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.

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".