Introduction

It was shown previously with a large dataset that the IRAC flat-field in Band 1 (the faintest, and hence hardest, band) could be derived with conventional means to an accuracy of 0.6% using a large amount of data. Unfortunately, this amount is a significant fraction (10 hours, or roughly 6%) of the time in a typical instrument campaign, and given a cap of 17% for all calibrations it would be desirable to only use what is actually needed. How much data do we actually need?

To answer this, I used the same dataset as before, only decimating it so that frames were eliminated equally from each of the 9 mapping positions. Since the random cycling dither pattern had been used, eliminating frames from each mapping position should not introduce any bias in residual structure. To briefly recap:

• The data were simulated using the ISDS. 100-second frames were used. A 9x9 mapping pattern with a 100" throw and a cycling dither were used. Data were taken in a region of high background (for signal), and in a low background region (for the dark).
• The truth images contained a model of the stars, galaxies, and background.
• A spatial filter was applied to the data to mask all the objects. The data in each field were combined using the masks and outlier rejection.
• The combined image from the low background region was subtracted from the high region, and the resulting image normalized to make the flat.

Results

Results from this exercise are shown below. Both the pixel-to-pixel errors and the large scale residuals vary roughly with the root of the number of frames, as expected. While one expects that on a pixel-wise scale, on larger scales one expects the larger-scale residuals to get worse as the number of dithers available to remove the stars decreases. Indeed, if one looks at the 2-hour case below, the solution is becoming noticeably grainy. One alternative to this experiment would be to examine the effects of increasing the number of dithers by lowering the exposure time while holding the total AOR time constant.

Total Hours	Images per AOR	Pixel-Pixel % Error	Large Scale % Error	Flat-Field	% Error
10.5	162	0.6	0.7
5	81	0.8	1.2
2	27	1.3	1.5

Explanation of columns:

1. Total Hours - the total wall clock time needed to acquire all the data needed to make the flat.
2. Images per AOR - to make the flat requires two AORs, one in a high background region, and one in a low.
3. Pixel-Pixel % Error - the error relative to the known input flat on pixel-size scales.
4. Large Scale % Error - the error relative to the known input flat on size scales of 30 pixels or larger.

Additional Fine-Tuning and Conclusions

Note that the ideal total times will hold the noise contributions from the "sky" and "dark" combined images about equal, since both contribute equally to the noise quadrature sum of the difference image. For channel 1 this is a ratio of roughly 4:1. Shown in the figure below are the results of subtracting a "sky" and "dark" made from 81 high background images and 27 low background images. This flat has a typical 1-sigma error of 0.9%, and large-scale deviations of about 1.3%.

From this I conclude that we can probably acquire a 1% flat in 3-5 total hours to collect all the needed data. Although our requirement states 0.5%, it also says that this number is for "sources", which neccessarily subtend more than one pixel. Our pixel-wise noise is probably adequate, then. Large-scale deviations are still higher than desired, and hopefully more careful tuning of the selected dither pattern and the target field can improve this.

Flat-Field	% Error
Flat made from 2.5 hours of "sky" data and 1 hour of "dark" data.