Astrometry

The second criterion used to evaluate the restoration methods is the accuracy in measuring stellar positions in the restored image. Accurate positions of the stars are important for aperture photometry in crowded star fields where small apertures must be used. The RMS errors (in pixels) in position measurements are given in Table 2 for the various restoration methods. Results are shown for different combinations of stellar magnitude ranges and separation of the stars from their nearest neighbor. Positions were measured using a 33 centroid centered on the brightest pixel in the star. Centroids using areas larger than 33 pixels gave slightly better results for well separated stars but gave significantly worse results in crowded regions.

The best astrometry results were obtained using the non-linear restoration and the hybrid methods, although none of the methods give very good results for stars fainter than 18.5 magnitudes. Stars between 17.5 and 18.5 magnitudes also gave significantly poorer results when the star's closest neighbor was within 3 pixels. RMS errors of 0.1 pixel were obtained for well separated stars with a magnitude brighter than 17.5.

Fig. 5 shows the astrometry errors for well separated, bright stars in the 1000-iteration R-L/Snyder restoration. The errors are plotted for various positions of the star with respect to the center of a pixel. The diamonds give the true star positions. Vectors are drawn to the measured position. Stars not centered on a pixel show systematic errors in the position measurements. These errors are partly due to the use of only a 33 centroid centered at the brightest pixel. When a 77 pixel centroid is used, some of the systematic errors remain with a magnitude on the order of 0.05 pixels. The systematic errors occur in all of the restoration methods and are slightly larger for the linear methods.