Global Self-Attention with Exact Fourier Propagation for Phase-Only Far-Field Holography

Abstract

Wavefront control underpins a wide range of technologies spanning imaging, communication, and light-matter interaction, yet remains fundamentally challenging due to the globally coupled nature of Fourier optical propagation. Computer-generated holography, using phase-only spatial light modulators, provides a widely used framework for wavefront manipulation. In the Fraunhofer (far-field) regime, propagation reduces to a Fourier transform, such that each modulator element influences the entire reconstructed field, rendering hologram synthesis a non-local inverse problem [1]. This coupling fundamentally limits conventional approaches. Iterative phase-retrieval methods [2-4] can stagnate and trade computation for quality, while camera-in-the-loop strategies remain tied to iterative refinement and near-field applications [5-7]. Learning-based approaches have accelerated hologram synthesis, yet largely rely on local inductive biases and Fresnel (near-field) models, leaving the fully coupled nature of the strict Fraunhofer regime unaddressed [8]. Here we show that the globally coupled structure of Fourier propagation maps naturally onto self-attention, enabling direct modeling of long-range dependencies in hologram synthesis. We demonstrate single-shot, high-fidelity phase-only hologram generation at inference in both simulation and experiment and show that integration with camera-in-the-loop training and a learnable phase corrector enables adaptive wavefront control under real optical conditions. These results establish self-attention as a scalable framework for wavefront control in complex optical systems and introduce attention-based modeling as a general approach to inverse problems governed by long-range interactions in wave physics.