The photometric calibration of IRAC is tied to point sources (calibration stars) measured within a standard aperture with a radius of 12 arcseconds. This point source calibration is applied to all IRAC data products during pipeline processing to put them into units of MJy/sr (1 MJy/sr = 10–17 erg s-1 cm-2 Hz-1 sr-1). This method results in a highly accurate calibration for point sources. However, transferring this calibration to extended sources is not straightforward. The discrepancy between the (standard) point source calibration and the extended source calibration arises from the complex scattering of incident light in the array focal planes. Our best understanding is that there is a truly diffuse scattering that distributes a portion of the incident flux on a pixel throughout the entire array.
The surface brightness of extended emission in IRAC images will tend to appear BRIGHTER than it actually is. The reason for this is two-fold. First, photons that would normally scatter out of the PSF aperture used to measure a point source are instead captured by an extended source. The scattering depends on the convolution between the IRAC PSF and how the light is distributed across the focal plane, which is usually quite complex for extended sources (galaxies, ISM, and nebulae). Second, photons are scattered into the aperture from the emission regions outside the aperture. As a thought experiment, one can imagine a single point source inside an aperture, which is easy to measure. But if four point sources are placed around it just outside the measurement aperture, each of them scatters light into the aperture, which leads to an overestimate of the real flux. For the extended source case, we can imagine the same experiment taken to the limit where all the regions have emitters in them.
For photometry of extended sources (over 1 arcminute in size), the calculated flux inside an aperture must be scaled by the ratio of the extended and point source throughputs. The scaling factors (fp/fex) to be used are given in Table 4.8 (the infinite aperture case). Note that these are not really throughputs, in the sense that they have anything to do with the number of photons reaching the detector. It is more accurate to think of them as a special type of an aperture correction. The values in Table 4.8 are for a very extended, red source like the Zodiacal light.
The more challenging case is correcting aperture photometry of extended objects with spatial scales between a point source and the very extended case, e.g., a relatively nearby galaxy. Here the underlying surface brightness distribution of the object is important. One technique is to determine aperture corrections via a curve-of-growth from actual data. Below, a detailed analysis of early-type spheroidal galaxies (chosen because of the relatively simple light profile of these stellar-dominated sources), ranging in size from 20 arcseconds to several arcminutes, is presented. The aperture corrections may, within limits, be applied to other galaxy types. Note that the large-aperture corrections derived here are fairly close to the infinite aperture corrections of Table 4.8.
A commonly encountered problem is that of measuring the total flux of extended objects that are still smaller than the standard aperture size used for the photometric calibration. For example, the background galaxies seen in all IRAC images are often slightly extended on size-scales of a few arcseconds. PRF-fitting photometry of such objects will obviously underestimate their fluxes. One methodology for handling such sources was developed by the SWIRE project; readers are referred to the data release document for SWIRE, especially section 8.4.2, at
Detailed analysis by SWIRE has indicated that Kron fluxes, with no aperture corrections applied, provide measurements of small extended sources that agree closely with hand-measured fluxes. Kron fluxes are provided as one of several flux measures in the popular SExtractor software (Bertin & Arnouts 1996). Note that it is important to determine that an object actually is extended before using the Kron flux, as it is ill-defined otherwise. This may be determined by using the stellarity and isophotal area as defined by the SExtractor software. Selecting limits on these parameters based on their breakdown as a function of signal-to-noise ratio generally will mimic SExtractor's own auto function.
To measure absolute flux on large scales (sizes of order the field of view), consider all the sources of flux that go into each pixel. The IRAC images are in surface brightness units. The flux of an extended object is the integral of the surface brightness over the solid angle of the object. The value of a pixel in an IRAC BCD is the real sky value plus a contribution from the zodiacal light minus the dark current value at that pixel. The dark current value is made from observations of a low background region at the north ecliptic pole and so it contains some small amount of flux of astrophysical origin. The darks have also had an estimate of zodiacal light subtracted from them before use. The (theoretically) estimated zodiacal light brightness during an observation is in the BCD header keyword ZODY_EST, and that for the sky dark observation is listed as SKYDRKZB. While it is possible using the above keywords to recover something similar to the absolute sky surface brightness, this brightness estimate is still limited by the accuracy of the underlying model of the zodiacal emission.
In practice, most extended source photometry will usually be performed with respect to a background region within the image (for example, large aperture photometry of galaxies, nebulae, etc.) and one does not attempt to measure the absolute sky brightness on large scales (like the zodiacal cloud). The median value of the pixels located in user-selected background regions is generally a reasonable estimator of the background.
