Digital holography based on multiwavelength spatial-bandwidth-extended capturing-technique using a reference arm (Multi-SPECTRA).

Digital holography based on multiwavelength spatial-bandwidth-extended capturing-technique using a reference arm (Multi-SPECTRA) Tatsuki Tahara,* Toru Kaku, and Yasuhiko Arai Faculty of Engineering Science, Kansai University, 3-3-35 Yamate-cho, Suita, Osaka, 564-8680, Japan * [email protected]

Abstract: Single-shot digital holography based on multiwavelength spatialbandwidth-extended capturing-technique using a reference arm (MultiSPECTRA) is proposed. Both amplitude and quantitative phase distributions of waves containing multiple wavelengths are simultaneously recorded with a single reference arm in a single monochromatic image. Then, multiple wavelength information is separately extracted in the spatial frequency domain. The crosstalk between the object waves with different wavelengths is avoided and the number of wavelengths recorded with both a single-shot exposure and no crosstalk can be increased, by a large spatial carrier that causes the aliasing, and/or by use of a grating. The validity of Multi-SPECTRA is quantitatively, numerically, and experimentally confirmed. ©2014 Optical Society of America OCIS codes: (090.0090) Holography; (090.1995) Digital holography; (090.1705) Color holography.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

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#215171 - $15.00 USD Received 3 Jul 2014; revised 18 Sep 2014; accepted 10 Oct 2014; published 19 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029594 | OPTICS EXPRESS 29594

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1. Introduction Holography [1,2] is a technique for recording the complex amplitude distribution of an object wave and then reconstructing the three-dimensional (3D) image of an object. A 3D image of any ultrafast physical phenomenon can be captured with a single-shot exposure using holography, and even a 3D motion-picture recording of light pulse propagation has been achieved [3]. Digital holography [4] is a technique capable of recording 3D information with a single-shot exposure of an image sensor and then reconstructing both the 3D and quantitative phase images of the object using a computer. It has been actively researched in the fields of quantitative phase imaging [5–7], microscopy [8–10], phase tomographic imaging [11], particle and flow measurements [12], object recognition [13], and single-pixel imaging [14]. In recent years, there has been increasing demand for multispectral imaging techniques, especially in the fields of Raman scattering microscopy [15], medical science [16], and improvement of color reproduction [17]. In digital holography, multiwavelength 3D information is obtained by recording waves with multiple wavelengths irradiated from light sources, which is called multiwavelength [18,19] or color digital holography [20,21]. Applications to color 3D microscopy [22,23], cell analysis using dispersion [24], colorreproduction improvement of a 3D space [25,26], simultaneous recording of visible and invisible light [27], and multispectral imaging [28,29] have been proposed. Kubota et al. and Ito et al. have reported that color reproduction is improved by recording more than three wavelengths in color holography [25] and color digital holography [30], respectively. From the viewpoints described above, a multiwavelength digital holographic technique capable of recording a large number of wavelengths, including visible and invisible ones such as infrared and/or ultraviolet light is required. Object waves with multiple wavelengths are captured by utilizing space-division multiplexing [20,21,27,31,32], time division [18,19,28,33–37], temporal frequency-division multiplexing [29,38,39], space division [40–43], and spatial frequency-division multiplexing [44–48]. Multiwavelength digital holography using space-division multiplexing is easily implemented by using an image sensor with a Bayer color filter array [20,21]. The wavelength selectivity of the technique depends on that of the color filter array. Crosstalk between the object waves with different wavelengths occurs, causing ghosts to appear if the wavelength selectivity is low [43]. Multiwavelength 3D imaging without the crosstalk can be done by time-division [18,19,28,33–37] and temporal frequency-division multiplexing [28,38,39] techniques at the cost of temporal resolution. However, these techniques are valid for static phenomena and are not suitable for both instantaneous measurement and motion-picture


