Due to the undersampled nature of the IRAC PRF, Channel 1 (3.6 µm), and to a lesser extent Channel 2 (4.5 µm), show intra-pixel gain variations that depend on the location of a star within a pixel. These cause systematic errors in aperture fluxes as a function of "pixel phase", the offset of the stellar centroid from the center of the central pixel in which it is located, (x_phase,y_phase) = (x,y) - ROUND(x,y). Early in the cryogenic mission, the point source aperture flux was fit with a radial function in pixel phase (Reach et al 2005). Later, Mighell et al 2008; Download PDF, 0.7 MB* found that the intra-pixel gain variation is better described by a two-dimentional function of (x,y) pixel phase, primarily because the peak of the response is not at the center of an IRAC Channel 1 pixel.

At the beginning of the warm IRAC mission, we found that the pixel phase response peak-to-peak variation increased by a factor of about 2 in both Channels 1 and 2. The larger dynamic range enabled us to model the intra-pixel gain in terms of the sum of gaussian functions in measured (xphase,yphase). See the warm IRAC documentation for more details. The pixel phase response function is normalized such that its (integral) average across a single pixel is unity.

We display below images of the pixel phase response for channels 1 and 2. This function was fit simultaneously with the Array Location Dependent photometric correction function using the entire cryogenic flux calibration star dataset. An IDL function for correcting aperture photometry for both these functions can be downloaded here. Pixel phase correction images (the inverse of the response) that can be applied (multiplied) to data can be downloaded in fits format here.

These images are subsampled in 0.01 pixel increments, starting at -0.5 and ending at +0.5 (in both xphase and yphase), and may be interpolated to the phase of a given stellar centroid and multiplied by the measured aperture flux.

IRAC cryogenic pixel response model, showing intra-pixel gain variations as a function of pixel phase. Only Channel 1 (3.6 m) and Channel 2 (4.5 m) have significant variations.

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