"Classic" Cassegrain telescopes
The "classic" Cassegrain has a parabolic primary mirror and a hyperbolic secondary mirror that reflects the light back down through a hole in the primary. Folding the optics makes this a compact design. On smaller telescopes, and camera lenses, the secondary is often mounted on an optically flat, optically clear glass plate that closes the telescope tube. This support eliminates the "star-shaped" diffraction effects caused by a straight-vaned support spider. The closed tube stays clean, and the primary is protected, at the cost of some loss of light-gathering power.
It makes use of the special properties of parabolic and hyperbolic reflectors. A concave parabolic reflector will reflect all incoming light rays parallel to its axis of symmetry to a single point, the focus. A convex hyperbolic reflector has two foci and will reflect all light rays directed at one of its two foci towards its other focus. The mirrors in this type of telescope are designed and positioned so that they share one focus and so that the second focus of the hyperbolic mirror will be at the same point at which the image is to be observed, usually just outside the eyepiece. The parabolic mirror reflects parallel light rays entering the telescope to its focus, which is also the focus of the hyperbolic mirror. The hyperbolic mirror then reflects those light rays to its other focus, where the image is observed.
In most Cassegrain systems, the secondary mirror blocks a central portion of the aperture. This ring-shaped entrance aperture significantly reduces a portion of the modulation transfer function (MTF) over a range of low spatial frequencies, compared to a full-aperture design such as a refractor or an offset Cassegrain.[8] This MTF notch has the effect of lowering image contrast when imaging broad features. In addition, the support for the secondary (the spider) may introduce diffraction spikes in images.
The radii of curvature of the primary and secondary mirrors, respectively, in the classic configuration are
and
where
- is the effective focal length of the system,
- is the back focal length (the distance from the secondary to the focus),
- is the distance between the two mirrors and
- is the secondary magnification.
If, instead of and , the known quantities are the focal length of the primary mirror, , and the distance to the focus behind the primary mirror, , then and .
The conic constant of the primary mirror is that of a parabola, . Thanks to that there is no spherical aberration introduced by the primary mirror. The secondary mirror, however, is of a hyperbolic shape with one focus coinciding with that of the primary mirror and the other focus being at the back focal length . Thus, the classical Cassegrain has ideal focus for the chief ray (the center spot diagram is one point). We have,
- ,
where
- .
Actually, as the conic constants should not depend on scaling, the formulae for both and can be greatly simplified and presented only as functions of the secondary magnification. Finally,
and
- .
Off-axis configurations
An unusual variant of the Cassegrain is the Schiefspiegler telescope ("skewed" or "oblique reflector"; also known as the "Kutter telescope" after its inventor, Anton Kutter[9]) which uses tilted mirrors to avoid the secondary mirror casting a shadow on the primary. However, while eliminating diffraction patterns this leads to several other aberrations that must be corrected.
Several different off-axis configurations are used for radio antennas.[10]
Another off-axis, unobstructed design and variant of the Cassegrain is the 'Yolo' reflector invented by Arthur Leonard. This design uses a spherical or parabolic primary and a mechanically warped spherical secondary to correct for off-axis induced astigmatism. When set up correctly the Yolo can give uncompromising unobstructed views of planetary objects and non-wide field targets, with no lack of contrast or image quality caused by spherical aberration. The lack of obstruction also eliminates the diffraction associated with Cassegrain and Newtonian reflector astrophotography.