1) Introduction

Previously I have reported on my efforts to derive the IRAC flat-field from simulated observations of the high and low zodiacal background. My attempts to do so using the Fixsen software were only marginally fruitful. In particular, attempting to derive both the gain and offset simultaneously from the data were complete failures. Therefore, the data was packed up and sent to Rick Arendt, in order to see what a true wizard of the algorithm could do with it. Rick made a number of changes, including (as I understand it) a change to the weighting scheme, selective weighting of the stars, and an additional constant offset term in the model to match something known to be in the sims (the "fluctuating bias" feature of the ISDS).

2) Results

Gains (Flat-field)

The input data for the solutions shown in Figures 1 and 4 were the two sets of high and low background "blank" fields. Specifically, for the following these consisted of 72 30-second frames in a high zody region, and 72 in a low zody region, using the Reuleaux dither pattern. Each AOR takes 51 minutes to execute, for a total of 1.7 hours of wall clock time.

Fig. 1 - Derived (top) vs. true (bottom) gainmaps for channels 1-4 (left->right).

The gainmaps look very similar to the known input calibration flats, albeit noisier. Figure 2 shows the percent error maps. Pixel-to-pixel errors are 3, 1.8, 1.1, and 0.4%. Several of the maps show large-scale gradients. The peak-to-peak amplitude of these gradients are 8, 19, 1.5, and 1.7%. The striping in Band 4 is due to an error in the simulator, which applied the relative gains of the separate readout channels twice to the data. It contributes much of the error in this band.

Fig. 2 - Percent error in Fixsen derived flats.

For a specific comparison to the previous results, figure 3 shows the gain derived from the "5hour" dataset. This consists of two sets of 162 100-second frames, and takes a total of 10.4 hours to collect (the name is a result of using 2 AORs which are of the maximum allowed length). Small-scale (pixel-to-pixel) errors are 0.4%. Large scale errors (in particular, the top-to-bottom gradient) are 1% peak-to-peak. The pixel-to-pixel error is better than what was acheived using the mask-and-coadd technique. The large-scale residuals at the very largest spatial frequencies are somewhat worse.

Fig. 3 - Band 1 input flat (left), fixsen derived flat (middle), and percent error (right).

Offsets (Darks)

Figure 4 shows the derived offsets for the test which used 1.7 hours of data. They don't look as good as the gains. The offsets probably aren't as tightly constrained. Also, the gradient in the channel 2 gainmap appears to arise from a corresponding degeneracy with the channel 2 offset.

Fig. 4 Derived (top) vs. true (bottom) offsets for channels 1-4 (left->right).

At this point I think a highly relevant question is whether these techniques are achieving the kind of performance we expect to get. To this end I show below the expected S/N vs. the collection time for a single AOR. I have assumed several things in this calculation:

• A slew model that taxes 3 minutes initially and 14.4 seconds per mapping/dither slew, which produces times fairly commensurate with SPOT.
• The data are taken with 100-second frames.
• The read noise is that given in the SOM.
• High and low zodiacal backgrounds are those given in the SOM.
• An equal number of frames are used for both the high and low background areas.

The expected errors based purely on photon counting statistics are 0.3% in Band 1 for the 162 frame case. Although a few frames are decimated by the spatial coadd filter, the total number of pixels in a given pixel stack lost this way is typically only 2.5%.

Fig. 5 - Expected error vs. time per AOR. Task requires 2 AORs. Shown are bands 1-4 (top to bottom). The marker indicates the expected result for the 5-hour dataset.

• With appropriate massging of the input weight functions, Fixsen can perform near the theoretical limit in reconstructing the pixel-to-pixel variance in the gain. The coadd technique is within a factor of 2 of this.
• The Fixsen reconstructions are suffering from large scale gradient errors. With a large data set these errors are around 1%, and are in the form of a tilted plane. The coadd approach typically has errors of 0.5% on spatial scales similar to the primary dither size.