A new algorithm is proposed for unwrapping interferometric phase maps. Existing algorithms search the two-dimensional spatial domain for 2π discontinuities: only one phase map is required, but phase errors can propagate outward from regions of high noise, corrupting the rest of the image. An alternative approach based on one-dimensional unwrapping along the time axis is proposed. It is applicable to an important subclass of interferometry applications, in which a sequence of incremental phase maps can be obtained leading up to the final phase-difference map of interest. A particular example is quasi-static deformation analysis. The main advantages are (i) it is inherently simple, (ii) phase errors are constrained within the high-noise regions, and (iii) phase maps containing global discontinuities are unwrapped correctly, provided the positions of the discontinuities remain fixed with time. The possibility of real-time phase unwrapping is also discussed.

The recently proposed technique of temporal phase unwrapping has been used to analyze the phase maps from a projected-fringe phase-shifting surface profilometer. A sequence of maps is acquired while the fringe pitch is changed; the phase at each pixel is then unwrapped over time independently of the other pixels in the image to provide an absolute measure of surface height. The main advantage is that objects containing height discontinuities are profiled as easily as smooth ones. This contrasts with the conventional spatial phase-unwrapping approach for which the phase jump across a height discontinuity is indeterminate to an integral multiple of 2pi. The error in height is shown to decrease inversely with the number of phase maps used.

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Projected fringes can be used to measure surface profiles unambiguously, even in the presence of surface discontinuities, if the fringe pitch is changed over time. We investigate by numerical, analytical and experimental means the reliability of two recently proposed algorithms for unwrapping the resulting phase histories. The first, which unwraps through a sequence of phase maps produced with a linear change in spatial frequency with time, is found to be superior to the second, which uses only the first and last maps in the sequence. A new method is proposed in which the spatial frequency is changed exponentially with time. It is shown to be significantly more robust than either of the other algorithms under most conditions. The computation time required to unwrap through a given phase range is proportional to log 2 ( /π ) and therefore also results in a reduction in computational effort by a factor log 2 ( /π )/( /π ) compared with the linear algorithm.