A Fast Autofocus System Based on the Advancement of the CGH Algorithm

Traditional CGH algorithms often face a trade-off between computational efficiency and reconstruction fidelity. In this study, we propose a hybrid hologram synthesis framework that combines geometric and physical optics to generate phase-only holograms for SLM. A freeform surface obtained from geometric optics provides a smooth continuous phase initialization for the iterative CGH solver, which substantially reduces the number of required iterations. We further improve the SGD-based optimization by introducing an adaptive step size factor and explicit phase constraints during the update process. These modifications guide the solution toward a smooth phase profile, thereby suppressing high-frequency phase noise and mitigating speckle artifacts. Compared with a standard CGH algorithm, the proposed method achieves an approximately four times improvement in computational efficiency while maintaining reconstruction quality. Finally, we integrate the resulting holograms into an eye tracker–based autofocus system, enabling real-time adaptation to changes in the human eye’s focal state.