Centroids computation and point spread function analysis for reverse Hartmann test

Abstract

This paper studies the point spread function (PSF) and centroids computation methods to improve the performance of reverse Hartmann test (RHT) in poor conditions, such as defocus, background noise, etc. In the RHT, we evaluate the PSF in terms of Lommel function and classify it as circle of confusion (CoC) instead of Airy disk. Approximation of a CoC spot with Gaussian or super-Gaussian profile to identify its centroid forms the basis of centroids algorithm. It is also effective for fringe pattern while the segmental fringe is served as a ‘spot’ with an infinite diameter in one direction. RHT experiments are conducted to test the fitting effects and centroiding performances of the methods with Gaussian and super-Gaussian approximations. The fitting results show that the super-Gaussian obtains more reasonable fitting effects. The super-Gauss orders are only slightly larger than 2 means that the CoC has a similar profile with Airy disk in certain conditions. The results of centroids computation demonstrate that when the signal to noise ratio (SNR) is falling, the centroid computed by super-Gaussian method has a less shift and the shift grows at a slower pace. It implies that the super-Gaussian has a better anti-noise capability in centroid computation.