Code for extracting FITS spectra from a simulation of an Arcus X-ray spectrum.

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Arcus is a proposed X-ray grating spectrometer for the ISS. This project will be python-based (more specifically largely astropy based) and will read the output of the simulator SIXTE (http://www.sternwarte.uni-erlangen.de/research/sixte/) when run for arcus and extract pha spectra.

This is outlined by David Huenemoerder:

1. Assume that we have a "Level 1" event file, which minimally contains the columns:

TIME, CCD_ID, CHIPX, CHIPY, ENERGY, DETX, DETY, X, Y,

DETX and DETY will be some focal plane coordinate system which tiles the CCDs (useful for looking at the whole field). X,Y will be some aspect-corrected coordinate system (for chandra this is a sky pixel, but that is not relevant here, except for zeroth order). [can we ignore aspect correction? that is, no dither, and we always have the same aim point (simulations)].

2. Define a region which contains the zeroth order, and determine it's centroid (in dither-corrected coordinates).

3. Define spatial regions (in X, Y) which will contain the dispersed spectrum for a given module.

4. For each event in the spectral region, transform coordinates (using the off-plane dispersion relation, zeroth order location, geometry, and aspect solution) to dispersion coordinates (essentially angles along dispersion and across). Assign an m*lambda (order times wavelength) to each event.

[We could probably do this in a fairly ad hoc way, by transforming the dispersion arc to a linear coordinate system, and not actually trying to locate the zeroth order or dispersed spectrum. So step 2 is moot, and step 3 is pre-determined.]

5. Use the CCD ENERGY to compute a real-valued order for each event. That is, we know (m*lambda) ~ (m/E).

We have an approximate E from the CCD ENERGY, so

m' = (m/E) * ENERGY.

Add this real-valued estimate of the order to the event file, call it tg_m_real. (we eventually would like tg_m, the integer order).

6. Before we bin the events, we now need to filter appropriately. We need to define a wavelength grid (low,high wavelength boundaries, per each order), a cross-dispersion width (which needn't be constant with wavelength, but for convenience a rectangle might be good enough), and order boundaries. The order filter should come from the CCD response and be chosen, for instance, to give some large fraction of the response, say 95%. So tg_m_real limits will in general be a function of energy. (For Chandra gratings, we tabulate in the CALDB the E_low( E ) and E_high( E ) and the enclosed fraction; here a rectangle might also be good enough.)

Given these regions we can filter and bin into a standard PHA-type spectrum file.

7. In order to analyze the data, we need the responses, and these need to correspond to the filter and include detector geometry and aspect information. For chandra gratings, the effective area is for a full spatial extraction aperture, but includes order-selection efficiency factor from the CCD response, and the detector geometry (chip gaps) and aspect solution (dither) for the efficiency vs wavelength.

The grating response matrix (RMF) includes the aperture-selection information. This is because in general the LSF and cross-dispersion efficiency do not factor --- if you change your spatial extraction width, you change the efficiency AND the profile. Hence, they are strongly coupled, and we interpolate in tables stored in the CALDB. The aperture efficiency factor is thus included in the RMF.

From Randy McEntaffer, the off-plane grating and LSF equations are: The current LSF based on measured SPO data is a double Gaussian, f:

ax = exp(-0.5*((xdata-coeffs[2])/coeffs[4])^2) bx = exp(-0.5*((xdata-coeffs[3])/coeffs[5])^2)

f = coeffs[0]*ax+coeffs[1]*bx+coeffs[6]

with coeffs=[1.5594215e+008, 20923465., 178.65726, 179.69612, 2.4961202, 15.360183, 1000003.4]

with 24 micron pixels at 20 m this produces a central Gaussian with 1.45" FWHM and a broader Gaussian at 8.95" FWHM. The broad Gaussian contains 45% of the power.

I've only recently been successful in forcing my raytrace to produce such a PSF in the telescope so I don't have an aberration function for the gratings yet. However, the dispersion equation is:

x(n,lambda) = nlambda2.87 (mm/ang)

So this gives you the x distance (in mm) from 0 order that you should expect a given wavelength (in angstroms) and order (n). To be clear, x is the linear dispersion distance not a distance along the arc.

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With Arcus in practice the zero-order centroid will rarely be used directly for analyis as outlined above, since position knowledge will need to be determed on the time scale of readouts (0.1 s) due to ISS motions. The centroid of the fully accumulated (i.e., many ks of exposure) will be used as a check but for the most part the metrology system + star trackers should be giving us steps 2 and 3 above so we will be assuming that here. Later we would like to add in the uncertainties in the positions of the zero-order and disperse spectrum.

The pyfits / astropy.io.fits package can read in the events list in a dictionary object. The x,y columns will initially be simply in the dispersion and cross-dispersion directions.