Iterative phase retrieval by combining modulus constraints and angle relationships

In coherent diffraction imaging, modulus is recorded and phase is lost. Phase retrieval is to recover the lost phase from the recorded modulus. Iterative Fourier algorittun (IFA) solves this problem by imposing modulus constraints to make the phase converge. Here we show a modulus angle joint phase retrieval method. When both amplitude and phase modulation are applied, the angle relationship, which denotes the Fourier phase difference, can be exactly derived from the measured intensities. Based on this angle relationship, a new form of IFA called angle iteration is developed, which exhibits a faster but unstable convergence compared with tradition IFA (modulus iteration). By modulus-angle combined iteration, the proposed method reaches a quick and stable convergence. With the same intensity measurements, it drops nearly 80% the phase retrieval errors by traditional IFA but costs the same CPU time. This work reveals the fact that changing the constraint format would improve the original iteration process.