Shape measurement temporal phase unwrapping: comparision of unwrapping algorithms

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 phi is proportional to log(2)(phi/pi) and therefore also results in a reduction in computational effort by a factor log(2)(phi/pi)/(phi/pi) compared with the linear algorithm.