Page 88 - Modern Optical Engineering The Design of Optical Systems

Chapter
5

The Primary Aberrations

5.1 Introduction
In the preceding chapters we discussed the image-forming character-
istics of optical systems, but we limited our consideration to an infinite-
simal thread-like region about the optical axis called the paraxial
region. In this chapter we will consider, in general terms, the behavior
of lenses with finite apertures and fields of view. It has been pointed
out that well-corrected optical systems behave nearly according to the
rules of paraxial imagery. This is another way of stating that a lens
without aberrations forms an image of the size and in the location
given by the equations for the paraxial or first-order region. We shall
measure the aberrations by the amount by which rays miss the paraxial
image point.
It can be seen that aberrations may be determined by calculating
the location of the paraxial image of an object point and then tracing a
large number of rays (by the exact trigonometrical ray-tracing equations
of App. A) to determine the amounts by which the rays depart from the
paraxial image point. Stated this baldly, the mathematical determina-
tion of the aberrations of a lens which covered any reasonable field at
a real aperture would seem a formidable task, involving an almost
infinite amount of calculation. However, by classifying the various types
of image faults and by understanding the behavior of each type, the
work of determining the aberrations of a lens system can be simplified
greatly, since only a few rays need be traced to evaluate each aberra-
tion; thus the problem assumes more manageable proportions.
Seidel investigated and codified the primary aberrations and
derived analytical expressions for their determination. For this reason,

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