recording of objects moving at high speeds. Space-division technique is implemented with multiple image sensors [40,42,43] or a stacked image sensor [41,43]. When using multiple image sensors, highly accurate alignments are required especially in cases where an object wave scattered from an object with a rough surface is recorded. In the space-division technique using a stacked image sensor, the wavelength selectivity of the sensor is a problem that has not been solved [43]. Lohmann has proposed a holographic technique for recording both multiwavelength and 3D information with a single-shot exposure on a monochromatic 2D plane by utilizing spatial frequency-division multiplexing [44]. As an implementation, multiwavelength information is multiplexed in the space domain by introducing multiple reference beams from different directions, and is separated in the spatial frequency domain by the differences between the carrier frequencies generated by the reference waves, which is called angular multiplexing [45–48]. Multiple reference arms were required for implementing angular multiplexing. As an alternative approach, a common-path multiwavelength interferometer that does not use any reference arms was proposed to record multiwavelength information by Lue et al. [24]. A part of the single laser beam containing multiple wavelengths works as reference waves and angular multiplexing is not done. In the techniques of [24,45–48], multiple wavelength information is separately extracted by using the Fourier fringe analysis [49]. However, the problems with the respective techniques are as follows. In the former, the optical setup was complicated as increasing the number of the wavelengths. This is because one reference arm was required for recording one wavelength. In the latter, it is difficult to construct a reflectiontype digital holographic system due to a common-path setup. As another issue, a large spatial carrier cannot be generated by an optical system that has no reference arm. As a result, the spatial bandwidths available for recording object waves become narrow, and the crosstalk between the object waves with different wavelengths cannot be avoided as increasing the number of wavelengths. In this article, we propose single-shot digital holography to capture both amplitude and quantitative phase distributions with multiple wavelengths simultaneously with a reference arm. The main ideas are the utilization of a single reference arm for recording single-shot multiwavelength digital holography, and the methods for extending the spatial bandwidth with no crosstalk. Spatial frequency-division multiplexing is utilized to record multiple wavelengths. The optical system is simplified by a single reference arm, which allows wavelengths to be increased easily. The validity of this proposal is quantitatively, numerically, and experimentally confirmed. 2. Digital holography based on multiwavelength spatial-bandwidth-extended capturingtechnique using a reference arm (Multi-SPECTRA) The basic concept of digital holography based on multiwavelength spatial-bandwidthextended capturing-technique using a reference arm (Multi-SPECTRA) is composed of three parts: a single reference arm to record multiple wavelengths and waves reflected from an object with a compact setup; utilization of intentional aliasing and the periodicity of a digital signal [50,51], and/or a grating, to improve the spatial bandwidth available for recording object waves without crosstalk, and to increase the number of wavelengths recorded with a single-shot exposure of a monochromatic image sensor; and spatial frequency analysis to extract each object wave in each wavelength selectively. In the recording process, a monochromatic image sensor records a wavelength-multiplexed hologram using an off-axis configuration with a reference arm. In the reconstruction process, each object wave at each wavelength is selectively extracted in the spatial frequency domain by the Fourier fringe analysis [49]. After the procedures of digital holography, complex amplitude distributions in multiple wavelengths with a wide spatial bandwidth are reconstructed from a single monochromatic image.


