Modulator refinement algorithm for coherent modulation imaging

Coherent modulation imaging (CMI) has been shown to be an effective lensless diffraction approach to imaging general extended samples with fast algorithmic convergence and high robustness to data imperfection. In the reported phasing algorithms of CMI, an exact knowledge of modulator is used as a priori. Extra characterization of the modulator is thus required before the CMI experiments are conducted and this can be cumbersome. Here we propose a modulator refinement algorithm that allows for modulator refinement in the same iterative process of image reconstruction. We demonstrate the method for both near-field and far-field geometries in simulations and for a far-field experiment. A relaxed requirement on exactly knowing the modulator would turn CMI into a standalone technique and make it much easier to implement, thus open up its wider applications in biology and materials science.