Computer-generated holography encoding via dynamic region segmentation and parallel phase difference inference

With the growing demand for high-performance imaging, freeform optical elements are increasingly used in optical systems. The computer generated hologram (CGH) designed for null interferometric testing often spans large areas and exhibits complex, high-density fringe patterns. In this context, the trade-offs between encoding accuracy, computation workload, and data size have become key constraints on the efficient and widespread adoption of freeform optics. This paper proposes a CGH encoding method that efficiently infers the phase values at the majority of sampling points by leveraging the structural characteristics of fringe patterns and the spatial continuity of the fringe phase. Theoretical analysis demonstrates that, whereas conventional methods exhibit quadratic growth in the number of explicit points with increasing encoding resolution or region size, our method reduces this to linear growth. In a representative case involving a 94mm-diameter CGH designed for testing an off-axis Bi-conic Zernike freeform mirror, while maintaining an encoding error below λ/200, the proposed method reduces runtime to only 1.32 hours and data size to 0.496 GB, corresponding to reductions of approximately 107.92 times and 99 times over conventional methods, demonstrating the method's high computational efficiency and low storage demand. Furthermore, the CGH encoded is applied in interferometric testing. The accuracy and effectiveness of the proposed CGH encoding method were verified through theoretical error modeling and analysis of interferometric measurement data. These results highlight the method's favorable trade-off among encoding accuracy, computational workload, and storage demand. This work offers a practical solution for high-precision CGH encoding in freeform optics null testing.