Page 108 - Modern Optical Engineering The Design of Optical Systems

The Primary Aberrations 91

curled inward. The wave front shown is “ahead” of the reference sphere;
the distance by which it is ahead is called the optical path difference,
or OPD, and is customarily expressed in units of wavelengths. The
wave fronts associated with axial aberrations are symmetrical figures
of rotation, in contrast to the off-axis aberrations such as coma and
astigmatism. For example, the wave front for astigmatism would be a
section of a torus (the outer surface of a doughnut) with different radii
in the prime meridians. For off-axis imagery, the reference sphere is
chosen to pass through the center of the exit pupil (in some calcula-
tions, the reference sphere has an infinite radius, for convenience in
computing).

5.7 Aberration Correction and Residuals
Section 5.4 indicated two methods which are used to control aberra-
tions in simple optical systems, namely lens shape and stop position.
For many applications a higher level of correction is needed, and it is
then necessary to combine optical elements with aberrations of opposite
signs so that the aberrations contributed to the system by one element
are cancelled out, or corrected, by the others. A typical example is the
achromatic doublet used for telescope objectives, shown in Fig. 5.18.
A single positive element would be afflicted with both undercorrected
spherical aberration and undercorrected chromatic aberration. In a
negative element, in the other hand, both aberrations are overcorrected.
In the doublet a positive element is combined with a less powerful
negative element in such a way that the aberrations of each balance
out. The positive lens is made of a (crown) glass with a low chromatic
dispersion, and the negative element of a (flint) glass with a high
dispersion. Thus, the negative element has a greater amount of chro-
matic aberration per unit of power, by virtue of its greater dispersion,
than the crown element. The relative powers of the elements are chosen
so that the chromatic exactly cancels while the focusing power of the
crown element dominates.
The situation with regard to spherical aberration is quite analogous
except that element power, shape, and index of refraction are involved
instead of power and dispersion as in chromatic. If the index of the

Figure 5.18 Achromatic doublet
telescope objective. The powers
and shapes of the two elements
are so arranged that each cancels
the aberrations of the other.