## 3 Image Quality in Relation to Bit Depth of Wavelength-Multiplexed Holograms
### Numerical Simulations  
To investigate image quality and validate the experimental evaluations, in the case that bit depth of the image sensor was from 1 bit to 16 bits, image quality of reconstructed images was numerically simulated for three-wavelength WSPS-DH. A random pattern was set as the phase distribution of the object wave because scattering object waves were assumed. For color-intensity images, a photographic image of a flower and grass was prepared. For wavelengths of red-, green-, and blue-color light sources, 640 nm, 532 nm, and 488 nm were assumed. In the simulation, the distance between the object and image sensor was set to 150 mm, pixel pitch to 2.2 \(\upmu\)m, and the number of pixels of the image sensor to 512 \(\times\) 512. It was assumed that phase shifts were generated by a mirror with a piezo actuator and the mirror was moved 0 nm, 61 nm, \(\pm\)244 nm, and \(\pm\)488 nm sequentially. The intensity ratio between object and reference waves was 1:4 at each wavelength. Resolution of the image sensor was changed from 1 to 16 bits. Six wavelength-multiplexed phase-shifted holograms were obtained numerically and three-wavelength object waves were reconstructed by WSPS-DH [50; 51]. Reconstructed images in the numerical simulation are shown in Figure 4. In the same manner as revealed by the experimental results, as bit resolution was decreased, the reconstructed images degraded gradually. However, a clear multicolor object image was reconstructed even when the number of bits was 6. As shown in Figure 5, CCs of the reconstructed amplitude images were more than 0.8 when bit depth of the image sensor was decreased to 6 bits. Furthermore, although the color of the reconstructed image differed from that of the object, a three-wavelength object image was reconstructed even when the image sensor had a 4-bit depth resolution. On the other hand, it was found that RMSE and CC of the reconstructed phase distribution were worse than those of the amplitude images. For phase measurement and 3D shape measurement with multiwavelength phase unwrapping, an image sensor with high dynamic range is required. Using an image sensor with resolution of more than 9 bits will result in performance of less than RMSE of \(\lambda/20\) [rad] in phase. Analysis for smooth phase distribution is a future work.  
Figure 4: Numerical results: Reconstructed images when bit depths of holograms are (**a**) 2, (**b**) 3, (**c**) 4, (**d**) 5, (**e**) 6, and (**f**) 7 bits.  
The experimental and numerical results indicate that a resolution of at least 2 bits per wavelength in each hologram is required to obtain a multiwavelength 3D-object intensity image, and a color 3D image with a small color shift can be reconstructed when the sensor has more than 2-bit resolution per wavelength. Measurement error is reduced as bit depth is increased in the same manner as an ordinary imaging system; however, a faithful object intensity image can be reconstructed in a case of resolution of much less than 8 bits. The numerical results also show that using a low-bit image sensor causes a large error in phase measurement; therefore, an image sensor with more than 9 bits is desirable in the case of 3D shape measurement with phase information at multiple wavelengths.