Photometric Analysis

A photometric analysis was made of the simulated images using two of the widely available reduction programs, ROMAFOT (Buonanno et al. 1983) and DAOPHOT (Stetson 1987). It should be noted that both packages have several tunable parameters which need careful attention in order to produce optimal results. Default values were initially used, followed by a range of parameter changes, in an attempt to optimize the functioning of the programs.

The output data from the photometric programs were compared to the original positions and magnitudes used to create the simulated images. A measured star was considered successfully detected if its position differed less than one pixel from its nearest neighbor with known position. If no neighbors were found within the one pixel radius the star was discarded.

It should be noted that the results from the programs were not edited, except that magnitude errors larger than two standard deviations were considered false identifications.

ROMAFOT

The version of ROMAFOT available under MIDAS 92NOV was used in our tests. The PSF was extracted from the image and the reduction followed the standard procedure for ROMAFOT. Analysis of the image generated using the Tiny Tim PSF gave substantial errors ( 0.1 mag) even for bright stars which also showed some instability. Fig. 5a shows the results with magnitude error as function of magnitude. The error bars represent spread in each magnitude interval. Measurements on the rebinned, expanded image showed only marginal improvements (Fig. 5b), the bright stars were not detected at all. In contrast, the (non-realistic) image generated with the Moffat PSF showed a marked improvement in accuracy (Fig. 6a). Here, the error for bright stars remained within 0.02 mag. This clearly implies a strong dependence on PSF shape, which is not unexpected since ROMAFOT uses analytical Moffat functions to fit the stellar images. A remarkable feature is the systematic underestimation of the intensities for the faint stars. The investigation also gave information regarding detectability of sources. This is seen in Fig. 6, which shows the fraction of found stars as function of magnitude. The total number of detected stars was about 17,000. Thus, the majority of very faint stars remained undetected.

DAOPHOT

The DAOPHOT version used was DAOPHOT II, which included enhancements up to October 1993. As for ROMAFOT, the PSF was derived from the image. Again, measurements made on the Tiny Tim PSF generated image gave unsatisfactory results. Bright stars showed errors of about = 0.05 mag and a zero point offset was seen for fainter stars (Fig. 7a). The rebinned and expanded image gave better results (Fig. 7b), with the smallest errors in the order of = 0.04. However, the brightest stars showed some anomaly. Similarly to ROMAFOT, the image with the Moffat PSF gave significantly better results than the image generated with the Tiny Tim PSF; the errors in the magnitudes of the brighter stars were around = 0.02. These results are slightly better than those obtained with the rebinned image. For the fainter stars however, the results are significantly better, with nearly twice as many detected stars, and about half the spread in the magnitudes of those stars.

The number of detected stars increased from 15,000 to 17,000 when measuring the rebinned and expanded image (Fig. 8a).

Positions were determined equally well in either the original or the rebinned image; slightly better in the image with the Moffat PSF. Fig. 8b shows the spread (with = 0.18 pixels) of position determinations on the original image.

Intrinsic DAOPHOT Errors

A simple test was done to see if DAOPHOT could produce consistent results with the complex given input data to determine if it was at all possible to reach the limiting S/N ratio. The results of DAOPHOT's allstar were fed as input to a new run of allstar. Ideally this should provide identical results. This was, however, not the case for the original image with the Tiny Tim PSF. Only 15%of the stars had identical positions and magnitudes after this second run. For the remaining stars the differences in position and magnitude were determined (Fig. 9a). A positional accuracy of better than 0.02 pixels is required to reach a photometric reproducibility of 5%. The fraction of stars that has positions that can not be determined sufficiently accurate includes a relatively large fraction of the brightest stars. The fact that the two runs gave different results probably depends on the size and shape of the PSF. In the tested case the centers of the stars could not be determined with sufficient accuracy, but it should be emphasized that the FWHM of the PSF is only 0.9 pixels and the fitting radius is only 3 pixels in this case, so the number of pixels with astrometric and photometric information is small.

Achieved vs. Possible Accuracy

In Fig. 9b is shown the theoretical signal to noise ratio limit for the simulation. This limit, valid for a 45 min exposure with filter F547M (Strömgren ), was determined using Poisson noise, sky background, dark noise, and read out noise, and assumed that the PSF deposited about 30%of the total stellar intensity in one pixel. The entire observation was assumed to be on a single exposure. Also shown are the measurements from ROMAFOT (dotted line) and DAOPHOT (dashed line) from the rebinned image, interpreted as signal to noise ratio.