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As in campaign D2, the data were processed through the DAT without any problems, and then left-right flipped. Efforts to use mips_enhancer to remove distortion from the images did not meet with much success, due to the very limited time available to test the software with actual CTA images. Eventually it was determined that the enhancer was correctly restoring images to a rectilinear grid, but that sampling effects were blurring the PSF by an amount larger than the FWHM variations in the original (distorted) images. As a result, there was no advantage to removing the distortion from focus images before PSF reconstruction.
The 24 micron focus determination is based on analysis of structure in the second dark Airy ring. Specifically, the radial profile of the observed star image is compared to radial profiles of model PSFs with different amounts of defocus. Ideally the observed profile would directly overly one of the model curves; but imperfect centering, imperfect flat fielding and background subtraction, and unmodeled optical or detector effects prevent this from happening. Instead, the observed radial profile crosses several of the model curves, and thus will be consistent with a range of defocus values. The radial profiles of the data and the models were calculated using the fortran program "mips24_focusdeter128a". This program subtracts background from the image; renormalizes the star to unit flux; assigns each image pixel to a radial bin; forms the radial profile from an azimuthal median of the image values in each radius bin; and normalizes the radial profiles against the radial profile of the in-focus SIRTF Tiny Tim model PSF.
As in campaign D2, we chose to work only with the data on K star HD 53501.
The first step in the focus analysis was to select only the dither positions from the upper left quadrant of the 24 micron array for analysis. These four showed the least image distortion (see Figure 1), so using them would minimize the effects of uncorrected distortion on the focus results. The star was observed as a four-position cluster target with large 3.5 pixel dithers, so four sets of upper left quandrant dither positions (16 positions total) were available for analysis. Since two cycles of 24 micron photometry were performed on the star, two exposures were made at each of the 16 preferred dither positions. These two images at each position were combined into a single coadded image with cosmic ray rejection (t= a+b - abs(a-b)). These sixteen coadded exposures were the basis of all further focus analysis.
The next step was to measure the centroid of the star image in each of the 16 coadded frames. IDP3 was used with Gaussian fitting. The sky background and its rms noise were measured in apertures left and right of the star images; these aperture locations were chosen to minimize the effect of the 3% vertical photometry gradient on the background estimate at the stellar position. Total counts on the star were measured and background subtracted. Values for the star centroid, total star counts, image background, and rms background were recorded in parameter files for use by the radial profile analysis program.
The data was then grouped in two different ways for the radial profile analysis:Single dither position images
Model PSFs were calculated using the SIRTF Tiny TIM software version 1.3. The specific pixel position measured for the star at each of the 16 dither positions was used as an input to Tiny TIM. This assured that field-dependent aberrations were properly accounted for in the PSF models. For each of the 16 dither postions, model PSFs were calculated for a range of defocus values, forming 16 focus libraries tailored to match the campaign E focus observations. All models were calculated on a 10x oversampled grid, then simultaneously rebinned to the native 2.55" pixel scale and translated so that the star centroid was aligned to within 0.02 pixel with the star centroid in the MIPS 24 sky images.
Coaddition of all 16 dither positions
Coadding all 16 dither positions had the benefit of increasing the S/N of the PSF in the images, enhancing the ability to measure brightness changes in the second dark ring. A coadded PSF model is needed for comparison to the coadded data. For each defocus position, we coadded all 16 of the 10x oversampled models calculated above, then rebinned them to the native 2.55" pixel scale. The next step was to build a single reconstructed image of the focus star from a combination of the 16 dithered images. IDP3 was not able to automatically align and centroid the images because the world coordinates in the fits headers were wrong. As a stopgap measure, the JPL spica package was used to automatically find the centroids of the largest bright object in the field above a specified isophote. The images were then shifted and medianed on a 4x oversampled grid, yielding a reconstructed image of HD 53501. This oversampled image was then resampled back to the native 2.55 arcsec per pixel scale, and in the process shifted so that the star centroid coincided with the centroid of model PSF in the coadded focus library.
Figure 1: Coaddition of 30 separate
dither frames from the first cluster target position, for K star HD 53501.
The PSF FWHM values are given in pixel units, and were measured by Gaussian fitting
in IDP3 using an aperture of 6 pixels radius. The numbers give the FWHM along
the X and Y axes of the detector array, respectively.
In the above figure, one can see how the apparent size of the MIPS 24 image core varies with dither position in the standard small-field photometry AOT. The larger image size the in X direction is fully consistent with pre-launch expectations for different plate scales in the X and Y directions: 2.4932 arcsec/pixel in X, and 2.5981 arcsec/pixel in Y from ray tracing (J. Keene, personal communication). The variation of the FHWM with field position is due to higher order distortion terms.
We now show five radial profile plots comparing the observed 24 micron PSF with SIRTF Tiny TIM models. In these plots, the sky data is represented by three solid lines. The central line is the median radial profile, and the upper and lower solid lines represent "error bars" to the median profile. The errors are calculated for +1 and -1 sigma changes in the sky background level, and do not include systematic effects. The dashed lines are the family of curves for model PSFs at negative focus positions, and the dotted lines are the same but for positive focus positions. The two vertical bold lines define the inner and outer boundaries of the second dark Airy ring, and thus bound the region of interest for the data/model comparison. If the SIRTF Tiny Tim models were exactly correct, if there were no systematic normalization or alignment errors in the radial profiles, and if MIPS was in perfect focus, then the median radial profile would appear as a flat horizontal line at radial profile ratio value = 1.
Figure 2: Radial profile of MIPS 24 micron PSF using the coaddition of two 3 second
exposures taken at pixel position 38.3, 84.7.
Figure 3: Radial profile of MIPS 24 micron PSF using the coaddition of two 3 second
exposures taken at pixel position 38.3, 89.3.
Figure 4: Radial profile of MIPS 24 micron PSF using the coaddition of two 3 second
exposures taken at pixel position 38.3, 93.8.
Figure 5: Radial profile of MIPS 24 micron PSF using the coaddition of two 3 second
exposures taken at pixel position 38.4, 80.1.
With the four plots in Figs 2-5 above showing large errors, we spent a good deal of effort to investigate how to get better agreement between the data and the models. The background measurements and centroid determinations were re-checked. We investigated whether an error in the assumed plate scale might lead to errors in the radial profile comparison; the SIRTF Tiny Tim models assume square pixels, whereas both raytracing and IOC measurements show a small scale difference between the X and Y axes. It was found that changing the plate scale of the Tiny Tim models by 1% did not substrantially change the quality of the radial profile fits. We also investigated whether the 24 micron bandpass in Tiny Tim was correct; eventually we verified that it was, although not until we had mistakenly believed for a few days that it wasn't.
Figure 6: Radial profile of the MIPS 24 micron PSF using the coaddition of
thirty-two 3 second exposure taken at various positions over the
upper left quandrant of the array.