IRAC: PSF

Core PRFs

The PRFs (here we use the language common in the optics field; the point spread function [PSF] is before sampling by the detector array, and the point response function [PRF] is after sampling by the detector array) are undersampled at the native IRAC pixel scale. These high dynamic range PRFs have a pixel sampling of 0.2 IRAC pixels, or 0.24 arcsec. The size of each PRF image is 279x279 pixels, covering an area of ~68x68 arcsec. The PRFs are centered within each image and volume normalized to unity in a 12.2 arcsecond aperture with a 14.4 to 24.0 arcsecond background annulus removed. This normalization is consistent with the standard calibration aperture of IRAC, and the PRFs should not need additional normalization.

Each of the 300 high-dynamic-range observations of the calibration star contain a short-exposure (0.6s/1.2s) and long-exposure (12s/30s). The Core PRFs were generated using prf_estimate.pl in the MOPEX package by first combining short-exposure frames and long-exposure frames separately. The short frames enabled the cores to be explored without saturation, while the long exposures allowed us to obtain higher signal-to-noise in the wings of the PRF out to 15 arcsec. The assembly required replacement of any saturated area in the long-exposure PRF with unsaturated data from the same pixel area of the short exposure frames. It also required the non-linear artifacts in the ch3 & ch4 data (i.e. electronic bandwidth correction) to be removed and replaced by short frame pixels. The "stitching" was completed using a 1/r algorithm requiring a percentage of each frame to be added together over a small annulus 2.4 arcsec in width just outside the saturated area. Each epoch was treated separately and then all three epochs were aligned and medianed to remove background stars.

• IRAC.Core.PRF

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. We display the PRFs with a logarithmic scaling to better show the whole dynamic range.

Extended PRFs

These Extended high dynamic range PRFs have a pixel sampling of 0.2 IRAC pixels, or ~0.24 arcsec. The size of each PRF image is 1281x1281 pixels, covering an area of ~5.1x5.1 arcmin. The PRFs are centered within each image. The PRFs are calibrated in MJy/sr as an unsaturated, very high S/N image of Vega: the flux contained within a 10 IRAC pixels aperture (50 HDR PRF pixels) with the sky level estimated in an annulus with 10 and 20 IRAC pixels inner and outer radii is equal to the flux of Vega according to the IRAC Data Handbook. The pedestal level of each image is set to zero in the corners of each PRF.

Observations of the stars Vega, epsilon Eridani, Fomalhaut, epsilon Indi and Sirius were used in construction of the Extended PRF. Each star was observed with a sequence of 12 sec IRAC full frames, using a 12 point Reuleaux pattern, with repeats to reach the final integration time (varying between 20 min and 1 hour per source/epoch).

The Core PRFs were aligned and rescaled to the extended PRFs by matching their overlapping area. The alignment was done to an accuracy of ~0.1 arcsec. The rescaling was made by forcing the cores (within a 10 IRAC pixel aperture), to have the same flux density of Vega (as the flux densities of the extended portion of the PRF were normalized to Vega). 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 PRF data were missing due to saturation cutoff), and the extended PRF.

The merged PRFs were then cropped to a final 5.1x5.1 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. Note: For these PRFs, the pixel sampling is 1/5th that of the native IRAC pixel size.

• IRAC.Extended.PRF

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. To determine a proper aperture correction, the aperture photometry should be performed on an image of a point source, that is, the portion of the PRF for a particular pixel phase. For a PRF with a factor of 5 sampling (the PRF samples 25 individual pixel phases), an image of a point source is given by extracting every fifth pixel in row and column directions (remember that you also need to multiply the pixel scale, arcsec/pixel, by the same factor of 5). Then perform aperture photometry within the 12.2 arcsec radius on the resulting point source image, and divide the resulting total counts value from that aperture with the total counts value in all the pixels in that image. The result is the correction factor that you should multiply your measured point source flux densities with.

IRAC provides diffraction-limited imaging internally. The image quality is limited primarily by the Spitzer telescope. The PRF has been created at the center, therefore use of these PRFs degrades as a function of distance from the center of the array. The PRF will vary by position on the array, including, but not limited to, the position of the optical ghosts at 3.6 and 4.5 um 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 aberrations are 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.

A much larger variation in the flux of sources measured in different parts of the array is due to the tilt of the filters, which leads to a different spectral response in different parts of the field of view. The flat field calibration is done with the zodiacal light, which is relatively red; blue sources have a flux variation of up to 10% from one side of an array to the other (see the IRAC Data Handbook or this web page for more details).

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