Subsections

• 5.1.1 HRMA Model
• 5.1.2 Post-HRMA Blurring
• 5.1.3 PSF Cropping and Aperture Correction

5.1 Point Spread Function Images

The point spread function (PSF) of the Chandra-ACIS system is obviously a fundamental calibration product useful in many ways for the analysis of point sources. AE makes use of the PSF in several ways, described elsewhere. Since the Chandra-ACIS PSF varies strongly with position on the detector and with energy, AE represents the PSF for each observation of each source individually by storing images (file source.psf) of the monochromatic PSF for several energy values that span the ACIS response.

5.1.1 HRMA Model

Several models of the HRMA component of the system PSF are available, including ChaRT, SAOTrace, MARX, and the mkpsf tool in CIAO. Routine use of ChaRT is infeasible in AE because it lacks a machine interface. At the current time (January 2008) SAOTrace is in beta release and has limited operating system coverage.

AE currently³models the HRMA using the MARX ray-trace simulator. Simulations are run for each observation of each source at several monochromatic energies. MARX dithers the simulated source using the observation's aspect file, allowing accurate modeling of distortions caused by the PSF dithering over the boundaries of the ACIS CCDs. (MARX does not however model the bad pixel table.)

Note that application of the CXC thread ``Improving the Astrometry of your Data: Correct for a Known Processing Offset'' will induce an offset between your data and the MARX PSF. We do not understand the header magic involved here, but fortunately this thread in not applicable to data re-processed after 2004.

5.1.2 Post-HRMA Blurring

The PSF of a real source observed by ACIS differs strongly (on-axis) from the HRMA-alone PSF due to three blurring effects:

• ACIS pixels are large compared to the HRMA PSF, leading to significant quantization effects.
• The reported positions of ACIS events are reconstructed from an aspect solution that measures the dither motion; this reconstruction has small errors.
• By default, the CIAO pipeline (acis_process_events) adds uniform random noise to the ACIS event positions.

These post-HRMA blurring effects are very significant on-axis (Proposers' Observatory Guide v.10, §4.2.1, 4.4). As of January 2008, these effects are unfortunately not as well modeled and calibrated by the mission as one would like. The documentation for the mkpsf tool completely ignores post-HRMA blurring effects. The recommended PSF construction work flows involving ChaRT, SAOTrace, and MARX confound the three blurring effects into a single Gaussian noise model, even though the two largest effects (ACIS quantization, pipeline randomization) are inherently uniform and bounded phenomenon. As of January 2008, recommended parameters for this Gaussian blur model are given only for the default case where pipeline randomization is present, not for the common case where the observer has removed this effect. Most importantly, no calibration provenance for the stated Gaussian blur model parameters is quoted, i.e. no comparison between the PSFs produced by the recommended work flows and Chandra-ACIS data is available.

Prior to version 3.163, AE also modeled post-HRMA blurring with a Gaussian model, i.e. mkpsf images were convolved with a Gaussian kernel. However, AE currently models the three effects separately:

• ACIS quantization is modeled by convolving the HRMA PSF image with a ``box kernel'', sized to match the ACIS pixel. For convenience, this image and kernel are defined on the sky coordinate system, which is not perfect since the actual ACIS pixel grid is rotated from the sky system. I feel this is a better model for pixel quantization than a Gaussian, although I do not have the calibration resources to quantify this.

• Aspect reconstruction errors are modeled by convolving the HRMA+ACIS image with a 2-D Gaussian kernel with $\sigma_x = \sigma_y = 0.07$ arcseconds. That parameter value is taken from the Image Reconstruction Performance Report and from the CXC Helpdesk ticket #6819.

• If the observer has declared that the ACIS data have pipeline randomization applied, then the HRMA+ACIS+aspect image is convolved with another ``box kernel'', precisely modeling the uniform random deviates added to the event positions in the pipeline.

I do not have the luxury of devoting resources to perform a thorough comparison between the PSFs produced by this work flow and Chandra-ACIS observations of point sources, both with and without the pipeline randomization option. Nor can I devote resources to compare the MARX and mkpsf results. I have compared the MARX-generated PSFs from AE version 3.167 to a few point sources in our own data, and I'm satisfied that they are better than in previous versions of AE. Observers are encouraged to use the AE tool ae_radial_profile (§7.20) to compare PSFs to their own observations.

5.1.3 PSF Cropping and Aperture Correction

The original and primary use of multi-energy PSFs in AE is to correct the mission's spectral response calibration for the effects of the finite aperture used to extract the source. As of January 2008 neither the CIAO tools nor threads address the aperture correction issue.

As far as I can tell, both the HRMA and ACIS effective area calibrations implicitly assume an infinitely large detector and extraction aperture⁴. I believe the HRMA simulations used to derive QE values count all rays exiting the HRMA, regardless of how far out in the wings of the source they fall. The ACIS QE was derived for flat illumination where there is no concept of an aperture.

AE attempts to imperfectly correct the ARF (§5.9) to account for the source events presumed to fall outside the extraction aperture, by measuring the fraction enclosed by that aperture on each of the mono-chromatic PSFs available. When the PSFs are constructed, AE tries to estimate how much total power the PSF contains, integrated to infinity⁵, and then records how much of that power has been cropped away by the finite size of the PSF images themselves. MARX simulations used to generate PSFs are run with the ACIS readout streak disabled, since that ``out of time'' effect is handled by the CXC via a reduction in the source's exposure time (via FITS keyword DTCOR).

One imperfection of our aperture correction arises from the fact that PSFs generated via MARX contain distortions caused by the dithered edges of the ACIS CCDs. For some uses of the PSF this is a good thing--MARX very nicely simulates the data one would observe on the real ACIS. For aperture correction however, the proper PSF to use would probably be one built assuming an infinite detector, since that is the assumption used in the HRMA and ACIS calibrations. We do not however have such a PSF available in AE. By using a PSF which exhibits chip edges, we should be under-estimating the PSF fraction of sources dithering off the detector, thereby over-correcting the ARF. The energy dependence of this over-correction has not been studied. The moral of this story is that calibration is difficult where ever the exposure map is varying over the scale of the PSF, and one should take a skeptical view of all properties derived for sources there.

The energy-dependence of the aperture correction--the correction to the shape of the ARF--can be significant. For example, a source far off-axis ($theta=8.7$ arcmin) extracted with a default aperture ($\sim$15 sky pixel radius) should have these corrections applied to its ARF:

Energy (keV)	PSF Fraction
0.277	0.91
1.496	0.90
4.510	0.85
6.400	0.77
8.600	0.63

A source nearly on-axis ($theta=0.4$ arcmin) extracted with a default aperture ($\sim$1.6 sky pixel radius) should have these corrections applied to its ARF:

Energy (keV)	PSF Fraction
0.277	0.96
1.496	0.90
4.510	0.80
6.400	0.81
8.600	0.80