Diffracto-Astrometry measurements: accuracy of the measuring algorithm

We present a theoretical analysis of the measuring algorithm we use when applying the Diffracto-Astrometry technique to Hubble Space Telescope Wide Field Planetary Camera 2 (WFPC2) saturated stellar images. Theoretical Point Spread Functions (PSFs) were generated using the Tiny Tim software for the four CCDs in the WFPC2 and for some of the available filters. These images were then measured with our Diffracto-Astrometry measuring algorithm using only their diffraction pattern, and positions for the simulated PSFs on each generated CCD-frame were obtained. The measuring algorithm recovers the original positions reasonably well ($\pm 0.1\ \rm{to} \ \pm 0.4$ pixels). However, slight deviations from the original values are observed. These also vary with position over the entire surface of the CCD. We adjust the difference between the real and the measured position with a quadratic function of the coordinates. The transformation coefficients also present a slight correlation with the filter effective wavelength. Application of these transformation coefficients allows us to determine the position of a stellar image with a precision of a few hundredths of a pixel.