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10. CATADIOPTRIC TELESCOPES WITH SUB-APERTURE CORRECTORS
As telescopes evolved, it has been discovered that performance of all-reflecting systems - especially those with more strongly curved surfaces - can be improved if mirrors are combined with lens elements. General term for telescope systems using both, reflective and refractive elements in order to form the prime image is catadioptric. Main working principle of a catadioptric telescope is that aberrations of reflecting and refracting elements cancel each other (kata=against, dioptric=refractive). Lens element(s) used in combination with mirrors can be either placed in the path of incoming light, when it is a full-aperture corrector, or in the converging cone produced by mirror element(s), when it is a sub-aperture corrector. Strictly talking, catadioptric telescope is designed as a synergy of reflective and refractive elements, requiring both for its functioning. That separates it from a mirror telescope using field-corrector, which can function without it. Systems with sub-aperture correctors are relatively infrequent and, in the commercial arena, often come with second-grade products. This doesn't mean that high-quality catadioptric systems with sub-aperture lens elements can't be built. One example is hyperbolic astrograph, consisting of a hyperbolic primary and either two (Rosin), three (Wynne) or four element (a pair of doublets) sub-aperture lens corrector. Even a single-element lens corrector in a form of equal or near-equal radii meniscus, can significantly improve performance of a fast parabolic mirror (FIG. 79A), or even fast sphere (FIG. 79B).
A simple doublet corrector of Jones-Bird type can also achieve a good overall correction level in combination with spherical mirror (FIG. 80). Another more recent sub-aperture corrector type for spherical mirror, incorporated in the Cape Newise telescope, consists of a pair of widely separated doublets (one in front of the diagonal, the other at the bottom of the focuser tube). It seems to be capable of very good performance. However, its specifications are not available.
Wynne-type corrector offers excellent correction level with either paraboloidal or hyperboloidal mirrors (it is also used in two-mirror systems), both in regard to monochromatic aberrations and chromatism. However, while one of the three lens elements is a simple plano-convex, the other two are strongly curved, thin menisci, very demanding in both, fabrication and positioning/centering. Still, the Wynne corrector is not out of reach for advanced amateur telescope makers and designers. Here is a working example of a Wynne-type corrector for a general paraboloid by C. Cavadore. While 3-element Wynne-type corrector is sufficient for smaller, or medium fast mirrors, large, fast mirrors require 4th element for highly corrected image (Fig. 81).
With smaller mirrors, it is easier to achieve high level of correction by combining sub-aperture corrector and hyperboloidal mirror. This is due to simple coma correctors generating under-correction, thus introducing one aberration while correcting for the other. Having the mirror hyperboloidal practically takes spherical aberration out of the equation, allowing corrector design to be optimized for correcting other aberrations. For that reason, hyperbolic astrographs can be designed to a high level of correction with quite simple doublets in place of the correcting element (FIG. 82).
FIGURE 82: Ray spot plot for a 10" f/4
hyperbolic astrograph with Rosin-type corrector designed by Mike I. Jones
(black circles represent the e-line Airy disc).
The corrector consists of a positive and negative meniscus, placed at
the bottom of the focuser base. The primary is a hyperboloid with the
conic K=-1.408. Evidently, image quality is excellent across the flat
1-degree field. The LA graph shows most colors focusing tightly together. Only
the violet end departs somewhat, resulting in the violet h-line blur of
approximately 12 microns in diameter (~0.2 wave RMS error), also
producing small lateral color error at this end of the spectrum. However,
it is still well above usual levels of correction, and can easily be remedied by using slightly different glasses, for instance
LAF9 for the front element.
Low level of aberrations allows for upscaling a system to
larger apertures. Schematics at the bottom shows the system layout. The two
corrector lens elements are of a simple form, easy to fabricate;
main fabrication difficulty is the relatively strongly aspherized
primary mirror. Needed in-focus distance for the corrector is relatively
small, allowing it to mounted onto the focuser
base. The final focus to corrector separation, on the other hand,
is large enough to accommodate use of various accessories, if desired. A
very good example of how successful can be combining
hyperboloidal mirror and relatively simple two-element sub-aperture
corrector in creating near-perfect photo-visual telescope/astrograph.
SPEC'S
Sub-aperture correctors can also be used
with two-mirror telescopes, usually with the goal of improving field
quality. As with Newtonian telescopes corrector, they can be either
integral part of a system, or an optional add-on. Typical sub-aperture
correctors in two-mirror systems are coma-corrector in Dall-Kirkham, or
astigmatism/field curvature corrector in aplanatic Cassegrain
(Ritchey-Chrétien) telescope. But they also can be used in systems with
full-aperture corrector, either to maximize performance, or to allow for
easier fabrication of the full-corrector, or both. One such example is
aplanatic Houghton-Cassegrain with both, full- and sub-aperture being a
plano-convex/concave lens pair (FIG.
115).
In general, aberrations induced by a
sub-aperture corrector are determined by its effective diameter, as well
as the element shape and power. Ideally, its monochromatic aberrations
would nearly balance out with those of the mirror (or mirrors), while
the chromatism it induces should be negligible. It is not always
possible; in principle, axial monochromatic correction is a priority,
followed by acceptable chromatic correction and correction of off-axis
aberrations. While sub-aperture correctors can be very complex, a simple
single-lens doublet, as illustrated with the above examples, can be very
effective. A brief overview of the aberration properties of a
thin-lens-element sub-aperture corrector follows.
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FIGURE
80: Ray spot diagram for a 200mm f/5.9 system with f/4 spherical
primary and Jones-Bird type corrector (Telescope Optics, Rutten/Venrooij),
placed in front of the flat. It is a single-glass lens doublet:
bi-concave lens in front, and a positive meniscus. Its strong
astigmatism and field curvature are actually advantageous for visual use, where they
largely offset these aberrations in conventional eyepieces. This also applies to
corrector's combination with a reducer lens which, being a positive lens
group, tends to generate astigmatism of the same sign and level as do conventional eyepieces. Chromatic correction
of the Jones-Bird is good - approximately a 4" f/30 achromat level - but
with excessive chromatism in the violet. As the LA graph shows, it is
mostly due to chromatic defocus (secondary spectrum).
Two-glass J-B corrector
gives better
results ( PFCB19-61 and FN11 combo
reduces the combined h/r error six fold). 
