Real-time compensation of projector lens distortion using a linear-grid model in fringe projection profilometry

In fringe projection profilometry, applying pre-distortion to fringe patterns reduces the errors caused by projector lens distortion. However, it is important to note that discontinuous fringe patterns, such as binary fringe patterns, introduce additional errors when using pre-distortion methods. While post-undistortion methods are applicable for discontinuous fringe patterns, the computation is typically time-consuming. We propose a linear-grid model for correcting lens distortion. First, we select multiple equidistant points within the grid to calculate the linear parameters and store them as look-up tables (LUTs). Second, by rounding down the captured distorted point to the nearest integer point, we obtain the index value for LUTs. Finally, we achieve real-time compensation for distortion error through linear expressions. The experimental results show that the proposed effectively mitigates the distortion by a factor of 6x in terms of root mean squared error. Additionally, it exhibits a computational speed of 409.50 fps, which is an improvement compared to the traditional iterative model at 39.48 fps and the scale-offset model at 264.48 fps.