Stitching of off-axis sub-aperture null measurements of an aspheric surface

Optical testing of a large convex aspheric surface, such as the secondary of a Ritchey-Chretien telescope, can be performed with a Fizeau interferometer that utilizes subaperture aspheric reference plates, each providing a null test of a subaperture of the larger mirror. The subaperture data can be combined or stitched together to create a map of the full surface. The region of the secondary mirror surface under test in each sub-aperture is an off-axis segment of the parent aspheric surface, therefore, the Fizeau reference requires a non-axi-symmetric aspheric surface to match it. Misalignment of the Fizeau reference relative to the parent in each sub-aperture will then result in aberrations in the measurements other than the ordinary terms of piston and tilt. When stitching sub-aperture measurements together, the apparent aberrations due to the null lens misalignment need to be fitted and subtracted. This paper presents an algorithm to perform this particular type of stitching.