Refraction error compensation method based on a pixel-deviation look-up table for fringe projection profilometry in the cross-media three-dimensional shape measurement

Refraction-induced image distortion produces large errors in cross-media three-dimensional (3D) shape measurement using fringe projection profilometry (FPP). In this Letter, a refraction error compensation method based on a pixel-deviation look-up table (PD-LUT) is proposed. First, pixel deviation with and without light refraction is constructed as PD-LUT. Then, with the PD-LUT and a tri-linear interpolation algorithm, error compensation values in measurement are determined for correcting the erroneous pixel coordinates of measured points. Finally, 3D data without refraction errors are retrieved with the corrected pixel coordinates and FPP. Compared with methods that need to determine the transmission trajectory of light and/or provide feature information for a refractive interface, the proposed method is simple and easy-to-implement, because the complicated and hard-to-implement processes of ray tracing and manually pasting features onto the interface are removed. Two experiments, including 3D shape measurement of a standard step and 3D shape measurement of a spherical object, are conducted to demonstrate the performance of the proposed refraction error compensation method based on PD-LUT.