Abstract
In this chapter, we introduce multiwavelength digital holographic techniques and a novel multiwavelength imaging technique. General multiwavelength imaging systems adopt temporal division, spatial division, or space-division multiplexing to obtain wavelength information. Holographic techniques give us unique multiwavelength imaging systems, which utilize temporal or spatial frequency-division multiplexing. Conventional multiwavelength digital holography systems have been combined with one of the methods listed above. We have proposed phase-shifting interferometry selectively extracting wavelength information, characterized as a multiwavelength three-dimensional (3D) imaging technique based on holography and called phase-division multiplexing (PDM) of multiple wavelengths. In PDM, wavelength-multiplexed phase-shifted holograms are recorded, and multiwavelength information is separately extracted from the holograms in the space domain. Phase shifts are introduced for respective wavelengths to separate object waves with multiple wavelengths in the polar coordinate plane, and multiple object waves are selectively extracted by the signal processing based on phase-shifting interferometry. Additionally, the system of equations needed to obtain a multiwavelength 3D image is solved with less wavelength-multiplexed images using two-step phase-shifting interferometry-merged phase-division multiplexing (2π-PDM), which makes the best use of 2π ambiguity of the phase and two-step phase-shifting method. The PDM techniques are reviewed and color 3D imaging ability is described with numerical and experimental results.
Keywords
- digital holography
- holography
- interferometry
- holographic interferometry
- phase-shifting interferometry
- multiwavelength interferometry
- color holography
- multiwavelength 3D imaging
- color 3D imaging
- multiwavelength imaging
- phase-division multiplexing of wavelengths
- 2π-PDM
1. Introduction
Holography [1–4] is a technique to record a wavefront of an object wave by utilizing interference of light as well as reconstruct a three-dimensional (3D) image of an object. The medium containing the information of an interference fringe image is called a “hologram”, which contains both the amplitude and phase information of an object wave. 3D image information is reconstructed using a hologram and diffraction theory. One of the most remarkable features in holography is that 3D motion-picture recording of any ultrafast physical phenomenon can be achieved, even for light propagation in 3D space [3]. Digital holography [5–8] is a technique to record a hologram digitally using an image sensor, and reconstruct both the 3D and quantitative phase images of an object using a computer or spatial light modulator. This technique has been researched for not only the observation of ultrafast phenomenon, but also for microscopy [9, 10], quantitative phase imaging [11, 12], and multimodal imaging [13, 14].
In recent years, there has been an increase in demand for multispectral imaging techniques. Multiwavelength information helps us to perceive, analyze, and recognize an object such as body tissue or a tumor. Wavelength of light has the ability to clarify color and material distributions of an object [15], visualize the localization and dynamics of molecules with Raman scattering [16, 17], and analyze the health of human skin [18]. In digital holography, the information of multiple wavelengths and 3D space is obtained by recording waves with multiple wavelengths that are irradiated from light sources, called multiwavelength/color digital holography [19, 20]. Multiwavelength digital holography has the ability for not only color 3D imaging [19, 20], but also dispersion imaging [21] and 3D shape measurement with a wide range by using multiwavelength phase unwrapping [22], due to the recording of quantitative phase information with multiple wavelengths. Temporal division [23–25], spatial division [26–28], and space-division multiplexing [19, 20, 29], which are generally adopted for multiwavelength imaging in an imaging system, can be merged into digital holography to record multiple wavelengths. In general imaging systems, wavelength information is temporally or spatially separated when recording image(s), as shown in Figure 1(a) – (e) . However, holographic techniques make it possible to record multiwavelength/color information using a monochromatic image sensor and to reconstruct it from wavelength-multiplexed image(s). In holography, multiple wavelength information is obtained also by utilizing temporal frequency-division multiplexing ( Figure 1(f) ) [30, 31] and spatial frequency-division multiplexing ( Figure 1(g) ) [32, 33]. In these techniques, Fourier and inverse Fourier transforms are required to separate wavelength information. In the former, many wavelength-multiplexed images and an image sensor with a high frame rate are needed. In the latter, the spatial bandwidth available for recording an object wave at a wavelength is restricted as the number of wavelengths is increased.
