An important question about any deconvolution algorithm is its linearity. In order to quantify this we followed the approach used by Busko (1993). This involves investigation of the photometric residuals as a function of the source brightness. Because of the crowded field of these simulations we only used the value of the restored object at the pixel locations given by the truth list. We defined the brightest source in the field, i.e., the bright star in the upper right quadrant, as having zero magnitude and normalized the photometry of the reconstructions to this source.
Fig. 5 shows the peak photometry for the ``raw'' data sets. Note the
difference before and after the correction for the spherical aberration. There
is still some power distributed into the PSF ``halos'' as is evidenced by the
mean offset from zero. The scatter of the residuals is due to the crowded field
where there are overlapping PSF's which contribute to increasing the
intensities. Fig. 6 shows similar plots but for the three restored
images shown in the previous section. Note that the three have means close to zero and that the dispersion of the residuals is substantially less than that for the ``raw'' images. The dispersion of the residuals increases with fainter magnitude. This behavior is to be expected as the SNR of the individual sources decreases with increasing magnitude. It can also be seen that as more input information is used, i.e., an increased number of observations, then the residual dispersion decreases showing a trend, based on the limited data presented here, which is proportional to the square root of the number of input images.
Acknowledgments
SMJ was supported by NSF Grant OPP-9219515. MWR was supported by an REU scholarship from the National Science Foundation.