we concluded that the [5.8] and [8.0] maps were too shallow to perform DIA and obtain reliable light curves, so our variability analysis is restricted to the [3.6] and [4.5] bands. 

Spitzer PSFs have a “triangular” shape with extended diffraction-like patterns (more precisely they are “multiplexer bleed” or “muxbleed,” “column pull-down,” and “banding” $^{2}$), and the PSF rotates between the epochs. DIA works best on simple quasi-Gaussian PSFs, so we pre-filtered the images to have a simpler PSF structure (Figure 1). For each region, we scaled and median combined the brightest stars to build an empirical model of the PSF, B . We then linearly filtered the image I to create a filtered image defined by the combination of Fourier transforms ˜ I$_{F}$ = ˜ G ˜ I/ ˜ B , that transforms the PSF from B to G , where G is a Gaussian broad enough to avoid noise amplification (i.e., ˜ G → 0 faster than ˜ B → 0 for small scales/large wave numbers). The filtering process conserves fluxes and was carried out on a 3 × 4 grid of 4040 × 4040 pixel regions that overlap by 20 pixels along their edges. To save some computation time, each of these 4040 × 4040 regions was then cut into smaller 2040 × 2040 pixel sub-images (again each with 20 pixels of margin) for the DIA analysis. We combined all four epochs to build the template images and these templates were scaled and subtracted from each epoch using DIA (Wo´ zniak 2000). The brightest stars in the field produce artifacts due to subtraction residuals, particularly from the “diffraction” spikes in the PSF. We therefore masked a region around all stars with K < 11 mag in the 2MASS catalog of point sources (Cutri et al. 2003). The masking radius was 260(1 − K/ 11) arcsec, which is large enough to include the spikes. We used the Two Micron All Sky Survey (2MASS) catalogs because these bright stars were saturated and not included in the SDWFS catalogs. The masked regions constitute ∼ 3% of the area. 

The [3.6], [4.5], [5.8], and [8.0] Vega magnitudes, and the coordinates (J2000.0) are taken from the SDWFS catalogs (Ashby et al. 2009). Throughout this paper, we use 4 arcsec diameter aperture magnitudes with aperture corrections to 24 arcsec. The original 3.6 µ m full SDWFS catalog contains 677,522 objects (catalog DR1.1), but we cropped it to 515,055 objects (hereafter called the “cropped sample”) as variations in coverage between epochs reduced the usable area for variability analysis by about 20%, to 8.1 deg $^{2}$. Using DIA’s PSF fitting routines, we could construct light curves (at least three epochs) for 492,420 objects simultaneously in both [3.6] and [4.5]. The final number of objects used in this analysis after masking regions around bright stars is 474,179. While we include the results for all objects from the cropped sample in Table 1, in the analysis that follows we consider only the sources with at least three epochs. Table 2 provides the DIA light curves for all SDWFS sources from the cropped sample. 

