Using an Objective Prism (a wedge prism placed in front of the telescope aperture) is a long established way of producing low resolution spectra.  A similar technique can be used with a diffraction grating, but large diameter gratings (and objective prisms) are expensive and the dispersion produced by even a coarse 100 lines/mm grating is unmanageably high with a typical telescope focal length. 

Using a camera lens instead of a telescope however gives a more reasonable dispersion and the smaller objective size of a typical camera lens means small affordable but efficient 1.25 inch diameter gratings such as the Star Analyser can be used. 

Of course using such a small aperture restricts the technique to brighter objects but because the light from the star is already collimated, it potentially can give significantly improved resolution (typically 3x) compared with the alternative simple technique of placing the grating in the converging beam between the telescope and the camera.

Making the most of this potential increase in resolution requires a higher dispersion than is normally used with the Star  Analyser, which means a larger camera detector if the full spectrum plus zero order is to be imaged. (Useful to aid focusing and calibration, particularly for beginners). A large format monochrome astro camera would be an ideal but expensive option. Alternatively Digital Single Lens Reflex cameras such as the Cannon 350D etc perform well under astro imaging conditions and can be used successfully in this application, though with restricted wavelength range towards the IR unless the internal IR blocking filter has been removed or replaced.

The choice of lens focal length depends on a number of factors:  

The dispersion increases proportionally with focal length but so does the size of the star image so  the resolution is largely independent of focal length.

A shorter focal length means a shorter, more concentrated spectrum and therefore fainter objects can be recorded.

With too short a focal length however, the star image will be undersampled (ie the star image will be smaller than a single pixel, remembering that for a colour camera like a DSLR, the effective pixel size is larger than a single pixel due to the Bayer pattern of pixel colour coding). Undersampling can produce severe artifacts in the spectrum, particularly with colour cameras.
  
 A short focal length  also means a greater area of sky is imaged giving a higher sky background brightness and an increased risk of interference from other stars and their spectra. 

(Note that using this technique with short focal lengths can be useful for recording spectra of fainter diffuse objects such as comets as seen here  bottom of the page.  In extreme cases it also be used to cover a wide field at ultra low resolution as in this meteor spectrum)

Too long a focal length and it will not be possible to fit the star (zero order) and spectrum in the frame. Tracking also becomes more critical at higher focal lengths.(Indeed, with modest focal lengths it is possible to produce "drift spectra" with a fixed camera)

The Setup

For these tests I used a 100 lines/mm Star Analyser grating with a Canon 350D camera fitted with a 75-300mm zoom lens at 200mm focal length which gives a dispersion of about 3.5A/pixel.  It was piggyback mounted on my main telescope. ((It is also possible to used a fixed camera on a tripod, orientating it so  the star drifts perpendicular  to the dispersion direction.)

To mount the grating,  I cut a hole in a lens cap and screwed the Star Analyser into it. To make it easier to rotate the grating independent of the focusing adjustment, I added a blank rotatable filter cell (from an inexpensive crossed polarising filter set) between the lens cap and the Star Analyser. An alternative could be to adapt a blank photographic filter cell the right size for the lens. This could be orientated by screwing the assembly in and out. The small grating aperture produced some vignetting but provided the calibration reference star is placed at the same position as the target this is not a problem .  (Note flats cannot be used in the conventional way with slitless spectroscopy like this. See here for some tips on how to avoid flat field defects in Star Analyser spectra)

A typical single 30sec exposure of  Epsilon Aurigae (7th full size)  Click on the image to view full size (1.5Mb)	Flat field

You need some means of operating the camera without getting camera shake and viewing the images immediately in full resolution to check for positioning, orientation and focus. I  control the camera and view the images on a laptop using a freeware program called  Focus Assist but you will  no doubt have your own favourite method if you are already astro-imaging with your camera.