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

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.

Sensitivity Analysis and Optimization of Gerchberg Saxton-based Neural Networks for Computer Generated Holography

The paper titled "Towards Robust and Generalizable Gerchberg Saxton based Physics Inspired Neural Networks for Computer Generated Holography: A Sensitivity Analysis Framework" examines the susceptibility of Gerchberg-Saxton-based Physics-Inspired Neural Networks (GS-PINNs) to variations in forward model hyperparameters (FMHs). The authors address the sensitivity of these neural networks, which can affect their generalization and adaptability in computer-generated holography (CGH), a field of significant interest for applications such as augmented reality, 3D displays, and neuroscience. Their framework employs Saltelli's extension of Sobol's method to quantify the influence of various FMHs on the performance of GS-PINN, providing concrete guidelines for improving neural network models in CGH tasks.

Key Findings and Methodology

1. Sensitivity Analysis:

   • The study finds that SLM pixel-resolution has the most significant impact on GS-PINN performance, surpassing other parameters like pixel-pitch, propagation distance, and wavelength. This insight aligns with the goal of understanding hardware-dependent sensitivity and guides configuration for optimal network performance.
   • Higher order interactions among SLM-related parameters contribute significantly to performance, implying the importance of joint parameter consideration during design and optimization processes.

2. Forward Model Evaluation:

   • A comparative analysis between free space propagation and Fourier holography models was conducted, revealing that GS-PINN trained with free space propagation forward models outperforms those based on Fourier holography in terms of generalization capability. Conversely, Fourier holography appears favorable for the traditional Gerchberg-Saxton algorithm due to its stability.
   • The distinct sensitivity profiles between the GS algorithm and GS-PINN underscore the importance of model selection and parameter tuning tailored to the intended application and underlying forward model characteristics.

3. Benchmarking and Standardization:

   • The authors propose a composite metric integrating GS-weighted, generalization, and resilience metrics to consistently evaluate neural network performance across varying FMH configurations. This metric addresses challenges of reliable comparisons and interpretable evaluations in the presence of FMH-dependent complexity.
   • Findings suggest that directly comparing neural networks trained on disparate FMH setups or benchmarking them against traditional algorithms like GS can result in unreliable conclusions due to the intrinsic complexity variability introduced by FMH differences.

Implications and Future Directions

By elucidating the sensitivity effects of FMH on CGH systems, this research advances the discourse on creating robust and generalizable GS-PINN models essential for practical implementation in diverse applications. The results emphasize the importance of selecting appropriate forward models based on the specific trade-offs desired in application contexts, such as performance stability versus generalization flexibility.

Furthermore, this work provides a foundation for developing standardized metrics to evaluate the performance of diverse neural networks in CGH contexts, ensuring fair benchmarking and fostering advancements in CGH algorithm design.

In conclusion, this paper makes a substantial contribution to computational holography by presenting a comprehensive sensitivity framework that informs better design and evaluation of neural networks tailored for holographic applications. Future research could explore extending this framework to other neural network variants and forward models, enhancing the scope of applicability in CGH-related tasks. These efforts may lead to the development of more sophisticated, interpretable AI systems capable of addressing the increasingly complex challenges in CGH and related fields.