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4.3 How Wide You Can Really Open the Slit: Anamorphic Demagnification

  Most of us are aware that the demagnification of a spectrograph (conversion from mm at the focal plane to mm at the detector) is dependent upon the relative f ratios of the camera and collimator. However, when there are significant collimator-to-camera angles there can be additional demagnification in the spectral direction due to the tilt of the grating. (This is nicely reviewed by François Schweizer in 1979 PASP 91, 149). The effect of this works in the astronomer's favor; at large grating tilts the slit can be opened wider (letting in more light) without degrading the resolution. Of course, at very high inclinations a point is reached where the grating becomes overfilled and the light above or below the grating is lost. A little consideration of the geometry involved will suggest that for a given wavelength, the higher the dispersion the more tilted the grating has to be.

The ``anamorphic demagnification" r can be computed from:

where t is the grating angle (relative to zero order) and is the camera-collimator angle. For the RC Spectrograph, ; for GoldCam, .

We give in Fig. 10 and Fig. 11 the anamorphic demagnification as a function of grating tilt. For the RC Spectrograph, we use ``encoder units" to measure the grating tilt (zero-order occurs at 6450 and there are 100 encoder units per degree); for GoldCam the units are in degrees with zeroth order being at 25.93. In practice, simply look up the encoder setting using the tables in the Appendix of this manual (Sec. A.1) and then use Fig. 10-Fig. 11 to see what additional fraction you can open the slit without degrading the resolution.

Remember that CryoCam, being a straight-through system, has no anamorphic magnification.

 
Figure 10:   The anamorphic demagnification as a function of grating tilt (in encoder units) for the RC Spectrograph. To obtain the encoder setting corresponding to a particular wavelength and grating, see the table in the Appendix.

 
Figure 11:   The anamorphic demagnification as a function of grating tilt for GoldCam; to obtain the tilt corresponding to a particular wavelength and grating, see the table in the Appendix.