Accurate residual distortion compensation of projector lens in fringe projection profilometry

In fringe projection profilometry, traditional parametric models for projector lens distortion offer simple implementation. However, the limited descriptive capability results in significant residual errors. Existing methods typically ignore coupled errors during residual distortion (RD) estimation, whereas compensation strategies accumulate nonlinearities and lack adaptability to various fringe patterns. To address these issues, we propose an RD computation method based on weighted least squares, where weight coefficients derived from the preliminarily corrected 3D point cloud guide the fitting process to calculate the residual errors robustly. With the RD map, we further develop two compensation methods using lookup tables: pre-distortion-based and linear-grid-based compensation methods. Experiments show that both compensation methods suppress full-field distortion errors by a factor of 20× and reduce errors by over 90% compared to results before RD compensation. The proposed methods achieve accurate and robust lens distortion correction without additional calibration complexity or hardware dependence.