The transfer of positional information from one dataset to another allows one to devise new methods of using the new generation of large ground based telescopes in conjunction with high resolution space telescopes such as HST.
One such method is a two channel photometric restoration method known as GIRA first conceived by one of us (L. B. Lucy) and which is under development at the ST-ECF (Pirzkal et al. 1999). A few, often just one, high resolution space based images are used to improve our ability to measure the brightness of the same objects in a seeing-limited image or set of images. In seeing-limited images, not all of the sources might be visible or easily detectable using conventional means due to the spreading of the available photons by the seeing and because the sources are likely to be much more blended together and hence harder to even successfully detect.
We start by modeling the true sky as the sum of two different components, or channels. The first channel is made up of all the stars in the field whose initial positions are known accurately (for example by using stellar positions obtained from higher resolution HST images). The second channel is the remaining diffuse emission, or background emission in the field. Hence,
If we denote an actual (noisy) observation of this field as , then an estimate of this observed image can also be written:
where represents the convolution operator, is an estimate of the PSF in , and G is a two dimensional Gaussian whose full width at half maximum determines the additional level of smoothness in . This extra level of smoothness is required in order to remove the degenerate solution of stellar objects represented by sharp peaks in the background channel while simultaneously dropping the flux of the objects to zero in . Consecutive estimates of and are computed using a scheme which maximizes the likelihood
using an iterative scheme developed by L. B. Lucy (Lucy 1974, Lucy 1991, Hook & Lucy 1991). This scheme ensures that the non-negativity of both and is enforced and that the total flux in is conserved. Initially, each channel is assigned half of the total flux observed in and all the stars in are assigned the same flux (half of the total flux divided by the number of stars).
Several aspects of this approach are noteworthy: First, this two channel restoration scheme does not produce ringing or other artifacts that are known to limit the accuracy of the photometry obtained with single channel restoration methods such as the classical Richardson-Lucy method. GIRA uses a general coordinate and brightness list to represent and not simply a set of functions at fixed integer pixel coordinates and regularizes the background channel using a single parameter instead of two free parameters as it is the case in the previous two channel restoration technique PLUCY. Second, nothing precludes an implementation of this algorithm which periodically adds automatic adjustments of the size of the chosen PSF , or moves objects around their original positions in order to increase the value of .
We wanted to assess GIRA's ability to measure stellar magnitudes of stars in NGC6712 and applied GIRA to a set of simulated 256x256 V and I images of this dense globular cluster. These images, with a PSF of 0.7'' and a pixel scale of 0.09'', closely matched the physical properties of real images of NGC6712 taken with the Test Camera during the Science Verification phase of UT1 VLT (ESO 1998). Each star was however assigned a set of known V and I stellar magnitudes drawn from a Tonry globular cluster model distribution (Tonry 1998). In Figure 2 we show that the magnitudes measured using GIRA suffer from no apparent systematic effects and that the amount of error is within what would be expected when photometric noise and stellar crowding effects are accounted for.
The ability of GIRA to adjust and correct object positions in an image is also demonstrated in Figure 3. In this test, GIRA was used for 1000 iterations on an image containing three stars of magnitude -2.0,-2.0,and -3.0, with a FHWM of 7.2 pixels and separated by at most 4 pixels (Coordinates are [64,66],[64.9,63.4],and [66.9,63.4] respectively). Despite positional errors added to the input object positions of 0.038, 0.207,and 0.298 pixel respectively, all three final stellar positions were adjusted to within 0.05 pixel of the true stellar positions.
ESO Messenger cover article, 93, 1998
Hook, R. N., Lucy, L. B. 1991, in The Restoration of HST Images and
Spectra-II (STScI/NASA publication)
Lucy, L. B. 1974, AJ, 79, 745
Lucy, L. B. 1991, in The Restoration of HST Images and Spectra-II (STScI/ NASA publication)(http://www.stsci.edu/stsci/meetings/irw/)
Pirzkal, N., Hook, R. N., Lucy, L. B. 1999, in ST-ECF WWW Newsletter, 1 (http://ecf.hq.eso.org/newsletter/webnews1/)
Tonry, J., personal communication, May 1998