Centroids analysis for circle of confusion in reverse Hartmann test

The point spread function (PSF) is investigated in order to study the centroids algorithm in a reverse Hartmann test (RHT) system. Instead of the diffractive Airy disk in previous researches, the intensity of PSF behaves as a circle of confusion (CoC) and is evaluated in terms of the Lommel function in this paper. The fitting of a single spot with the Gaussian profile to identify its centroid forms the basis of the proposed centroid algorithm. In the implementation process, gray compensation is performed to obtain an intensity distribution in the form of a two-dimensional (2D) Gauss function while the center of the peak is derived as a centroid value. The segmental fringe is also fitted row by row with the one-dimensional (1D) Gauss function and reconstituted by averaged parameter values. The condition used for the proposed method is determined by the strength of linear dependence evaluated by Pearson's correlation coefficient between profiles of Airy disk and CoC. The accuracies of CoC fitting and centroid computation are theoretically and experimentally demonstrated by simulation and RHTs. The simulation results show that when the correlation coefficient value is more than 0.9999, the proposed centroid algorithm reduces the root-mean-square error (RMSE) by nearly one order of magnitude, thus achieving an accuracy of $\sim 0.01$ pixel or better performance in experiment. In addition, the 2D and 1D Gaussian fittings for the segmental fringe achieve almost the same centroid results, which further confirm the feasibility and advantage of the theory and method. (paper)