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In this appendix the properties of the ISIS gratings are presented in graphical form; the grating setting, slit to detector reduction factor, vignetting factor, and reciprocal dispersion (Å/mm) are presented as a function of wavelength for all red and blue gratings. For completeness graphs for both blaze-to-collimator and blaze-to-camera are presented, although only use of the former is recommended, and graphs for grating H2400B in the red arm are also presented, although this is not a particularly efficient combination. The explanation and the program used to generate the plots are due to C.R. Jenkins.
The grating equation is:
for a first-order spectrum. The camera-collimator angle in ISIS, , is nominally 40 degrees, although the exact value will be slightly different for each channel.
(with appropriate sign conventions for and ). Solving these two equations gives:
where the positive sign corresponds to the normal condition for ISIS, namely blaze to collimator. The grating setting for each channel is then given by multiplying (in degrees) by 100 and adding an offset (which is the autocollimation angle for each grating mount). These offsets are 30800 for the blue channel and 35500 for the red. In solving for the grating setting, one has to check for the cases where the angle of incidence exceeds 90 degrees, or where the discriminant becomes imaginary (corresponding to the wavelength where constructive interference cannot be achieved).
The reduction factor follows simply; it is:
where is 1650 mm and is 500 mm.
The gratings in ISIS are 200 x 150 mm, and the cameras have sufficient aperture to accommodate the fully dilated 200 mm beam. Most of the vignetting (excluding refinements of matching central obstructions between camera and telescope pupil) occurs simply because light misses the grating at high angles of incidence. The fractional loss is:
where is given by:
This internal vignetting only exceeds 1% for the 1200 and 2400 gratings.
The dispersion is given by: