IRAC Instrument Handbook - IRSA - California Institute of Technology

IRAC Instrument Handbook
coefficients that are in the world coordinate system of each image. The main effect is that the PSF 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 Section 4.5 in this Handbook for more details).
Table 2.1: IRAC image quality properties.
Channel Noise
pixels
(mean)
FWHM
(mean;”)
FWHM of
centered
PRF (“)
Central
pixel flux
(peak; %)
Instrument Description 7 Description of Optics
Pixel
size
(“)
1 7.0 1.66 1.44 42 1.221 1.3
2 7.2 1.72 1.43 43 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
Maximum
distortion (pixels
relative to square
grid)
Table 2.1 shows some properties relating to the IRAC image quality. These numbers were derived from
in-flight measurements of bright stars. PRF is the “Point Response Function”, further discussed in Section
4.7.
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 13×13 pixel portion of an unconfused
image and assuming the PRF is perfectly known. In more detail, 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 i FP I −
χ = Σ
σ
2
i
2
i
where σi is the measurement uncertainty in pixel i. We will assume here that σi is independent of pixel
2
and set σi = σ. Now we take the derivative of χ with respect to the source flux and set it to zero to find
the optimum value. We find
0
= Σ
( Ii − FPi
) Pi