## 4 The Verification of CGH
### Generation of Modified Off-Axis Reference Beam CGH
Figure 17: Lee-encoded continuous grayscale reconstructed images under varying Gaussian noise coefficients (_ef_1 = 0.0–1.0). Figure 15: The flowchart of Lee-encoded continuous grayscale CGH encoding. Results (Figure 18) demonstrate stage-specific noise impacts on image quality metrics. PSNR decreases rapidly by 29% (27.88 dB\(\rightarrow\)19.79 dB) at noise coefficients 0.1-0.5, followed by marginal attenuation (0.7 dB, 19.79\(\rightarrow\)19.09 dB) in the high-noise regime (0.5-1.0), confirming its \"saturation attenuation\" approaching the theoretical noise-dominant limit. In contrast, SSIM exhibits a 3.9% reduction (0.9749\(\rightarrow\)0.9365) at 0.1-0.3 noise and merely a 1.5% decline (0.9365\(\rightarrow\)0.9216) at 0.3-1.0, sustaining structural fidelity >0.92 throughout, which verifies its exceptional robustness under intense noise. A mechanistic analysis reveals that the accelerated PSNR decay originates from linear noise energy accumulation directly degrading SNR, whereas SSIM stability arises from effective preservation of macroscopic structural features (edges, textures) and contrast characteristics under noise interference. (3) Lee-encoded binary CGHs  
In Figures 19-21, the flowchart of Lee-encoded binary CGH encoding, Lee-encoded binary CGHs under varying Gaussian noise coefficients (_e_f1 = 0.0-1.0), and Lee-encoded binary reconstructed images under varying Gaussian noise coefficients (_e_f1 = 0.0-1.0) are displayed. Pure phase noise (_e_f1) randomizes the phase of the object wavefront's complex amplitude, inducing amplitude distribution shifts in the four decomposed basis components and localized adjustments to subgrid apertures. Figure 19: The flowchart of Lee-encoded binary CGH encoding. Figure 12:0 PSNR and SSIM values of Lee-encoded continuous grayscale reconstructed images under varying Gaussian noise coefficients (_e_f1 = 0.0-1.0). Experimental results (Figure 22) reveal that PSNR exhibits continuous attenuation, declining by 29% (22.34 dB\(\rightarrow\)15.83 dB) as noise increases from 0.1 to 1.0, with a sharper reduction of 16.8% (22.34\(\rightarrow\)18.61 dB) in low-noise regimes (0.1-0.4) versus 13.6% (18.32\(\rightarrow\)15.83 dB) at higher noise levels (0.5-1.0), indicating SNR saturation under noise dominance. In contrast,  
Figure 12:1 Lee-encoded binary reconstructed images under varying Gaussian noise coefficients (_e_f1 = 0.0–1.0). Figure 12:2 PSNR and SSIM values of Lee-encoded binary reconstructed images under varying Gaussian noise coefficients (_e_f1 = 0.0–1.0). SSIM shows only a 3.9% overall decline (0.9294\(\rightarrow\)0.893), with an anomalous 0.2% increase (0.9131\(\rightarrow\)0.9153) at 0.4-0.5 noise. As a result of noise-content interactions, low-contrast distortion masking at specific noise levels and edge-sharpening effects induced by high-frequency noise may temporarily enhancing structural similarity. These findings demonstrate SSIM's superior robustness to noise interference compared to PSNR. At noise coefficients of \(ef_{1}\geq\) 0.5, PSNR enters a slow-decay noise-dominant state, while SSIM maintains its structural fidelity above 0.89, underscoring its evaluative advantage in noisy scenarios.