Since 2013, we have presented a novel multiwavelength imaging technique utilizing holography and wavelength-multiplexed images [34–39]. The presented technique gives phase-shifting interferometry [40–51] the function to extract wavelength information such as wavelength dependencies of amplitude, phase, and polarization state selectively from wavelength-multiplexed phase-shifted holograms. It is especially important to record not only phase images but also amplitude distributions of object waves at multiple wavelengths in order to achieve multicolor and multispectral 3D imaging of multiple objects. By making use of holography for multiwavelength imaging, 3D space information is simultaneously captured. In this chapter, we explain the proposed technique, phase-shifting interferometry selectively extracting wavelength information: phase-division multiplexing (PDM) of multiple wavelengths and two-step phase-shifting interferometry-merged phase-division multiplexing (2π-PDM).
2. Phase-shifting interferometry selectively extracting wavelength information: phase-division multiplexing (PDM) of wavelengths
Figure 2
illustrates the schematic of the proposed multiwavelength 3D imaging technique in the case where the number of wavelengths
Figure 3 describes the principle that wavelength information is selectively extracted by the signal processing in the space domain. As seen in Figure 3 , different phase shifts for respective wavelengths are given to object waves with multiple wavelengths, and then wavelength information is separated in the polar coordinate plane. Although this separation is used to extract an object wave from a hologram in general phase-shifting interferometry, in the proposed technique, the separation is utilized to remove not only the conjugate images and 0th-order diffraction wave, but also undesired wavelength information. This means phase-division multiplexing (PDM) of wavelengths. Figure 3 shows the case where specific phase shifts are used [34–36], but this concept is also applicable to the case where arbitrary phase shifts are introduced [39].
Figure 4 illustrates optical implementations of the proposed digital holography. Multiple lasers irradiate laser beams with multiple wavelengths simultaneously. A device for shifting the phase of light, such as a mirror with a piezo actuator, a spatial light modulator, or wave plates, is placed in the path of the reference arm. A monochromatic image sensor records the required wavelength-multiplexed phase-shifted holograms sequentially. An optical system based on PDM has the following features: the spectroscopic sensitivity of the optical system can be extended in comparison to the system with a color image sensor; full space-bandwidth product of an image sensor can be used to record object waves with multiple wavelengths; a bright color image can be obtained due to no spectroscopic absorption, while wavelengths filters required in conventional systems absorb light to obtain a color image; and measurement time is shortened by the wavelength-multiplexed recording in comparison with temporal division technique.
Figure 5
illustrates the image reconstruction algorithm [34–36]. A wavelength-multiplexed phase-shifted hologram
here
Only the complex amplitude distributions of object waves with dual wavelengths
Here, when
As shown in Eqs. (5) and (6), subtraction between holograms, which is based on phase-shifting interferometry, is calculated and the unwanted wavelength component
3. Numerical simulation
Numerical simulations were conducted to verify the effectiveness of the proposed technique. Figure 6 shows the amplitude and phase distributions of the object wave at each wavelength. As shown in Figure 6(b) , a color object with rough surface was assumed. 640 and 532 nm were assumed as the wavelengths of the light sources. Red and green color components of a standard image “pepper” were used as amplitude images at 640 and 532 nm, respectively. In these simulations, the distance between the object and image sensor was assumed as 200 mm, pixel pitch was 5 μm, resolution was 10 bits, and number of pixels was 512 × 512. Figure 7 shows the images reconstructed by the proposed technique. Faithful images were reconstructed at each wavelength, and crosstalk between object waves with different wavelengths was not seen. The color synthesized image in Figure 7(c) indicates color 3D imaging ability. Thus, the validity of the proposed technique was numerically confirmed. Detailed numerical analyses and an experimental demonstration using an image sensor with 12-bit resolution were reported in Ref. [36].
