## 1 Introduction
Spatial division is being actively researched because neither temporal nor spatial resolutions are sacrificed. However, in the case of space division, alignment of multiple image sensors is a problem. Numerical correction is reported to solve this problem effectively [29]. On the other hand, holographic multiplexing makes it possible to record multiwavelength/color information by using a monochrome image sensor and to reconstruct it from wavelength-multiplexed image(s). In the 1960s, [PERSON] presented the concept of recording a multidimensional image by holographic multiplexing [37], which is based on spatial frequency-division multiplexing [34; 35; 36]. This multiplexing enables single-shot multidimensional holographic sensing and imaging; however, it sacrifices the spatial bandwidth available for recording each object wave at each wavelength as the number of wavelengths is increased. As another means of holographic multiplexing, temporal frequency-division multiplexing has been researched, and it provides a wide spatial bandwidth regardless of the number of wavelengths [29; 30; 31]. As for temporal frequency-division multiplexing technique, Fourier and inverse Fourier transforms are calculated for each pixel to separate wavelength information. To obtain a color 3D image, however, many wavelength-multiplexed images and an image sensor with a high frame rate are needed. Since 2013, we have been proposing an interferometric technique which selectively extracts wavelength information by using wavelength-multiplexed phase-shifted interferograms to measure multiwavelength object waves without using a color-filter array [9; 38; 39; 40; 41; 42; 43]. As for the proposed interferometry, multiwavelength information is multiplexed both on the space and in the spatial-frequency domain, and it is then separated in the polar coordinate plane by using wavelength-dependent phase shifts. Hereafter, multiwavelength DH based on the proposed interferometry is termed wavelength-selective phase-shifting DH (WSPS-DH). Applying the WSPS-DH provides a full space-bandwidth product of an image sensor at each wavelength regardless of the number of wavelengths measured. Moreover, operations to change the wavelengths of light to form a hologram are not required. When the number of wavelengths is \(N\), only 2\(N\)+1 wavelength-multiplexed images are required for multiwavelength 3D image sensing [9; 38; 39; 40], while 3\(N\) holograms are recorded in the temporal division. Recordable wavelength bandwidth is determined by the spectral sensitivity of the monochrome image sensor. Therefore, both wavelength and spatial bandwidth of the WSPS-DH are greater than those of the space-division multiplexing with a color image sensor. After the initially reported WSPS-interferometry was reported, WSPS-DH utilizing 2\(N\) wavelength-multiplexed images was proposed [41]. In the primitive scheme [38; 39; 40; 41], phase ambiguity of 2\(\pi\) was utilized to selectively extract multiwavelength object waves, and then a technique employing arbitrary phase shifts for rigorously retrieving object waves at multiple wavelengths by using 2\(N\)+1 holograms was proposed [9; 42; 43]. Although Doppler phase-shifting color DH [31; 32] has also been proposed as another holographic multiplexing technique with a full space-bandwidth product, it requires the recording of a large number of images. WSPH-DH requires only 2\(N\) holograms at least [41] by employing two-step phase-shifting interferometry [44; 45; 46; 47; 48; 49], while 512 holograms are required for Doppler three-wavelength phase-shifting DH [32]. Therefore, WSPH-DH accelerates measurement speed by more than 80 times when recording three wavelengths [39; 41]. The proposed DH has the potential to obtain a multiwavelength holographic 3D image with a small number of recordings without any color absorption. It thus enables multimodal cell imaging with low light intensity when applied to biological microscopy. Moreover, in principle, it alleviates light damage to living cells during multidimensional holographic imaging.