Efficient phase retrieval based on dark fringe recognition with an ability of bypassing invalid fringes

This paper discusses the noisy phase retrieval problem: recovering a complex image signal with independent noise from quadratic measurements. Inspired by the dark fringes shown in the measured images of the array detector, a novel phase retrieval approach is proposed and demonstrated both theoretically and experimentally to recognize the dark fringes and bypass the invalid fringes. A more accurate relative phase ratio between arbitrary two pixels is achieved by calculating the multiplicative ratios (or the sum of phase difference) on the path between them. Then the object phase image can be reconstructed precisely. Our approach is a good choice for retrieving high-quality phase images from noisy signals and has many potential applications in the fields such as X-ray crystallography, diffractive imaging, and so on.