The IRAC optics specifications limited the wavefront errors to < λ/20 in each channel. IRAC provided diffraction-limited imaging internally, and image quality was limited primarily by the Spitzer telescope. The majority of the IRAC wavefront error was a lateral chromatic aberration that was most severe at the corners of the IRAC field. The aberration was due to the difficulty of producing an achromatic design with a doublet lens over the large bandpasses being used. The effect was small, with the total lateral chromatic dispersion less than a pixel in the worst case. The sky coordinates of each pixel were accurately measured in the cryogenic mission using an astrometric solution from the ultra-deep GOODS Legacy data (PI Mark Dickinson), resulting in distortion coefficients that are in the world coordinate system of each image. The main effect was that the PSF (point spread function) and distortion may be slightly color-dependent, which may be detectable for sources with extreme color variation across the IRAC channels. See Section 2.2.4 below for more information about the distortion correction in the cryogenic and warm mission images.
A large variation in the flux of sources measured in different parts of the array is due to the filters, which led to a different spectral response in different parts of the field of view. The flat-field calibration was done with the zodiacal light, which was relatively red; blue sources have a flux variation of up to 10% from one side of an array to the other (see Section 4.5 in this Handbook for more details). This is called the “array location-dependent photometric correction” in the IRAC documentation.
Table 2.1: IRAC image quality properties. The second set of numbers for channels 1 and 2 are for the warm mission, and the rest of the numbers are for the cryogenic mission. Noise pixels are defined in Section 2.2.2.
Channel
Noise pixels (mean)
FWHM (mean; ”)
FWHM of centered PRF (”)
Central pixel flux (peak; %)
Pixel size (”)
Maximum distortion (pixels relative to square grid)
1
7.0/7.22
1.66/1.95
1.44/1.78
42/37
1.221
1.3
2
7.2/7.33
1.72/2.02
1.43/1.80
43/34
1.213
1.6
3
10.8
1.88
1.49
29
1.222
1.4
4
13.4
1.98
1.71
22
1.220
2.2
Table 2.1 shows a few properties of the IRAC image quality. The cryogenic numbers were derived from in-flight measurements of bright stars during the cryogenic mission. PRF is the “Point Response Function,” further discussed in Section 4.9. The warm mission values were determined from the ≈ 4000 observations (0.4 second frames) of the calibration star that was used for the PRF/focus measurements in the warm mission after the final biases and temperatures were set. In the warm mission, the FWHM values were obtained from a Gaussian fit to the PRF profile, and the peak central pixel fluxes were the average of stars that were within 0.09 and 0.15 pixels from being centered, in each channel.
The noise pixels column in Table 2.1 gives the equivalent number of pixels whose noise contributes to a linear least-squares extraction of the flux of a point source from a 13 pixel × 13 pixel portion of an unconfused image, assuming the PRF is perfectly known. The quantity is derived as follows: let the PRF in pixel i be Pi and the intensity of an image in pixel i be Ii. If a point source with flux F is present in the image, then Ii= FPi. If we do a least-squares fit to determine F, then we minimize
(2.1)
where σi is the measurement uncertainty in pixel i. We will assume here that σi is independent of pixel and set σi = σ. Now we take the derivative of with respect to the source flux and set it to zero to find the optimum value. We find
(2.2)
solving for F, we find
(2.3)
Now we derive the uncertainty in the flux. Using the well-known theorem for the propagation of errors
(2.4)
and applying it to the result above, we find that
(2.5)
or, equivalently, where , which is the definition of noise pixels.
There are two columns for the full width at half-maximum (FWHM) of the PRF in Table 2.1. The mean FWHM is from observations of a star at 25 different locations on the array. The FWHM for the “centered PRF” is for cases where the star was most closely centered in a pixel. The fifth column in Table 2.1 is the fraction of the flux in the central pixel for a source that is well centered in a pixel. It was determined from the images of the focus star (after the telescope was focused) that were the most symmetric and concentrated. These values for the flux in the central pixel can be used in the saturation predictions (see Section 2.5.2 below). The flux in the central pixel for a random observation is likely to be lower, because the Spitzer PRF was undersampled at the IRAC pixel scale.
with respect to the source flux and set it to zero to find the optimum value. We find 
where 
, which is the definition of noise pixels.