CONSTRUCTION METHOD OF FREEFORM SURFACE SHAPE BASED ON XY-POLYNOMIAL

摘要

A construction method of freeform surface shape based on XY-polynomial obtains a plurality of data points of a freeform surface according to an object point and an imaging point in a three-dimensional Cartesian coordinates system Oxyz. Each of the plurality of data points comprises a coordinate value Q_i and a normal vector N_i. A first sum of squares e₁(P) of coordinate differences in z direction between the coordinate value Q_i and the freeform surface is applied, and by a second sum of squares e₂(P) between the normal vector N_i of the data points and a normal vector n_i of the freeform surface, a modulus of vector differences is acquired. An evaluation function ƒ(p)=e₁(P)+we₂(P) is proposed and a plurality of freeform surface shapes obtained by selecting and applying different weightings. A final freeform surface shape Ω_opt is chosen from the plurality of freeform surface shapes.