Optical Design

primary mirror

secondary mirror


concave parabolic

Dall-Kirkham Cassegrain

concave elliptical

convex spherical
Classical Cassegrain

concave parabolic

convex hyperbolic
Ritchey-Chretien Cassegrain

concave hyperbolic

convex hyperbolic

There are hundreds, if not thousands, of optical designs. The four listed above are some of the most common and well known for mirror-based systems.

A spherical figure is questionably the easiest to produce. Next is the slightly deeper and therefore more difficult to produce elliptical figure. Deeper still is a parabolic and even further still is the varying degrees of hyperbolic. A sphere has a K-constant of 0/zero. A parabolic has a K-constant of -1. Anything between a 0 and -1 is some form of an elliptical shape. Anything past a -1 (i.e.: -1.25) is a hyperbolic.

A f3 primary mirror has a steeper curve than a f4. This is true no matter what the desired figure: sphere, elliptical, parabolic or hyperbolic. One of the hardest mirrors to figure is a fast hyperbolic. Some cutting edge applications have called for focal ratios as fast as f0.85. Most large, 3 meter and larger, telescopes in the past five years have used primary mirrors of f1.7 to f1.25.

Typically the focal ratio on most commercially available, under 1 meter, Cassegrains is f3.

Most convex surfaces are expensive and therefore difficult to test. The exception being the spherical convex as used by the Dall-Kirkham design. This design in particular uses a primary mirror that is only slightly more work to produce than a sphere, yet less work than a parabolic. The secondary on the Dall-Kirkham is also much more feasible to produce and test. Of the three Cassegrain types listed above though, the Dall-Kirkham has by far the worst off-axis image quality. It can be an inexpensive, specific purpose on-axis instrument. Both the Classical Cassegrain and the Ritchey-Chretien Cassegrain offer a more diverse instrument with better inherent optical quality across a field.

Any four of these designs can be built from the ground up with a corrector in mind. The corrector can greatly enhance the optical quality of the instrument at the focal plane/eyepiece. Correctors have and will continue to be utilized on optical systems. There use will continue to grow as more become aware of the dedicated corrector's potential. Even the refractor has not been isolated from the correctors use. Both in add on correctors for refractors but also inherent correctors that have become part of the optical system, i.e.: doublets of the previous century being replaced by triplet designs. The third lens element is arguably a corrector that was blended into the design.