image enhancement techniques, to significantly improve the perceived image quality for biological applications. Figure 11(c) and (f) shows 3D pseudocolor reconstructed phasecontrast images of stripy sarcomere of Figure 11(a) and (d), respectively. Although phase images tend to suffer from the coherent noise to a significantly less degree compared to the amplitude images, the sarcomeres are hardly viewed in Figure 11(c) because of the existence of coherent noise at the background. In contrast, Figure 11(f) shows that the stripe structures of 10 sarcomeres are clearly viewed in the phase-contrast image because of no coherent noise in the background image. The phase profiles extracted along white lines in the phase-contrast image of Figure 11(c) and (f) are shown in Figure 12, indicating the cross-sectional profile of two sarcomeres. As shown from Figure 12, the phase profile of the proposed technique (red color) is free from noise, and the sarcomere cross section can be calculated precisely with no need of image enhancement techniques, which in turn takes time to enhance the image to some amount.

The phase profiles have been measured at different locations, and the average phase profile of the proposed method was found to be in good agreement with nominal values of the sarcomere depth. The contrast (axial resolution) of the proposed method is estimated from Figure 12 to be two times better than the contrast of He-Ne phase-based result. It is noted that the mismatching in the peaks of the phase profiles shown in Figure 12 is due to difference in magnifications of the captured off-axis holograms of both He-Ne and femtosecond pulse light. To enhance the differentiation of the sarcomere structure within the reconstructed amplitude map, the 3D reconstructed amplitude maps of both He-Ne laser light and femtosecond pulse light may be displayed in a false color representation as shown in Figure 13(a) and (b), respectively.

It is noted that these 3D reconstructed amplitude maps were flipped upside down to see the sarcomeres from different views. In Figure 13(a), existence of coherent noise in the background image makes it difficult to visualize the structure of the sarcomeres. On the other hand, Figure 13(b) shows the high quality and contrast of structure detail on the sarcomeres and

was captured at nearly same region of FOV. Comparison of these images indicated that the image brightness of DHM with the femtosecond pulse light was higher than that of the He-Ne laser light due to temporally localized energy of the femtosecond pulse light. Figure 11(b) and (e) shows one filtered spectrum from the three spectra in frequency domain when two-dimensional fast Fourier transform (2D-FFT) has been used for the off-axis interferogram as shown in Figure 11(a) and (d), respectively. Note that the three spectra appearing in the filtered one spectrum are due to the off-axis fringes of the sarcomere sample itself. Figure 11(b) shows the appearance of both spurious and speckle noises, while such noise was totally disappearing by using our setup as shown in Figure 11(e). In order to see the effectiveness of our setup compared to the conventional DHM with He-Ne laser light, we have not applied any of the numerous image enhancement techniques, to significantly improve the perceived image quality for biological applications. Figure 11(c) and (f) shows 3D pseudocolor reconstructed phasecontrast images of stripy sarcomere of Figure 11(a) and (d), respectively. Although phase images tend to suffer from the coherent noise to a significantly less degree compared to the amplitude images, the sarcomeres are hardly viewed in Figure 11(c) because of the existence of coherent noise at the background. In contrast, Figure 11(f) shows that the stripe structures of 10 sarcomeres are clearly viewed in the phase-contrast image because of no coherent noise in the background image. The phase profiles extracted along white lines in the phase-contrast image of Figure 11(c) and (f) are shown in Figure 12, indicating the cross-sectional profile of two sarcomeres. As shown from Figure 12, the phase profile of the proposed technique (red color) is free from noise, and the sarcomere cross section can be calculated precisely with no need of image enhancement techniques, which in turn takes time to enhance the image to some

Figure 11. Off-axis holograms of layered structure of sarcomeres taken by (a) He-Ne laser light and (d) femtosecond pulse light. (b) and (e) are filtered 2D-FFT spectrum of (a) and (b), respectively. (c) and (f) are 3D pseudocolor reconstructed

phase-contrast image of stripy sarcomere with He-Ne laser light and femtosecond pulse light, respectively.

amount.

284 Holographic Materials and Optical Systems

Figure 12. Phase profiles extracted along white lines of two sarcomeres in phase-contrast images of both Figure 11(c) (blue color) and Figure 11(f) (red color).

