Measurement uncertainty of Carré-type phase-stepping algorithms

Abstract

Phase retrieval techniques are powerful tools used in interferometry, fringe projection, and other methods of image and signal analysis. The popular linear phase stepping algorithms combine weighted sums of signal values to obtain sine and cosine parts of the phase of interest. The coefficients and phase step angles are chosen to minimize the measurement uncertainty due to some experimental influence quantities. While a general treatment of measurement uncertainty for linear phase stepping algorithms has been given elsewhere, in this article a treatment of non-linear, Carré-type algorithms is given. We show that such algorithms can be viewed as a geometrical mean of linear phase stepping algorithms, and we express the measurement uncertainty in terms of the measurement uncertainty of an equivalent linear phase-stepping algorithm. Using the general expression for the measurement uncertainty, we show explicitly that the influence of a linear phase step miscalibration is suppressed.