Geometrical-physical optics modeling and inverse design for coherent optical field control with freeform elements.

We propose a geometrical-physical optics framework for coherent optical field propagation and inverse design in freeform optical systems. By interpreting geometrical optics as the stationary phase approximation (SPA) of physical-optics propagation operators, the proposed framework establishes an asymptotic connection between wave-optics propagation and ray-based optical modeling. A pointwise Fourier transform formulation is introduced to describe the asymptotic mapping between spatial and spatial-frequency domains under the SPA. Based on this formulation, a geometrical-physical optics phase retrieval algorithm is developed by extending the iterative Fourier transform algorithm into regimes with sufficiently large phase gradients. The method is further applied to the inverse design of freeform optical elements for coherent beam shaping. Numerical examples demonstrate that the proposed framework can effectively approximate coherent optical field propagation and achieve coherent beam shaping through freeform inverse design. The proposed approach provides a computationally efficient framework for coherent freeform optical design and may be useful for coherent beam shaping and wavefront engineering applications.