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9. REFRACTING TELESCOPES   ▐    10.1. Sub-aperture corrector aberrations
 

                             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).


FIGURE 79: (A) Ray spot plot for a fast paraboloid with meniscus-type coma corrector. With the coma nearly corrected, dominant aberration is astigmatism, limiting diffraction-limited field to 0.18° radius, over three times that of the paraboloid alone; since the astigmatism offsets with that of the eyepiece, actual visual field is larger, limited by eyepiece astigmatism. (B) Ray spot plot for a fast sphere with sub-aperture meniscus corrector. This one has slightly different radii, which is needed to generate sufficient corrective spherical aberration at a reasonable lens thickness (mirror alone has 1.4 wave of spherical aberration). Both correctors offer similar diffraction-limited field (angular), and near perfect longitudinal chromatic correction. Lateral chromatism is more noticeable in the latter, due to a thicker meniscus, but still within tolerable. Neither corrector is fully optimized, but should illustrate most of their potential. While appearing quite simple to make, they require very high surface radius accuracy for given meniscus thickness, which has nearly as tight tolerance itself. This is partly offset by greater simplicity of mounting and collimating a single element.  Black circle represents the e-line (546nm) Airy disc.                      SPEC'S

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.

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).        SPEC'S

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).


FIGURE 81
: Wynne-type corrector designed by M. I. Jones. It uses a single common crown glass (BK7) to achieve near perfect correction over 0.4° field radius (raytrace by OSLO EDU). Black circles represent the Airy disc diameter  for the corresponding wavelength, with the one for the combined blur being that in the e-line (546nm).                              
SPEC'S

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.


9. REFRACTING TELESCOPES   ▐    10.1. Sub-aperture corrector aberrations

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