Page 89 - Modern Optical Engineering The Design of Optical Systems

72 Chapter Five

the primary image defects are usually referred to as the Seidel
aberrations.

5.2 The Aberration Polynomial
and the Seidel Aberrations
With reference to Fig. 5.1, we assume an optical system with symme-
try about the optical axis, so that every surface is a figure of rotation
about the optical axis. Because of this symmetry, we can, without any
loss of generality, define the object point as lying on the y axis; its dis-
tance from the optical axis is y h. We define a ray starting from the
object point and passing through the system aperture at a point
described by its polar coordinates (s, ). The ray intersects the image
plane at the point x′, y′.
We wish to know the form of the equation which will describe the
image plane intersection coordinates y′ and x′ as a function of h, s, and
; the equation will be a power series expansion. While it is impractical
to derive an exact expression for other than very simple systems or for
more than a few terms of the power series, it is possible to determine
the general form of the equation. This is simply because we have
assumed an axially symmetrical system. For example, a ray which

Figure 5.1 A ray from the point y h, (x 0) in the object passes through the optical
system aperture at a point defined by its polar coordinates, (s, ), and intersects the
image surface at x′, y′.