Fig. 3.5. The function f (m2) = (m2+1Hm2-1)2 curve refers to Cassegrain solutions, the right-hand curve to Gregory solutions, if the image is real f(m2)
for DK telescopes. The left-hand
Substituting from (3.123) gives
for the normal focal case. Similarly, Eq. (3.68a) or Table 3.6 give for the afocal case the particularly simple form in terms of J1 and d1:
With the normalized geometry of Table 3.2, the DK case with m? = -4 gives from (3.131)
(E^Ir) = -3.63281 - 0.5 = -4.13281 , the value appearing in Table 3.3, Case 5. This must be compared with the value -0.5 for a classical Cassegrain and shows the high price that must be paid for the manufacturing convenience of the DK solution: the field coma is increased by a factor of over 8 compared with the classical Cassegrain with this typical geometry! Since field coma as a third order aberration varies linearly with field, it follows that, for a given acceptable coma limit, the field area is reduced by almost two orders of magnitude.
The field astigmatism of the DK telescope is given in the focal case by Eq. (3.61) or Table 3.5. The fourth term is again zero with E SI =0, but the third term is only zero if spr1 is zero, i.e. the stop is at the primary. Assuming spri = 0, we have
giving with (3.123)
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