Solving differential equations for phase retrieval in Fourier-transform methods

Details Solving differential equations for phase retrieval in Fourier-transform methods Solving differential equations for phase retrieval in Fourier-transform methods

Apr 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010aipc.1236..118m&link_type=abstract

INTERNATIONAL CONFERENCE ON ADVANCED PHASE MEASUREMENT METHODS IN OPTICS AND IMAGING. AIP Conference Proceedings, Volume 1236,

Physics

Optics

Fourier Transform Optics, Phase Transfer Function, Interference, Partial Differential Equations, Interferometry, Fourier Optics, Phase Retrieval, Interference, Partial Differential Equations, Holographic Interferometry, Other Holographic Techniques

Scientific paper

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[iø(x,y)] is first calculated from a certain interference pattern given by a(x,y)+b(x,y).cosø(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 ∇ø(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 ø(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.

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