Figure 1 shows examples of optical implementations in reflection digital holography. Here we assume that the number of wavelengths is N, where N is an integer and N≥2. Figure 1(a) shows an implementation that uses a single reference beam. By using a single reference arm, a reflection-type multiwavelength digital holography system can be constructed. Also, by use of the single reference arm, it is easy to increase the recorded wavelengths regardless of the number of wavelengths. A large 2D spatial carrier is introduced by tilting the mirror with a large angle. The spatial frequency of interference fringes f is determined by f = sinθ / λ , (1) where θ and λ are the angle between the optical axes of the object and reference waves, and the wavelength used for recording a hologram, respectively. Equation (1) shows that a large θ extends the difference of the spatial frequencies between object waves with different wavelengths, in the system using a reference arm. f in the shortest wavelength is the highest before recording a hologram. However, in the case of (2M + 1)/(2d) < | fx |, | fy | < (M + 1)/d as shown in Fig. 1(a), where M is an integer and M ≥ 0, and d is the pixel pitch of an image sensor, the spatial frequency of the shortest wavelength in a recorded hologram is modulated to the lowest by utilizing a high spatial carrier frequency. This is done by using the aliasing and the periodicity of a digital signal [50,51]. When the spatial frequency of interference fringes is more than double the spatial sampling frequency, sampling theorem is not satisfied and fringes cannot be recorded correctly. After recording a hologram and a 2D fast Fourier transform (FFT), replicas of the object waves appear in the spatial frequency domain due to the periodicity of digital signals. In Fresnel digital holography, experimental demonstrations were presented in [51–53]. As a result, object waves are recorded even in case where the sampling theorem is not satisfied, and crosstalk can be avoided by widening the distance between object-wave spectra with different wavelengths. In cases where the spatial bandwidth is limited by the design of the optical system, the number of wavelengths recorded with a single-shot exposure can be increased by introducing a larger angle. Note that attenuations of the amplitude distributions of object waves occurs when a high spatial carrier is introduced and the fill factor of an image sensor is large [54–56]. This is because the visibility of interference fringes decreases to zero by increasing the value of the multiplication of the spatial frequency with the fill factor. An image sensor with a small fill factor should be chosen to suppress attenuations. Figure 1(b) shows another implementation of Multi-SPECTRA. Spatial-bandwidth extension and the increase of the recordable number of wavelengths can be achieved by not only the tilt of the mirror, but also a grating used for implementing angular multiplexing with a single reference arm. Either a reflective or a transmission grating can be used. In Fig. 1(b), the reference waves with different wavelengths are separated by a grating placed in the reference arm, then the waves are introduced to the image sensor from different directions. This implementation is based on angular multiplexing, but the system does not become complicated due to a single reference arm regardless of the number of wavelengths.

Fig. 1. Schematic of optical implementations in Multi-SPECTRA. Examples of the systems when using (a) a single reference beam and (b) a grating. A spatial carrier is generated by both a mirror and a grating.


Fig. 2. Incident angles of reference waves to generate a spatial carrier and spatial frequency distributions of holograms recorded by Multi-SPECTRA. (a) and (b) show cases using a reference beam with a large 2D spatial carrier, and small and large 1D spatial carriers, respectively. Aliasing occurs when using a large spatial carrier and the object-wave spectra are 1/d shifted by the periodicity of the digital signal. (c) and (d) show cases using a grating utilized to change the 2D and 1D propagation directions of the reference waves, respectively.

Figure 2 shows the relationship between the incident angles and spatial frequency distributions of a wavelength-multiplexed hologram in Multi-SPECTRA. In the system shown in Fig. 1(a), alias is introduced to 2D or 1D direction by 2D large or 1D large and 1D small spatial carriers, as shown in Figs. 2(a) and 2(b), respectively. Object-wave spectra are well separated in the spatial frequency domain. In the system shown in Fig. 1(b), 2D or 1D propagation direction is changed by use of a grating to separate object-wave spectra in the spatial frequency domain, as shown in Figs. 2(c) and 2(d). Spatial frequency in the shortest wavelength is the highest when θ along the x-axis direction is the same in each wavelength, as derived from Eq. (1). By changing the 2D propagation direction, the spectra arrangement shown in Fig. 2(c) can be generated. 3. Quantitative evaluation of the recordable spatial bandwidths in Multi-SPECTRA In this section, we theoretically derive the recordable maximum spatial information in multiple wavelengths when using a reference beam. Figure 3 shows that the spatial information is related to the maximum incident angle of object waves against the optical axis α. Both the field of view and the resolution in a Fresnel digital holography system are improved by enlarging α. From Fig. 3(a),

tanα = L / ( 2Z obj ) ,

(2)

where L is the diameter of an image sensor and Zobj is the distance between the object and the image sensor. Indeed the spatial bandwidth can be limited by enlarging Zobj. However, the resolution of the system is decreased if the distance is increased, because the numerical aperture of the system is decreased as shown in Eq. (2). If the image-sensor area and the pixel pitch are not changed, there is a tradeoff between the field of view and resolution of the system, as described in [57]. Also, Pavillon et al. explains the importance of recording a wide spatial bandwidth to improve the resolution in digital holographic microscopy [58]. A large value of α is required to improve the imaging ability of the system.


Fig. 3. Schematics of (a) the resolution and (b) the field of view in an off-axis configuration.

