2 images with similar (good) seeing were picked from each of our three most widely used telescopes for comparison between several photometric reduction methods.
seeing(=gauss sig = 1.3) -> FW = 3 pixels; 0.55 arcsec/pixel
kp4m (feb494kp4m14ebs.fts,feb494kp4m15ebs.fts); sig=1.2 -> FW=3 pixels
seeing(=gauss sig = 1.2) -> FW = 3 pixels; 0.47 arcsec/pixel
kp2m (oct1194kp2m103dbs.fts,oct1194kp2m104dbs.fts); sig=2 -> FW =5 pixels
seeing(=gauss sig = 2) -> FW = 5 pixels; 0.304 arcsec/pixel
Aperture photometry was obtained with Deepsearch IDL-based routines as well as IRAF software for each of the six images for comparison. The 'reduceimage' and 'aperture' routines were used in IDL to compute photometry whereas the 'phot' task in the digiphot.daophot package was used for obtaining photometry with IRAF. Similarly, IDL-based weighted photometry was undertaken for comparison with the IRAF point-spread function (psf) photometry.
For any given pair of images from the same telescope reduced by the same method (eg. IRAF aperture photometry or Deepsearch Weighted Photometry), ratios of the flux of the same objects were calculated. A dispersion in percent of these ratios was then calculated for specific magnitude ranges spanning from 16 mag to 26 mag. A plot of magnitude versus percent dispersion is available for aperture photometry comparisons as well as daophot point-spread function in comparison with Deepsearch Weighted photometry.
A test for linearity was also performed by comparing photometry between the two analysis systems. This is demonstrated for aperture and psf photometry for the INT images.
NOTE: (1) IRAF has a predefined zeropoint magnitude offset. (2) for future reference, the value of zmag(=zero point magnitude) is dependent upon the IRAF package the user is in while running the 'phot' task.
Deepsearch Aperture Photometry is calculated as follows:
mag = zmag - 2.5*log10(aperture)
NOTE: (1) IDL-based photometry routines are performed on sky subtracted images. (2) Zero point magnitude is calculated using the entire image.
Unfortunately, all the images have problems with point spread function (psf) spatial variance across the field of view, the kp4m being the worst of the three while the INT is the least problematic. Iraf daophot offers a number of different choices for the psf model in trying to deal with this problem. In most cases, one would probably prefer to create an empirical psf comprised of one or more look-up tables in addition to an analytic function. Iraf also offers the option for a purely analytic psf model although this is not recommended except for severely undersampled data (large uncertainties in the computed look-up table and resulting fit due to interpolation errors may be problematic for undersampled data fit with something more complicated). For all the images involved, a number of different reductions were performed. It was found that a two-dimensional elliptical gaussian function aligned along the x and y axes of the image was sufficient for the analytic portion of the psf. More complicated analytic functions were found to have produced a fit with less scatter without having actually improved the results. A series of psf models were tested that consisted of the gaussian function as the analytic component and 1, 3, or 6 look-up tables that describe parameters of the psf as a function of position in the image. These include a constant psf model (ie. the psf model has the same shape everywhere in the image) comprised of the analytic portion and one look-up table, a linearly variable psf (ie linearly variable with position in the images) consisting of the analytical component and 3 look-up tables, and a quadratically variable psf consisting of 6 look-up tables in addition to the analytic component. For the empirical variable psf models, it is the values in the look-up table that are varied spatially, not the analytic portion.
The agreement for aperture photometry between IDL and Iraf reduction methods is good for the INT , kp2m , and kp4m telescopes. Results are also in agreement with theoretical predictions based on Poisson statistics. This applies to both aperture photometry obtained for standards in the field as well as standards and galaxies combined, as is expected for aperture photometry.
It was found for the photometry of the INT images that a linearly variable psf did not provide any improvements in dispersion over a constant psf model. In addition, at these faint magnitudes, the IDL-based weighted photometry gave results with less dispersion than the Daophot psf. This may be attributed to the different methods by which the sky is calculated. Daophot uses an annulus to calculate the sky whereas the IDL-based algorithms use the whole image for the sky calculation. At magnitudes brighter than 22, daophot psf and IDL-based weighted give similar results. Results agree with theoretical predictions.
Similar results were found for the kp4m images as for the INT even though the kp4m had the most problems with spatial variance. In addition however, the agreement between daophot psf and deepsearch weighted is good even at faint magnitudes. This may be attributed to the larger size of the image which provides more objects for comparison as well as the fact that the kp4m images are deeper which provides for a better signal at fainter magnitudes. Dispersion measurements for the photometry are a bit worse than theoretical predictions. However, due to the problems with the kp4m images, this is not unexpected. It was also found that a quadratically variable psf did not approximate the actual stellar psf well for these images; this may be due to the possibility that the spatial variance in the kp4m images are actually cubic. The daophot software only give options for a linear or quadratically variable fit.
Due to the smaller size of the kp2m images as well as the fact that we choose fields to specifically avoid stars, there was not an adequate number of stars to perform an accurate statistical analysis like that done for the INT and kp4m images. However, an aperture photometry comparison that included both stars and galaxies was performed to show good agreement between the two aperture methods as well as good agreement with theoretical predictions.
The decrease in dispersion of Iraf daophot psf photometry over Iraf aperture photometry is about 20% at fainter magnitudes ( fainter than or equal to 22 mag); a similar improvement applies for the Deepsearch aperture photometry compared with the Deepsearch weighted photometry. At magnitudes brighter than 22, the IRAF and weighted IDL are comparable.
It is apparant from this analysis that the Iraf and Deepsearch IDL-based routines are essentially equivalent for the images under study. For our lightcurves, we use aperture photometry in preference to weighted photometry for simplicity in error calculation. The analysis shows that this is adequate. We should in the future implement the weighted photometry especially if we plan to observe at fainter magnitudes. This is not a crucial step for now.