Robustness of reduced temporal phase unwrapping in the measurement of shape

The predictions of success rate and depth uncertainty for the negative expo nential sequence used for temporal phase unwrapping of shape data are gener alized to include the effect of a reduced sequence and speckle noise in sin gle-channel and multichannel systems, respectively. To cope with the reduct ion of the sequence, a scaling factor is introduced. A thorough investigati on is made of the performance of this algorithm, called the reduced tempora l phase-unwrapping algorithm. Two different approaches are considered: a si ngle-channel approach in which all the necessary images are acquired sequen tially in time and a multichannel approach in which the three channels of a color CCD camera are used to carry the phase-stepped images for each fring e density in parallel. The performance of these two approaches are investig ated by numerical simulations. The simulations are based on a physical mode l in which the speckle contrast, the fringe modulation, and random noise ar e considered the sources of phase errors. Expressions are found that relate the physical quantities to phase errors for the single-channel and the mul tichannel approaches. In these simulations the single-channel approach was found to be the most robust. Expressions that relate the measurement accura cy and the unwrapping reliability, respectively, with the reduction of the fringe sequence were also found. As expected, the measurement accuracy is n ot affected by a shorter fringe sequence, whereas a significant reduction i n the unwrapping reliability is found as compared with the complete negativ e exponential sequence. (C) 2001 Optical Society of America.