## 1 Introduction  
Conventional hologram generation algorithms rely on precise phase and amplitude information, yet practical limitations such as noise and computational complexity often degrade reconstruction quality [1]. Unlike traditional optical holography requiring intricate interferometric setups, computer-generated holography (CGH) integrates computational techniques with modern optics, replacing physical interference devices with numerical simulations [2, 3]. This approach eliminates optical alignment errors and environmental disturbances while enabling rapid hologram generation, easy modifications, and large-scale data processing. Advances in digital holography have expanded CGH's applications in holographic displays [4, 5, 6] and optical information processing [7, 8]. CGHs are categorized by encoding techniques into detour-phase, modified off-axis reference, kinoform, and computational interference holograms.  
Recent progress in computer-generated holography (CGH) includes the work by [PERSON] et al. [9], who derived a cylindrical diffraction formula in the spectral domain to model light propagation from the outer holographic surface to the inner object surface. This framework enabled the analysis of pixelation effects, leading to a high-order diffraction model that effectively suppresses artifacts in CGH-generated images. Additionally, [PERSON] et al. [10] proposed an adaptive layer-based (ALB) method for rapid generation of CGHs with precise depth information. Their approach achieved high-fidelity reconstruction within 8.7 s using 52 adaptive layers. Despite these advancements, noise interference from environmental factors remains a critical challenge, degrading both amplitude and phase information in reconstructed wavefronts.  
Current noise suppression studies in CGH predominantly rely on single-metric evaluations. For instance, [PERSON] and [PERSON]. [11] developed a wavelet-based image fusion technique utilizing peak signal-to-noise ratio (PSNR) and the universal image quality index (UQI), demonstrating superior performance of discrete wavelet transform (DWT) over discrete cosine transform (DCT). [PERSON] and [PERSON] [12] further established a theoretical link between the structural similarity index (SSIM) and L2-norm measurements for image similarity. Although recent studies, such as [PERSON] et al. [13], have integrated SSIM and PSNR to assess compressed image quality in DCT-based systems, these metrics still exhibit limitations. Specifically, PSNR focuses on global intensity distortion but fails to capture structural degradation, while SSIM emphasizes local perceptual features but lacks sensitivity to noise saturation effects.  
Despite these efforts, a systematic analysis of noise impacts under varying encoding methods -- particularly for complex CGH architectures such as detour-phase, modified off-axis, kinoform, and interferometric holograms -- remains unexplored. Existing studies often overlook the interplay between encoding parameters (e.g., aperture geometry, quantization levels) and noise intensity, limiting their applicability to real-world scenarios with dynamic interference. This gap motivates the need for a comprehensive evaluation framework that combines multi-metric assessments with adaptive encoding optimization.  
This study employs Matlab simulations with dual metrics (PSNR and SSIM) to systematically investigate noise impacts on reconstruction quality across these four CGH types.