4. Two-step phase-shifting interferometry-merged phase-division multiplexing (2π-PDM)
In a wavelength-multiplexed hologram, 2
The optical setup required for 2π-PDM is the same as that for other PDM techniques. Therefore, the systems in
Figure 4
are applicable to 2π-PDM. In 2π-PDM, various types of two-step phase-shifting methods [52–56] can be employed. When merging Meng’s two-step method [53] into 2π-PDM, intensity distributions of reference waves
From the extracted object wave
If the sum of the intensities of the 0th-order diffraction waves is equal to |
From the obtained
where,
Thus, the object waves at the desired wavelengths are extracted selectively from four wavelength-multiplexed phase-shifted holograms and intensity distributions of the reference waves. In this way, in the case where the number of wavelengths is
Note that an arbitrary phase shift at
5. Experimental demonstration of 2π-PDM
We have demonstrated 2π-PDM experimentally to show color 3D imaging ability [38].
Figure 10
shows a completed model of the optical system illustrated in
Figure 4(a)
. Four wavelength-multiplexed phase-shifted holograms were recorded sequentially by using a mirror with a piezo actuator. Before/after that, two intensity images of two reference waves were sequentially recorded only once. The wavelengths of the lasers were
Figure 11
shows the experimental results. Wavelength-multiplexed monochromatic images such as
Figure 11(a)
were captured, and wavelength information was superimposed on space and spatial frequency domains as seen in
Figure 11(a)
and
(b)
.
Figure 11(c)
and
(d)
were the images focused digitally at a distance of 320 mm from the image sensor plane and reconstructed by diffraction integral alone and 2π-PDM, respectively. Blue and red color films attached to the sheets absorbed red and blue light, respectively. However,
Figure 11(c)
, which was obtained from a wavelength-multiplexed hologram, indicated the superimpositions of not only the 0th-order diffraction wave and the conjugate image but also image components given by the crosstalk between
6. Discussions and summary
We have proposed phase-shifting interferometry selectively extracting wavelength information as a novel multiwavelength imaging technique. In this technique, not only multiwavelength images but also the information of 3D space are simultaneously captured by the combination with holography. The technique is characterized as phase-division multiplexing (PDM) of wavelengths, and wavelength information is separately extracted in the space domain from the information of multiple wavelength-multiplexed images. 2π-PDM is the technique to analytically and completely solve the system of equations with 2
As future works, constructions of three-color digital holography and multidimensional holography systems are important to realize full-color 3D imaging and multidimensional holographic sensing.
Figure 12
shows an example of the required holograms in three-wavelength 2π-PDM [38] and numerical results for theoretical validation. Phase shifts indicated in
Figure 12(a)
mean that three-color 3D imaging with 2π-PDM is capable, when a spatial light modulator or wave plates are used as phase shifter(s) as described in Ref. [38]. Also, a combination of a piezo and a wave plate or a spatial light modulator will be applicable as another implementation.
Figure 12(b)
–
(i)
shows the results of a numerical simulation for three-wavelength 2π-PDM. In this simulation, a three-color object “pepper” with a smooth surface shape, red, green, and blue color wavelengths of 640, 532, and 473 nm, and 200 mm distance between image sensor and object planes, an image sensor with the pixel pitch of 5 μm, 512 × 512 pixels, ideal bit resolution, and
The next step of the PDM techniques is the extension to multicolor holographic 3D image sensing, simultaneous imaging of color and 3D shape with multiwavelength phase unwrapping, dispersion imaging of a 3D specimen, and multidimensional holographic imaging. This technique has prospective applications to multispectral microscopy to observe 3D specimens with a wide field of view, quantitative phase imaging, multicolor lensless 3D camera, multidimensional holographic image sensors, and other multiwavelength 3D imaging applications.
Acknowledgments
We appreciate Kris Cutsail-Numata for checking the English grammar in this chapter of the book. One of the authors would like to sincerely thank Shu Tahara for encouragement. This research was supported by Japan Science and Technology Agency (JST), PRESTO, Konica Minolta Science and Technology Foundation, The Okawa Foundation, Research Foundation of Tokyo Institute of Technology, the Japan Society for the Promotion of Science (JSPS), MEXT-Supported Program for the Strategic Research Foundation at Private Universities (from 2013 to 2018), and Research Foundation for Opt-Science and Technology.
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