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within 0.4 arcsec in the range 330 nm to 1000 nm. The spot-diagrams of Fig. 4.18 may be compared with those shown in Fig. 4.14(b) for the original Wynne-type corrector, for which the field performance in the blue part of the spectrum is much inferior to the 1 arcsec specification. It should be emphasized that the new corrector, like its predecessor, only uses spherical surfaces. The circular field covered is marginally smaller, 0.9° diameter instead of 1.0°. However, this field size is solely determined by the detector: a larger field, at least 1° , would be perfectly feasible. The limitation in all prime focus correctors lies not with the monochromatic aberrations, but with the chromatic effects. A balance between the lateral chromatic aberration and the higher order chromatic aberrations of coma and astigmatism presents the usual limitation.

Delabre has also designed a similar 4-lens PF-corrector for a 3.6 m telescope with a parabolic primary of f/3.8 [4.76]. The lack of overcorrection of spherical aberration given by an RC primary is a disadvantage that is compensated by the lower relative aperture. The field covered is 1.4° circular (1.0° by 1.0° square). Both the monochromatic performance and the chromatic performance are comparable with the system of Fig. 4.18.

4.3.2 Secondary focus correctors using lenses

4.3.2.1 Origins. Secondary focus correctors normally refer to Cassegrain foci but are, of course, also relevant to Gregory telescopes. The normal application is to Cassegrain foci, either in the classical form or in RC or quasi-RC form.

Sampson's first paper in 1913 [4.1] was the first proposal to be made for a corrector which was substantially afocal with a view to correcting field aberrations. Sampson's design used an f/5 primary whose asphericity was allowed to vary to correct the spherical aberration, the final form being an ellipse close to the parabola. The Cassegrain secondary, which he called the "reverser", was of a Mangin-type with a spherical back reflecting surface and weak negative lens effect. A spaced, nearly afocal doublet was then placed about 2/3 of the distance to the primary. Sampson calculated an image diameter, strictly circular, within 2.2 arcsec for a field diameter of 2°. The final f/ratio was f/14.05.

In modern terms, Sampson's design was effectively a Dall-Kirkham telescope with a Mangin secondary and afocal doublet corrector. (We recall from Chap. 3 that the Dall-Kirkham telescope with spherical secondary also has an elliptical primary fairly near the parabola). In this sense, it was not a corrector for a classical Cassegrain telescope, but a new - and remarkable -telescope design. His aim was similar to Schwarzschild's telescope, but in a more practical form.

Sampson's work was followed in 1922 by the analysis of Violette [4.3], immediately succeeding the invention of the RC telescope and closely following the approach of Chretien discussed in Chap. 3. Although Violette's point of departure was the RC telescope, his approach was, in fact, the same as Sampson's in that he designed a complete system with a doublet corrector in which the forms of both mirrors were allowed to depart from the RC asphericities. His aim, then, was a telescope fulfilling all four conditions Si = Y1 Sii = Y Siii = Y1 Siv = 0. Since the RC system did not satisfy the last two, Violette's corrector required finite negative power to correct the Petzval sum. He used two different glasses for achromatism, supposing thin lenses, and noted the inevitable secondary spectrum. He applied thin lens theory for the lenses and the Eikonal approach of Chretien (following Schwarzschild) for the mirrors. He noted a spare degree of freedom for limiting distortion. Another solution, following Sampson, to eliminate the secondary spectrum, was proposed for a Cassegrain with equal radii on the two mirrors, giving a mirror system with Siv = 0. This permitted an afocal doublet with a single glass. We have considered a Cassegrain with Siv = 0 in Chap. 3: its major disadvantage is the large obstruction ratio Ra for acceptable image positions.

Surprisingly, the pioneer work of Sampson and Violette attracted little attention until Bowen [4.41] in 1961 proposed Cassegrain foci of the order of f/8 with f/3 primaries in order to have acceptable "speed" at the Cassegrain with photographic plates. This led to proposals for RC telescopes to extend the Cassegrain field and to corrector systems for further extension for various telescope forms.

4.3.2.2 Third order theory for classical Cassegrain and RC telescopes. We can apply the same thin lens theory to the Cassegrain (or secondary focus in general) that we have applied above to the PF corrector case. Wynne [4.23] analysed the situation in a similar way already in 1949. While the same theory is applicable, there is an important difference. The PF case was dominated by considerations of spherical aberration and coma, arising from the appreciable relative aperture; astigmatism and field curvature of the primary only played a minor role. In the Cassegrain case, we have an opposite situation: since the relative aperture is weak and the telescope is often aplanatic or near to that state, the corrector's role is dominated by astigmatism and field curvature, above all because the field curvature concave to the incident light of the secondary is usually far stronger than the opposite field curvature of the primary.

Let us consider first the general case of a Cassegrain telescope with correction by a thin lens. Combining Eqs. (4.31), omitting asphericities, with Eqs. (4.47) for lenses and adding the field curvature condition from Table 3.5, we have:

E S/// = f'( f + + d2 C + (S///)cor + 2E(S/j)cor + E2(S/)C

As before, the quantities f' and L are defined as positive quantities in a Cassegrain telescope with normalization to f' = 1, while is negative. The quantity E, expressing the position of the corrector relative to the stop at the primary, was given for an aspheric plate corrector by (4.34) as f' f + di

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