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

Abstract

Phase-only computer-generated holography (CGH) seeks a phase pattern for a spatial light modulator (SLM) whose propagated optical field reproduces a desired intensity distribution. In the far-field (Fraunhofer) regime, optical propagation reduces to a Fourier transform, such that each hologram pixel contributes to the entire reconstructed intensity distribution. When restricted to phase-only modulation, intensity must be shaped through global phase interference effects, making the inverse mapping from target intensity to phase highly non-linear and sensitive to local minima. We present a proof-of-concept physics-in-the-loop approach in which a transformer maps a target intensity image to a phase-only SLM field and is trained end-to-end through exact FFT-based propagation embedded directly within optimization. We further observe that patch tokenization strongly shapes the optimization geometry: coarse tokenization acts as an implicit spectral regularizer that stabilizes training and suppresses checkerboard-like attractors, while finer tokenization increases spatial degrees of freedom but benefits from curriculum or hierarchical refinement. Despite training on limited primitives and a single digit class (only digit 6), the learned generator exhibits out-of-distribution (OOD) generalization to unseen digits and hand-drawn target patterns. These results suggest that transformer architectures, whose self-attention enables global token interactions, are a natural fit for far-field holography and provide a viable foundation for scalable physics-grounded hologram generation.