Fig. 3.73. 3-mirror system due to Paul (1935), see also footnote on p. 324 concerning Mersenne above is instructive, but too unwieldy to be of wide application in practice, even though it is simplified by the assumption of the entrance pupil at the primary. (Of course, the stop position is uncritical, to the third order, for an anastigmatic telescope). However, the forms of Fig. 3.72 proposed by Korsch are the two most interesting 3-mirror systems: (a) because of the final image position behind the secondary, giving stray light baffling by M2; and (b) because of its 2-axis nature and the general potential of 2-axis systems - see
The system of Fig. 3.72 (a) given by Korsch is, in fact, a more generalised form of a system already proposed in 1935 in a classic paper by Paul [3.74], shown in Fig. 3.73. The essential properties of this system and further developments are excellently treated by Schroeder [3.22(b)]. The original Paul form starts off with a Mersenne afocal anastigmatic beam compressor defined by Eq. (3.97) and Table 3.6 as a Cassegrain system of two confocal paraboloids (Fig. 1.3). Paul added a spherical tertiary mirror to this beam compressor as shown in Fig. 3.73, placed so that its centre of curvature is at the vertex of the secondary. This tertiary, of course, introduces spherical aberration, but otherwise functions as a Schmidt primary receiving an anastigmatic beam from the exit pupil of the beam compressor, if the exit pupil is placed at the secondary. Paul then corrected the spherical aberration by the following elegant and simple concept: he defined r3 = r2 and, instead of correcting E Si by making the tertiary parabolic, he achieved the same correction by removing the parabolic form of the secondary, thereby making it also spherical.
We can now apply the "aspheric plate theory" of § 3.4 to show that the field aberrations coma and astigmatism are also corrected. Let the exit pupil of the beam compressor be placed at the vertex of the secondary. (This assumption has no effect on the anastigmatism of the beam compressor, since from Eqs. (3.213) a stop shift has no effect on the third order terms apart from distortion). Then the removal of the parabolic form from the secondary to correct E Si is the equivalent of adding an aspheric plate to the unchanged secondary to achieve the same effect. Since the pupil is at the secondary and the tertiary is concentric with it, the addition of such an equivalent "Schmidt system" has no effect on E Sii and E Siii which are zero from the original anastigmatic beam compressor, as follows from Eqs. (3.214). If the exit pupil of the beam compressor is now shifted to its normal position behind the sec
ondary, corresponding to the usual stop position at the primary, Eqs. (3.213) show there is no effect on Sj, Sjj and Sjjj due to this stop shift. The Paul system is therefore anastigmatic with Sj = Sjj = Sjjj = 0, but the field is not flat, and has a curvature of Pc = 1//.
Baker [3.23(d)] [3.75] modified the Paul system into what is known as the Paul-Baker system by setting the condition |r3| > |r2| such that the Petzval sum is zero and a flat field is achieved. The third order theory of this Paul-Baker form is simple and elegant.
From the definitions leading to Eq. (3.20) we have for the field curvature
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