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• W1998553792 abstract "In this paper, a method for phase retrieval by using Fourier analysis and techniques to solve differential equations is presented. From the technique proposed by Takeda et al., the function c(x,y) = (1/2)⋅b(x,y)⋅exp[io/(x,y)] is first calculated from a certain interference pattern given by a(x,y)+b(x,y)⋅coso/(x,y). By deriving c(x,y) and c*(x,y) with respect to x and y, it is then possible to find the corresponding phase gradient ∇o/(x,y), from which a Pfaff equation can be obtained. In this paper, we show that the solution of the Pfaff equation is the desired phase function plus a constant phase offset accordingly to the theory of differential equations. From this point of view, the phase function consists of a family of potential functions, which are orthogonal to a vectorial field which is the phase gradient. With this technique, the phase function o/(x,y) can be calculated from an interference pattern without the need of any phase unwrapping stage. A theoretical analysis and both numerical and experimental results are shown." @default.
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• W1998553792 date "2010-01-01" @default.
• W1998553792 modified "2023-09-25" @default.
• W1998553792 title "Solving differential equations for phase retrieval in Fourier-transform methods" @default.
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• W1998553792 doi "https://doi.org/10.1063/1.3426096" @default.
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