Figure 13. 3D pseudocolor reconstructed amplitude-contrast image of (a) He-Ne laser light and (b) femtosecond pulse light.

provides accurate profile edges of hexagonal shape of the sarcomeres. This makes our technique preferable in featuring such sandwiched biological samples, which is quite difficult to investigate using atomic force microscope (AFM).

Our deductions were verified by applications of apodization technique [10], to estimate the coherent noise level in the reconstructed amplitude maps of the off-axis holograms generated by both He-Ne and femtosecond pulse light, respectively. Apodization is the same topic as windowing in signal processing. The transmission of the apodized aperture function is completely transparent in the large central part of the profile. At the edges, the transmission varies from zero to unity following a curve defined by a cubic spline interpolation. The 2D transmission size of (480 +480) pixels of the apodized aperture function is multiplied with the off-axis holograms (480 +480) pixels of both He-Ne laser light and femtosecond pulse light, respectively. Normalization of intensity distribution of four sarcomeres at the middle of the off-axis hologram of the He-Ne laser light before and after application of apodization is shown in the left side of Figure 14. Normalization of intensities distribution of four sarcomeres at the middle of the off-axis hologram of the femtosecond laser light before and after application of apodization is shown in the right side of Figure 14.

As seen from the left figure, the variation in intensities before and after application of apodization function indicates that there is a coherent noise in the reconstructed amplitude of He-Ne off-axis hologram. Such coherent noise is totally disappearing in the right figure, whereas no variation in intensities before and after application of apodization. This confirms that the reconstructed amplitude of femtosecond pulse light off-axis hologram is free from coherent noise. Due to the short coherence length of the pulsed light, only fraction of hologram shows high-contrast fringe, resulting in a good reconstruction in this region as shown in Figure 13(b) which is corresponding to the off-axis hologram of Figure 11(d). The contrast of the fringes in Figure 11(d) reduces from center to two sides diagonally, which indicates the zero-path-difference point is nearly in the middle of the sensor. To obtain a high-brightness full-field image, we can move the center of the fringes diagonally and collect holograms with different zero path difference. Twelve off-axis holograms were generated diagonally by varying the optical path length of the interferometer to cover a sarcomere sample of around 45 +45 micrometers in the field of view (FOV) with high-contrast fringes at different regions in the

Figure 14. Normalization of intensities distribution of four sarcomeres with (a) and without (b) apodization taken at the middle of the off-axis holograms of He-Ne laser light (left) and femtosecond pulse light (right).

provides accurate profile edges of hexagonal shape of the sarcomeres. This makes our technique preferable in featuring such sandwiched biological samples, which is quite difficult to

Our deductions were verified by applications of apodization technique [10], to estimate the coherent noise level in the reconstructed amplitude maps of the off-axis holograms generated by both He-Ne and femtosecond pulse light, respectively. Apodization is the same topic as windowing in signal processing. The transmission of the apodized aperture function is completely transparent in the large central part of the profile. At the edges, the transmission varies from zero to unity following a curve defined by a cubic spline interpolation. The 2D

respectively. Normalization of intensity distribution of four sarcomeres at the middle of the off-axis hologram of the He-Ne laser light before and after application of apodization is shown in the left side of Figure 14. Normalization of intensities distribution of four sarcomeres at the middle of the off-axis hologram of the femtosecond laser light before and after application of

As seen from the left figure, the variation in intensities before and after application of apodization function indicates that there is a coherent noise in the reconstructed amplitude of He-Ne off-axis hologram. Such coherent noise is totally disappearing in the right figure, whereas no variation in intensities before and after application of apodization. This confirms that the reconstructed amplitude of femtosecond pulse light off-axis hologram is free from coherent noise. Due to the short coherence length of the pulsed light, only fraction of hologram shows high-contrast fringe, resulting in a good reconstruction in this region as shown in Figure 13(b) which is corresponding to the off-axis hologram of Figure 11(d). The contrast of the fringes in Figure 11(d) reduces from center to two sides diagonally, which indicates the zero-path-difference point is nearly in the middle of the sensor. To obtain a high-brightness full-field image, we can move the center of the fringes diagonally and collect holograms with different zero path difference. Twelve off-axis holograms were generated diagonally by varying the optical path length of the interferometer to cover a sarcomere sample of around 45

micrometers in the field of view (FOV) with high-contrast fringes at different regions in the

Figure 14. Normalization of intensities distribution of four sarcomeres with (a) and without (b) apodization taken at the

middle of the off-axis holograms of He-Ne laser light (left) and femtosecond pulse light (right).

