go to Page 2

### -3-

short distance ahead of the focal plane, gives a very satisfactory instrument. Another variation employs
a tilted simple lens of very long focal length located in the light path ahead of the primary mirror. Where
reasonably good optical performance is required, all of these designs are limited to rather small
apertures and rather long focal lengths.

For instruments of large apertures and top optical performance, one or the other of two additional stratagems must be employed. Either the surface curves of one or both mirrors must have predetermined amounts of astigmatism figured into them, or a properly designed and adjusted warping harness must be applied to one of the mirrors.

Although the equations and comments contained herein may be applied to more than one of the
variations just described, the bulk of the material of this paper is concerned with the harness-warped-secondary Yolo reflector.

## General Equations

The effective focal length, F, is given as follows (see Figure 1):

where R_{1} and R_{2} are the radii of curvature of the primary and secondary mirrors, respectively, and S is
separation distance (slant-distance) from the center of the primary to the center of the secondary.

Equation (3) gives the diameter of the illuminated area of the secondary, D_{2}:

where D_{1} is the illuminated aperture of the primary.

go to Page 4