In the past LSF_PARMS products were made based on an earlier version of MARX simulated datasets. Each MARX dataset contained a simulation of mono-energetic point-source beam; and a 2-D line profile per grating (HEG, MEG, or LEG) per order (+1 or -1, etc) was extracted and used to analyze its projected 1-D profile in both dispersion and cross-dispersion directions. The profile was fitted with single Gaussian and Lorentzian functions, though a linear combination of these functions was not quite adequate to describe the line profile at any wavelength.

The fundamental process of LSF_PARMS production is still valid. So we have repeated the process with a new set of MARX (version 4.0.3) data. A major technical change we have made here is that, instead of using single Gaussian and Lorentzian functions (total of 2 components), we have decided to describe a line profile with two Gaussian and two Lorentzian functions (so total of 4 components). Of four components, one Gaussian component dictates the goodness of fitting (I call it as "the principal Gaussian component" in figures). Other components are essential, though their contributions are only important to its waist and wing part of the line profile. Figure 1a and b give examples of the fitting results for HEG and MEG (with ACIS-S) at E = 1.5keV. These examples are fairly representative of our results. Typically about 20+ mono-energetic energy beams are simulated (from 0.8 -- 12keV for HEG; from 0.4 -- 12keV for MEG; for LEG, TBD). That's done per single extraction width. We now choose 5 different extraction widths (previously 3 widths were used) per grating. So the total of 20+ times 5 times 2 = 200+ fitting procedures are performed to make LSF_PARMS for HEG and MEG.

Figure 1a: Example of 2 Gaussians + 2 Lorentzians Fitting (HEG). The dotted blue line is the principal Gaussian component that matters most; the dotted red line is the secondary Gaussian component to fit the wing+core part; and the dotted light-blue and magenta lines are two Lorentzian components that fit the extended wing. The light-green curve gives the sum of all four components. Here MARX is not designed to address grating scatter, so trying to fit the wing below the 1e-3 normalization level is really moot.

Figure 1b: Example of 2 Gaussians + 2 Lorentzians Fitting (MEG). See the caption for Figure 1a for details.

Oh by the way, the fitting is not always flawless. Sometimes 4 components ain't just enough. Take a look at this example from MEG +1 at E=0.450keV.

Figure 1c: Example of 2 Gaussians + 2 Lorentzians Fitting (MEG) at E=0.450keV.

In this example, the fitting result is rather poor, as four components alone cannot describe its wing distribution very well.

So this document is being written in order to keep readers in mind on what works with the new LSF_PARMS product and what limitation or caveats exist for using the products.

For those who are interested in line width of the principal Gaussian component, here are the plots for both HEG and MEG. The estimated width values are consistently below the acclaimed resolutions listed in POG (0.012 and 0.023AA for HEG and MEG, respectively). This is because the principal Gaussian component alone is inadequate for describing the core of a line profile.

Figure 2a: FWHM Gaussian line width for the principal Gaussian component (HEG). Note that this is not a representative of line resolution for the instrument.

Figure 2b: FWHM Gaussian line width for the principal Gaussian component (MEG). Note that this is not a representative of line resolution for the instrument.

This page was last updated Aug 13, 2002 by Bish K. Ishibashi. Accessibility To comment on it or the material presented here, send email to bish@space.mit.edu.