Error-reduction methods for shape measurement by temporal phase unwrapping

Temporal phase unwrapping is a method of analyzing fringe patterns in which the fringe phase Φ at each pixel is measured and unwrapped as a function of time t. We propose two methods for improving the signal-to-noise ratio of the total phase change by incorporating data from the intermediate phase values. The first involves fitting the expected curve to the measured phase history; the second involves Fourier transformation of the corresponding phasors. The performance of these methods is compared both experimentally, with data from a fringe projector based on a spatial-light modulator, and numerically. It is shown that the optimum performance is given by the Fourier transform method. The best way to use the first method is with Φ decreasing exponentially with time from its maximum value to zero; this provides significant improvements in reliability, accuracy, and computation time compared with the original temporal unwrapping algorithm.