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Astigmatism
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.
Next Page - Field
Curvature
Optics 101 Aberrations Page
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