Figure 4 shows the arrangements of spatial frequency spectra in Multi-SPECTRA using a reference beam. Those of holograms recorded with a low carrier [24] and a high carrier that satisfies the sampling theorem are also shown for the spatial bandwidths comparison purposes. We evaluate the spatial bandwidths without either crosstalk or the superimposition of the unwanted images, the 0th-order diffraction waves and the conjugate images. | fx |, | fy | < 1/d was adopted in this evaluation for simplicity. The crosstalk occurs between neighboring wavelengths used to record a hologram, and therefore we investigate the spatial bandwidths of λN and λN-1. The spatial carrier frequencies fλN and fλN-1, and the spatial bandwidths fobjλN and fobjλN-1 in neighbor wavelengths λN and λN-1 are expressed as

Fig. 4. Spatial frequency conditions in (a) Multi-SPECTRA using a single reference beam and (b) a low and (c) a high spatial carrier that satisfies the sampling theorem.

f λN =

f λ N −1 =

sin θ

λN

,

(3)

sin θ

, (4) λ N −1 sin α , (5) f objλ N = λN sin α . (6) f objλN −1 = λ N −1 From Eqs. (5) and (6), the spatial bandwidth is extended in proportion to the increase of α. However, one should consider the problems of the crosstalk and the superimposition of the unwanted images. Therefore, boundary conditions to avoid the problems are geometrically derived as (7) f λ N − f λ N −1 ≥ f obj λ N + f obj λ N −1 ,


f λN + 3 f objλN ≤

2 , d

(8)

where the condition λN < λN-1 is set. By substituting Eqs. (3)–(6) to formulas (7) and (8), sin θ

λN

sin θ

−

λ N −1

λN

sin α

λN

λ N −1 + λ N

sin θ ≥

sin θ

≥

λ N −1 − λ N

+

3 sin α

λN

≤

+

sin α

λ N −1

sin α ,

(9)

2 d

2λ N

sin θ ≤

(10) − 3 sin α . d When the value α reaches a certain point, formulas (9) and (10) are changed into equations. Therefore, the maximum angle αmax is specified from Eqs. (9) and (10) as λ N −1 + λ N 2λ N sin α max = − 3 sin α max λ N −1 − λ N d

λ N (λ N −1 − λ N ) , 2 (2λ N −1 − λ N )d

sin α max =

 λ (λ  N N −1 − λ N )  .  2 ( 2λ N −1 − λ N )d 

∴α max = sin −1 

(11) (12)

In the same manner, the maximum angle θmax is also specified by substituting Eq. (11) into Eq. (10). 2λ N 3λ N (λ N −1 − λ N ) − sin θ max = d 2 (2λ N −1 − λ N )d =

λ N ( λ N −1 + λ N ) 2 ( 2 λ N −1 − λ N ) d

,

 λ (λ  N N −1 + λ N )  .  2 ( 2λ N −1 − λ N )d 

∴θ max = sin −1 

(13) (14)

For comparison, the conditions using a low spatial carrier shown in [24] and a high carrier that satisfies the sampling theorem are derived. In the former shown in Fig. 4(b), fλN is fixed as 1/(2 2 d) because the object wave spectrum of the optical axis in the shortest wavelength is set as ( ± 1/(4d), ± 1/(4d)) or ( ± 1/(4d), ∓1/(4d)). Boundary conditions are geometrically derived from Eq. (7) and as f λ ≥ 2 f objλN + f objλ1 , (15) 1

1 . (16) 2 2d Under the condition that the difference between λN and λ1 is small and Eq. (15) can be ignored, αlow and θlow are derived from Eqs. (3)–(7) and (16). λ sin θ low = N , (17) 2 2d f λN =




∴θ low = sin −1 

2 

λN 2 2d sin α low

λN 2d

   

,

λ N −1 + λ N sin α low , λ N −1 − λ N λ N (λ N −1 − λ N ) , = 2 2 (λ N −1 + λ N )d

(18)

=

(19)

λN (λN −1−λN )  (20) .   2 2 (λ N −1 +λN )d   In the latter case shown in Fig. 4(c), the boundary conditions to avoid the superimposition are geometrically derived from formula (7) and the following expressions. 

∴α low = sin −1 

f λ1 ≥ 2 f obj λ N + f obj λ1 ,

fλ

(21)

1

N . (22) + f objλN ≤ 2d 2 In the same manner as Eqs. (3)–(6) and (9)–(14), and assuming that the difference between λN and λ1 is small, the angles αhigh and θhigh are derived.



