Parametric registration of cross test error maps for optical surfaces

It is necessary to quantitatively compare two measurement results which are typically in the form of error maps of the same surface figure for the purpose of cross test. The error maps are obtained by different methods or even different instruments. Misalignment exists between them including the tip-tilt, lateral shift, clocking and scaling. A fast registration algorithm is proposed to correct the misalignment before we can calculate the pixel-to-pixel difference of the two maps. It is formulated as simply a linear least-squares problem. Sensitivity of registration error to the misalignment is simulated with low-frequency features and mid-frequency features in the surface error maps represented by Zernike polynomials and spatially correlated functions, respectively. Finally by applying it to two cases of real datasets, the algorithm is validated to be comparable in accuracy to general non-linear optimization method based on sequential quadratic programming while the computation time is superiorly incomparable.