Summary

Observations of the asteroid Harmonia were analyzed and compared to STinyTim models to characterize the 160µm PSF and determine aperture corrections. This analysis is based on photometry-mode observations run through the MIPS DAT (v. 2.8), using a subsampling factor of x2 to generate the final mosaics. The prime purpose was to measure aperture corrections, so comparisons were performed using radial profiles of the observed and model PSFs, not detailed comparison of the 2D distribution of signal. (The analysis was not intended to generate model PSFs for use in deconvolution or PSF removal, but does probably provide useful insight into the types of PSF that might be appropriate for those uses.) The primary results are:

• The STinyTim model does not replicate the observed 160µm PSF unless the model PSF is suitably smoothed.
• For an STinyTim model PSF with oversampling of x5 (3.2" per model pixel), the appropriate boxcar smoothing width is approximately 9 model pixels.
• The smoothed model PSF was used to computer aperture corrections because it is noise-free and it is trivial to normalize to the total flux.
• The aperture corrections are available as a table here

NOTE: The PSFs of concern here ARE NOT impacted by the near-IR spectral ghost. This report does not attempt to address the strength, position, or any other aspect of the spectral ghost, and its impact on photometry or imaging. Blackbody sources with temperatures in excess of 1000K are likely to be contaminated by the spectral ghost.

This page, all images, all fits images, and the routine used to compute the aperture corrections can be downloaded as a gzipped tarball here (~1Mb).

Observations

The main-belt asteroid Harmonia was observed in MIPS campaigns 10, 11, and 12 using the standard 160µm photometry AOR, and in campaign 11 using the large-field AOR. The data were reduced in the usual way using the DAT. The campaign X3 160µm illumination correction was used, no electronic non-linearity correction was applied, a subsampling factor of x2 (i.e. -s 0.5) was used to create the mosaics. An asteroid was used because there is no contamination of the PSF by the near-IR spectral ghost in the 160µm band.

The Campaign 11 (11MC) large-field mode PSF (top image in triptyche below) was the truth image against which model PSF were compared. While there appear to be some differences in the core of the PSF compared to the 12MC small-field PSF (bottom image above), they are minor, as is shown later.

Figure 1: Observed and Model PSF Images
	Harmonia Large-field mode observation from 11MC. The off-source DCEs have been subtracted from the on-source DCEs to remove time-varying detector effects. The slight NE/SW elongation of the PSF core may be related to a slight WCS issue in large-field mode. Fits file is here.
	The smoothed STinyTim PSF that best reproduces the radial profile from the large-field observation above is for an 80K blackbody source: Fits file here. A smoothed PSF appropriate for a 10K source: Fits file here. A smoothed PSF appropriate for a 30K source: Fits file here. A smoothed PSF appropriate for a 1000K source: Fits file here.
	Harmonia small-field mode observation from 12MC. A constant background was removed from the final mosaic to simulate the near zero background obtained in the large-field mosaic. Fits file here.

Analysis

Radial profiles for the 11MC and STinyTim PSFs were computed and overplotted to determine what model PSF to use for computing aperture corrections. The model PSF is desireable because the total flux in the image is known exactly, there is no noise, and there are no background sources or structure to cloud the results. Figure 2 shows the radial profile from the observed PSF and profiles for various degrees of smoothing of the STinyTim model PSF. The model PSF was computed for blackbody spectra with temperatures of 1000, 80, and 10K. 1000K is about as hot a blackbody source as can be observed without the near-IR spectral ghost contaminating the PSF. Figure 2 shows results for the the 80K model profile. A point is plotted for every pixel in the input images to show the range of values as a function of radial distance. Distance in all cases is measured from the centroid of the PSF. Smoothing of the STinyTim PSF was done using a boxcar of the specified width (the IDL smooth function was used). The width is given in model PSF pixels, which were 3.2" on a side.

Figure 2: Observed vs. Smoothed STinyTim Radial Profiles

Figure 3 shows the same data as Figure 2, but average values within radial bins are given. For the observed PSF error bars show the 1σ deviation of the data falling within each bin. From this figure it is clear that in the core of the PSF the data fall between the models smoothed by 9 and 11 pixels. However, near the first Airy minimum the observed PSF is much more closely approximated by the model PSF smoothed by 9. Beyond the first Airy ring the x9 and x11 models are quite close, and both agree with the data very well. On the basis of this figure, a composite model PSF, constructed by averaging the x9 and x11 smoothed model PSFs, was chosen as the basis for computing aperture corrections. It should work well for apertures smaller than the first Airy minimum, where it is most critical, and it makes little difference which model is used for larger apertures.

Figure 3: Observed vs. Smoothed STinyTim Average Radial Profiles

The effect of source temperature on the PSF is shown in Figure 4. The hottest source considered is a 1000K blackbody, as sources hotter than that will have a significant contribution from the near-IR spectral ghost. The temperature of the observed asteroid was about 250K. As the figure shows, a 250K blackbody is equivalent to a 1000K blackbody for the purposes of aperture corrections. Vertical lines are labeled showing distance in the native pixel scale of 16"/pix for comparison with the apertures defined in the results section below.

Figure 4: Effect of Temperature on Model PSFs

Results

The aperture corrections were computed using the IDL astronomy library procedure aper.pro. The aperture correcion is the total counts in the model image normalized by the counts in the object - sky apertures. That is, to correct photometry done using one of the apertures defined below, the user must multiply their measured counts by the aperture correction to derive the total flux of the object. The effect of the source temperature is only 5.4% in the 20" aperture, well below the absolute calibration of the 160µm data, and the effect is smaller for larger apertures. Note that some of the combinations of object and sky apertures defined here actually overlap, and so probably wouldn't be used in practice.

160µm Aperture Corrections
		Background Annulus Radii
Aperture Description	Aperture Radius	None	first Airy ring	first Airy min.	large
	(arcseconds)		32"-56" (2-3.5 pix)	40"-75" (2.5-4.7 pix)	75"-125" (4.7-7.8 pix)
10K (red) source
0.5 x HWHM	10.000	10.083	10.663	10.718	10.094
1 x HWHM	20.000	3.124	3.350	3.372	3.128
1.5 x HWHM	30.000	1.931	2.130	2.150	1.935
2 x HWHM	40.000	1.601	1.857	1.884	1.605
center 1st Airy minimum	50.000	1.470	1.833	1.875	1.476
1000K (blue) source
0.5 x HWHM	10.000	9.381	10.003	9.960	9.389
1 x HWHM	20.000	2.962	3.215	3.197	2.966
1.5 x HWHM	30.000	1.874	2.110	2.093	1.877
2 x HWHM	40.000	1.575	1.891	1.866	1.579
center 1st Airy minimum	50.000	1.437	1.886	1.848	1.442
An ASCII table with these (and others) is here.