Subassembly predictions for the Gratings

Getting the data files

Using detailed bar shapes derrived from the subassembly data, the grating average efficiency into different orders on a shell-by-shell basis was calculated using John Davis's s/w. The 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; for HETG gratings it includes the polyimide but not the effect of gaps between the frames.)

The results are available at MIT and XRCF in the following directories:

location:

  At MIT:  /nfs/spectra/d6/effic_tables/

  At XRCF: /data/asc3/MIT_HETG/eff0c_tables/

files:
        HETG (1.5 Mb each):
                  HETG_shell1_multi.dat
                  HETG_shell3_multi.dat
                  HETG_shell4_multi.dat
                  HETG_shell6_multi.dat

        LETG (3.3 Mb each):
                  LETG_shell1_multi.dat
                  LETG_shell3_multi.dat
                  LETG_shell4_multi.dat
                  LETG_shell6_multi.dat

The .dat 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.

The calculations were done using John Davis's eff s/w using the .sl files in these directories (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.

Using the data files

These efficiencies are the average for a given shell, energy, and order. In order to compare these to the measured XRCF efficiencies two additional effects need to be included: i) mirror-shell weighting and ii) facet-level vignetting.

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 a 
               "baseline" set of tables for these values, at aperture
               diameters of 200, 500, 1000, 10000 um for example.)

 Eff_Gn(E,m)   is the membrane efficiency (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 LETG
               shells a value of 0.7 to 0.75 is reasonable, for HETG shells
               a value of 0.93 is reasonable.

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 [  V_Gn * A_n(E,ap) * Eff_Gn(E,m)  ]


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

        where the sums are over appropriate n in the case of HEG or MEG and
        the aperture size is assumed to be much larger than grating-induced
        PSF effects.

The efficiencies generally mentioned for flight performance are for large values of "ap".