Page 91 - Modern Optical Engineering The Design of Optical Systems

74 Chapter Five

are called transverse aberrations. They represent the distance by which
the ray misses the ideal image point as described by the paraxial imaging
equations.
The B terms are called the third-order, or Seidel aberrations. B 1 is
spherical aberration, B 2 is coma, B 3 is astigmatism, B 4 is Petzval, and
B 5 is distortion. Similarly, the C terms are called the fifth-order aber-
rations. C 1 is fifth-order spherical aberration; C 2 and C 3 are linear
coma; C 4 , C 5 , and C 6 are oblique spherical aberrations; C 7 , C 8 , and C 9
are elliptical coma; C 10 and C 11 are Petzval and astigmatism; and C 12
is distortion.
The 14 terms in D are the seventh-order aberrations; D 1 is the seventh-
order spherical aberration. A similar expression for OPD, the wave
front deformation, is given in Chap. 15.
As noted above, the Seidel aberrations of a system in monochromatic
light are called spherical aberration, coma, astigmatism, Petzval curva-
ture, and distortion. In this section we will define each aberration and
discuss its characteristics, its representation, and its effect on the
appearance of the image. Each aberration will be discussed as if it
alone were present; obviously in practice one is far more likely to
encounter aberrations in combination than singly. The third-order
aberrations can be calculated using the methods given in Chap. 6.

Spherical aberration
Spherical aberration can be defined as the variation of focus with
aperture. Figure 5.2 is a somewhat exaggerated sketch of a simple lens
forming an “image” of an axial object point a great distance away.
Notice that the rays close to the optical axis come to a focus (intersect
the axis) very near the paraxial focus position. As the ray height at the

Figure 5.2 A simple converging lens with undercorrected
spherical aberration. The rays farther from the axis are brought
to a focus nearer the lens.