Abstract
Crossed-grating phase-shifting profilometry (CGPSP) has great utility in three-dimensional shape measurement due to its ability to acquire horizontal and vertical phase maps in a single measurement. However, CGPSP is extremely sensitive to the non-linearity effect of a digital fringe projection system, which is not studied in depth yet. In this paper, a mathematical model is established to analyze the phase error caused by the non-linearity effect. Subsequently, two methods used to eliminate the non-linearity error are discussed in detail. To be specific, a double five-step algorithm based on the mathematical model is proposed to passively suppress the second non-linearity. Furthermore, a precoding gamma correction method based on probability distribution function is introduced to actively attenuate the non-linearity of the captured crossed fringe. The comparison results show that the active gamma correction method requires less fringe patterns and can more effectively reduce the non-linearity error compared with the passive method. Finally, employing CGPSP with gamma correction, a faster and reliable inverse pattern projection is realized with less fringe patterns.
Highlights
Phase shifting profilometry (PSP), with non-contact, full-field, high-resolution and high-precision advantages, is a popular three-dimensional (3D) shape measurement technique based on fringe projection [1,2,3]
The comparison results show that the active gamma correction method requires less fringe patterns and can more effectively reduce the non-linearity error compared with the passive method
Crossed-grating phase-shifting profilometry (CGPSP) with gamma correction, a faster and reliable inverse pattern projection is realized with less fringe patterns
Summary
Phase shifting profilometry (PSP), with non-contact, full-field, high-resolution and high-precision advantages, is a popular three-dimensional (3D) shape measurement technique based on fringe projection [1,2,3]. In PSP, the height information of a tested object is encoded within the phase of the projected fringe patterns. The phase retrieved from the captured deformed fringe patterns by phase shifting algorithm is wrapped within the range from −π to π [7]. A phase unwrapping algorithm must be conducted to obtain a continuous phase map. Spatial phase unwrapping implemented on a single wrapped phase map is normally dependent on the unwrapping path. Temporal phase unwrapping can solve the phase ambiguity problem by using multi-wrapped phase maps, in which phase unwrapping is performed at each pixel independently
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