Gratings Littrow configuration

Apart from using the grating in zero order so that it works like a mirror, maintaining a (compact) round beam at the camera (A = 1) requires that the spectrograph adopt the Littrow configuration for which Tf = 0 and the incident and diffracted rays are parallel. From equations 6 and 9, the resolving power at blaze in the Littrow configuration is... 

Figure 4. The efficiency of gratings used in the Gemini Multiple Object Spectrograph (CMOS) from measurements by the vendor in Littrow configuration.

Figure 11. Left Littrow configuration for an echelle grating. Right example of the layout of orders (labelled by m) on the detector showing the wavelength ranges covered.

Some of the relevant facts about the angular dispersion of a grating may be derived from the following equation, which is a close approximation when the grating is used in the Littrow configuration small in Figure 2-12) ... 

All the mirrors are gold coated. The grating has 150 grooves per mm and a blaze of 8.6° (A = 2 m at the first order) and is used in the Littrow configuration the back side is a plane mirror that can be used to obtain images of faint sources. 

This Littrow grating equation is generally useful because 0[ and 9a can be regarded as approximately equal in many applications of reflection gratings, even when the optical configuration is not strictly Littrow. 

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