# Simulating Aspect with marx¶

Motion or change, and identity or rest, are the first and second secrets of nature.

– Ralph Waldo Emerson

## Introduction¶

In the course of a normal science observation, the Chandra line-of-sight pointing position on the sky moves. This “dither” motion serves several purposes including sub-sampling of the point spread function as well as averaging over uncertainties in quantum efficiency from detector element to element. In the case of the HRC MCPs, it also evenly distributes the dosage received over many microchannel pores extending the life of the detector. Typically this dither motion will follow a Lissajous pattern over an area up to 20 arcsec in size and is referred to as Normal Point Mode (NPM) (http://cxc.harvard.edu/proposer/POG/html/chap5.html). The Chandra Aspect camera system provides pointing information over the course of this dither motion and, when processed through the CXCDS Aspect pipeline, allows the effects of dither to be removed from the final image. marx provides the capability to include the effects of dither motion in Chandra simulations.

The net result of dither motion is that the image of a given source will move in the Chandra focal plane as a function of time. When all photons from the observation are combined, the resulting image will be blurred in the Focal Plane (FP) coordinate systems. These system corresponds to the CHIP, DET, or TDET columns in the FITS events file. The CXCDS Level 1 pipeline corrects for this blurring and produces “aspect–corrected” Sky pixel coordinates. These coordinates appear in the FITS events file as the X and Y columns. marx computes a simple approximation to the Level 1 pipeline aspect correction. For a more detailed discussion of these coordinate systems, the user is referred to http://cxc.harvard.edu/contrib/jcm/ncoords.ps.

If dither is selected for the simulation, images created from the CHIP, DET, or TDET pixel positions will reflect the motion of the Chandra line-of-sight. marx also emulates the aspect pipeline and calculates aspect-corrected Sky X and Y values. These sky pixel values are written to the standard output directory specified by the OutputDir parameter in the native binary format files sky_ra.dat and sky_dec.dat. If the marx2fits post-processing tool is used, the aspected-corrected Sky pixel values are written to the FITS events file in the X and Y columns. For simulations with no dither, the FP and Sky coordinate positions are equivalent.

For actual Chandra flight data, residual errors in the reconstruction are expected to add a “blurring” to detected photon positions which is essentially Gaussian. This is simulated by marx through the use of the AspectBlur parameter, which has a default value of 0.07 arcsec. The detector pixelization and randomization blurs are simulated by marx2fits, where the user may specify several types of pixel randomization using its --pixadj option.

marx provides two options for simulating dither motion. The choice of dither model is determined by the value of the DitherModel parameter. The two models are discussed individually below. By default Dithermodel=INTERNAL and dither motion is included. The following parameter in marx.par controls which type of dither model is used:

DitherModel

(default: INTERNAL) Dither Model [NONE, INTERNAL, FILE]

AspectBlur

(default: 0.07) Uncertainty of the Aspect reconstruction (sigma - arcsec). Number taken from http://cxc.harvard.edu/cal/ASPECT/img_recon/report.html (version: 06/29/11).

Simulation showing the effects of the internal dither model in marx. The panel on the left shows an image of a typical marx point source simulation with no dither included in Focal Plane (FP) coordinates. The right panel shows the same simulation with marx INTERNAL dither mode turned on. Note that in Sky X and Y coordinates the images would both resemble point sources due to the aspect correction. The color scales have been adjusted and are not identical in the two panels.

## marx Internal Dither Model¶

marx provides an emulation of the NPM Lissajous dither pattern. This internal model is selected by setting DitherModel=INTERNAL. The form of the dither pattern is determined by the amplitude, phase and period for both the RA and DEC axes. marx also includes the ability to “dither” the roll angle of the spacecraft during the simulation. In general, the roll angle of Chandra during a science observation will not vary; however, there may prove to be some small variations and this capability allows their effects to be studied.

When using the internal model, the deviations applied to the position of the line–of–sight over the course of the simulation are calculated using the following expressions:

$\Delta Pos = A ~\sin \biggl(\frac{2 \pi t}{P} + Phase \biggr)$
$\theta = \theta_0 + A ~\sin \biggl(\frac{2 \pi t}{P} + Phase \biggr)$

The first equation corresponds the deviations along the RA and DEC axes, while the second gives the expression for the roll angle deviation. In both equations, $$A$$ and $$P$$ correspond to the amplitude and period of the variations and $$t$$ is time. $$\theta_0$$ represents the nominal roll angle of the simulation.

Each of these parameters is controlled by an entry in the marx.par parameter file. An example of the effects of dither on a simulated ACIS-I point source observation is shown in Example of a dither file. The images are displayed in Focal Plane (FP) coordinates.

The marxasp tool will create an ASPSOL file containing the aspect motion for a simulation which used the marx internal dither model. This ASPSOL file can be used in conjunction with normal CIAO tool asphist to produce an aspect histogram file. See marxasp for more details.

Set DitherModel=INTERNAL and use the parameters described in Dither/Aspect Parameters in marx.par to control the internal dither model.

The variation in the declination of the simulated Chandra aimpoint with time as encoded in an ASPSOL file produced using marxasp.

## Aspect File Mode¶

In addition to its internal dither calculation mode, marx can generate simulations using aspect solution files created by the CXCDS aspect pipeline. For each observation, the CXCDS produces an aspect solution giving the Chandra pointing as a function of time. These files are FITS binary tables of the format described in in the table below (CXC ASPSOL ICD, Rev 2.4). The ASPSOL (or PCAD) files for a given Chandra observation can be retrieved from the CXC Archive. Set DitherModel=FILE and the file to be used is determined with the DitherFile parameter:

DitherFile

(default: obsid_105/data/asol1.fits) ASPSOL File

If the input file is not a valid ASPSOL file, marx will exit with an error message. The time interval covered by the ASPSOL file must equal or exceed the requested exposure time of the simulation. If the end of the ASPSOL file is reached before the requested exposure time, marx will truncate the simulation at that point.

For reference, the following table lists the columns in an ASPSOL file:

Column Type Comment Units
time double Time s
ra double RA of MNC frame (x-axis) deg
dec double DEC of MNC frame (x-axis) deg
roll double ROLL of MNC frame deg
ra_err float Uncertainty in RA deg
dec_err float Uncertainty in DEC deg
roll_err float Uncertainty in ROLL deg
dy float dY of STF frame - FC frame mm
dz float dZ of STF frame - FC frame mm
dtheta float dTHETA of STF frame - FC frame deg
dy_err float Uncertainty in dY mm
dz_err float Uncertainty in dZ mm
dtheta_err float Uncertainty in dTHETA deg
q_att double S/C attitude quaternion
roll_bias float Roll bias rate deg/s
pitch_bias float Pitch bias rate deg/s
yaw_bias float Yaw bias rate deg/s
roll_bias_err float Roll bias rate error deg/s
pitch_bias_err float Pitch bias rate error deg/s
yaw_bias_err float Yaw bias rate error deg/s