Subassembly Efficiency Analysis

Overview

The steps in getting the sub-assembly efficiency predictions are summarized here and described in more detail below:

• X-GEF Test and Analysis at MIT
  • Acquire X-GEF data on facet
  • Analyze X-GEF data to get count rates in line-orders
  • Transfer known reference grating efficiency to facet being tested by count rate ratios.
  • Fit facet line-order efficiencies with John Davis multi-vertex model
  • Save model parameters
• Assemble model parameters from all regions of all gratings on each shell (HETG_shellX_multi.rdb files)
• Run John Davis's multi.sl slang procedure on the 'multi files to get the shell average "membrane" efficiency data.
• The current efficiency files used optical constants defined by the input file optical-constants.dat for HETG and optical-constants.dat for LETG.
• Add rdb headers to these membrane 'effic files for further processing (locally in /spectra/d6/effic_tables)
• Run the IDL procedure cip_weights_and_errors.pro to calculate and write the CIP efficiency files (made available on web as .rdb.gz files)

Similar steps are carried out for the LETG, using instead the procedure letg_cip_etc.pro.

X-GEF Test and Analysis

For general operating principles of the X-GEF see the X-GEF section of the Sub-assembly Measurements description. The analysis of the X-GEF data has been carried out at MIT using IDL code. The X-GEF analysis proceeds through a variety of steps as indicated by the key-word-gated sections of the top level procedure: xgef_analysis.pro.

• X-GEF_log.txt : Summary log of X-GEF tests covering date codes 950610 through 961206.

The Facet-by-Facet Model Parameters

The X-GEF model parameters are collected into shell-by-shell data files:

Shell	multi-grating File
HETG 1	HETG_shell1_multi.rdb
HETG 3	HETG_shell3_multi.rdb
HETG 4	HETG_shell4_multi.rdb
HETG 6	HETG_shell6_multi.rdb

[For LETG the bar FWHM, height, and slope have been determined by NIR spectrophotometer method. These values were used by leg_to_multi.pro to create similar rdb files for the LETG gratings:

Shell	Period-Width-height-slope file	multi-grating File
LETG 1	LETG_shell1_whs.txt	LETG_shell1_multi.rdb
LETG 3	LETG_shell3_whs.txt	LETG_shell1_multi.rdb
LETG 4	LETG_shell4_whs.txt	LETG_shell1_multi.rdb
LETG 6	LETG_shell6_whs.txt	LETG_shell1_multi.rdb

]

Calculating the Average Efficiencies

Using the 'multi.rdb files of detailed bar shape parameters, the grating average efficiency into different orders on a shell-by-shell basis is calculated using John Davis's multi.sl routine. At MIT, the calculations were done using John Davis's eff s/w using the .sl files in /spectra/d6/effic_tables (see the file do_em_all). The input to these calculations is the bar parameters for each facet which are given in the *_multi.txt files (the 'multi.rdb files without the header information).

The resulting efficiencies are the "membrane efficiency" - that is the efficiency of the grating membrane itself (i.e., for LETG this includes the support structure but not the effect of the circular facet shape(see below, however); for HETG gratings it includes the polyimide but not the effect of gaps between the frames.)

These membrane efficiency files are processed by cip_weights_and_errors.pro to produce the final products: shell efficiency files which include the vignetting terms, and HEG/MEG/HETG mirror weighted efficiency files. Error files are created for these as well.

For the LETG, the "membrane" efficiency files include one factor of 0.809, in order to produce files with the efficiency into the central "0,0" order only, an additional factor of 0.81 is included along with the facet vignetting terms (which shell average to 0.8346) due to the circular facets; these calculations are performed by letg_cip_etc.pro.

The results files ('effic.rdb) are available at MIT (/nfs/spectra/d6/CIP/) and SAO (TBD).

Grating Shell	Efficiency File
HETG 1	HETG_shell1_effic.rdb
HETG 3	HETG_shell3_effic.rdb
HETG 4	HETG_shell4_effic.rdb
HETG 6	HETG_shell6_effic.rdb
LETG 1	LETG_shell1_effic.rdb
LETG 3	LETG_shell3_effic.rdb
LETG 4	LETG_shell4_effic.rdb
LETG 6	LETG_shell6_effic.rdb

The 'effic.rdb files have a row per energy. The first column of each row is the energy in keV and subsequent columns are the predicted diffraction efficiencies in order order, e.g., -11, -10, ... , -1, 0, +1, ..., +10, +11. The HETG shells are calculated for orders -11 to +11 and the LETG shells are calculated for orders -25 to +25. Each HETG file is 1.5 Mb and the LETG files are 3.3 Mb each.

Mirror-area-weighted efficiencies

The efficiencies tabulated above are the average for a given shell, energy, and order. In order to predict flight effective areas or to compare these to the measured XRCF efficiencies it is useful to apply mirror-shell weighting.

Define the following:

A_n(E,ap)

is the HRMA effective area for shell n at energy E into an aperture of diameter ap. (We should try to identify an XRCF "baseline" set of tables for these values, at aperture diameters of 200, 500, 1000, 10000 um for example.)

V_Gn Eff_Gn(E,m)

This product is the content of the shell efficiency tables above, where the terms are defined below:

Eff_Gn(E,m)

is the membrane efficiency (NOT the tables above) at energy E and diffraction order m. G is either "H" or "L", indicating HETG or LETG grating and n is the shell.

V_Gn

is the vignetting factor for shell n of grating G; for HETG the vignetting values are close to 0.935.

Then the expected effective area and efficiency for the grating spectrometer at energy "E", order "m", and into an aperture "ap" are given by:

  Grating                       
    effective area (E,m,ap)  =  sum over n [  A_n(E,ap) * V_Gn * Eff_Gn(E,m)  ]


  Grating                       sum over n [  A_n(E,ap) * V_Gn * Eff_Gn(E,m)  ]
        efficiency (E,m,ap)  =  ----------------------------------------------
                                          sum over n [  A_n(E,ap)  ]