The Fourier-transform method is often used to evaluate fringe patterns. The fundamental limitations of its accuracy are examined. Special filter functions leading to an improved spatial definition and a fringe-extrapolation algorithm that reduces the errors at the border of the pattern are presented. Numerical simulations predict an accuracy of the phase evaluation of less than 6 mrad under certain conditions. We investigated the reproducibility by experiments with a Michelson interferometer. Deviations of approximately 10 mrad were found. In a second test a Ronchi ruling was imaged, and a well-defined phase change was introduced. We deduce an accuracy of less than 5 mrad rms.
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