Recently, a reader of these pages asked me what I meant by “distortion”
— a word I use frequently here. My initial impuse was to ask,
“Don't you have a dictionary?” But when I looked at several on-line
dictionaries, I was dismayed to find that most of them never explain the
uses of this word in optics.
Two kinds of “distortion”
To begin with, it's used in two different ways. In connection with
mirages and other phenomena of atmospheric optics, it means the
changes in shape of the images of distant objects, which are usually
either stretched or compressed by changes in
It's important to notice that atmospheric refraction displaces images only
in the vertical direction, because the surfaces of constant density in the
air are very nearly horizontal. It's the gradient in refractivity that
shifts images; and that gradient is nearly always close to vertical. (The
main exception is very close to inclined or vertical surfaces, where the
direction of the gradient is perpendicular to the surface — as in
mural mirages ,
In this context, distortion refers to the vertical
compression of images in
stooping, and the
vertical expansion of images in
But the atmospheric distortion of images is usually a lot more complicated
than that; see the
of mirages — especially, those of
— for examples.
The word is also used in connection with lens design, where “distortion”
is one of the five classical aberrations of lenses. Here again, the term
refers to the deformation of images; but in the optics of lens systems
with rotational symmetry, the image displacements are in the radial
direction, toward or away from the axis of the system. Distortion in lens
systems changes the magnification with distance from the axis, so that
straight lines in object space become curved in image space.
If we regard the refracting atmosphere as a lens, it's a very astigmatic
one: almost all of its power in in the vertical, and the horizontal power
is negligible. From that point of view, we can say that the vertical
deformations produced by the atmosphere are something like the
lens-makers' astigmatism; but in the context of lenses, the word
distortion is restricted to a particular effect of the
third-order term in the expansion of the sine function, while the
atmospheric kind of distortion encompasses all orders, and usually
involves such high-order terms that the idea of a series expansion is
Other ambiguous words
While we are thinking about ambiguous terminology, maybe it's worth
mentioning the word aberration , which appears in two
different contexts here.
In the previous section, I mentioned optical aberrations, one of which is
distortion. There are five different aberrations — to be precise,
five different third-order aberrations — that texts
on lens design deal with: spherical; coma; astigmatism; distortion; and
field curvature. Each of these arises from the third-order term
in the series expansion of the sine function. (There are two angles to be
considered, so we have several effects that result from their interactions.)
Notice that distortion is just one of the five classical third-order
aberrations. I was disgusted to find an on-line dictionary that said the
words aberration and distortion were synonyms;
distortion is just one of five third-order aberrations.
In addition, lens designers have to deal with chromatic aberration,
which is due to the
of all transparent physical media, whether solid, liquid, or gaseous.
(Green flashes are caused by a combination of the dispersion and the
distortion of atmospheric refraction.)
But astronomers also deal with a different image displacement, which is
due to the relative motion between a light source (such as a star or
planet) and the observer. Historically, this effect was named the
aberration of light . It was discovered by James Bradley in
1727, though its effects had been noticed earlier; Bradley managed to find
a sensible explanation for it. (You will find that Wikipedia has a long
page that will tell you more than you want to know about this.)
Today, Bradley's explanation is regarded as obsolete and incorrect.
Properly, the aberration of light is a relativistic effect that
requires the Special Theory of Relativity to be understood correctly.
Fortunately, we need not go into its details here.
Just remember that most of the mentions of aberration in the
refer to this kind of “aberration”, not the kinds lens designers have to
© 2023 Andrew T. Young
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