Focal Reducers

A focal reducer is a camera which changes the focal ratio, or the scale, of the telescope. It is simply a reimaging system which demagnifies the telescope focal plane. In its simplest form, it consists of just two lenses: the collimator and the camera lens. The collimator lens has the same focal ratio as the telescope, and converts the telescope beam into a collimated beam. The camera lens then refocuses the light light with the desired focal ratio. The magnification of the system is given by:

$$m = {f_{camera}\over f_{collimator}}$$

Consequently, the focal length of the entire system (telescope plus focal reducer) is:

$$f_{system} = f_{telescope} m$$

$$f_{system}= f_t {f_{cam}\over f_{col}}$$

$$f_{system}= F_t D_t {F_{cam} D_{cam} \over F_{col} D_{col}}$$

$$f_{system}= D_{tel} F_{cam}$$

where we have used the fact that $F_{col} = F_t$ (or else it won't collimate the light) and that the diameters of the beams on the camera and collimator are the same. Consequently, the scale in the image plane of the focal reducer is just the scale in the telescope focal plane multiplied by the ratio of the focal ratio of the camera to that of the telescope.

Note that with a focal reducer, one does not just get a new scale ``for free''. The focal reducing system may introduce additional aberrations giving reduced image quality. In addition, one always loses some light at each additional optical surface from reflection and/or scattering, so the more optics in a system, the lower the total throughput.