Three-dimensional shape measurement of aspheric mirrors with fringe reflection photogrammetry

Three-dimensional (3D) shape measurement of an aspheric mirror with fringe reflection photogrammetry involves three steps: correspondence matching, triangulation, and bundle adjustment. Correspondence matching is realized by absolute phase tracking and triangulation is computed by the intersection of reflection and incidence rays. The main contribution in this paper is constraint bundle adjustment for carefully dealing with lens distortion in the process of ray intersection, as compared to the well-known grating reflection photogrammetry. Additionally, a free frame is proposed to alleviate troublesome system geometrical calibration, and constraint bundle adjustment is operated in the free frame to refine the 3D shape. Simulation and experiment demonstrate that constraint bundle adjustment can improve absolute measurement accuracy of aspheric mirrors.