High-precision calibration of a fringe projector based on Gaussian bicubic interpolation and orthogonal constrained homography

A grating projection system consists of a projector and a camera, where the projector functions as the inverse imager of the camera. Achieving high-precision calibration remains a major challenge. This study proposes an improved high-precision projector calibration technique. First, the grating fringe features of the calibration plate are enhanced using the Gaussian bicubic interpolation algorithm, and the projector pixel coordinates are calculated using the phase mapping formula, forming point pairs with the camera pixel coordinates. Then, a linear system of equations is constructed using the orthogonal constrained homography transformation equation. The optimized homography matrix and precise projector pixel coordinates are iteratively obtained to complete the calibration. This method eliminates the need for bundle adjustment to find optimal parameters, improves calibration accuracy and robustness, and reduces time costs. Experiments show that the calibration accuracy is approximately 0.02 mm, an 89% improvement over the traditional direct mapping method. This technique is suitable for fast 3D reconstruction and significantly improves the calibration accuracy of projectors.