Point source fitting to IRAC data has proven problematic as the point spread function (PSF) is undersampled, and, in channels 1 and 2, there is a significant variation in sensitivity within pixels. To deal with these problems, we have developed Point Response Functions (PRFs) for IRAC. A 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 single detector pixel increments, an estimate of the detector point source response can be obtained for a source centered at any given subpixel position.
In-flight PRF FITS files (August 2008)
The IRAC point response functions (PRFs)
at 3.6, 4.5, 5.8 and 8.0 microns. The PRFs were generated
from models refined with in-flight calibration test data
involving a bright calibration star observed at several
epochs (see Hoffmann 2005 for more information). Central
PRFs for each channel are shown above with a logarithmic
scaling to help display the entire dynamic range. The PRFs
are shown as they appear with 1/5th the native IRAC pixel
sampling of 1.2 arcseconds to highlight the core structure.
The FITS files of the core PRFs can be obtained by clicking on the links listed below. These core PRFs can be used for PRF-fitting photometry and source extraction in BCDs for all but the brightest sources. Aperture photometry is recommended in all instances except in crowded fields and regions with a strongly varying background.
Please see Appendix C of the IRAC Instrument Handbook for directions on how to best perform PRF-fitting photometry.
(includes details of the creation, testing, and proper use of the PRFs supplied on this page in IRAC images).
The PRFs are provided in two different samplings, 1/5th and 1/100th native pixels. The 1/100th native pixel sampling have been created by interpolating the 1/5th sampled PRFs onto a finer grid. These PRFs are designed to work with the SSC-provided photometry extraction software APEX. The 1/5th pixel sampling versions are the originally derived versions and are appropriate for use with custom prf-fitting software, but not APEX. For both versions of sampling, the PRFs are provided for 25 positions in a 5x5 grid upon the array for each channel. The PRFs are normalized such that the flux is unity in a 10 pixel radius aperture around each point source with the zero pixel phase instance (centered on a pixel).
The extended IRAC point response functions (PRFs) at 3.6, 4.5, 5.8 and 8.0 microns with high signal to noise out to the edge of the array. The extended PRFs are displayed with a logarithmic scaling to reveal the whole dynamic range.
1. Cryogenic IRAC Extended PSFs
The FITS files of the images shown above can be obtained by clicking on the link listed below. In order to gain high signal-to-noise out to the edge of the arrays, PSFs were generated from a combination of on-board calibration and science observations of stars with different brightness, joined together to produce extended high dynamic range (HDR) observational PSFs. These PSFs have two main components: a core HDR PSF created by the observations of a reference star, and the extended region from observations of a set of bright stars that saturated the IRAC array. They can be used to perform source extraction and PSF-fitting photometry of bright, highly saturated stars with extended wings. The core of the extended PSF was generated using the prf_estimate module of Mopex which has been shown to be inadequate for making good PSFs for IRAC. As a result, the extended PSF should not be used for PSF-fitting photometry and source extraction of non-saturated point sources. Instead, the core PRFs discussed above are more appropriate. Also, note that the detailed structure of the center of saturated sources fitted using the extended PSF will not be correct in detail.
These extended HDR PSFs have a pixel size of 0.2 IRAC pixels, or ~0.24 arcsec. The size of each PSF image is 1281x1281 pixels, covering an area of ~5.1 arcmin x 5.1 arcmin. The PSFs are centered within each image. The PSFs are calibrated in MJy/sr. The PSFs represent an unsaturated, very high S/N image of Vega, and the flux density contained within a 10 native IRAC pixel aperture radius (50 HDR PSF pixels), with the sky level estimated in a radial annulus from 10 to 20 native IRAC pixels, is equal to the flux density of Vega. The pedestal level of each image is set to zero in the corners of each PSF.
To produce the core portion of the HDR PSF, 300 HDR observations of a calibration star were obtained during three separate epochs, each observation consisting of short exposures (0.6 sec/1.2 sec) and long exposures (12 sec/30 sec). The HDR PSFs were generated by first combining short-exposure frames and long-exposure frames separately. The short frames enabled the cores to be constructed without a saturation problem, while the long exposures allowed the construction of a higher signal-to-noise PSF in the wings out to 15 arcseconds. The assembly required the replacement of any saturated areas in the long-exposure frames with unsaturated data from the same pixel area of the short-exposure frames. It also required the replacement of a few pixels in the long-exposure frames by the corresponding pixels in the short-exposure frames to mitigate the non-linear bandwidth effect in channels 3 and 4. The "stitching" of the two components of the HDR PSF was completed using a 1/r masking algorithm requiring a percentage of each frame to be added together over a small annulus two IRAC pixels in width just outside the saturated area. Each epoch was treated separately and then all three epochs were aligned and a median was taken to remove background stars.