 λ N (λ N −1 − λ N ) .  {(2 + 2 )λ N −1 − ( 2 − 2 )λ N }d 

(23)

 λ {(2 + 1 / 2 )λ  N N −1 − ( 2 − 1 / 2 )λ N }  . {(1 + 2 )λ N −1 − (1 − 2 )λ N }d  

(24)

α high = sin −1 

θ high = sin −1 

Thus, the incident angle of the reference wave against the optical axis of the object wave θ and the maximum angle of the object wave α are quantitatively derived. From Eqs. (12), (14), (18), (20), (23), and (24), it is clarified that a larger angle α is obtained by Multi-SPECTRA and the recordable spatial bandwidth is extended quantitatively. As an example, when recording 640, 532, and 473 nm with an image sensor with the pixel pitch d = 2.2 μm, αlow = 2.56 × 10−1, αhigh = 4.72 × 10−1, and αmax = 8.70 × 10−1 degrees, respectively. So, αmax /αlow = 3.40 and αmax /αhigh = 1.84 and both the resolution and the field of view are quantitatively improved by enlarging α. θmax = 15.0° is required for obtaining αmax. θ means (θ x 2 + θ y 2 )1 / 2 and therefore θxmax = θymax = 10.6° should be set. The detailed analysis of the system using a grating requires further work in future. 4. Numerical simulations We conducted numerical simulations to verify the effectiveness of Multi-SPECTRA. Figure 5 shows the amplitude distributions in multiple wavelengths and the phase distribution of the object waves. The phase distribution shown in Fig. 5(d) means that strongly scattering object waves were assumed. Figure 5(e) shows the color-synthesized image of the object waves. To show the capability for recording object waves with wide spatial bandwidths, an object wave having a wide spatial frequency area was assumed for each wavelength. N = 3 was assumed and λ1 = 640 nm, λ2 = 532 nm, and λ3 = 473 nm were set. The pixel pitch d, the number of bits, and the number of pixels of an image sensor were 2.2 μm, 12 bits, and 2048(H) × 2048(V), respectively. The fill factor of the image sensor was set at a sufficiently small number. The distance between the image sensor and an object z was 200 mm. Three wavelengthmultiplexed holograms that were obtained with a low spatial carrier fx = fy = 1/(4d), which satisfies the sampling theorem, and with the systems of Figs. 1(a) and 1(b) were assumed, in


order to compare the qualities of the reconstructed images. In the system shown in Fig. 1(a), θx = θy = 10.4° are assumed. In this simulation of Fig. 1(b), the grating has a spatial frequency of 900 lines/mm and is tilted at 10 degrees from the y axis to the in-plane direction. A blazed grating was assumed. Reference waves with multiple wavelengths illuminate a grating with the angles in x- and y-axis directions 20° and 60° against the normal line of the grating plane, and then these waves are separated. Object and reference waves interfere on the image sensor plane with the angles between the optical axes of the waves θx = 5.08° and θy = −4.53° at 473 nm, θx = 5.66° and θy = −1.23° at 532 nm, and θx = 6.73° and θy = 4.62° at 640 nm. Figure 6 shows the numerical results under the condition described above. In the case where the crosstalk is shown in the spatial frequency domain due to a low spatial carrier frequency, the reconstructed object images are severely degraded by the crosstalk. Although multiple wavelength information can be simultaneously recorded by using a reference arm even for a reflective object, recordable

Fig. 5. Amplitude distributions at (a) 640 nm, (b) 532 nm, and (c) 473 nm and (d) phase distribution of the object waves in the numerical simulation. (e) Color-synthesized image of the object waves.

Fig. 6. Numerical results. (a) Spatial frequency distribution of the hologram, amplitude distributions at (b) 640 nm, (c) 532 nm, and (d) 473 nm and (e) color-synthesized image of the object waves, which is obtained by the spectrum arrangement shown in Fig. 4(b). (f) Spatial frequency distribution of the hologram, amplitude distributions at (g) 640 nm, (h) 532 nm, and (i) 473 nm and (j) color-synthesized image of the object waves, which is obtained by MultiSPECTRA using a single reference beam. (k) Spatial frequency distribution of the hologram, amplitude distributions at (l) 640 nm, (m) 532 nm, and (n) 473 nm and (o) color-synthesized image of the object waves, which is obtained by Multi-SPECTRA using a grating. The areas circled by red, green, and blue lines shown in (a), (f), and (k) show the object wave spectra at 640 nm, 532 nm, and 473 nm, respectively.


