C.1 Use of the Five Times Oversampled PRFs Outside of APEX
As supplied in the documentation website, the PRFs are oversampled by a factor of five in Delta_x and Delta_y. This allows for 5*5=25 independent realizations of a point source, corresponding to 25 different pixel phase combinations (five each in x and y; see also Figure C.5). An IRAC pixel image (point source realization) can be obtained by overlaying the IRAC pixel pattern on the higher resolution PRF grid. The value on the PRF grid at the center of a given IRAC pixel is taken for the pixel value. If the IRAC pattern is not registered exactly with the PRF grid, the values must be interpolated between grid points. Thus, lower numbered PSRs result from overlaying the IRAC pixel pattern lower and to the left on the PRF grid, so the source appears on the top right; and vice-versa. To obtain any given point source realization (PSR), the PRF needs to be sampled every fifth pixel in x and y at the appropriate phase, i.e.,
where i,j are integers running from 1 to n in the case of a PRF table which is 5n * 5n in size. The current PRF table available on IRAC web pages at IRSA has a size of 128,128. You may copy this to, e.g., a 125,125 array so that the peak pixel is in the center pixel of this new array. In this case, PSR13 corresponds to the source landing in the center of a pixel. Note that the PRF should not be block averaged, as this will result in the loss of the pixel phase information.
These PRFs may be implemented directly by those willing to write their own code. In IDL, for example, a point source realization may be generated using the /SAMPLE switch in rebin, e.g,
psr = rebin(phasedPRF,n,n,/SAMPLE)
where phasedPRFis the 5n x 5n PRF shifted to the appropriate pixel phase in both dimensions. In IRAF, use:
imcopy PRF.fits[1:5n–4:5,1:5n–4:5] PSR1.fits
Note that the PSRs are normalized to unity at infinity, not to the IRAC 10 pixel calibration aperture. Fluxes obtained with these thus need to be multiplied by the appropriate infinite aperture correction. These have been determined to be 0.943 in channel 1 and 0.929 in channel 2, based on measurements of the PRF, and can be compared to direct measurements of 0.944 and 0.937. Estimates from the PRF are unavailable in channels 3 and 4, but the corrections given in this Handbook are 0.772 and 0.737, respectively (Table 4.8).
C.2 Modifications to the IRAC PRFs for Use with APEX
The IRAC PRFs are centered relative to the optical axis, so they are slightly off center in array coordinates due to array distortion. APEX assumes that the PRF is centered on its array, so to use the PRFs with APEX requires them to be re-centered. APEX also requires odd-valued axes.
APEX performs PRF fitting by varying the position and flux of a source using a modified simplex technique (see the APEX manual). However, for IRAC data, particularly in channels 1 and 2, where the PRF is undersampled, the default 5x sampling of the PRF is insufficient to obtain a sufficiently accurate position for fitting.
Therefore, the following transformations were applied to the PRFs:
i) The PRFs were magnified (using linear interpolation) by a factor of 20 (so the resultant PRF sampling is x100).
ii) The last row and column were removed to give odd-valued axes.
iii) In the cryogenic mission, the PRF was re-centered on a first-moment centroid measured using the array values within a 250 (resampled) pixel border. In the warm mission, the PRF was recentered to ensure that the point source realization centered on entry [1279, 1279] of the 2559 x 2559 PRF array will appear to be perfectly centered on a pixel. In other words, its first moment centroid will be measured to have a phase of [0, 0] (in zero-based indexing).
iv) The PRF was zeroed out in a 50 (resampled) pixel border (to avoid wrapping problems).
v) Information describing the PRFs and their modifications was added to the headers.