Quantifying Mirror Distortion
Name: Enrique C.
How can the distortion of an image viewed in a
mirror be stated, or quantified?
As you may already know, introductory and advanced physics textbooks contain
many mathematical formulas that relate to how and where an image is produced
by lenses and mirrors.
However, "distortion of an image" is in the eye of the beholder -- it can be
described, but not "quantified." For example, is the distortion to which you
refer the result of an out-of-focus condition, astigmatism, lack of
contrast, barrel distortion, pincushion distortion, spherical or chromatic
aberration etc.? That which constitutes distortion in the eye of a person
with perfect eyesight might not even be noticed by one with less than
If you mean a flat mirror, then the distortions are just a result of it
not being flat. These can be quantified in terms of how many wavelength
different are the various paths to the image. After all, if an mirror
is to reflect, all "rays" from a object point should make it to the
image with the same optical path, and the mirror should not be so wavy
that it throws other light into the path. If you want to go further,
then a flat mirror is just a special case of a curved mirror.
The distortions of a curved mirror are quantified the same as the
distortions in a lens. This means that with few changes to the math,
applying the same equations, you can understand mirrors as easily as
lenses, for optics. Under the heading of 5th order aberrations or
corrections, people came up with 5 distortions: spherical aberration
(SA), coma, astigmatism, field distortion, curvature of field long ago
(before computers). These are called the Siedel aberrations I think.
But again this was a way to explain problems with optics in an age
before exact computations were easy. So people spent much time on
this, and there are chapters in optics books on the subject, with lots
These aberrations produce very recognizable distortions. SA makes the
image dot sort of a fuzzy circle, but symmetric. (Its what the Hubble
Space Telescope had when first launched, and they needed to correct by
going back with astronauts). Coma leads to a "comet" like tail on the
image. Astigmatism can be seen sort of if you rotate the lens -- take a
pair of glasses from someone who has astigmatism, and rotate them, but
continue to look through the lens, and look at a piece of graph paper.
You will see the lines of the graph paper wave around. Now try this with
a pair of reading glasses from K-mart (no astigmatism correction), you
do not see the same. Distortion makes a piece of graph paper look like a
barrel instead of a square grid etc, etc.
I doubt many people know these equations by heart anymore, but the
affects are still useful to simplify things. (It is not much fun to
just tell people go run a computer code, it helps to know how things
scale, or change if you "tweak" on this or that).
The useful thing here is the simple equations guide you. You see that
some aberrations cannot be seen if the light is basically going through the
center of the lens. In this case, in the day time, your pupils
contract, you only use the center of the lens, and you do not see the
effect (same with camera on a bright sunny day). But if you need to
open up the lens more, then more of the glass is being used, and you
pick up the effects. Of course modern cameras have these things pretty
I refer you to almost any college level book on optics, but do not bother
too much with the math, look for pictures of how the image gets
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Update: June 2012