The same equations, in a slightly different form and adapted to his sign convention, are given by Bahner [3.5]. Other treatments have been given by Conrady [3.109], Marechal [3.110], Slevogt [3.111], Baranne [3.112] and Schroeder [3.22(d)].

In the thirties, Ritchey built the first major RC telescope, with an aperture of 1 m, for the US Naval Observatory in Washington. A short account is given by Riekher [3.39(h)] and the basic data by Bahner [3.5]. This important telescope is discussed further in Chap. 5. Its sensitivity to decentering coma was higher than normal Cassegrain telescopes of the time, but this was due more to its optical geometry than its RC form. The general form for the angular decentering coma of Eq. (3.363) shows that, for any form of 2-mirror telescope, the most important parameter in producing decentering coma is the f/no. of the primary. This is particularly clear if |m2| ^ 1, since the terms containing m2 then vanish if N2 is replaced by N and f' by f'. (The dominant role of the primary, in the normal case where |Ra| ^ 1, is also clear from the basic Schiefspiegler formula (3.356) in which the first term from the primary is dominant). Ritchey's telescope had a primary of f/4.0 and the very fast final relative aperture of f/6.8 because he wished to have a fast photographic telescope. The corresponding m2 was very low, only —1.7. The two terms in the bracket of Eq. (3.364) are then 1.89 and 1.67 respectively, with Ra = 0.40. With this low m2, therefore, the aplanatic form did indeed almost double the decentering coma compared with the classical telescope form. However, for a given value of decenter the aplanatic form only gave 33% more angular coma than a typical classical telescope would have given with the same primary and m2 = —4.

Another interesting case is the Dall-Kirkham (DK) telescope with a value (bs2)dk = 0. Eq. (3.362) then gives

Comparison with (3.358) shows that the decentering coma of the DK form is 2 (m2 + 1)/(m2) times that of the classical Cassegrain, a substantial gain.

Similarly, using (3.137) for (bs2)sp, the decentering coma for a telescope with a spherical primary is derived from (3.362) as in which the first term in the bracket corresponds to the classical Cassegrain case (3.358). With the values of Table3.2 for m2 and RA (—4 and 0.225), the second term is dominated by Ra compared with the first, giving a (Comai)jisp value —1.370 times that of the classical Cassegrain.

The angular tangential coma [(Su'p)comat] s due to transverse decentering according to Eq. (3.363) is given in arcsec in Table 3.20 for the 2-mirror telescopes listed in Table 3.2, using the same parameters |m2| = 4, |Ra| = 0.225 and |f '| = 1. The formulae above are also valid for Gregory telescopes with

Telescope type |
Angular transverse decentering coma (arcsec) |

Classical Cassegrain (C) |
+2.320 |

Ritchey-Chretien (RC) |
+2.520 |

Dall-Kirkham (DK) |
+0.870 |

Spherical Primary (SP) |

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