Towards Robust and Generalizable Gerchberg Saxton based Physics Inspired Neural Networks for Computer Generated Holography: A Sensitivity Analysis Framework

TL;DR

This work tackles the ill-posed inverse problem of phase retrieval in computer-generated holography by introducing a Saltelli Sobol-based sensitivity framework to quantify how forward-model hyperparameters FMHs influence GS-PINN performance. By comparing Fourier holography and free-space angular spectrum based propagation, the study shows that free-space FMHs generally improve GS-PINN generalization, while Fourier holography can offer stability for GS algorithms. A composite benchmarking metric is proposed to fairly evaluate and compare CGH-enabled neural networks across diverse FMH configurations, revealing limitations in cross-configurability and emphasizing hardware-driven parameter importance. Collectively, the framework guides forward-model selection, neural architecture design, and robust evaluation in CGH, enabling more interpretable and generalizable holographic systems. The work advances practical decision-making in CGH research by linking physics-based forward models with interpretable AI in phase retrieval tasks, underpinned by explicit variance-based sensitivity analyses and standardized benchmarking standards.

Abstract

Computer-generated holography (CGH) enables applications in holographic augmented reality (AR), 3D displays, systems neuroscience, and optical trapping. The fundamental challenge in CGH is solving the inverse problem of phase retrieval from intensity measurements. Physics-inspired neural networks (PINNs), especially Gerchberg-Saxton-based PINNs (GS-PINNs), have advanced phase retrieval capabilities. However, their performance strongly depends on forward models (FMs) and their hyperparameters (FMHs), limiting generalization, complicating benchmarking, and hindering hardware optimization. We present a systematic sensitivity analysis framework based on Saltelli's extension of Sobol's method to quantify FMH impacts on GS-PINN performance. Our analysis demonstrates that SLM pixel-resolution is the primary factor affecting neural network sensitivity, followed by pixel-pitch, propagation distance, and wavelength. Free space propagation forward models demonstrate superior neural network performance compared to Fourier holography, providing enhanced parameterization and generalization. We introduce a composite evaluation metric combining performance consistency, generalization capability, and hyperparameter perturbation resilience, establishing a unified benchmarking standard across CGH configurations. Our research connects physics-inspired deep learning theory with practical CGH implementations through concrete guidelines for forward model selection, neural network architecture, and performance evaluation. Our contributions advance the development of robust, interpretable, and generalizable neural networks for diverse holographic applications, supporting evidence-based decisions in CGH research and implementation.

Figures (29)

• Figure 1: GS-Physics Inspired Neural Network (GS-PINN) with Phase Initialization, Wavefront and Phase Adjustment Neural networks ( \ref{['algorithm:unrolled_GS_PINN']}). The laser constraints consist of a linearly polarized beam with uniform amplitude, and the 'star' symbol represents the formation of a complex wavefront.
• Figure 2: Forward Models (FM) and Forward Model Hyperparameters (FMH). For Fourier holography SLM pixel-resolution is the FMH ( \ref{['eq:Fourier_forward_model']}). For free space propagation wavelength of light, propagation distance, SLM pixel-resolution and pixel-pitch are the FMH ( \ref{['eq:ASM_forward_model']}).
• Figure 3: Normalized hyperparameter space with Inner, Mid and Outer points. Sampling for SA was performed using Saltelli's extension of Sobol's sequence sobol2001globalSALTELLI2002280will_usher_2016_160164. For $\textbf{h}_{\textup{mid}}$, $N_{\textbf{h}_{\textup{mid}}} = 1024$, generated $10240$ FMH configurations with $k = 4$ parameters. For $\textbf{h}_{\textup{outer}}$ and $\textbf{h}_{\textup{inner}}$, $N_{\textbf{h}_{\textup{outer|inner}}} = 256$ producing 2560 experiments each. (Resolution: $M \Delta x$)
• Figure 4: Sobol's samples for SLM pixel-resolution within the bounds [128,4000] to analyze sensitivity of FMs.
• Figure 5: FMH-induced parameter complexity and the composite metric. Top panel represents the inconsistency in performance of different algorithms for similar set of FMH configurations, complicating benchmarking. In the bottom panel, the composite metric addresses variability in model performance across similar FMH configurations, enabling more reliable benchmarking.