Phase increment-based pixel-independent phase–height model for the measurement range extension of projection moiré

Projection moiré is a high-resolution, high-precision three-dimensional (3D) profilometry, but the phase-height model constrains its measurement range and accuracy. This study introduces a pixel-independent (P-I) phase-height model for projection moiré to expand the measurement range. A P-I model is derived regarding the moiré phase increment, eliminating the challenges posed by inconsistent distortion between the fringe pattern and the reference grating. The model further accounts for reception system distortions by modeling the system as a two-stage back-projection process. The proposed model can accurately represent the phase-height relationship across the entire reference plane by addressing the distortions on moiré phases associated with both the fringe and grating phases. Experimental results show that the proposed model achieves high accuracy over a measurement range four times the calibration range, doubling that of the conventional pixel-dependent (P-D) model.