Analytical Fresnel Phase Compensation for Rapid Retargeting of Phase-Only Holograms

Computer-generated holography (CGH) for near-field diffraction displays often becomes bottlenecked by the computational latency of iterative hologram optimization algorithms. This limits real-time or adaptive updates to the reconstruction conditions. We propose a closed-form phase-compensation method derived from the Fresnel transform. This method reuses an existing phase-only function (POF) to retarget the propagation distance z, the wavelength λ, their coupled z-λ variations, and tilted-plane reconstructions without rerunning iterative procedures. Analytically derived compensation operators are applied directly to the POF. Numerical evaluations demonstrate that the compensated holograms reproduce the baseline reconstructions, achieving correlation coefficients greater than 0.995 and peak signal-to-noise ratios (PSNRs) greater than 20 dB. Notably, once a baseline POF is initially generated via MGSA, the subsequent retargeting computation time is reduced from several seconds to the millisecond range, offering a significant speed enhancement of approximately 150× for dynamic updates. Unlike deep-learning-based CGH generation, our approach requires no training data, is fully interpretable, and can be integrated with existing CGH pipelines. This method offers a low-latency and stable approach to real-time and adaptive holographic displays, including head-up display (HUD) systems.