970724 Focus Tests:
Extended Source Detection

T. Jarrett, IPAC
(970731)


On the night of 970724 a series of scans (all of the same area of the sky) were acquired under sequentially changing focus setting. The purpose of these tests was to impart a non-symmetric distortion to the PSF -- starting from horizontally flattened profile (actually, it is more diagonal, from 30 to 50 degrees) to symmetric profile (i.e., in focus), to a vertically flattened profile. The performance of the point source and extended source processors can then be assessed with a diverse (re: good to horrible) PSF.

To properly assess the performance of extended source processor, it is necessary to have several galaxies of differing flux and orientation in the field of study. Unfortunately, the field chosen for the focus tests of 970724 was devoid of any galaxies brighter than K = 13.5 or so. (There was one galaxy with an integrated mag of about 13.8, and another galaxy fainter still. Other than these two extended sources. the field consists of stars.) Thus, it will not be possible to address the question of extended source completeness or repeatibility. It will, however, be possible to address the question of reliability, or rather, to quantify the relative difference in the number of false extended source detections with the quality of the PSF. This memo presents the results of this analysis. The completeness question will have to wait for additional focus test data (hopefully of a field with a galaxy cluster).

Final caveat: the effect of seeing on the results presented here is ignored. It is surely present (the best seeing is not very good, perhaps 3 arcsec) and mucking with the results. This experiment optimally requires good seeing, which we will have to await for future observations.

DATA

Scans 95 to 155 on the night of 970724 comprise the focus tests. A log of the proceedings can be viewed here: observing log, 970724 . The focus setting to start the experiment (-9670) resulted in a horizontal-diagonal flattened PSF . Six scans were taken at this focus setting (each scan 1 degree in length). The focus was then upped 20 steps (i.e., -9650), and six scans were taken. The experiment was continued in the fashion, passing through the correct focus and beyond at which the profile was distorted along the verticle (inscan) direction. This distortion is easily measured with the second moment ratio (ratio between the X and Y second moments) and with the axis ratio (as determined by fitting an ellipse to the PSF). A plot of the moments and axis ratio is given below.

The "seeing" is measured using the "sh" parameter, which measures the symmetric radial extent of the PSF (note: it does not measure assymtries, unlike the second moment ratio, and thus is not as sensitive to the assymetric distortions). A plot of the "sh" versus scan can be seen below. Note that the correlation between "sh" and the axis ratio is rather weak.

Images

In order to see the affect of the distortion, the following images show some representative "false" galaxy detections (they are all stars that pass star-gal separation thresholds).

Notice that the distortion at focus setting -9670 (krat = 1.47) is along the diagonal (from 30 to 50 degrees up from horizontal). For the intermediate focus settings, the distortion cannot be seen with the naked eye. For the lower focus settings, -9530, -9510 & -9490, corresponding to krat < 0.8, the distortion is lined up vertically and its magnitude is greater than that of the first focus settings (particularly at J band, the difference is readily apparent). Thus, the focus setting test is not symmetric about the proper focus (in this case, the best focus is around -9600 to -9610).

Results

Each extended source candidate was visually inspected and compared with the DSS counterpart to classify the object (e.g., galaxy, star, double star, artifact, etc). At the sensitivity limit, most of the candidates cannot be classified and are left as "unknown" and no further tracking is made on these objects.

Only one galaxy was found in the field with K < 14 mag, the remainder of the extended source candidates were either isolated stars or double stars. The following plot shows the number of "detections" of extended sources as a function of the second moment ratio (or the focus, if you prefer). The solid white line (histogram) shows the galaxy detections (i.e., one galaxy, which can repeat six times) and the dashed red line the false extended source detections. The number of detections consists of the cummulative count of sources with (J < 15.5, H < 15.0, K < 14.0).

The reason that the galaxy is does not appear at least siz times (six repeats) for the K band results is due to statistical scatter in the mag (the galaxy is only a 6 or 7 SNR detection). It is in fact detected, but with a fainter mag than the limits set for the histogram.

Most of the false detections occur in the faintest bins, J > 14 mag and K > 13 mag.

Notice that the best "sh" value seems to occur at 2nd mom ratio of about 1.1, not 1.0 (as would be expected).

The number of false detections appears to be about the same for 2nd moment ratios between 1.2 and 0.85 or so. The reliability is quickly going to hell for 2nd moment ratios less than 0.85 or so.

Bottom Line

It is clear that the reliability of the extended source database will be compromised by image data with a PSF distortion less than 0.85, as measured by the 2nd moment X-Y ratio. The results also suggest that the reliability is poor for distortions greater than 1.3 or so, as measured by the 2nd moment X-Y ratio. The focus tests are not sufficient to address the question of galaxy repeatibility or completeness.