ASTR 511 (O'Connell) Lecture Notes
TELESCOPE OPTICAL DESIGN
Hevelius 140foot Telescope (ca. 1675)
Telescope optical design is covered in detail in ASTR 512, so we give only
a flavor of what is involved here.
A. Overview
The usual goal of telescope optics design is to bring all light rays,
arriving at the primary element from a large range of field angles, to
a sharp focus in a flat focal plane. The image should be a faithful
onetoone reproduction of the angular distribution of light in the
source with minimal geometric distortion and image blur. The image
representation should be independent of the wavelength of the light
rays (i.e.
achromatic).
But it is
not possible to accomplish this. One can never build
a perfect optical device. Any realized design is always a compromise
because it is not possible to control for all
optical
aberrations at will.
Therefore, modern telescope design is essentially a process of
successive approximations in
aberration control in 3
dimensions. Fortunately, a number of highly capable software packages
are now available to mitigate the pain of doing this. In the case of
large mirrors or multiplemirror designs, continual mechanical surface
correction and alignment devices must be included.
The picture at the top of this page shows how early telescope builders
tried to control for two major aberrations in crude lenses: (1)
chromatic aberration and (2)
spherical aberration. The effects of both of these
aberrations diminish with focal length....hence the extraordinarily
long focal length of Hevelius' telescope.
The modern solution to chromatic aberration (the fact that the focal
point depends on the wavelength) in refractive optics is to
use
mirrors rather than lenses, and most large telescopes
employ mirrors as their primary optics. However, most optical
instruments must also include refractive elements in order to achieve
wavelength selection or widefield images, so chromatic aberration is
still almost always an issue.
The modern solution to spherical aberration (the fact that parallel
light rays striking the surface of a sphere do not come to a single
focus) is to use
nonspherical optics  e.g. paraboloids and
hyperboloids. Rays parallel to the axis of a parabolic reflector come
to a perfect focus. Unfortunately, offaxis rays do not, and this
leads to a cometshaped aberration known as
coma,
which becomes worse with field angle.
 Coma can be reduced by using a refractive corrector near the
focal plane of a parabolic primary.
 A widelyused alternative is the
RitcheyChretien design, a Cassegrain system that employs two
hyperbolic mirrors yielding zero firstorder coma and spherical
aberration. RC's are affected, however, by thirdorder coma,
astigmatism, and field curvature (at larger field angles).
 Another famous alternative for control of spherical aberration over a
wide field with a spherical primary is to use a special fullaperture
refractive correcting plate called a Schmidt corrector. The
Schmidt skysurvey telescopes employ these.
B. Sample Ray Traces
Click below for illustrations of ray traces for spherical and
parabolic reflectors. These show light paths for parallel incoming
rays in a plane containing the symmetry axis of the mirror. They are
for fast optical systems (small f/ ratios, where f/ = Focal
Length/Diameter), so that aberrations are larger than for typical
designs and can be seen in the diagrams. You can see that, except for
the case of a parabola and paraxial rays, it is not possible to find a
good focal point anywhere in these systems.
STANDARD TELESCOPE OPTICAL CONFIGURATIONS
TYPE 
PRIMARY MIRROR 
SECONDARY MIRROR 
COMMENTS 
PRIME FOCUS

Parabola


Focus inside telescope.
Add refractive corrector for
wide field.

NEWTONIAN

Parabola

Flat

Focus at side/top of telescope.

CASSEGRAIN

Parabola

Hyperbola (convex)

Focus below primary.

GREGORIAN

Parabola

Ellipse (concave)

Primary mirror focus before secondary. Focus below primary.

RITCHEY CHRETIEN

Hyperbola

Hyperbola (convex)

Focus below primary.
Zero coma & spherical aberration.

COUDE

Various

Various

Tertiary flat directs light
to fixed focus below polar
axis.

NAYSMITH

Various

Various

(AltAz): Tertiary flat directs light
to focus outside altitude axis.

SCHMIDT

Spherical


Catadioptric: Uses refractive corrector to provide wide field without
spherical aberration. Focus inside telescope body.

Last modified
November 2020 by rwo
Copyright © 20002020 Robert W. O'Connell.
All rights reserved. These notes are intended for the private,
noncommercial use of students enrolled in Astronomy 511 at the
University of Virginia.