Optical distortion is a significant (measurable) effect in IRAC data. The » 1% distortion in all channels is due principally to IRAC being offset from the optical axis of Spitzer, with additional components from the telescope and camera optics. In addition to varying the effective pixel size, there are also higher-order terms such as skew (the two axes are not exactly perpendicular) and a difference in the pixel scales between the two axes. Failure to account for the distortion will lead not only to errors in photometry (described below), but also shifts in astrometric position, approaching 1 arcsecond near the array corners.
Optical distortion corrections in each of the IRAC FOVs have been implemented in the (C)BCD FITS header keywords using a standard method described by Shupe et al. (2005). This method places the center of the distortion at the center of each detector array, in particular at CRPIX1 and CRPIX2. The linear terms and any skew are represented in the CD matrix header keywords (CD1_1, CD1_2, CD2_1, and CD2_2), while the distortion keywords provide the second and higher order terms. Importantly, these distortion corrections apply to the array coordinates, prior to the transformation to sky coordinates. This means that all IRAC data for a given detector share the same distortion keywords. In addition, we also provide a separate set of header keywords representing the “reverse” transformation from sky to array coordinates.
The form of the optical distortion that is encoded in the (C)BCDs is read properly by several standard tools available to the general astronomical community, e.g., the Spitzer mosaicker (MOPEX), WCSTools, and DS9 (except for grid overlays).
The optical distortion was fit independently for each IRAC detector. Originally a second-order fit was used, but an improved fit to third order was derived from the GOODS data by S. Casertano. The (C)BCD coefficients remove the distortion to 0.1 arcsecond accuracy.
4.11.2 Pixel Solid Angles
As a result of the optical distortion described above, the detector pixels did not all subtend the same projected solid angle on the sky. The variation in projected pixel solid angle was roughly 1.5%.
This size variation is accounted for in the flat-fielding process because the flats were derived from actual sky measurements. As a result, after flat-fielding, the (C)BCD images were calibrated in units of true surface brightness (MJy/sr). This poses a difficulty because virtually all software assumes that the pixels are in units of flux per pixel, and simply sum the pixel values. In order to properly measure fluxes from an image in surface brightness units, one must multiply the pixel value by the pixel size. Failure to do so could induce photometric errors at the 1% level, depending on the location on the array. Unfortunately, older photometry software cannot read the FITS-standard WCS distortion keywords written in the (C)BCD headers and properly account for the sizes of the pixels.
The simplest solution to this problem is to reproject the images onto an equal area (or nearly so) projection system (such as TAN – TAN) using suitable software that can understand the distortion keywords in the WCS header (e.g., MOPEX). MOPEX also has the significant advantage that it understands how to properly handle surface brightness images during coaddition. After processing, the pixels will all subtend the same solid angle, and hence any standard photometry software can produce the correct result.
However, some data users may prefer alternative approaches, in particular if they wish to measure photometry directly from the (C)BCD images. Therefore, we supply maps of the pixel size in the “Calibration and Analysis Files” section of IRSA’s IRAC documentation website that can be used to correct the pixel solid angles in BCD images if any measurements are being directly made on them. Note that this correction is built into the “location-dependent photometric correction” image (see Section 4.5), also available on the website, so multiplying by this correction map (intended to provide correct photometry for point sources with stellar-like SEDs) will also produce the correct result