Improved convergence for CCD gain calibration using simultaneous-overrelaxation techniques

Simple modifications to the analysis used in the Kuhn, Lin, & Loranz flat-field CCD calibration method yield significant improvements in both speed and accuracy. In this method, multiple exposures are taken of a time-independent signal at different spatial positions. The flat field is then expressed in the form of a Jacobi relaxation solution to Poisson's equation. By applying the technique of simultaneous overrelaxation, we have improved the convergence rate to require approximately the square root of the number of iterations (√r) needed by the Jacobi method. For large arrays, where r is correspondingly large, this improvement is significant. Furthermore, we have improved the accuracy by extending the method to account for fractional pixel shifts.