Relaxation of mask design for single-shot phase imaging with a coded aperture

We present a method of relaxing the conditions of mask design in single-shot phase imaging with a coded aperture (SPICA), for extending the applications of SPICA. SPICA, based on compressive sensing, enables the acquisition of wide, high-resolution optical complex fields in a single exposure without the need for reference light. In our previous work on SPICA, a coded aperture (CA) was implemented with only amplitude modulation, resulting in a low transmission factor and low light efficiency because of the need for an independent phase retrieval process in the reconstruction. We attempt to alleviate these limitations by adapting a reconstruction algorithm to directly associate the phase-retrieval process with a sparsity-based reconstruction. With this approach, it is possible to realize SPICA with an amplitude-modulation-based CA having a high transmission factor, a phase-modulation-based CA, and a complex-amplitude (amplitude and phase)-modulation-based CA. We verified the effectiveness of these relaxed CA designs numerically and experimentally.