The technique we have proposed in this paper is very general and is applicable for images of arbitrary shape. It can also provide a decent reconstruction for features that are several hundred times more intense than noise. However, the problem of image reconstruction still remains for low contrast features with noise. We believe that the knowledge of the actual point spread function, as gained by the parametric search described in this paper, will provide tight constraints on iterative deconvolution schemes for very noisy images which can start with a guess for the noise distribution and converge to the true distribution of noise. This belief is yet to be verified. On the other hand, there are a number of applications where the determination of the psf itself would be of vital importance. One example is the determination of daytime "seeing" at a new astronomical site. All that would be required is a sequence of long exposure pictures of the sun taken through a filter of reasonable bandwidth like 5 nm or 10 nm. Another example is the need to determine the broadening mechanisms of spectral lines. We hope that this technique would be able to detect small departures from a gaussian profile, which has great implications for the detection of non-thermal or supra-thermal distributions. The quality of spectra that are expected from SOHO, for example, would perhaps be good enough for such investigations.
This technique was used to estimate the Fried's parameter in the image of the globular cluster. The results are discussed in Appendix 1. The main result in appendix is the practical demonstration of the successful working of the parameter search method. The choice of a star cluster to test the method is very appropriate because the entire object occupies several isoplanatic patches while each stellar member of the cluster provides a point source to provide an unambiguous psf. We see here that the conventional method of fitting a Gaussian profile and FWHM of the Gaussian fit used as a measure of the Fried's parameter matches well with the Fried's parameter obtained using the parameter search method.
We would like to thank Prof. Ram Sagar and Mr. Alok Gupta for providing with the image of the globular cluster NGC 1409. We would like to thank the anonymous referee for useful suggestions and comments.