F f f

showing that the monocentric Cassegrain system has the same equivalent focal length for all finite separations d1 as the "thin-lens" combination with d1 = 0. Now from Table 3.5 the right-hand side of (3.295) also represents the Petzval sum Pc of the system, so that

and the field curvature Siv is the reciprocal of the equivalent focal length of the system, exactly as for a classical single-mirror Schmidt, normalizing H2 = 1 in Table 3.5. This is a price to be paid for the concentric form, but the system must be anastigmatic from its spherical symmetry about the plate centre (stop) and has the advantage of having purely spherical mirrors.

We will now derive the asphericity required on the plate. For simplicity, we shall assume that the final image is at the pole of the primary, i.e. b = 0 in Fig. 3.43. Then from Eqs. (2.67) and (2.72)

with b = 0. From Table 2.2, the quantities f1i, f2i and d1 were defined as negative in a Cassegrain telescope. From the monocentricity and Eq. (3.293):

giving from (3.297)

If f2 is now substituted in Eq. (3.295), we obtain 1 1 /! — Ra

f f V1 + Ra. But from (3.297) we have f =-f '{ iRRa) (1301)

Eliminating f from (3.300) and (3.301) gives Ra = 1/3 , a value slightly more favourable than the value 0.35 for the Baker systems with an image position in front of the primary. The obstruction ratio must be more favourable, since the secondary is more strongly curved than in the Baker flat-field solutions.

If b = 0 in Fig. 3.43, we have P = —f and Eq. (2.84) becomes

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