480) pixels of the apodized aperture function is multiplied with the

480) pixels of both He-Ne laser light and femtosecond pulse light,

+45

investigate using atomic force microscope (AFM).

+

+

apodization is shown in the right side of Figure 14.

transmission size of (480

286 Holographic Materials and Optical Systems

off-axis holograms (480

Figure 15. 3D pseudocolor reconstructed amplitude-contrast image from superimposing of (a) 1 hologram, (b) 2 holograms, (c) 3 holograms, (d) 4 holograms, (e) 5 holograms, (f) 6 holograms, (g) 7 holograms, (h) 8 holograms, (i) 9 holograms, (j) 10 holograms, (k) 11 holograms, and (l) 12 holograms produced by femtosecond pulse light by using linear direct method.

image. The full-field image can be obtained by adding multiple such single reconstructions on the intensity basis as shown in Figure 15(a)–(l). The synthesized image map is shown in Figure 15(l). Because of the holograms' shifting process, the reference and object beam will have some phase shifts when the second hologram is recorded. When the second hologram is subtracted from the first hologram, the zero order is removed. Subtractions among successive holograms were superimposed using a direct linear addition method to constitute a full-field, high-quality synthesized hologram as shown in Figure 9. The intensity of the synthesized hologram I can be written as follows:

$$I\_{\text{synth}} = \sum\_{i=1}^{N/2} \left( h\_N - h\_i \right) + \sum\_{i=1}^{N/2} \left( h\_i - h\_N \right), \tag{22}$$

where i takes from 1 to N, whereas N is the total number of off-axis holograms = 12.

#### 5. Off-axis terahertz DH using continuous-wave THZ radiation

Terahertz (THz) radiation is an electromagnetic radiation lying between the microwave and infrared portions of the spectrum as shown in Figure 16. THz radiation can be produced by many techniques such as quantum cascade lasers (QCLs). QCLs are semiconductor heterostructures that can emit continuous-wave (CW) THz radiation [10]. QCLs are electron-only

Figure 16. Spectrum of waves showing the location of THz radiation.

Figure 17. Experimental setup of CW THz-DH: OC is optical chopper and M is a mirror.

devices that exploit transitions between conduction band states. The conduction band offsets between neighboring materials in the superlattice create a series of quantum wells and barriers. The most widely used QCL designs are based on GaAs/AlGaAs superlattices. The word cascading means that one electron can produce many photons in the superlattice periods. A significant advantage of THZ radiation is that it can easily inspect sealed packages for contrasting metal and plastic objects, testing pharmaceutical tablets for integrity, detecting skin cancers, etc.

In Section 5, we present the usage of THz radiation for 3D surface characterization via a digital holography (DH) technique [11]. Since the usual DH uses a visible light, it is difficult to visualize 3D internal structure of visibly opaque objects due to their limited penetration depth. The compelling advantage of THz radiation is that it has a good penetration capability; thus, 3D visualization of both surface shape and internal structure in visibly opaque object can be achieved [12]. We constructed off-axis THz digital holography (THz-DH) system equipped with CW-THz radiation generated by QCL, and the THz digital hologram is captured by a THz camera.

Figure 17 illustrates a schematic diagram of off-axis THz-DH system. An optical chopper (OC) is positioned in front of the QCL to reduce the noise. The radiation was collimated by a Teflon lens (f = 300 mm). The collimated THz beam of diameter around 60 mm is divided into a signal THz beam and a reference one by a silicon beam splitter (BS). Figure 18(a) shows 2D intensity distribution of the THz beam without the sample. Figure 18(b) shows the dark frame captured

Figure 18. (a) A 2D intensity distribution of the THz beam without the sample, (b) dark frame captured by the THz camera when there is no illumination, (c) off-axis hologram, and (d) 3D phase-contrast image reconstructed by angular spectrum method.

by the THz camera when there is no illumination. The signal THz beam passed through a sample (here, the sample is a letter T from paper), while a reference THz beam is reflected by a mirror (M). Then, these two THz beams were spatially overlapped at a certain off-axis angle to generate 2D fringe of THz beams. Finally, the off-axis THz digital hologram is captured by a THz camera as shown in Figure 18(c). The off-axis THz hologram has been reconstructed with angular spectrum method to extract both amplitude and phase. Figure 18(d) shows the 3D reconstructed phase of the sample.