Table 1. Cross correlations and root-mean-square errors of the reconstructed images.

λ = 640 nm

λ = 532 nm

λ = 473 nm

CC

RMSE

CC

RMSE

CC

RMSE

Using a reference arm and a low spatial carrier

0.543

100

0.438

133

0.555

122

Multi-SPECTRA using a reference beam

0.996

6.79

0.963

22.6

0.967

28.4

Multi-SPECTRA using a grating

0.999

3.58

0.999

3.37

1.00

3.25

spatial bandwidth with no crosstalk is limited without combination of another optical technique. Crosstalk is avoided by use of Multi-SPECTRA even though a single reference arm and a monochromatic image sensor are used to record a hologram containing multiple wavelength information. As a result, the quality of the reconstructed image is remarkably improved as shown in Figs. 6(f)–6(o). We calculated cross correlations (CCs) and root-meansquare errors (RMSEs) of the images shown in Fig. 6 to analyze the image quality quantitatively. Table 1 shows the calculation results and indicates significant image-quality improvement by Multi-SPECTRA, verifying its effectiveness. The errors in Multi-SPECTRA using the system shown in Fig. 1(a) was larger than that in Fig. 1(b) because the differences of spatial carriers in Fig. 1(a) was less than those in Fig. 1(b). However, the system shown in Fig. 1(a) is more easily constructed with a compact setup. 5. Experiments We conducted experiments for a macroscopic object, and microscopic reflective and transparent specimens to demonstrate Multi-SPECTRA. Figure 7 is a schematic of the constructed optical system based on Fig. 1(a). This time the system shown in Fig. 1(b) was not constructed, because we did not have a grating. The required 2D spatial carrier was generated by a mirror placed in the path of the reference arm in Fig. 7. Two CW lasers were used as light sources and the wavelengths of the lasers were λ1 = 640 nm and λ2 = 532 nm. A monochromatic CMOS image sensor whose d, the number of bits, and the number of pixels were 2.2 μm, 12 bits, and 2592(H) × 1944(V) was used to record a hologram. A Japanese coin with a diameter of 23.5 mm was set as a color object. The distance between the image sensor and the object z was 620 mm. In Multi-SPECTRA, the angles θx = 10.3° and θy = 10.8° were set, although less than θx = θy = sin−1(0.532/4.4) = 6.94° should be set to satisfy the sampling theorem in 532 nm wavelength. Figure 8 shows photographs of the object taken by the CMOS image sensor and an imaging lens. Figures 8(a) and 8(b) are the images of the object illuminated by CW laser beams whose wavelengths are 640 nm and 532 nm, respectively. After removing the imaging lens from the image sensor, a hologram was obtained by using the optical setup shown in Fig. 7. Multiwavelength object waves were reconstructed from a single monochromatic hologram by Multi-SPECTRA, and then the quality of the reconstructed color image was investigated. Figure 8 shows the spatial frequency distribution of the hologram and the images reconstructed by Multi-SPECTRA. For comparison, the images were obtained with the low spatial carrier. As shown in Fig. 8, the quality of the reconstructed images is severely degraded by the crosstalk when using a single reference arm and the low spatial carriers that satisfy the sampling theorem. The spectra of the object waves should be separated with a large spatial carrier difference when recording a wide spatial bandwidth using a single reference beam. The crosstalk problem was solved by MultiSPECTRA, and faithful object images in multiple wavelengths were obtained. Thus, the effectiveness of Multi-SPECTRA was experimentally demonstrated.


Fig. 7. Schematic of the optical setup for this experiment.

