## 4 The Verification of CGH  
### Generation of Lohmann-III Detour-Phase Cgh  
Figure 4 illustrates the flowchart of Lohmann Type III detour-phase CGH encoding. The object (\"\(\%\)\" in Chinese) was initially 512 \(\times\) 512 pixels but resized to 64 \(\times\) 64 pixels for accelerated Matlab computation on PC platforms. Additive white Gaussian noise (AWGN) was injected with intensity controlled by the coefficient \(ef_{1}\). To suppress the spectral dynamic range, tunable parameters include noise factor \(ef_{1}\) and aperture width \(w\). The object wavefield undergoes Fourier transformation followed by modulus normalization with a threshold coefficient \(ef_{2}\) = 1.5. Sampling units are then embedded into the CGH via detour-phase encoding. As demonstrated in Figures 5 and 6, the reconstructed images are derived from the synthesized CGH spectrum.  
For computational efficiency, each CGH unit comprises \(s\times s\) pixels, with aperture width \(w\) = \(s\)/2 yielding a final CGH dimension of (64 \(\times s\)) \(\times\) (64 \(\times\) \(s\)) pixels.  
Figure 4: The flowchart of Lohmann Type III detour-phase CGH encoding.  
Figure 3: Matlab simulation flowchart for calculating PSNR and SSIM metrics.  
The results (Figure 7) reveal distinct trends: PSNR monotonically decreases with the noise coefficient (18.2 dB at 0.1 to 11.59 dB at 1.0, a 36.3% reduction). A rapid decline occurs in low-noise regimes (0.1-0.3: 18.2\(\rightarrow\)14.56 dB), while high-noise regimes (0.7-1.0) exhibit saturation (merely 0.71 dB reduction), indicating heightened sensitivity to low-intensity noise. SSIM shows an overall decline (0.7936\(\rightarrow\)0.5925, 25.3% reduction), with minor fluctuations (0.648\(\rightarrow\)0.6395) at noise coefficients 0.3-0.4, reflecting nonlinear structural degradation.  
(2) Assume a fixed _ef\({}_{1}\)_ = 0.8 and _ef\({}_{2}\)_ = 1.5, with \(w\) adjusted from 4 to 12. The Lohmann Type III detour-phase CGHs and their reconstructed images under varying aperture widths \(w\) (_w_ = 4-12) are presented in Figures 8 and 9, respectively.  
The corresponding PSNR and SSIM values for the Lohmann Type III hologram under varying aperture widths (_w_ = 4-12) are shown in Figure 10.  
Aperture width significantly impacts imaging quality (Figure 10). Increasing the aperture width from 4 to 12 enhances PSNR (10.4\(\rightarrow\)20.2 dB, +94.2%) and SSIM (0.5895\(\rightarrow\)0.8611, +46%), showing near-linear trends: each 2-unit aperture increase improves PSNR by -2.45 dB and SSIM by -0.07.  
This phenomenon originates from multiple effects induced by aperture enlargement. (1) Increased photon flux effectively suppresses sensor dark current noise, thereby enhanc  
Figure 8: Lohmann Type III detour-phase CGHs under varying aperture widths \(w\) (_w_ = 4-12).  
Figure 10: PSNR and SSIM values for Lohmann Type III hologram under varying aperture widths (_w_ = 4–12).  
Figure 9: Lohmann Type III detour-phase reconstructed images under varying aperture widths \(w\) (_w_ = 4-12).  
ing signal-to-noise ratio (SNR). (2) Larger apertures substantially mitigate diffraction artifacts inherent to small apertures, achieving resolution improvement from blurred states to a structural fidelity level of 0.8611. (3) Aperture expansion potentially optimizes system aberration correction capabilities.  
Notably, smaller apertures (widths of 4-8) yield the most significant gains (PSNR: +64%; SSIM: +30%).  
The dynamic range of the spectrum is controlled by adjusting pure-phase noise intensity (via coefficient _ef\({}_{1}\)_) and aperture width \(w\). Combined optimization of these parameters effectively balances noise suppression and imaging fidelity.