Ideally, in measuring effective area or grating efficiency, a monochromatic source is used so that detected counts represent counts at the energy of interest (assuming background counts are removed). In practice the source of X-rays is not monochromatic and so "measured counts" consists of counts due to many energies. Likewise when using a detector with a finite aperture to measure a focussed beam, the measured counts reflect only a portion of the full spatial distribution of counts (i.e., an encircled energy correction is needed.)
By using a spectrum that has lines, detectors with some energy resolution, and analysis schemes with some finesse, it is possible to create an experimental setup with the property that the observed counts from the analysis are to first order most sensitive to the effective area or efficiency over a small range of energies. This range is given by the smaller of the width of the source line or (for a continuum source,say) the energy resolution of the detector.
If the source, optical system, detector, and analysis method can be modeled then it is possible to calculate, through simulation, a correction factor applicable to the measured data:
all counts due to "the feature" correction factor = -------------------------------------- observed counts output from analysisNote that the analysis method is itself part of the system. Of course there is a chicken-and-egg problem here because the calculated correction factor depends on the very unknowns we're trying to measure (e.g., the energy dependent effective area and efficiency) but this just lets us use wonderful words like "iteration" and "self-consistent" and we keep on analyzing!
Why do I say "the feature" instead of "line"? Because some lines are broad, some lines have very close satellite lines and because the continuum under a line is at the same energy as the line, it can be tricky to specify, operationally, what "the line" is. A feature can be more clearly specified:
"the feature" = all photons with an energy within 1% of the nominal line energy, i.e., in IDL: where( ABS(energies-Eline) LT 0.01*Eline )This definition has the property that it is spectrally narrow (and for many sources the feature may come from an effectively smaller range of energies) and it is unambiguous: given an incident source spectral model the "feature" photons can be counted without the complexities of continuum subtraction, satellite lines, broad lines, etc.
MARX simulations were carried out for most of the measurements used for zero and and plus/minus first-order eae analysis. Because of the HXDS stage tilt there may be a slight plus/minus order difference in the simultaions.
The simulation includes a realistic source spectrum, finite source distance, XRCF grating geometry, and, currently, a "MARX 2.21" HRMA model. The source models are empirical and based on HSI-Grating Source Spectra. The non-flight detectors have been modelled using a flat focal-plane (the HRC-I with Ideal QE offset to the correct focal-plane location) and post-MARX processed to include the detector QE. The Y and Z locations (w.r.t. detector center) and unblurred energies of photons detected in a 12 mm by 12 mm region around the detector center are saved for analysis.
More specific details are available in the software section below under eae_sim.pro and xrcf_sim.pro.
After a measurement is simulated, a useful summary .gif is made containing three plots. These plots are available by clicking on the aperture field in the eae_wfracs.html listing or, for some example plots, by clicking on the links in the Table below.
number of all feature counts in the order feature-fraction = ------------------------------------------- number of ROI countsand it explicitly includes any "encircled energy" correction. (Though the correction is referenced to the Order region diameter.)
|Table of Sn-La,Snx2 ROI Feature-fraction Examples|
|* EE correction|
|NONE||D-IXF-3D-22.017/970124/110081/i0||0.4238 <-- click!||0.4179||1.014||13.9 %|
|MEG, 0||D-HXF-3D-22.019/970124/110084/i1||0.4130 <-- click!||0.4065||1.016||14.6 %|
|LEG, 1||D-LXF-3D-22.018a/970124/110083/i0||0.4424 <-- click!||0.4250||1.041||13.6 %|
|MEG, 1||D-HXF-3D-22.019/970124/110084/i0||0.6137 <-- click!||0.6017||1.020||28.1 %|
|HEG, 1||D-HXF-3D-22.020/970124/110085/i0||0.9109 <-- click!||0.9037||1.008||1.6 %|
eaeIndex - the zero-based index (line number) of the eae file fracNom - the feature fraction at nominal aperture size/location fracDplus - the feature fraction for diameter = diameter + 0.025 mm fracDminus - the feature fraction for diameter = diameter - 0.025 mm fracYplus - the feature fraction for Y_center = Y_center + 0.050 mm fracYminus - the feature fraction for Y_center = Y_center - 0.050 mm fracZplus - the feature fraction for Y_center = Y_center + 0.050 mm fracZminus - the feature fraction for Y_center = Y_center - 0.050 mm Nfeature - the number of events in the full feature ObsFeatFrac - the observed feature fraction is the ratio: number of feature events in the aperture ---------------------------------------- number of ROI events (EE correction)- The EE correction is not explicitly given in the file but can be calculated as: EE correction = fracNom / ObsFeatFracThe additional columns beyond fracNom are present to allow some estimates of an error for the value of fracNom.
The value of the feature-fraction depends on the full simulation used to generate it and hence on all aspects of modeling the measurement. The procedure feat_frac_err.pro calculates a "df/f" fractional error from the feature_fractions.rdb file and other internal parameters - see the code for specifics. The error terms currently included are described briefly here:
This page is http://space.mit.edu/HETG/eae/feat_frac.html
Return to http://space.mit.edu/HETG/eae/eae.html