Propagation-adaptive 4K computer-generated holography using physics-constrained spatial and Fourier neural operator

Computer-generated holography (CGH) offers a promising method to create true-to-life reconstructions of objects. While recent advances in deep learning-based CGH algorithms have significantly improved the tradeoff between algorithm runtime and image quality, most existing models are restricted to a fixed propagation distance, limiting their adaptability in practical applications. Here, we present a deep learning-based algorithmic CGH solver that achieves propagation-adaptive CGH synthesis using a spatial and Fourier neural operator (SFO-solver). Grounded in two physical insights of optical diffraction, specifically its global information flow and the circular symmetry, SFO-solver encodes both target intensity and propagation distance as network inputs with enhanced physical interpretability. The method enables high-speed 4 K CGH synthesis at 0.16 seconds per frame, delivering an average PSNR of 39.25 dB across a 30 mm depth range. We experimentally demonstrate various-depth 2D holographic projection and an adjustable multi-plane 3D display without requiring hardware modifications. SFO-solver showcases significant improvements in the flexibility of deep learning-based CGH synthesis and provides a scalable foundation to fulfill broader user-oriented requirements such as dynamic refocusing and interactive holographic display.