Generalized virtual wave propagation model for a configurable DMD-based multiple-plane phase retrieval method

Image acquisition time in multiple-plane phase retrieval can be considerably reduced by replacing mechanical camera translations with equivalent virtual wave propagations at a fixed plane. This can be done by uploading digitized transfer functions at the Fourier plane of a 4f system to a high-speed digital micro-mirror device (DMD). While previous studies used DMDs with orthogonal mirror layouts, virtual wave propagations using alternative DMD models with diagonal mirror layouts that induce scaling distortion have yet to be demonstrated. Furthermore, the influence of the 4f system magnification on the virtual wave propagation remains unexplored. In this study, it was demonstrated that virtual wave propagations using a diagonal-mirror DMD in a 4f system with non-unity magnification fail to replicate the field obtained by manual camera translations. To resolve the discrepancy, a novel virtual wave propagation model, to our knowledge, based on Fourier analysis that accounts for both the magnification and scaling distortion, is proposed. A systematic calibration method to determine the compensating factors and misalignments is also presented. The proposed model was validated through simulations and experiments and provides a generalized framework for DMD-based phase retrieval regardless of the DMD mirror layout and 4f magnification.