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Thus, in 1636, without knowing it and without the necessary theory of field aberrations to be able to understand its significance, Mersenne invented not only the first aplanatic telescope form, but also the first anastigmatic form [3.13]. We shall see that these properties of an afocal telescope are of great significance for the further development of modern forms of reflecting telescope, see also footnote on page 324 concerning Mersenne.

The field curvature £ S/v of the classical telescope is given in various forms by Eq. (3.62) and in Table 3.5 for the focal case; in Table 3.6 for the afocal case. In the Cassegrain case, if the telephoto effect T is large according to Eq. (2.57), then L ^ / and the second form of Eq. (3.62) shows that the field curvature from the secondary will be far higher than that of the primary. This gives the high values of the Cassegrain solutions of Table 3.3 compared with the 1-mirror telescope. This Cassegrain field curvature is concave towards the incident light. The last column of Table 3.3 gives the effective field curvature for best imagery in the presence of £ S/// and £ S/v . We see that the astigmatism increases the effective field curvature.

If the curvatures of Mi and M2 in a Cassegrain telescope are made equal, the system will yield a flat field with £ S/v = 0. However, this leads to an optical geometry which is rarely practicable from the point of view of the final image position or obstruction. This is easily demonstrated from Eq. (2.64):

Setting Ra = 1/3, a typical value, gives

If £ S/V = 0, then (3.101) and (3.102) give m2 = —1.5 (3.103)

for a flat field with Ra = 1 /3. This is the inevitably low value of m2 associated with a weakly curved secondary. The consequence for the position of the image b relative to the primary is given by Eq. (2.65):

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