Spitzer Documentation & Tools
IRAC Instrument Handbook

 

 

2.2.2        IRAC Image Quality

The IRAC optics specifications limit the wavefront errors to < λ/20 in each channel. IRAC provides diffraction-limited imaging internally, and image quality is limited primarily by the Spitzer telescope. 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 were accurately measured in the cryogenic mission using an astrometric solution from the ultra-deep GOODS Legacy data, resulting in distortion 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. The second set of numbers for channels 1 and 2 are for the warm mission, the rest of the numbers are for the cryogenic mission.

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 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 warm mission values were determined from the ~ 4000 observations (0.4s frames) of the calibration star that was used for the PRF/focus measurements in the warm mission after the final bias and temperatures were set. In the warm mission, the FWHM values were obtained from a Gaussian fit to the PSF 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 13×13 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

 

 

 

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

 

 

solving for F, we find

 

 

 

Now we derive the uncertainty in the flux. Using the well-known theorem for propagation of errors

 

 

 

and applying it to the result above, we find that

 

 

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 “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 2.4 below). The flux in the central pixel for a random observation is likely to be lower, because the Spitzer PRF is rather undersampled at the IRAC pixel scale.