Camera-in-the-loop gradient descent hologram generation for Fraunhofer diffraction
Year: 2026
Type: article
Abstract: Gradient descent (GD) is a common method for computing phase-only holograms in the Fraunhofer regime (far-field), where the ideal replay field is the Fourier transform of the modulator field. Optimized against a simulated forward model, GD produces holograms of high simulated fidelity, but that fidelity is not obtained on an optical setup. We demonstrate full hologram generation for the far-field using GD with camera-in-the-loop (GD+CITL), which corrects for the discrepancy between the forward model and the optical setup, across 18 targets in a single optimization per target. GD+CITL takes into account the optical setup while generating the hologram. Using a liquid-crystal-on-silicon (LCoS) spatial light modulator (SLM) with a camera at the focal plane of a Fourier lens, we used this method under two forward models: an ideal Fourier transform, and a physically faithful model accounting for the pixel-aperture sinc envelope and the replay-plane bandwidth. To establish the mechanism, we first emulate an aberrated system in simulation, injecting Zernike wavefront error of known RMS magnitude into the measurement while the optimizer’s own forward model stays clean, so that the aberration is sensed only through the feedback loop. Correction is confined to a band between the diffraction limit and a realistic bench. At 0.05 waves RMS of combined aberration, feedback recovers a median 2.28 dB (95% confidence interval (CI) 1.29 to 2.73) over an uncorrected baseline when simulation-seeded and 0.95 dB (0.68 to 1.15) from a uniform random phase, falling to 0.61 and 0.34 dB at 0.20 waves. Once the aberration-independent piston floor is subtracted, both went to zero beyond ∼0.3 waves. A piston mode serves as a null control and isolates 0.34 dB of the simulation-seeded gain as aberration-independent refinement rather than correction. On the physical system, 750 iterations of per-iteration GD+CITL improve reconstruction quality from a uniform random phase by a paired median of 1.82 dB (95% CI 1.25 to 3.42) under the faithful model, improving 17 of 18 targets, and 2.34 dB (95% CI 1.68 to 3.35) under the ideal model, improving 16 of 18. Simulation-seeded runs give 1.80 dB (95% CI 1.42 to 3.53) and 2.73 dB (95% CI 1.71 to 3.55) on the same targets. All four survive Benjamini-Hochberg correction. Because every iteration costs one physical exposure, we also quantify the method’s capture cost. We initialize the optimizer from a converged simulated hologram and reduce the iteration of best reconstruction from a median of 168 to 75, a median per-target reduction of 2.11×, improving all 18 targets, cutting camera time from 5.5 to 2.5 minutes per target, at a negligible paired quality difference of 0.03 dB (95% CI 0.01 to 0.12).
Source: Optics Express
DOI: 10.1364/oe.613770
Language: English
Subfield: Media Technology
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,270
OpenAlex ID: W7224096724