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 2N holograms against 2N + 1 variables contained in each hologram. An experimental demonstration was conducted and clear color 3D imaging ability was successfully shown. Note that detailed analyses against both the experimental demonstration and the theory in 2π-PDM were reported in Ref. [38].

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-

Figure 12. (a) An example of holograms required for three-wavelength 2π-PDM and (b)–(i) its numerical results. (b) Amplitude and (c) phase distributions of the assumed object wave and (d) one of three-wavelength-multiplexed phaseshifted holograms. Reconstructed amplitude images at the wavelengths of (e) 640 nm, (f) 532 nm, (g) 473 nm, and (h) phase image at 640 nm. (i) Color synthesized image obtained from (d)–(f). In the results, wave plates are assumed as phase shifters as described in Ref. [38]. The image-reconstruction procedure is in the same manner of dual-wavelength 2π-PDM, which is explained in Section 4.

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 α1, α2, α<sup>3</sup> = π/2 were assumed. These assumptions can be satisfied with the optical system with five quarter wave plates, which is illustrated in Ref. [38]. Numerical results indicate that multiwavelength holographic 3D imaging can be done with high image quality from grayscale wavelength-multiplexed images, if successfully constructed. Improvements on the measurement principle and/or an image-reconstruction algorithm are important to simplify the construction; this is one of the main issues to be solved. From the viewpoint of multidimensional holographic imaging, PDM and 2π-PDM have the potential for not only multiwavelength, but also polarization-imaging digital holography [37] and instantaneous measurement [35], as implementations are described in these references. It is expected that simultaneous imaging of 3D structures, multiple wavelengths, and polarization distribution can be demonstrated with 2π-PDM.

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.
