Biomedical Engineering Reference
In-Depth Information
15
Aberrations
Virtually all optical systems have aberrations that degrade the quality of the image
they create. If an aberration can be produced with a single wavelength of light, it
is referred to as a
monochromatic aberration
. In comparison,
chromatic aber-
rations
occur only with polychromatic light, which is composed of multiple wave-
lengths.
1
Aberrations are an important consideration in the design of spectacle
lenses and the correction of refractive errors.
THE PARAXIAL ASSUMPTION
AND SEIDEL ABERRATIONS
The paraxial equation (i.e., vergence relationship) is very useful because it allows us
to readily locate the images produced by spherical optical systems. It is only accu-
rate, however, for light rays that make a sufficiently small angle of incidence with the
refracting surface, commonly referred to as
paraxial rays
because they are close to
the optical axis. For these rays, we can make an assumption that sin
(in radians).
This paraxial assumption, which is made in the derivation of the paraxial equation
(refer to Appendix E for the derivation), becomes less accurate as the angle of inci-
dence increases. A better estimate of sin
θ
=
θ
θ
is given by the following expansion:
θ
θ
θ
⎛
⎝
3
3!
⎞
⎠
⎛
⎝
5
5!
⎞
⎠
⎛
⎝
7
7!
⎞
⎠
+
…
sin
θ
=
θ
−
−
+
3
/3!)] is used, image formation dif-
fers from what is predicted by the paraxial equation in five ways. These interrelated
deviations, which are referred to as
Seidel
,
or
classic
,
aberrations
, are spherical
aberration, coma, oblique (sometimes called radial or marginal) astigmatism, cur-
vature of field (power error), and distortion.
When the third-order approximation [
θ
-
(
θ
1. White light is polychromatic.
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