Page 115 - Modern Optical Engineering The Design of Optical Systems

98 Chapter Five

For simple uncorrected lenses the first term of Eq. 5.8 is usually
adequate to describe the aberration. For the great majority of
“corrected” lenses the first two terms are dominant; in a few cases
three terms (and rarely four) are necessary to satisfactorily represent
the aberration. As examples, Figs. 5.3, 5.24a, and 5.24b can be repre-
3
sented by TA′ c tan U′, and this type of aberration is called third-
order spherical. Figure 5.24c, however, would require two terms of the
3
expansion to represent it adequately; thus TA′ c tan U′ d tan U′.
5
The amount of aberration represented by the second term is called the
fifth-order aberration. Similarly, the aberration represented by the
third term of Eq. 5.8 is called the seventh-order aberration. The fifth-,
seventh-, ninth-, etc., order aberrations are collectively referred to as
higher-order aberrations.
As will be shown in Chap. 6, it is possible to calculate the amount of
the primary, or third-order, aberrations without trigonometric ray-
tracing, that is, by means of data from a paraxial raytrace. This type
of aberration analysis is called third-order theory. The name “first-
order optics” given to that part of geometrical optics devoted to locating
the paraxial image is also derived from this power series expansion,
since the first-order term of the expansion results purely from a longi-
tudinal displacement of the reference plane from the paraxial focus.

Notes on the interpretation of ray
intercept plots
The ray intercept plot is subject to a number of interesting interpreta-
tions. It is immediately apparent that the top-to-bottom extent of the plot
gives the size of the image blur. Also, a rotation of the horizontal (abscis-
sa) lines of the graph is equivalent to a refocusing of the image and can
be used to determine the effect of refocusing on the size of the blur.
Figure 5.23 shows that the ray intercept plot for a defocused image
is a sloping line. If we consider the slope of the curve at any point on
an H–tan U ray intercept plot, the slope is equal to the defocus of a
small-diameter bundle of rays centered about the ray represented by
that point. In other words, this would represent the focus of the rays
passing through a pinhole aperture which was so positioned as to pass
the rays at that part of the H–tan U plot. Similarly, since shifting an
aperture stop along the axis is, for an oblique bundle of rays, the equiv-
alent of selecting one part or another of the ray intercept plot, one can
understand why shifting the stop can change the field curvature and
coma, as discussed in Sec. 5.4.
The OPD (optical path difference) or wave-front aberration can be
derived from an H–tan U ray intercept plot. The area under the curve
between two points is equal to the OPD between the two rays which