## Optical calculations

To calculate the position and magnification of the image formed by a focal reducer, see Figure 6.1 and Table 6.1. If you look back at Table 5.1 on p. 52, you'll see that one of the formulae has been rearranged to avoid giving negative numbers in this situation. Both tables are equally valid if you follow the instructions.

Table 6.1 Calculations for compression, arranged to avoid negative numbers. (Compare Table 5.1, p. 52.)

Compression

A = distance from focal reducer lens to sensor or film F = focal length of focal reducer lens

Projection magnification F — A Additional back focus required = B — A

Projection magnification (always less than 1) = — = —-—

Focal length of system = focal length of telescope x projection magnification f -ratio of system = f -ratio of telescope x projection magnification exposure time without reducer

Exposure time needed with focal reducer =

(projection magnification)2  Figure 6.2. Schmidt-Cassegrains, Maksutov-Cassegrains, and related telescopes focus by moving the main mirror, shifting the focal plane over a wide range and overcoming the problem in Figure 6.1. Telescope focal length increases when this is done.

The projection magnification with a focal reducer is always less than 1, typically 0.3-0.7. A magnification of 0.707 will double the image brightness and cut your exposure time in half.

You must generally find F, the focal length of the compressor lens, by experiment; Figure 6.4 shows how to do so. Make sure the light source is really distant - at least on the other side of the room - and measure from the middle of a multi-lens focal reducer. F is always appreciably greater than A and B. Figure 6.3. The Trifid Nebula (M20). Stack of four 3-minute exposures at ISO 400 with a Canon Digital Rebel (300D) through an 8-inch (20-cm) f /10 Schmidt-Cassegrain telescope with x 0.63 focal reducer giving effective f /6.3. Cropped from a larger image; processed with MaxIm DL, Photoshop, and Neat Image.

Figure 6.3. The Trifid Nebula (M20). Stack of four 3-minute exposures at ISO 400 with a Canon Digital Rebel (300D) through an 8-inch (20-cm) f /10 Schmidt-Cassegrain telescope with x 0.63 focal reducer giving effective f /6.3. Cropped from a larger image; processed with MaxIm DL, Photoshop, and Neat Image.

Distant light source, as far away as possible

Figure 6.4. To find the focal length of a compressor lens (focal reducer), use it to form an image of a distant light source.

Compressor lens Image of

(focal reducer) light source 