reference : chief ray
Fig. 4.6. Spot-diagrams ESO 3.6 m telescope (f/3
for a quasi-RC telescope with Gascoigne plate corrector and field flattener based on the geometry of the -f/8)
large values of E, such as 31.4167 above, mean that the principal ray is E-times higher than the aperture ray for the normalized telescope with f/0.5 and upr = 1. For a real telescope with f/10 and a field diameter of 1.5°. the real value Erea; = 8.225. The aspheric form in Eq. (3.221) defining the plate depends on y4 and the aspheric constant is determined by S over the axial beam width. So Srea; must be multiplied by (Erea;)4 = 4577 for Ereai = 8.225. This gives an asphericity of about 1 mm from Eq. (3.221) for n' = 1.5 and a 3.5 m telescope at f/10. The compensating y2 term, as in the Schmidt plate, reduces this to about one quarter, i.e. « 250 ^m. We see that a 3° diameter field would require an asphericity 16 times as high, becoming prohibitive from a manufacturing viewpoint. In practice, such plate strengths will anyway lead to unacceptable chromatic effects. Schulte [4.17] gives the maximum departure from the nearest sphere as ± 64 ^m for the corrector plate of the 1.52 m telescope for Cerro Tololo. Scaling the telescope size from 3.5 m and allowing for his use of fused silica with n' ~ 1.46, this is in excellent agreement with the value above of about 250 ^m for a 3.5 m telescope. Chromatic effects are worse for Cassegrain telescopes with a high m2 because the angle upr of the emergent principal ray is magnified by the same order. But this is the angle of incidence of the principal ray on the plate as shown in Fig. 4.1 and the chromatic differences of astigmatism and coma will increase with it.
220.127.116.11 Cassegrain correctors consisting of 2 or more aspheric plates. It is clear that similar considerations apply to the Cassegrain focus as to the prime focus, but with the important difference that the relative aperture is far lower for the Cassegrain and, in consequence, the factor E is much higher.
A classical Cassegrain presents an identical situation to a parabolic primary of the same relative aperture, whereas an RC combination has no PF equivalent. With 2 plates at the Cassegrain, 2 conditions can be fulfilled. As in the PF case, the only interest (in principle) would be the correction to achieve E S// = E S/// = 0 with free parameters for Z or £, or both. The correction of the astigmatism of a strict RC, maintaining the other two conditions, would require a 3-plate corrector.
We have seen above that the limitations of the single Gascoigne plate in the Cassegrain with a quasi-RC solution are set only by the plate strength due to high values of E and the corresponding chromatic aberrations of higher order. We have also seen that multi-plate correctors, because of the nature of the aberration compensations in the solution matrix, must have far higher individual plate strengths than is the case for single-plate correctors, leading to increased higher order chromatic aberrations. For these reasons, although the 3-plate case for an RC telescope does not appear to have been formally designed for a practical case, it seems very unlikely that it would be a viable solution.
Nevertheless, for special cases, 2- or 3-plate correctors may be of considerable interest. One such case, considered briefly in § 3.4, was the correction of spherical aberration in the Hubble Space Telescope (HST). In that case, since the error was on the primary at the pupil, there was no effect on coma or astigmatism. Since the RC astigmatism was corrected at the individual instruments the correction required is only in Sj. This is the opposite case from a 3-plate corrector mentioned above to correct astigmatism in an RC telescope, but the principle is the same. An excellent optical solution was possible, but the logistics of its mounting in space would have presented major technical problems and dangers of failure, as was also the case for other technically interesting solutions. For these reasons, a 2-mirror corrector (COSTAR) was preferred, which also has the advantage of avoiding spherochromatism and other higher order chromatic effects [4.19]. More details are given in RTO II, Chap. 3.
4.3 Correctors using lenses
4.3.1 Prime focus (PF) correctors using lenses
18.104.22.168 Theory of basic solutions. Reference has been made above to the early work of Sampson [4.1]. Gascoigne [4.7] [4.8] and Wynne [4.5] give excellent reviews of this and later work.
In 1913 Sampson was concerned with a corrector for a Newton telescope with an f/5 parabolic primary. Following his work on a 3-lens corrector for a Cassegrain telescope (see below), he investigated the possibilities of a PF corrector consisting of 3 thin lenses of a single glass, effectively afocal, the largest being at a distance 0.215 / from the focus, the smallest at 0.175 / , in front of the Newton flat. The lens spacings were therefore quite small and arbitrarily selected. Sampson set up the three third order equations for Sj, Sjj and the "curvature" combination of Sjjj and Siv and realised he could not, with practicable lens shapes, satisfy the condition Sj = 0 as well as the other two conditions with the parabolic primary; or indeed meet the conditions ^2 Sj = ^2 Sjj = 0. He proposed, therefore, to abandon the parabolic form, replacing it by a hyperboloid "nearly as far beyond the paraboloid as the paraboloid is beyond the sphere" (bs1 = -1.944 in our notation). This permitted correction of the coma and the curvature conditions. The central lens had opposite sign from the two outer ones, a principle applied in later successful systems.
Apart from establishing the fundamental difficulty of correcting spherical aberration and the field aberrations with a parabolic primary, Sampson also pointed out the well-known advantage of eliminating secondary spectrum by the use of a single glass in an effectively afocal corrector system.
In 1933 Ross [4.20] published results of astrometric investigations with the 60-inch Mt. Wilson reflector, to which a prime focus corrector of his design had been added to the parabolic primary. This seems to be the first PF corrector to be made and applied in practice. It consists of a compact (effectively "thin") doublet system which is of a single glass and roughly afocal. In the above paper, Ross refers to the problem of residual spherical aberration and believed at that time that an aspheric surface could improve this.
In 1935 he wrote a second paper [4.21] with a complete optical analysis of the system. He drew attention to the important fact, well-known from lens theory, that it is impossible to correct both first order chromatic aberrations, longitudinal and transverse, with separated lenses, whether or not the corrector is afocal. This is easily proved from the theory given in Eq. (3.222) where the two first order chromatic coefficients were termed C, and C2. From Hopkins [4.22] for two lenses
£Ci = [Ei(Ci)i + £2(ci)2] H) in which the Lagrange Invariant H = 1 for our usual normalization and
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