Phase microscopy using band-limited image and its Fourier transform constraints

In this Letter, we present a new, to the best of our knowledge, form of single-exposure quantitative phase microscopy based on the phase retrieval method by recording the band-limited image and its Fourier image simultaneously. Applying the intrinsic physical constraints of microscopy systems in the phase retrieval algorithm, we remove the inherent ambiguities of the reconstruction and achieve a rapid iterative convergence. In particular, this system does not require tight support of the object and the oversampling needed in coherent diffraction imaging. We have demonstrated that, in both simulations and experiments, the phase can be rapidly retrieved from a single-exposure measurement using our algorithm. The presented phase microscopy provides a promising technique for real-time quantitative biological imaging.