Efficient phase retrieval based on dark fringe extraction and phase pattern construction with a good anti-noise capability

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 apply the information of extracted dark fringes and its relationship with designed phase patterns. Here the dark fringes are extracted from the image plane, rather than the Fourier/focal plane, and the invalid extracted fringes can be tactfully bypassed to improve the anti-noise capability. 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 broad prospects in practical applications such as X-ray crystallography, diffractive imaging, and so on.