in our normalized case, giving finally from Eq. (3.170) 1

It follows that, for the classical Cassegrain, the locus of points PC for different incident ray heights falls on the circle of radius 2f instead of f as required for aplanatism, i.e. that

The above construction shows clearly the difference in geometrical function of the aplanatic RC telescope from the classical Cassegrain. If the same construction is performed for the spherical primary (SP) telescope, the incident ray is reflected from the primary at Asp and meets the oblate spheroidal secondary at the point Bsp well below Be. The corresponding sphere P0 PSp then lies well to the left of the plane PqPQ .

3.2.7.2 The Couder 2-mirror (aplanatic) anastigmat In 1926, Couder [3.25] [3.24(b)] proposed a modification of the Schwarzschild telescope above in which E Siv was left uncorrected, but E Siii was reduced to zero by applying the condition (3.146) also given by Schwarzschild

5 Equation (3.169) is the normalized equivalent of Eq. (3.198) below for (Su'p)coma , which, however, gives the diameter of the angular aberration, whereas (3.169) gives the radius. Eq. (3.198) also supposes y1 = ym, the maximum aperture height. If y1 = ym, then (3.198) assumes the general form

If, with our present normalization, we set ym = f/ = 1, then (apart from the factor 2 because we now express the radius of the angular aberration), the general form of (3.198) is identical with (3.169). As a result of the normalization, Y1 is dimensionless, so that Eq. (3.169) is dimensionally correct.

which results from Eq. (3.119) for (E S///)Ap!an. Couder argued that E S/y could be corrected by a positive field-flattening lens. We shall consider such correctors in detail in Chap. 4. This is optically a much superior solution to Schwarzschild's. However, a severe price is paid in the length of the system: 2/ instead of 1.25/ in the case of Schwarzschild. In practice, a further tube extension is required in both cases to prevent direct light reaching the detector. In the Couder case, a total tube length of about 2.5/ is needed.

The Couder telescope is defined by the zero-astigmatism condition (3.174) of the aplanatic telescope, together with the conditions (3.109) and (3.114) defining the mirror forms to give aplanatism. If (3.174) is substituted in these, together with (2.75), we can derive at once

relations which leave m2 as a free parameter to be chosen. Couder gave this system the same final f/no as Schwarzschild, f/3.0, and for a normalized / =1 defined /1 = -3.25, thereby determining m2 = -0.30769

from (2.55). The primary thus has an even weaker curvature (f/9.75) than the Schwarzschild telescope. The values of (6s1)co«d. and (6s2)co«d. are, from (3.175) and (3.176), -14.204 and -0.554 respectively. The first value is not excessive because of the weak curvature. From (2.75) and (3.174), we have

giving Lcoud. = Ra = +0.38462 since / =1. Similarly, from (2.90) and (3.177)

This leads to the Couder telescope shown in Fig. 3.12 and the constructional data of Table 3.9. Although the design is essentially similar to the Schwarzschild telescope, the Couder system is obviously markedly longer.

The field curvature of the Couder telescope is given from Table 3.5 with H2 = 1 as

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