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1. Introduction

Turbulence in the earth's atmosphere degrades the true object intensity distribution of astronomical sources. The thermal gradients in the air produce random phase delays in the wavefront that cause blurring of images.

Usually all images which are exposed for several time scales of the atmospheric turbulence are classified as long-exposure images. As a general rule of thumb, the exposure times in excess of a few hundredths of a second are considered as long exposure images. In long-exposure images the high spatial frequency information is attenuated because the recorded image is the source convolved with the time average of the point spread function (psf).

A straightforward method to measure the atmospheric psf is to measure the size of the intensity profile of an unresolved source close to the object under study. Here we assume that the medium through which the imaging is done behaves in the same way for both the object under study and the point source. If one has to get the true point spread function then the point source and the object under study should be within an isoplanatic patch.

For the sun, we do not have access to a point source for comparison. Furthermore, for extended sources like the sun, the atmospheric point spread function will not be the same on all parts of the image. We have a problem of an image for which each part of the object has been convolved with different point spread functions. Hence a single point spread function will not be a correct characterisation of the point spread function for an extended object.

Another technique (Collados 1987) of solar image reconstruction uses the limb of the moon in the photographs taken during partial solar eclipse. In the absence of earth's atmosphere the moon's limb would be seen as a sharp edge against the bright Sun's surface. When imaged using a ground based telescope, the moon's limb is blurred because of the atmospheric point spread function. The gradient of the blurred limb profile of the moon gives the point spread function of the telescope and atmosphere. The point spread function thus found is used for deconvolving the point spread function from the entire image. This point spread function can be used to remove blurring only near the limb of the moon and within the isoplanatic patch which encompasses the moon's limb. Use of this point spread function for deconvolution elsewhere in the image will not give true reconstruction.

Night time observers can have single stars for deconvolution. To get a reconstruction which is close to the true object intensity distribution, the star used for determining the point spread function of the atmosphere and the object under study have to be within the same isoplanatic patch. In the case of photometry of extended objects like clusters of stars, algorithms like Daophot are used (Stetson 1987) where nonisoplanaticity effects are not considered.

The conventional method is to make a gaussian fit to these observed profile and the full width at half maximum of the fitted gaussian is used to characterise the point spread function. This creates spurious features if the true point spread function is not a gaussian. In fact, there is theoretical and experimental evidence for the non gaussian nature of the atmospheric psf (Roddier 1980).

We propose a method of estimating the point spread function at any arbitrary part of an extended image based on a parameter search. We assume a class of convolving kernels involving one or two parameters and look for the number of zeros and negative pixel values in the reconstruction as a function of the parameters. We show that it is possible to retrieve the unknown parameters of the kernel. The technique proposed here has been rigourously tested on simulations and also on real images.

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