Research on freeform surface detection by high precision normal measurement method based on laser confocal fixed-focus

To address the issue of freeform surface profile scanning measurement relying on high-precision linear motion datum, this paper proposes a high-precision normal vector measurement method based on laser confocal fixed-focus (NVM-LCFF) for freeform surface detection. This method utilizes the precise correspondence between the peak position of laser confocal axial response and objective lens focus. Through axial scanning, it simultaneously acquires both the laser confocal axial response and the spot centroid position detected by the position-sensitive detector (PSD). Capitalizing on the spot centroid measurement accuracy at the focus is the highest, this method acquires spot centroid at the focus by computationally the focus position of the laser confocal axial response, and effectively eliminates defocus-induced errors in centroid positioning. By leveraging the rotation-translation invariance of distances between sampling points and angles between normal vectors of sampling points. This method performs pre-registration by pre-scanning the coordinates and normal vectors of at least 4 sampling points. Through nonlinear least-squares optimization, an initial estimation of the position of freeform surface is obtained, thereby substantially reducing the precision requirements of position adjustment. Initial experimental verification demonstrates that this approach achieves freeform surface measurement with accuracy better than ±50 nm, effectively reducing the influence of straightness errors on measurement accuracy, and eliminating the dependence on the ultra-precise height measurement references in traditional freeform surface metrology.