Robust gamma correction based on chord distribution coding considering projector defocusing

In phase-measurement profilometry (PMP), the gamma effect can cause severe nonlinear distortion of the phase pattern (i.e., water ripples on the surface profile). Gamma correction is an effective method to eliminate the gamma effects of commercial projectors. However, projector defocusing on the suppression of higher harmonics inevitably results in an estimated gamma deviation from the true value. In this study, gamma mapping is constructed using the duty ratio (DR) to code the chord distribution of the simulated distorted phase while considering projector defocusing. With the known gamma mapping, the accurate gamma is calculated by DR coding of the actual distorted phase under projector defocusing. Simulated experiments verified that the relative errors of the gamma calculated by the proposed method under different degrees of defocus were less than 3.5%. Furthermore, the experimental results demonstrate that the proposed gamma calculation method is robust to the defocus effect of the projector and that a smoother surface can be reconstructed after gamma correction.