Fig. 8. Object and experimental results. Images of the measured object illuminated by lasers at the wavelengths of (a) 640 nm and (b) 532 nm. (c) Color-synthesized image obtained from (a) and (b). (d) Spatial frequency distribution of a hologram based on the arrangement in Fig. 3(b), images obtained from the spectra in the areas circled by (e) red and (f) green lines. The areas surrounded by blue lines indicate the unwanted images caused by the crosstalk noise. (g) Color-synthesized image obtained from (e) and (f). (d) Spatial frequency distribution of a hologram obtained by Multi-SPECTRA, object images at the wavelengths of (i) 640 nm and (j) 532nm. (k) Color-synthesized image obtained from (i) and (j).

The applicability of Multi-SPECTRA on multiwavelength digital holographic microscopy was experimentally investigated. Figure 9 shows the constructed optical setups of reflectionand transmission-type multiwavelength digital holographic microscopy. A reflective object - a high-resolution USAF1951 positive test target - was set as a microscopic specimen and was


recorded by the system shown in Fig. 9(a). The test target was tilted to demonstrate 3D imaging of a specimen. Lasers and wavelengths were the same as that of the experiment for a macroscopic object, and a high-resolution monochromatic CMOS image sensor whose d, the number of bits, and the number of pixels are 1.67 μm, 12 bits, and 3840(H) × 2760(V) was used to record a hologram with a wide spatial bandwidth. An afocal magnification system was used to achieve 3D imaging of fine structures with a constant magnification regardless of the depth difference between the specimen and the microscope objective. The magnifications in the in-plane and depth directions were 35 and 1225. The distance between a part of the magnified image of the specimen and the image sensor was estimated as 1.5 mm, and angularspectrum method was used for refocusing [59] because there was no Fresnel region. In MultiSPECTRA, the angles θx = 15.3° and θy = 13.8° were set and thus θ was 20.6°. Figure 10 shows the microscopic images obtained by Multi-SPECTRA. For comparison, the images were also obtained with a low spatial carrier. Interference fringe patterns generated by the object waves with different wavelengths are shown in Figs. 10(e) and 10(f), due to the crosstalk between the object waves. Spatial-bandwidth limitation is a method to avoid crosstalk and we applied narrow filters not to cause crosstalk. However, this was at the cost of the resolution, as shown in Figs. 10(g) and 10(h). The crosstalk and tradeoff problems were solved by Multi-SPECTRA and any aberrations from introducing high spatial carriers were not seen. Furthermore, fine structures with 775 nm apertures in the group 9 line 3 was resolved in each wavelength and different depths. Next, a spicule of Holothuroidea de Blainville was set in the system shown in Fig. 9(b), to demonstrate the effectiveness of multiwavelength transmission digital holographic microscopy. The lasers, image sensor, and afocal magnification system used were the same as those in the constructed reflective digital holographic microscopy. The distance was estimated as 2 mm. The angles θx = 4.79° and θy = −15.7° were set in the Multi-SPECTRA experiment, and thus θ was 16.4°. For comparison, holograms and reconstructed images were also obtained by the single reference-arm techniques using a low and high spatial carrier that satisfies the sampling theorem. Figure 11 shows experimental results. As shown in Figs. 11(d)–11(g), the crosstalk was seen in the whole area due to the superimposition of the object-wave spectra. By using a high spatial carrier, some of the crosstalk was avoided when measuring a transparent specimen, even though the sampling theorem was satisfied. However, as clarified in section 3, the range of spatial bandwidths without crosstalk were extended by Multi-SPECTRA, and the crosstalk was also completely removed when measuring a transparent specimen. Therefore, the applicability to digital holographic microscopy was experimentally demonstrated.

Fig. 9. Schematic of the constructed (a) reflection- and (b) transmission-type multiwavelength digital holographic microscopy based on Multi-SPECTRA.


Fig. 10. Experimental results for a high-resolution reflection USAF1951 test target that is tilted to the depth direction. Spatial frequency spectra of the holograms obtained by (a) the arrangement shown in Fig. 4(b) and (b) Multi-SPECTRA. (c)-(f) and (g), (h) are images obtained from λ2 = 532 nm spectrum of the areas circled by green solid and dotted lines shown in (a), respectively, for comparison. (i)-(p) are images obtained by Multi-SPECTRA. (i)-(l) Whole images reconstructed from a single hologram. (i) and (j) are obtained from λ1 = 640 nm component shown in (b), and (k) and (l) are obtained from λ2 = 532 nm component shown in (b). The depth difference between (i),(k) and (j),(l) was 1755 nm in the object plane. (m)-(p) are magnified images of (i)-(l). The areas surrounded by red lines in (i)-(l) indicate the areas of (m)-(p). The areas surrounded by blue rectangles indicate the areas in focus. Group 9 line 3 in a high-resolution USAF 1951 has 775 nm width or height and these structures are resolved as shown in Figs. (m) – (p).


