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◄ 10. CATADIOPTRIC TELESCOPES   ▐    10.1.2. Single-lens field flattener ►

10.1.2. Sub-aperture corrector examples (1)

Systems with sub-aperture correctors are relatively infrequent and, in the commercial telescope 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. Sub-aperture Schmidt corrector can also be used to enhance off-axis performance of a telescope (for instance, to reduce or cancel astigmatism in the Ritchey-Chrétien), but it is seldom used for this purpose in amateur telescopes.

Even a single-element lens corrector in the form of equal or near-equal radii meniscus, can significantly improve field performance of a fast paraboloidal mirror (FIG. 98A), or even make possible to use fast spherical mirror (FIG. 98B). Since paraboloid forms good near-axis image on its own, the former is a hybrid catadioptric. The latter is a true catadioptric, since fast spherical mirrors alone are pretty much useless for astronomical use. In both instances the corrector is placed in front of the diagonal flat.

FIGURE 98: (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 somewhat greater in the latter, due to the 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. The black circle represents e-line (546nm) Airy disc.   SPEC'S

Sub-aperture meniscus corrector for a single mirror can be also placed closer to the focal plane, at the bottom of the focuser. Off-axis correction here is nearly as good as with the corrector placed in front of the diagonal flat, while offering advantages of smaller meniscus and lighter, smaller diagonal flat assembly.

A simple doublet corrector of Jones-Bird type can also achieve a good overall correction level in combination with spherical mirror (FIG. 99). Even simpler version, a split meniscus concave toward mirror, with the front surface somewhat stronger (intermediate form toward the above meniscus corrector) , also corrects for spherical aberration and coma, while introducing strong astigmatism and field curvature. It offers better control of secondary spectrum, but has some lateral color.

 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 99: Ray spot diagram for 200mm ƒ/5.9 system with ƒ/4 spherical primary and Jones-Bird type corrector (Telescope Optics, Rutten/Venrooij), placed in front of the flat. Black circle is the e-line Airy disc. The corrector is a single-glass lens doublet: bi-concave front lens and positive meniscus. Its strong astigmatism  and field curvature can be advantageous for visual use, to partly offset these aberrations in conventional eyepieces (also those of a typical reducer lens). Chromatic correction of the Jones-Bird is good - approximately a 4" ƒ/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 near plano-convex or PCX, 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. Large, fast amateur mirrors in particular benefit from a corrector of this type (FIG. 100).


FIGURE 100: Three-element Wynne-type corrector for fast paraboloid designed by Richard Snashall (optical design pages). It uses a single common crown glass (BK7) to achieve near perfect correction over 0.5° field radius (raytrace by OSLO EDU). Black circle represents the e-line (546nm) Airy disc. Corrector performance further improves with reducing the aperture, and more so with the relative aperture reduction. This level of correction probably reaches near-limit with a 3-element Wynne corrector made of a single common glass. While it is safe to assume that even better correction level is possible if using different glasses, that wouldn't result in practical benefit to an average user, since the size of corrected field is already exceeding standard requirements, and the aberration level is well below detectable (even without considering much greater magnitude of the seeing error). Note that this type of corrector can also be used to correct hyperboloidal mirror, with similar results (it is used to correct prime focus image of large observatory Ritchey-Chrétien telescopes). While the correction level achievable with Wynne corrector is impressive, these lenses pack large amounts of aberrations - astigmatism, coma and chromatism - thus require tight fabrication and mounting standards. The raytrace indicates that they are well worth the effort and time.                     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. 101).


FIGURE 101: Ray spot plot for 10" ƒ/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 1o 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. However, it is still quite small, and can easily be remedied by using slightly different glasses, for instance LAF9 for the front element. Low level of aberrations allows upscaling to significantly larger apertures. The two corrector lens elements are of a simple easy to fabricate; main fabrication difficulty is the relatively strongly aspherised primary mirror. Needed in-focus distance for the corrector is relatively small, allowing it to be mounted below 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 the above examples of the 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. 138).

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.


◄ 10. CATADIOPTRIC TELESCOPES   ▐    10.1.2. Single-lens field flattener ►

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