Above: Spot diagram of a star at the edge of the field affected by astigmatism
Like coma, astigmatism is an off-axis aberration. Unlike coma, it is a symmetrical aberration. For professional astronomers this can be an important distinction, since asymmetrical aberrations do not allow accurate astrometric (positional) measurements to be made. For amateur astronomers viewing the sky and taking pretty pictures, it is hard to choose one aberration over the other (and preferably neither would be present).
Understanding how astigmatism arises can be somewhat difficult. An optical system has two planes, the tangential and the sagittal planes, which are perpendicular to each other. If you imagine an optical diagram (below) that shows the optical path from the side, the tangential plane corresponds to the flat plane of the diagram (the computer screen) while the sagittal plane corresponds to the plane along the optical axis at a 90-degree angle--in other words the sagittal plane sticks out of the screen at 90 degrees to the screen itself.
Above: Optical diagram viewed along the tangential plane of the system. The sagittal plane sticks straight out of the screen at 90 degrees to the tangential plane.
Imagine then that the telescope has a different power (focal length) in each plane. For example, the telescope may focus closer along the tangential plane and farther along the sagittal plane. This is shown in the diagram below.
Above: Astigmatism arises from a difference of optical power in the two optical planes, tangential and sagittal
This effectively creates two focal surfaces, one corresponding to each plane. Seen from the side, as in a normal optical diagram, the two focal surfaces are normally curved (see the Field Curvature section on the next page) and coincide only at the optical axis.
Above: Two distinct focal surfaces exist in the presence of astigmatism, a tangential focal surface and sagittal focal surface
If astigmatism is eliminated, the focal surfaces will coincide across the entire field of view.
Telescope Designs with Astigmatism
Very few telescope designs have significant astigmatism. The most popular telescope with this aberration is the Ritchey-Chrétien (RC). RCs trade coma for astigmatism for the purpose of positional measurements. Hence the popularity of the design among professional astronomers. The Hubble Space Telescope, the Keck Telescope, and many other large professional telescopes are RCs. These designs have become popular with advanced amateur astronomers for CCD imaging, but for the purposes of pretty pictures there is little advantage to astigmatism over coma. In fact, the preference would be to not have either aberration. For this reason most RCs employ a correcting lens to eliminate the residual astigmatism.
Telescope Designs Free from Astigmatism
Most telescope designs are free from noticeable astigmatism. Parabolic mirrors such as those used in Newtonians do not suffer from astigmatism. Most two-mirror Cassegrain telescopes are designed specifically to eliminate astigmatism (again the RC being the exception). However, these designs suffer instead from coma.
Note that while few telescopes have astigmatism, many eyepiece designs, especially inexpensive wide-field designs, suffer from fair amounts of astigmatism. Often the poor edge quality seen in many wide-field eyepieces is attributed to coma in the telescope design while it is actually the result of eyepiece astigmatism. Fancier wide-field designs such as the TeleVue Nagler eyepieces are designed to minimize eyepiece astigmatism and hence sharpen stars at the edge of the field.