Fig. 11. Experimental results for a transparent specimen in multiwavelength digital holographic microscopy using a reference arm. Spatial frequency distributions of holograms with (a) a low spatial carrier, (b) a high spatial carrier that satisfies the sampling theorem, and (c) MultiSPECTRA. (d)-(g), (h)-(k), and (l)-(o) are obtained from (a), (b), and (c), respectively. (d), (h), (l) Amplitude and (e), (i), (m) phase images at 640 nm. (f), (j), (n) Amplitude and (g), (k), (o) phase images at 532 nm. The areas surrounded by orange lines in (h)-(k) indicate areas with crosstalk noises. The scale bar shown in (o) is 10 μm.

6. Discussion We discuss the possibility of ultrafast multispectral 3D image recording. When using a femtosecond or attosecond pulsed laser, it is expected that multispectral 3D imaging is achieved with extremely high temporal resolution. However, although multiple wavelengths are contained in pulsed light, the difference between the wavelengths is minimal. Due to the tradeoff between the spatial bandwidth and the crosstalk, it might be required to not only introduce a large spatial-frequency difference, but also extract wavelengths selectively before recording. With optical setups such as Fig. 12, it is considered possible to achieve ultrafast multispectral 3D image recording and imaging with no crosstalk. With the combination of the system shown in Fig. 1(b) and an aperture array as shown in Fig. 12(b), which is set to extract #215171 - $15.00 USD Received 3 Jul 2014; revised 18 Sep 2014; accepted 10 Oct 2014; published 19 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029594 | OPTICS EXPRESS 29608

the wavelengths selectively, interference fringe patterns are selectively generated on the image sensor plane. Light with wavelengths that are shut by the aperture array cannot be recorded as a hologram and only intensities of object waves are recorded by an image sensor. In the spatial frequency domain, object waves that are recorded as a hologram generate 0thand ± 1st-order spectra while those that are recorded as intensities generate only 0th-order spectra. As a result, the crosstalk is suppressed even when using a pulsed light. A spatial light modulator is considered as an implementation of the aperture array.

Fig. 12. (a) An optical implementation for 3D multispectral imaging with a femtosecond pulsed laser. (b) The detail of the reference arm for selectively extracting wavelengths.

7. Conclusion We have proposed single-shot digital holography to capture both amplitude and quantitative phase distributions of object waves in multiple wavelengths simultaneously with a reference arm. Multi-SPECTRA is implemented by a compact optical setup that uses a single reference arm, methods for enlarging the spatial frequency difference, and a single-shot exposure of a monochromatic image sensor. A wide spatial bandwidth without the crosstalk in each wavelength was numerically and experimentally demonstrated. The validity of MultiSPECTRA was quantitatively, numerically, and experimentally confirmed. In future work, it is expected to apply Multi-SPECTRA to achieve ultrafast multispectral 3D image recording and imaging by use of a femto- or atto-second pulsed laser as a light source. Also, multispectral 3D sensing of visible and invisible light containing infrared wavelengths is another next step. This has prospective applications to multispectral microscopy for 3D motion-picture recording of dynamically moving specimens, quantitative phase imaging, high-speed multicolor 3D camera for imaging of objects moving at high speeds, and other multiwavelength 3D imaging applications.


Acknowledgments The authors appreciate Prof. Adrian Stern and the reviewers for the helpful comments and kind editorial procedures. Also we thank Ryo Kato and Kris Cutsail for checking the English grammar of this article. This study was partially supported by Research Foundation for OptScience and Technology, The Murata Science Foundation, Research foundation of Tokyo Institute of Technology, Grant-in-Aid for Research Activity Start-up 25886014 of the Japan Society for the Promotion of Science (JSPS), and MEXT-Supported Program for the Strategic Research Foundation at Private Universities.


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