Subaperture stitching computation time optimization using a system of linear equations.

Measurement of large or aspheric optical surface shapes as a single aperture using interferometry is problematic for many reasons. A typical problem is the numerical aperture limitation of the interferometer transmission element and the surface slope deviation of aspheres. This deviation typically causes vignetting and spatial aliasing on the camera. A solution is subaperture measurement and subsequent subaperture stitching. A stitching algorithm, in principle, uses overlaps between subapertures to eliminate aberrations of each subaperture to obtain a full aperture for further analysis. This process is computation time demanding and requires optimization in order to obtain a result in a reasonable time to reduce, in turn, the overall manufacturing time. In this paper, a novel, to the best of our knowledge, and fast stitching method based on a system of linear equations is proposed and mathematically described. The developed method was compared with other algorithms, and theoretical computation complexity was calculated and compared. The method was tested practically, with real data measured on spherical surfaces using QED ASI (QED Technologies aspheric stitching interferometer) and an experimental interferometer, and the results are presented. Stitching quality was quantified for results and compared to other algorithms.