## 4 Numerical Analysis of the Wavelength Resolution Against Dynamic Range of Holograms  
The relation of wavelength resolution to bit resolution of holograms was numerically investigated. It was assumed that the optical setup is based on three-wavelength phase-shifting DH using a monochrome image sensor and a mirror with a piezo actuator under the following conditions. It was assumed that three-wavelength WSPS-DH with six wavelength-multiplexed holograms [50,51] was used and the mirror was moved 0 nm, 61 nm, \(\pm\)488 nm, and \(\pm\)732 nm sequentially. A color image and a rough surface were set as amplitude and phase distributions in 3D space, respectively. To investigate image quality quantitatively, CC and RMSE of the reconstructed images were calculated. It was initially assumed that the three wavelengths of light sources were \(\lambda_{1}\) = 640 nm, \(\lambda_{2}\) = 532 nm, and \(\lambda_{3}\) = 488 nm. After that, wavelength \(\lambda_{1}\) was set as 607, 589, 561, 556, 552, 546, 540, 534, 533, or 532.5 nm to investigate wavelength resolution of WSPS-DH. The wavelengths were determined from commercially available continuous wave (CW) lasers with long coherence lengths. Pixel pitch was 2.2 \(\upmu\)m, and the number of pixels was 512 \(\times\) 512. The wavelength resolution under the three conditions was investigated: an image sensor having 8-, 12-, and 16-bit resolutions. To investigate wavelength resolution of WSPS-DH under ideal conditions, no random noise such as incoherent stray light and dark-current noise was added to holograms.  
Reconstructed images obtained by this numerical simulation are shown in Figure 6, and graphs of calculated RMSE and CC of the amplitude and phase images at \(\lambda_{2}\) are plotted in Figure 7. High CC  
Figure 5: Quantitative evaluations for numerical results: CC of reconstructed (**a**) amplitude and (**b**) phase images and RMSE of reconstructed (**c**) amplitude and (**d**) phase images.  
means that faithful images were obtained and low RMSE indicates that multiwavelength 3D image measurement was high precision. The numerical results clarify that high CC was obtained even when the wavelength difference was less than 10 nm when an 8-bit image sensor was used. However, in the case an 8-bit image sensor was used, it was difficult to observe an object image clearly when the wavelength difference was within 2 nm. The difference between phase shifts added at neighboring wavelengths was small and the wavelength dependency of the intensity change induced by the wavelength-dependent phase shifts also became small. It is considered that an 8-bit image sensor could not detect weak wavelength dependency of the intensity change by the quantization. In contrast, in the cases of using an image sensor with 12- and 16-bit resolutions, object waves were successfully reconstructed because the image sensor captured weak wavelength dependency of intensity changes by phase shifts. An image sensor with 16 bits can record smaller intensity changes; therefore, higher CC and lower RMSE were obtained. These results indicate that wavelength resolution can be improved by increasing the bit depth of an image sensor. It is worth noting that this feature is characteristic of WSPS-DH. Thus, a guideline for selecting an appropriate image sensor was confirmed successfully.  
Figure 6: Numerical results concerning wavelength resolution in relation to the bit depth of an image sensor. Reconstructed images when (**a**–**d**) 8-bit, (**e**–**h**) 12-bit, and (**i**–**l**) 16-bit image sensors were used. Wavelength differences are (**a**,**e**,**i**) 0.5 nm, (**b**,**f**,**j**) 1 nm, (**c**,**g**,**k**) 2 nm, and (**d**,**h**,**l**) 8 nm.