Although laser sources offer more advantages over white light sources in some phase-shifting projected fringe profilometry applications, these advantages are at the cost of speckle. This paper presents some basic statistics of the speckle-induced phase measurement errors that are investigated based on the multiplicative-noise model for image-plane speckles. The dependence of the phase error distribution and measurement uncertainty on the speckle size and grating pitch is found based on the Karhunen-Loeve expansion of speckle field. This analysis shows that phase errors caused by speckles can be modeled as additive white Gaussian noise. Based on these simulation results we can discuss the designs of the optical system and noise reduction algorithms.
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