Examples and Photometric Tests

This method has been tested on many kinds of data both real and simulated. Here we present three examples in which the structure of the background is of increasing interest and photometry of point sources of diminishing importance. All three examples use simulated data from the collection prepared by the STScI Image Restoration Project and available from the STEIS anonymous FTP service (Hanisch 1993). A final example illustrates how the ``blind iterative restoration'' option may be used to obtain a PSF image from a data frame.

A Crowded Field Observed With HST WFC

Photometry of crowded fields is a very important problem for which many highly developed and thoroughly tested codes exist. Most of these were developed for ground based images and there may be special problems with handling HST data where images are badly undersampled and the greater extent of the PSF wings makes the crowding problem very severe. The photometric performance of the new algorithm has been tested using the WFC star cluster simulation which is available from STEIS. We used just the lower left quadrant of the image which includes the very dense core. The image was expanded by a factor of four in and before processing. Fig. 1 shows the results of this and Fig. 2 shows the photometric accuracy and also a histogram of the background image. These can be compared to similar graphs given for different restoration methods by Busko (1993). The photometry is seen to be highly linear and to lack bias. The scatter is larger than predicted from pure noise considerations because of the high degree of crowding.

Stars Superimposed on a Galaxy

Many interesting problems in astronomy involve trying to do photometry of point sources on a highly structured background. An important example is the photometry of Cepheid variables in nearby galaxies. The new algorithm is particularly suited to this problem because it can effectively model any background simultaneously with measuring the point source magnitudes. There is no assumption about the background structure except that it must be smooth to some (user controllable) degree. A good test for this kind of work is shown in Fig. 3 where the input data is a ground-based image of the nearby galaxy M51 on which some point sources of known brightness have been added. Fig. 4 shows the quality of the resulting photometry. The output image (upper left) also illustrates how the regularization effectively suppresses the speckles in the background which are so prominent in the standard restoration (lower right).

A QSO ``Fuzz'' Simulation

In an important class of problem there is only a single point source but this is so bright as to swamp interesting structure lying underneath. Fig. 5 shows the results of processing a simulated PC image of a QSO with an

underlying spiral galaxy. Although conventional restoration manages to recover the spiral arms well, there is still an inaccurate restoration of the regions close to the nucleus and the familiar speckles. This method has also been found to be among the most effective for this kind of work on real images obtained from the ground (Stockton &Ridgway 1993).

Blind Iterative Restoration

In many cases the PSF cannot be reliably predicted and must be obtained directly from the data image. The two channel method may be generalized to simultaneously improve both the estimate of the true object intensity distribution and the PSF. This is more stable and effective than other blind iterative methods because the point sources are at designated positions. Fig. 6 shows an example of obtaining an improved PSF from

a subset of the simulated WFC image which was used in the crowded field example given above. More details of the method are given in Lucy (1994).