Observations of the stars Vega, epsilon Eridani, Fomalhaut, epsilon Indi and Sirius were used in the construction of the extended portion of the PSF. Each star was observed with a sequence of 12 sec IRAC full frames, using a 12-point Reuleaux dither pattern with repeats to obtain the required total integration time (the stars were typically observed for 20 - 60 minutes during each epoch). The images were aligned, rescaled to the observation of Vega, and then averaged together with a sigma-clipping algorithm to reject background stars.
The core HDR PSFs were aligned and rescaled to the extended PSFs by matching their overlapping area. The alignment was done at best to an accuracy of ~0.1 arcsec. The rescaling was made by forcing the cores to have the same flux density, that of Vega, within a 10 native IRAC pixel radius aperture. The stitching was made using a mask with a smooth 1/r transition zone, 2.4 arcsec wide, between the core (contributing where the extended PSF data were missing due to saturation cutoff), and the extended PSF.
The merged extended PSFs were then cropped to a final 5.1 arcmin x 5.1 arcmin size, and a pedestal level was removed in order to have a surface brightness as close as possible to zero in the corners of the images. For these PSFs, the pixel size is 1/5th that of the native IRAC pixel size.
2. Warm IRAC Extended PSFs
Several bright stars were observed in the warm IRAC mission to derive the
extended PSFs in a manner similar to the cryogenic extended PSFs. The warm
mission data that were used are from the Spitzer program ``Search for Planetary
Mass Companions of Nearby Young Stars'' (Program ID 80071, P.I. M. Marengo). The
warm mission PSFs were constructed from these data by Massimo Marengo, Alan
Hulsebus, Rebecca Park, Denise Wood, and Joseph Hora. The stars were observed
with a 12 second full-array frame time, using a 36-point small Reuleaux triangle
dither pattern, and four repeats at each position, with the exception of Altair,
that was observed with 6 second frames and eight repeats. At this frame time,
the stars were generally saturated to different levels in the core but this
allowed a high S/N measurement of the extended PSF. Each star was observed in
two different epochs (and field rotations).
Mosaics of each star were created with 0.24 arcsec/pixel scale, and saturated areas were masked in each mosaic (pixels above 50% full well). The mosaics were then aligned and rescaled to a common reference star. After that any stars with close companions or other bright sources in the field were rejected. Finally, the aligned and rescaled mosaics were coadded together using outlier rejection.
The core portions of the extended PSFs were derived from a set of warm
mission standard star observations that were not saturated. The IRAC standard
star BD+67 1044 was observed with a 0.4 sec full array frame time at ten epochs
of 122 frames with sub-pixel dithering. The data were reduced and combined using
the same steps as described above for the extended PSF, except no saturation
masking was necessary. The core PSFs were then aligned and rescaled to the
extended PSFs by matching their overlapping area using the same method as
described above for the cryogenic extended PSFs. Images of the warm extended
PSFs are shown below. More information about the construction of extended PSFs,
together with a comparison of cryogenic and warm IRAC extended PSFs, can be
found in Hora et al. (2012).
The warm IRAC extended point spread functions (PSFs) at 3.6 (left) and 4.5 (right) microns with high signal to noise out to the edge of the array. The extended PSFs are displayed with a logarithmic scaling to reveal low-level emission that extends to the edge of the ~ 5 arcmin x 5 arcmin field that is shown here.
Point Source Fitting Photometry
The PRF is not an oversampled representation of a point source. Rather it is a map of the appearance of a point source imaged by the detector array at a sampling of pixel phases (positions of the source centroid relative to the pixel center). For that reason, performing aperture photometry directly on the PRF is not strictly correct. Please refer to the Appendix C of the IRAC Instrument Handbook for more details on the comparison of aperture and PRF-fitting photometry.
IRAC provides diffraction-limited imaging internally. The image quality is limited primarily by the Spitzer telescope. For more information about the IRAC image quality, including the FWHM ("spatial resolution") values, please see the IRAC Instrument Handbook page on IRAC image quality. The core PRFs are provided for 25 positions in a 5x5 grid on the array for each channel. Interpolating to the nearest position is needed. The extended PRFs have been created at the center of the array. Therefore use of these PRFs degrade as a function of distance from the center. The PRFs will vary with position on the array, including, but not limited to, the relative position of the optical ghosts in channels 1 and 2, and the diffraction spikes in all channels. The majority of the IRAC wavefront error is a lateral chromatic aberration that is most severe at the corners of the IRAC field. The aberration is due to the difficulty of producing an achromatic design with a doublet lens over the large bandpasses being used. The effect is small, with the total lateral chromatic dispersion less than a pixel in the worst case. The sky coordinates of each pixel have been accurately measured in flight using astrometric observations of an open cluster, resulting in distortion coefficients that are in the world coordinate system of each image. The main effect is that the PRF and distortion may be slightly color-dependent, which may be detectable for sources with extreme color variations across the IRAC bands (please see the IRAC Instrument Handbook or Array-Location-Dependent Photometric Corrections for more details).