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The most advanced method for characterizing the properties of the Chandra PSF is by simulating the PSF of the optics from the HRMA via ray tracing techniques in order to obtain a good model of the Chandra PSF for a given observation.

There are two primary means to simulate the HRMA PSF: SAOTrace (formerly SAOSAC) and the Model of AXAF Response to X-rays (MARX).

• SAOTrace is a flexible system used to simulate the as-built X-ray optics with on-ground calibration by ray tracing; it is directly derived from the engineering tools used to design Chandra. While users can install SAOTrace on a local system for the greatest control and customization, the primary means most users will use SAOTrace is through the web-based interface Chandra Ray Tracer (ChaRT). ChaRT is based on the most detailed physical model of the mirror geometry. This level of detail is especially important for off-axis sources or to study the wings of the PSF out to several arcseconds; and the latest version can incorporate an aspect solution which is necessary to treat sub-pixel effects, which are important for the shape of the PSF within ~1 arcsec.

• MARX is a suite of executables that is fairly easy to compile, allowing users to quickly run a large number of ray tracing simulations on a local system; MARX-generated rays can also be used to perform sub-pixel analysis. While the MARX model uses a slightly simplified (and faster) description of the HRMA, this is often sufficient for most simulations; if more detail is required, MARX can be used to project simulated HRMA rays produced by SAOTrace on to a detector-plane, accounting for detector effects. MARX was created as a PSF simulator, and not an observation simulator; therefore, not all CIAO tools are currently guaranteed to work on MARX simulated events files.

  The most recent detailed comparison of the PSFs produced by MARX v4.3 and SAOTrace v1 can be found in the Appendix of Primini et al. (2011), Statistical Characterization of the Chandra Source Catalog .

If a high fidelity model of the PSF is not required by the scientific goal of the analysis, a third method exists:

• The CIAO arfcorr tool can be used to generate an image of a simulated, circularly symmetric, mono-chromatic PSF. The PSF is derived to have have the correct encircled counts fraction at each radius, using the CalDB enclosed counts fraction for a given input energy. A detailed description of the algorithm used to generate the approximate PSF image can be found in the tool's ahelp file.

The table below shows a quick comparison between the different modeling tools.

	SAOTrace	ChaRT	MARX	arfcorr
user interface	command-line	web interface to SAOTrace	command-line	command-line
how to obtain?	download → compile → install locally	web-based, no installation required	download → compile → install locally or using the conda package manager.	CIAO tool
how many sources?	multiple sources	individual point sources	multiple sources	individual point sources
current limitations	does not run on the latest Linux and Mac platforms	limited number of available parameters (but sufficient for typical use cases)	does not include all of the fine HRMA details	only mono-chromatic sources supported
pros	flexible and powerful; definitive HRMA model	easy to use	high fidelity, and yet easy to use; portable; includes models for HRMA, gratings, and detectors	simple, quick tool
cons	complex installation and usage; only includes the HRMA model	need to wait for output	not as high-fidelity as SAOTrace for HRMA	circular approximation of the PSF

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From PSF Model to an Events File

The HRMA ray tracing simulations produce files that must be projected to a detector-plane and include blurring effects in order to visualize the Chandra PSF. MARX-generated rays are generally projected in tandem with the ray tracing run. In the case of SAOTrace/ChaRT results may be projected using MARX on to an instrument-specific detector-plane (including gratings arms), or to a semi-infinite detector-plane with the psf_project_ray CIAO tool.

The psf_project_ray tool produces an events file as output, while the marx2fits routine should be used after running a MARX simulation to obtain an events file.

Examples of using these packages and tools to simulate and project a PSF, as well as its direct analysis use, may be found in the PSF Simulations Analysis threads.

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Below is a summary of the Chandra PSF modeling tools and related threads.

Tool/Script	Description	Related Threads
ChaRT v2 & SAOTrace	Produces the best non-sub-pixel PSF for a point source at any off-axis angle and for any mono-chromatic energy or spectral energy distribution using the best calibration data available.	Preparing to Run ChaRT Using MARX to Create an Event File Accounting for PSF Effects in 2D Image Fitting
MARX	A suite of tools to run a large number of ray tracing simulations on a local system. May be obtained and installed using conda.	Using MARX to Simulate an Existing Observation Using MARX to Simulate a Planned Observation
arfcorr	Tool used to determine the approximate PSF fraction enclosed by a region and can apply a correction to an ARF. Alternate mode generates an image of a mono-chromatic, circular PSF for a given sky position derived from the integrated enclosed counts fraction. arfcorr-Generated Mono-Chromatic Circularly Symmetric PSF [Version: full-size] arfcorr-Generated Mono-Chromatic Circularly Symmetric PSF An on-axis point source (left) and its corresponding circularly symmetric, 2.3 keV PSF generated by arfcorr.	Calculate source count rates and fluxes Extract Spectrum and Response Files for a Pointlike Source Extract Spectrum and Response Files for Multiple Sources
psf_project_ray	Used for visualization; takes the rays generated by ChaRT/SAOTrace and projects them on to a semi-infinite detector plane.