## Chief

Fig. 3.7. Spot-diagrams for an SP Cassegrain telescope with the geometry of the ESO 3.5 m NTT (f/11; ra2 = -5), for a flat field. Compare with Fig. 3.6 with field times larger and Fig. 3.4 with field 45 times larger technical simplification in manufacture and test of the concave secondary compared with the convex secondary in the Cassegrain case, and the sign of the field curvature which is favourable for the compensation of that of auxiliary instruments.

It should be remembered that the technical price for the compactness of the Cassegrain telescope compared with the longer 1-mirror telescope is the associated problem of the severe centering tolerances (see § 3.7.2) unless the centering is actively controlled (see RTO II, Chap. 3). But the RC form of the Cassegrain offers a field correction which is impossible with a 1-mirror telescope.

3.2.7 Other forms of aplanatic 2-mirror telescopes (Schwarzschild, Couder)

3.2.7.1 The Schwarzschild original aplanatic telescopes. The fundamental contribution of Schwarzschild in 1905 [3.1] with the extension of aberration theory to field aberrations of reflecting telescopes was briefly discussed in § 3.2.6.1. Its significance has been further discussed from a historical viewpoint by the author [3.13]. Schwarzschild set up Eqs. (3.109) and (3.114) defining an aplanatic telescope in a somewhat different form and thereby recognised their validity for any chosen geometry. His initial aim, however, was more ambitious: he sought a 2-mirror solution permitting the correction of the first 4 Seidel conditions, S/ = S// = S/// = S/y = 0. In fact, his equations led him to such a solution, but he realised at once that it was not practicable for telescopes since the primary is convex, giving a secondary larger than the primary. Nevertheless, this solution has found application in somewhat modified form in spectrograph optics under the name "Bowen camera".

Having satisfied himself that no practical 2-mirror solution was available which satisfied more than the two conditions given by the "Schwarzschild theorem", Schwarzschild then sought an aplanatic solution (S/ = S// = 0) giving a "fast" telescope (f/3.0) for the slow photographic emulsions of the time. Had he applied his equations to the Cassegrain geometry of the 60-inch reflector for Mt. Wilson, under construction at that time by Ritchey, he would certainly have identified the RC solution seventeen years before it was formally published by Chretien [3.14]; although Chretien states elsewhere [3.21] that studies were already proceeding at Mt. Wilson in 1910, confirming the review of the situation given in § 5.2. Since the 60-inch reflector had a primary of f/5 and m2 = —3, the field coma as a classical telescope was by no means negligible, so the advantage of an aplanatic solution would already have been clear in 1905. But, for Schwarzschild, the resulting aperture ratio of f/15 was much too slow.

Before we consider Schwarzschild's aplanatic system, it is most instructive to repeat his argument proving the impossibility of a practical telescope fulfilling the four conditions E S/ = E S// = E S/// = E S/y = 0.

The aplanatic requirement Si = Sii = 0 is embodied in the apla-natic solution of § 3.2.6.3 (b) above, by the Eqs. (3.109) for bs2 and (3.114) for bs 1. For Sm = 0, we must satisfy from (3.119)

For Siv = 0, we have the condition from Table 3.5 1 = m-2 + 1= m-2 + 1 f L mf — m2d1 '

from (2.75) and (2.55), which reduces to f' = — m2d 1 (3.148)

Substitution from (3.147) then gives f = ± f' V2 (3.150)

## Telescopes Mastery

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