An Iterative Sub-pixel Interpolation Centroid Algorithm

Positional measurement of stars with high accuracy from digitized CCD imagesis one of the important objectives of astronomical observations. The most often-usedcentering algorithms are Gaussian-fit, Modified Moment method and median routines,but the FWHM of stars in the image must be more than2pixels at least. Although theHubble Space Telescope (HST) is not affected from the atmosphere, but its imagingsystem still has diffraction limitation and relatively short focal length, the FWHM of astellar image is less than2pixels, thus the image is under-sampled. Thisunder-sampled image will cause system error in positional measurement of stars.Therefore research of high precision centering algorithm for under-sampled image isof practical significance.Anderson and King proposed ePSF method to deal with the positionalmeasurement of HST under-sampled images, but it was very complex. Quine et al.proposed a sub-pixel interpolation centroid algorithm. This method is simple, and it isa new way to solve the problem of high precision location in under-sampled image,but there still exits system error due to ignoring higher order terms.This paper proposed a new iterative algorithm based on the method of Quine etal. Gray values of star were assumed to have a Gaussian distribution, and then anonlinear equation could be derived by the brightest pixel and the next brightestneighboring pixel. The lower root of the equation was set as the initial value, and thenan iterative method was performed. When the absolute difference of the two adjacentsolutions was small enough, the solution was just assumed as the center of the star.Specifically, we first produced simulative images according to the work of Quine,and then found centers of a star by Quine’s method and by the proposed iterativealgorithm, respectively. In addition, a contrast was made between the ModifiedMoment method and the proposed algorithm. We also discussed the affect of totallight and standard deviation of star to the centering precision. Our simulation resultsshow that the precision of the proposed algorithm is significantly better than the original one by Quine. And the new proposed algorithm had even better precision thanModified Moment method on the average.In the actual images, under-sampled images are obtained by pixel binning toactual over-sampled images, center coordinates of a star measured by Gaussian fittingare used as reference ones, and then we used the proposed centering algorithm. At thesame time, Gaussian-fit is applied to under-sampled images. According to theexperiment results, the precision of Gaussian-fit is found better than the proposediterative centering algorithm, but only a few stars can be processed by Gaussian-fit.However, the proposed interpolation algorithm could avoid this defect.