Template matching of freeform surfaces based on orthogonal distance fitting for precision metrology

Freeform surfaces are widely used in advanced optical and mechanical devices. In order to
assess the form quality of a freeform surface, it is required to match the measurement surface
with the design template. To improve the matching efficiency and accuracy, the whole procedure is divided into two stages: rough matching and final fitting. A new rough matching method, called the structured region signature, is proposed. The structured region signature is a generalized global feature which represents the surface shape by a one-dimensional function.
The template location occupying the best matching signature is considered to be the correct
rough position of the measurement surface. After that the motion parameters are updated
iteratively based on the orthogonal distance fitting. The dependence between the foot-point
parameters of the projection points and the motion parameters is derived from the closest-distance relationship between correspondence point pairs. Numerical experiments are given to demonstrate the validity of this approach.