Statistically constrained optimization for quantized computer-generated holography

Computer-generated holography enables precise modulation of optical fields, while generating high-quality quantized holograms remains challenging due to the non-differentiable quantization operation. In this Letter, we propose a gradient-based optimization algorithm with a statistical constraint strategy for quantized hologram generation. By incorporating the characteristics of the phase modulator, a statistical constraint is introduced during the optimization process to encourage phase values to cluster around target quantization levels. This strategy improves the optimization stability and bridges continuous optimization with discrete modulation. Numerical simulations and optical experiments demonstrate that the proposed method consistently improves reconstruction quality across a wide range of quantization bit depths.