Partially Coherent Ambiguity Functions for Depth-variant Point Spread Function Design

The ambiguity function (AF) provides a convenient way to model how a camera with a modified aperture responds to defocus. We use the AF to design an optimal aperture distribution, which creates a depth-variant point spread function (PSF) from a sparse set of desired intensity patterns at different focal depths. Prior knowledge of the coherence state of the light is used to constrain the optimization in the mutual intensity domain. We use an assumption of spatially coherent light to design a fixed-pattern aperture mask. The concept of a dynamic aperture mask that displays several aperture patterns during one image exposure is also suggested, which is modeled under an assumption of partially coherent light. Parallels are drawn between the optimal aperture functions for this dynamic mask and the eigenmodes of a coherent mode decomposition. We demonstrate how the space of design for a 3D intensity distribution of light using partially coherent assumptions is less constrained than under coherent light assumptions.