A gamma correction method based on constant-intensity images in phase-measuring profilometry

Phase-measuring profilometry (PMP) is an important technique for image analysis in optical non-destructive testing (NDT). Its measurement accuracy is significantly affected by gamma distortion in the projector, which makes the projected sinusoidal fringe patterns non-sinusoidal. In order to address this issue, a generic gamma non-linearity model based on constant-intensity images is proposed in this paper. In the proposed model, system defocus and noise are considered and analysed. It is demonstrated through theoretical derivation that the constant-intensity images remain unchanged, with no additional frequency being produced. For this reason, system defocus is not modelled in the proposed gamma calibration model and the related defocus parameters need not be calculated, which reduces the complexity of the calculation. Any noise that exists in the optical measurement system is another main factor influencing the greyscale levels of the image. A mutual information (MI)-based denoising method is proposed to reduce the noise and improve the accuracy of the gamma calibration. Furthermore, with the defocus analysis and the noise reducing method, a robust pixel-wise gamma calibration method is introduced. The experimental results in this paper show that the proposed gamma calibration method is able to accurately calibrate the gamma non-linearity of the system. Moreover, the phase precision is significantly improved and a higher quality measurement is achieved for the measured surfaces.