Design of a classical grating spectrograph

Introduction
Calculating the parameters
Mechanical considerations

A "classical grating spectrograph" has a simple optical principle, as shown in Figure 1.
The light from the star image in the telescope's focal plane (optionally constrained by a slit) is collimated by a first lens (the collimator), then diffracted by a grating, and then focussed by a second lens (the camera) on the detector.
In most cases the grating will be reflective, which leads to a layout as shown in Fig.2a.
Other designs, such as the Littrow design (Fig 2b), are based on a similar principle (the Littrow uses one lens simultaneously as collimator and camera, which can be handled by the same optical principle, with the restriction that the focal length of camera and collimator must be the same).

-highest optical throughtput, matched to telescope and detector (CCD).
-detector (CCD camera) most expensive part of the instrument. Most amateurs will already have a camera, and in the following we will assume the CCD is given and we design the spectrograph around it.

For amateur spectroscopy, the design is driven primarily by two tradeoffs:
- a tradeoff between resolution and wavelength coverage
- a tradeoff between efficiency (throughput) and size (bigger = heavier and more expensive)

The resolution

Several manuals on spectrograph design start with a laborious calculation of diffracted angle (from the grating towards the camera) as function of incidence angle (from collimator on the grating). However, this is of little practical value since the angles are fixed by the placement of the lenses (colli and camera) and the orientation of the grating. The angle between incoming and outgoing lightbeam to/from the grating should simply be kept as small as possible (this is extreme in the Littrow design where the angle is zero) to obtain the highest diffraction efficiency. This angle is in practice limited by the size of the lenses or the diameter of the lightbeam. The orientation of the grating will then be immediately obvious once it is inserted in the lightbeam: