Imaging with other Telescope Designs
Other Telescope Designs
While the Schmidt-Cassegrain, Newtonian, and refractor are the most common optical designs used for CCD imaging and observing in general, other types are becoming increasingly popular.
Classical Cassegrain
Above: Optical layout of a Classical Cassegrain telescope
The Classical Cassegrain is actually a fairly uncommon type of telescope, but we discuss it since it is the basis for a variety of other designs. A Cassegrain telescope consists of a paraboloidal primary mirror (just like a Newtonian), with a convex secondary mirror (specifically a hyperboloidal shape). The secondary reflects light back through a hole in the center of the primary mirror and out to the eyepiece or camera. The secondary is held in place by a spider (as in a Newtonian). Focusing is usually achieved by an external Crayford or rack-and-pinion type system similar to what a refractor would have.
The Classical Cassegrain is generally designed to have a long focal ratio (f/12-f/20 is common), and is most often intended as a planetary telescope. Because of its slow focal ratio, the Classical Cassegrain in not usually employed for deep-sky CCD imaging, although it is possible to design a Cassegrain with a faster focal ratio (f/8 or so). Cassegrains tend to be much longer than other folded optical designs since their primary mirrors often have focal ratios of around f/4 (whereas an SCT is usually about f/2). Another disadvantage is that Classical Cassegrains tend to be much more expensive than other designs, the better models currently manufactured rivaling apochromatic refractors in cost (around $1000 per inch of aperture).
The Classical Cassegrain suffers from coma and field curvature, similarly to a standard Schmidt-Cassegrain telescope (SCT). These aberrations require a field flattener lens for optimum performance with a camera.
PROS
- Long focal length is good for planetary imaging and other small targets
- More compact than equivalent focal length Newtonian
CONS
- Long optical tube relative to other Cassegrain variations
- Generally very expensive
- Slow focal-ratio makes for longer exposure times
- Suffers from coma and field curvature, normally requires field corrector
Ritchey-Chrétien
Above: Optical layout of a Ritchey-Chrétien telescope
This is an interesting variation on the Cassegrain and a very popular system for advanced CCD imagers. The Ritchey-Chrétien (RC) telescope uses two hyperboloidal mirrors. This design allows the system to be free of the aberration known as coma, unlike the Classical Cassegrain or SCT. The advantage of this design, for professional astronomers especially, is that the stars all appear round, even at the very edges of the field (unlike the comet-shaped stars in a system suffering from coma). This means extremely precise astrometric (positional) measurements are possible. Most professional telescopes, from the Keck to the Hubble Space Telescope, are Ritchey-Chrétien designs. This also means they are often very expensive, as these aspherical mirrors are very difficult to make. Also, RCs still suffer from astigmatism and field curvature and thus do not give perfectly round stars at the edge of the field. For professionals measuring stellar positions, this is preferable to coma, but for imaging is not any real improvement. Most RCs require the use of field correctors that eliminate the residual astigmatism and field curvature.
Above: Three stars as they would appear at the edge of a field of view. On the left, a scope suffering from coma (center of the field is down) such as a Classical Cassegrain. Middle star is from a scope with astigmatism, such as an RC. Right star is unaberrated, as might be the case in an RC with a field corrector or other sophisticated design.
There are several manufacturers of amateur RC telescopes, and these instruments have gained in popularity in recent years. RCs have the same advantages as the Schmidt-Cassegrain systems: compact design, relatively long-focal length (provides good image scale for small targets), and a relatively fast focal ratios (at least compared to Classical-Cassegrains and Maksutov-Cassegrains). High-end RCs rival apochromatic refractors in price (about $1000 per inch of aperture) and since they are rarely built smaller than 10" in size, it is unlikely that one could be had for less than a 5-digit price. Recently, less expensive imported RC telescopes have become popular at a much lower price point.
PROS
- Compact optical tube
- Very good image quality
- f/7-f/9 focal ratio means shorter exposure times than other typical Cassegrain designs
CONS
- Good quality ones are expensive
- Long focal length limits wide-field imaging
- Suffers from field curvature and astigmatism, requires a field corrector for large CCD chips
Corrected Dall-Kirkham
Above: Optical layout of a Corrected Dall-Kirkham telescope
The Dall-Kirkham (DK) is a design variation on the Classical Cassegrain. By using an ellipsoidal primary mirror, it is possible to make a system free from spherical abberation by using a spherical secondary mirror, which is much easier to make and test than the hyperbolic secondary in a Classical Cass or RC. The drawback is the off-axis coma grows to pretty unacceptable levels. A standard DK telescope is usually designed as a very long focal length planetary scope.
The Corrected Dall-Kirkham (CDK), uses a pair of corrector lenses ahead of the focal plane to eliminate basically all aberrations. The result is a relatively easy-to-make telescope that has exceptional performance. CDKs have largely replaced high-end RCs as the telescope of choice for advanced imagers wanting a high-resolution instrument.
PROS
- Excellent optical quality
- Less expensive than a comparable quality RC
- f/7-f/8 focal ratio is modestly fast for a Cassegrain
CONS
- Most available models are still high end telescopes and not inexpensive
Harmer-Wynne
Above: Optical layout of a Harmer-Wynne telescope
The Harmer-Wynne (HW) design was originally published by two professional opticians in 1976. Only one professional telescope of the design was made, but it occurred to us at Starizona that the design was ideal for an amateur telescope. Like the CDK it has relatively easy to make optics: a parabolic primary, spherical secondary, and two corrector lenses ahead of the focal plane. We produced the first amateur Harmer-Wynne telescopes as our Hyperion series.
The HW gives incredible performance, diffraction-limited spots over a very large field of view (optimized for 70mm in the Hyperions). This allows its use with huge format CCD cameras. The performance is as good or better than a field-corrected RC, long the standard of comparison, but the optics are much easier to manufacture. The spherical secondary also relaxes the alignment tolerances on that mirror, making collimation easier.
PROS
- Excellent optical quality
- Less expensive than a comparable quality RC
- f/7-f/8 focal ratio is modestly fast for a Cassegrain
CONS
- Most available models are still high end telescopes and not inexpensive
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Understanding Mirror Shapes A variety of shapes are used in manufacturing various telescopes. Below are the different possible shapes for mirrors and the telescopes that use certain combinations of mirrors and the reasons for those mirror choices in a design. Spheroidal -- The simplest curved mirror shape is that of a sphere. Simply grinding two pieces of glass together will yield a spheroidal shape. Paraboloidal -- A parabola is a slightly more complex shape than a sphere, but is not too much more difficult to make. Simplest of the aspheric (non-spherical) shapes. Hyperboloidal -- A hyperbola has a more complex shape than a parabola and is thus very difficult to manufacture. Hyperbolas are larger than parabolas (see below). Ellipsoidal -- Ellipses are smaller than parabolas but are still difficult to manufacture. The image below shows the mathematical shapes behind each mirror design.
Above: The black line represents a flat mirror. Only two shapes have exact specifications: the sphere and the parabola. The orange line represents a sphere, which is defined by only one mathematical equation. The green line represents a parabola, also defined by a specific equation. Ellipses and hyperbolas, on the other hand, have infinite variety. The blue line represents a specific hyperbola, but any curve in the blue section of the graph would be a hyperbola. Likewise the yellow curve represents a prolate ellipse (in which the foci are parallel to the optical axis, in other words, the ellipse's long axis runs along the optical axis), but all the curves within the yellow area would be prolate ellipses. The same is true for the oblate ellipse family, which inhabits the red part of the graph. Oblate ellipses have their long axes perpendicular to the optical axis. Newtonian -- Paraboloidal primary mirror, flat secondary. Simple design, suffers from coma. Classical Cassegrain -- Paraboloidal primary, hyperboloidal secondary. More complex design, suffers from coma. Ritchey-Chrétien -- Hyperboloidal primary and secondary. Complex design, suffers from astigmatism but not coma. Dall-Kirkham -- Ellipsoidal primary, spheroidal secondary. Spherical secondary simplifies design, suffers from coma. Pressman-Camichel -- Spheroidal primary, ellipsoidal secondary. Spheroidal primary greatly simplifies design, suffers extreme coma. Schmidt-Cassegrain/Maksutov Newtonian -- Spheroidal primary and secondary (in most commercial designs). Simple design, requires corrector lens to eliminate spherical aberration, suffers from coma, using an aspheric secondary eliminates coma. Schmidt-Newtonian/Maksutov-Newtonian -- Spheroidal primary, flat secondary. Requires corrector lens to eliminate spherical aberration, less coma than standard Newtonian. Corrected Dall-Kirkham -- Ellipsoidal primary, spheroidal secondary, two-element corrector. Easier to make and less expensive than RC, better performance. Harmer-Wynne -- Parabloidal primary, spheroidal secondary, two-element corrector. Easier to make and less expensive than RC, excellent performance. |
