Speckle-induced phase error in laser-based phaseshifting projected fringe profilometry

Laser sources offer advantages over white-light sources in some phase-shifting projected fringe profilometry applications. These benefits, however, are gained at the cost of incurring speckle noise. Some basic statistics of speckle-induced phase-measurement errors are investigated based on the multiplicative noise model for image-plane speckles. First, the dependence of phase-error distribution and measurement uncertainty on speckle size and grating pitch is numerically studied, based on the Karhunen–Loève expansion method. Then an analytical expression that relates phase-error distributions to optical system parameters is derived as a direct extension of the simulation results. This expression is useful for system design and optimization. Analysis shows that phase noise caused by speckles can be modeled as additive white Gaussian noise. Optical system design and noise-reduction algorithms are also briefly discussed, based on the simulation results.