Geometry-aware phase compensation for sampling-efficient angular spectrum method

We present a geometry-aware, phase-compensated angular spectrum method (GAPC-ASM) framework for efficient wave optical modeling of thick refractive and diffractive systems. Conventional ASM demands dense lateral grids and fine axial sampling, which limits scalability for wide angle and large aperture configurations. To overcome these bottlenecks, we unify carrier frequency shifting and global phase compensation, and introduce a new local phase compensation mechanism that models geometry dependent path length variations in thick refractive elements. Together, these components allow single-slice ASM to reproduce thickness induced geometrical distortion and, when used within multi-slice ASM, significantly reduce the required axial sampling. The resulting framework is efficient, differentiable, and well suited for gradient based inverse design. We validate the approach through inverse design and verification of spherical and aspherical lenses, and through the task driven design and fabrication of a freeform phase mask for lensless imaging. The fabricated mask produces point spread functions that closely match simulations and improve reconstruction quality, demonstrating that the proposed framework is a reliable and physically consistent tool for wave optical design of thick and hybrid optical systems.