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Fig. 3.98. Schiefspiegler with spherical primary and insensitive to lateral decenter [3.114]

Fig. 3.98. Schiefspiegler with spherical primary and insensitive to lateral decenter [3.114]

type of compensation occurs in any 2-mirror telescope for which the field coma is not corrected, i.e. all forms except the RC and aplanatic Gregory.

The system of Fig. 3.98 is a special case of the general excentric system of Fig. 3.95.

The TC,0 form, free from lateral decentering coma, is simply a limit case of a Schiefspiegler with zero field angle at the primary and lateral shear of the secondary. As a Schiefspiegler, such a limit solution is normally illusory, as it does nothing to reduce the central obstruction; but the freedom from translation (lateral) decentering coma has considerable merit for special cases.

For 2-mirror telescopes with solutions bs2 > +(m2 — 1)/(m2 + 1), we see from (3.385) that the bracket becomes negative and the CFP lies in front of the secondary in the Cassegrain case. The shorter the distance zcfp from the secondary, the worse the lateral decentering coma. The SP solutions with normally acceptable values of Ha have shorter distances from (3.384) than the corresponding values for the RC, classical and, above all, DK solutions. With normal obstruction values, therefore, the SP solutions are not only the worst for field coma, but also for lateral decentering coma. As we have seen, only with |Ra| > 0.5 can this situation be remedied.

In general, the position of the CFP is of great importance in the design of systems for active correction of decentering coma. This will be dealt with in RTO II, Chap. 3.

3.7.2.4 Schiefspiegler with three or more mirrors. An analysis of 3-mirror Schiefspiegler and excentric uniaxial systems for telecommunication purposes has been given by Sand [3.115], for which the central obstruction of centered systems is a serious disadvantage (see § 3.10). Sand concludes that the 3-mirror Schiefspiegler of the Kutter form does not yield the necessary quality, although it is not clear why this is the case for the "axial" (centre field) image. He gives a 3-mirror excentric (uniaxial) solution equivalent to Fig. 3.95, in which the four conditions Si, Sn, Shi and Siv are fulfilled as in the systems of Paul-Baker, Korsch and Robb discussed above in § 3.6.5. The MTF (see § 3.10) is virtually perfect over a field of 1° or more because of the removal of central obstruction. System parameters are less sensitive than in the 2-mirror case. The baffling situation is favourable because of a fourth plane mirror giving the brachy-form.

Schiefspiegler with three or more mirrors clearly offer an enormous variety of solutions. Robb and Mertz [3.116] have investigated a scheme for an Arecibo type fixed spherical primary with a Gregory secondary and a corrector consisting of two oblique powered mirrors. For the steep primary considered, this design was not adequate because of higher order aberrations, although it represented a good third order solution. The authors reverted to a centered corrector.

The above system of Sand is an off-axis system in aperture. More recently, an off-axis version in field of the 3-mirror Paul telescope (Fig. 3.73) has been proposed by Stevick [3.166]. Since the Paul telescope has excellent field correction (coma and astigmatism corrected to the third order, residual field curvature which may be of little consequence for amateur use), the Stevick-Paul telescope yields very good imagery while avoiding the serious contrast loss (see Fig. 3.111) due to the central obstruction of a normal, centered Paul telescope.

In § 3.6.5.1 new work by Rakich [3.162] [3.163] was described, whereby an automatic program investigates the whole parametric space of 3-mirror solutions, of which two are spherical and one aspheric. Most of the interesting solutions revealed and discussed are normal centered, or folded, systems. However, Rakich also gives 4 new flat-field anastigmatic Schiefspiegler solutions. One of these is a flat-field modification of the Stevick-Paul telescope, giving excellent performance over a 0.5° circular field. If the primary is modified to become an ellipsoid (bs = -0.95) as well as the liberation c2 = c3 to achieve the flat field, the system is called by Rakich a flat-field Paul-Rumsey arrangement, giving further improved quality. Other interesting flat-field systems given have the aspheric on the secondary (f/7.9), an all-spherical mirror system (f/12.25), a further system with aspheric on the secondary (f/8.22), and finally a Schiefspiegler of a type attributed to L.G. Cook (1987), for which the primary is an off-axis portion of an ellipsoid (f/13). A second version is shown with two folding flats to reduce the length.

A most interesting analysis of 4-mirror Schiefspiegler solutions has been performed by Schafer [3.117]. All the solutions are anastigmatic, free from obstruction, and contain only spherical surfaces. The starting basis for the designs is an inverted form of the Burch anastigmatic telescope [3.118], a modification using two concentric spheres of Schwarzschild's original design of Fig. 3.8.

Such proposals have in the past met with little interest. With modern progress in improvement of the reflectivity of larger mirrors, together with the stimulus to 3-mirror Schiefspiegler systems by the recent proposals of Stevick and Rakich above, there may well be considerable scope for further design work and realisation of 4-mirror Schiefspiegler solutions (see also § 3.6.5.1).

3.8 Despace effects in 2-mirror telescopes 3.8.1 Axial despace effects

Excellent treatments are given by Bahner [3.5] and Schroeder [3.22(e)].

3.8.1.1 Gaussian changes. There are three basic (independent) parameters of a 2-mirror telescope which are subject to error: fl, f and d1. These errors will be determined by manufacturing and test procedures and tolerances, or, in the case of d1, by the mechanical assembly conditions. The signs are as defined in Table 2.2 (and Table 2.3 for further derived quantities). For the axial despace characteristics, we require some relations from Chap. 2 (see Figs. 2.11 and 2.12). From (2.54) and (2.55): fi f i f1 = fi f2 d = m2f1 (3.390)

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