Gamma-distorted fringe image modeling and accurate gamma correction for fast phase measuring profilometry

In fast phase-measuring profilometry, phase error caused by gamma distortion is the dominant error source. Previous phase-error compensation or gamma correction methods require the projector to be focused for best performance. However, in practice, as digital projectors are built with large apertures, they cannot project ideal focused fringe images. In this Letter, a thorough theoretical model of the gamma-distorted fringe image is derived from an optical perspective, and a highly accurate and easy to implement gamma correction method is presented to reduce the obstinate phase error. With the proposed method, high measuring accuracy can be achieved with the conventional three-step phase-shifting algorithm. The validity of the technique is verified by experiments.