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

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