Page 38 - Modern Optical Engineering The Design of Optical Systems

Chapter
2

Gaussian Optics:

The Cardinal Points

2.1 Introduction
The action of a lens on a wave front was briefly discussed in Sec. 1.4.
Figures 1.8 and 1.9 showed how a lens can modify a wave front to form
an image. A wave front is difficult to manipulate mathematically, and
for most purposes the concept of a light ray (which is the path
described by a point on a wave front) is much more convenient. In an
isotropic medium, light rays are straight lines normal to the wave
front, and the image of a point source is formed where the rays converge
(or appear to converge) to a concentration or focus. In a “perfect” lens
the rays converge to a point at the image.
For purposes of calculation, an extended object may be regarded as
an array of point sources. The location and size of the image formed by
a given optical system can be determined by locating the respective
images of the sources making up the object. This can be accomplished
by calculating the paths of a large number of rays from each object
point through the optical system, applying Snell’s law (Eq. 1.3) at each
ray-surface intersection in turn. However, it is possible to locate optical
images with considerably less effort by means of simple equations
derived from the limiting case of the trigonometrically traced ray (as
the angles involved approach zero). These expressions yield image
positions and sizes which would be produced by a perfect optical
system; they are paraxial or first-order.
The term “first-order” refers to a power series expansion equation
which can be derived to define the intersection point of a ray in the

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