Page 109 - Modern Optical Engineering The Design of Optical Systems

92 Chapter Five

negative element is higher than the positive, the cemented inner
surface is divergent, and will contribute overcorrected spherical to
balance the undercorrection of the outer surfaces.
Aberration correction usually is exact for only one zone of the aper-
ture of a lens or for one angle of obliquity, because the aberrations of the
individual elements do not balance out exactly for all zones and angles.
Thus, while the spherical aberration of a lens may be corrected to zero
for the rays through the edge of the aperture, the rays through the other
zones of the aperture usually do not come to a focus at the paraxial
image point. A typical longitudinal spherical aberration plot for a “cor-
rected” lens is shown in Fig. 5.19. Notice that the rays through only one
zone of the lens intersect the paraxial focus. Rays through the smaller
zones focus nearer the lens system and have undercorrected spherical;
rays above the corrected zone show overcorrected spherical. The under-
corrected aberration is called residual, or zonal, aberration; Fig. 5.19
would be said to show an undercorrected zonal aberration. This is the
usual state of affairs for most optical systems. Occasionally a system is
designed with an overcorrected spherical zone, but this is unusual.
Chromatic aberration has residuals which take two different forms.
The correction of chromatic aberration is accomplished by making the
foci of two different wavelengths coincide. However, due to the nature
of the great majority of optical materials, the nonlinear dispersion
characteristics of the positive and negative elements used in an achro-
mat do not “match up,” so that the focal points of other wavelengths do
not coincide with the common focal point of the two selected colors. This
difference in focal distance is called secondary spectrum. Figure 5.20
shows a plot of back focal distance versus wavelength for a typical
achromatic lens, in which the rays for C light (red) and F light (blue)
are brought to a common focus. The yellow rays come to a focus about
1/2400th of the focal length ahead of the C-F focal point.

Figure 5.19 Plot of longitudinal
spherical aberration versus ray
height for a “corrected” lens. For
most lenses, the maximum under-
correction occurs for the ray the
height of which is 0.707 that of the
ray with zero spherical.