Comparison With Other Techniques

There have been several investigations of the photometric properties of HST image restoration techniques utilizing a range of different algorithms. While we do not intend to describe each in detail, it is interesting to compare the results of our simulation with those obtained using some other methods. Holtzman et al. (1991) studied the use of the Richardson-Lucy method (Richardson 1972, Lucy 1974) in restoration of PC images. They used that technique to restore a simulated image of a crowded field. The scatter in the magnitudes measured in the deconvolved data was comparable to that in the original blurry image, so the restoration did not provide a quantitative improvement. Additionally, they found a systematic nonlinearity of several tenths of a magnitude over a 4 mag range. In their deconvolution of an actual image of stars in the 30 Doradus nebula, the errors in the deconvolved photometry judged by calculated sigmas and residuals were worse than those in the original image. Additionally, the deconvolved image was noisier and revealed no new sources not present in the original image.

Cohen (1991) investigated the reliability of the Maximum Entropy method (Skilling 1989, Gull 1989) in restoring astronomical images while preserving photometric accuracy. Her investigations involved restoring simulated images created by blurring point sources with a 3 pixel FWHM Gaussian. She discovered that the Maximum Entropy software systematically recovered the fainter objects as too faint. This nonlinearity was a function of the degree of contrast of the object with the sky and the degree of crowding. She concluded that then currently available Maximum Entropy software could not be used where photometric reliability was required.

Finally, while it is more difficult to compare the previous results with those from Faint Object Camera (FOC) data, primarily because of its lower signal-to-noise ratio (SNR), Thomson et al. (1992) studied photometric techniques with FOC images. They used Maximum Entropy and did one test with the Richardson-Lucy method. They found that they needed a magnitude-dependent aperture correction, a nonlinearity correction (to account for the nonlinearity of the Maximum Entropy method which systematically underestimated the flux in point sources by about 1 standard deviation) and a zero-point correction which depended on the SNR of the observed image. Their photometric error was typically about 0.1 mag from the deconvolved data, comparable to what they derived using standard profile-fitting photometric techniques on the original images (see Stetson 1987, 1993).

Busko (1993) has performed a systematic investigation of the photometric properties of several restoration algorithms including the iterative/recursive algorithm presented here. He found that photometry performed on images restored with the iterative/recursive algorithm produced the best results in terms of linearity and reduction in confusion between neighboring stars. Thus, it is not surprising that in comparison with the studies mentioned above, our simulation indicates that photometric results from the iterative/recursive procedure may be more reliable (and certainly less complicated) than those obtained with either the Richardson-Lucy or the Maximum Entropy algorithms. An application of the iterative/recursive algorithm to HST images of the globular cluster NGC 6352 is presented elsewhere in this volume (Fullton 1993) and demonstrates the excellent photometric restoration possible with this algorithm.