Appendix C. Point Source Fitting IRAC Images with a PRF
This Appendix discusses the use of point source response functions (PRFs) for fitting sources in IRAC data. For true point sources, it is possible to obtain agreement between PRF-fitted and aperture photometry flux measurements at better than the 1% level. In this Appendix, we describe validation tests on point sources in IRAC data using the PRFs in combination with the MOPEX/APEX software. The procedure for using the PRFs in conjunction with MOPEX/APEX is given in the form of a “How To” description, and the necessary corrections to the resulting flux densities are detailed.
Point source fitting is a valuable tool for characterizing images. If the image consists of true point sources, PRF fitting can make optimal use of the information in the image, thus improving astrometric and photometric results beyond what is achievable using other techniques. PRF fitting also allows point sources to be subtracted from an image (for example, using the apex_qa task in MOPEX/APEX), enabling any diffuse background emission to be more easily characterized. Point source fitting is less useful in fields containing large numbers of partially-resolved objects (as typically seen in IRAC extragalactic survey fields), and aperture photometry is recommended in such fields. (In principle, model fitting could be used for extended sources by convolving a source model with the appropriate point source realizations, but such techniques lie outside the scope of this Appendix.) For isolated point sources on featureless backgrounds aperture photometry and point source fitting should give almost identical results.
Point source fitting to IRAC data has proven problematic as the PSF is undersampled, and, in channels 1 and 2, there is a significant variation in sensitivity within pixels. Techniques for dealing with these problems were developed for the WFPC2 and NICMOS instruments on HST (Lauer 1999; (Anderson, J. & King, I. R., 2000) (Franceschini, A. et al., 1991), see also Mighell et al. 2008). These techniques involve building a “point response function” (PRF; Anderson & King use the alternative terminology “effective PSF”), and users interested in the detailed theory of the PRF should refer to these papers. In summary, the PRF is a table (not an image, though for convenience it is stored as a 2D FITS image file) which combines the information on the PSF, the detector sampling and the intrapixel sensitivity variation. By sampling this table at regular intervals corresponding to the grid of pixel phases sampled, an estimate of the detector point source response can be obtained for a source at any given pixel phase.
PRFs for IRAC have been created by William Hoffmann of the University of Arizona, a member of the IRAC instrument team. The starting point for these PRFs was the Code V optical models for Spitzer/IRAC, made at the Goddard Space Flight Center [see also the technical memo “25 Position Model Pixel Response Functions (PRF) Description and Quality” by Hoffmann in the IRAC Papers section at
These were constructed on a 5 × 5 grid of sub-pixels covering each of the IRAC arrays. Observations of a calibration star made during the in-orbit checkout at each of these 25 positions per array were then deconvolved by their respective optical models. The results were averaged into a single convolution kernel per array which represents additional PRF scatter from unmodeled optical effects and spacecraft jitter. A paper by Hoffmann et al. “Simfit and Focus Diversity: Methods for determining the focus of the SIRTF telescope in space without a focus slew” gives more details and is included in the IRAC Papers section of IRSA’s Spitzer website. The intrapixel sensitivity function was estimated using a polynomial fit as a function of pixel phase. The PRFs were then transposed, and flipped in x and y to align them with the BCD coordinate system.