End-to-end design for large-aperture HDOE cameras by zone-parameterized differentiable ray tracing

Large-aperture harmonic diffractive optical elements (HDOEs) offer low mass and high angular resolution, making them attractive for spaceborne imaging and motivating end-to-end (E2E) design for centimeter-scale elements. Existing E2E approaches face two limitations: wave-optics models become computationally prohibitive at large-apertures, while ray-based order decomposition treats diffraction orders as independent refractive channels, reducing multi-order fidelity and providing an impractical optimization parameterization. To overcome these limitations, we propose a zone-decomposition differentiable design framework that preserves the efficiency of ray tracing. A double-sided HDOE is partitioned into concentric annular zones, each represented by a compact set of polynomial sag coefficients and optimized in a differentiable ray tracing engine. The resulting forward model is physically consistent with the fabricated zonal structure and remains fully differentiable. Combined with a RAW-domain imaging model and a reconstruction network, the framework enables E2E optimization of a 50-mm-aperture broadband achromatic HDOE in the visible-band. Experimental results demonstrate that the proposed method provides a physically credible solution for E2E joint design of large-aperture HDOEs.