Page 340 - Modern Optical Engineering The Design of Optical Systems

Optical System Layout 319

This is the minimum value for the numerical aperture; as indicated below
and in Fig. 13.23, skew rays have a larger NA than do meridional rays.
Again, with reference to Fig. 13.22, it is apparent that if the meridi-
onal ray had entered the cylinder well above or well below the axis, it
would have emerged with a slope angle of U. The path of a pair of
skew rays is indicated (in an end-on view) in Fig. 13.23. Note that
a skew ray is rotated with each reflection and that the amount of
rotation depends on the distance of the ray from the meridional plane.
Thus, a bundle of parallel rays incident on one end of a cylinder will
emerge from the other end as a hollow cone of rays with an apex angle
of 2U. If the diameter of the cylinder is small, diffraction effects may
diffuse the hollow cone to a great extent. It is also worth noting that
since the skew rays strike the surface of the cylinder at a greater angle
of incidence than the meridional rays, the numerical aperture for skew
rays is larger than that for meridional rays.
If the light-transmitting cylinder is bent into a moderate curve, a
certain amount of light will leak out the sides of the cylinder. However,
the major portion of the light is still trapped inside the cylinder, and a
simple curved rod is occasionally a convenient device to pipe light from
one location to another.
Optical fibers are extremely thin filaments of glass or plastic.
Typical diameters for the fibers range from 1 to 2 m to 25 m or
more. At these small diameters, glass is quite flexible, and a bundle of
optical fibers constitutes a flexible light pipe. Figure 13.24 shows a few
of the applications of fiber optics. Figure 13.24a indicates the basic
property of an oriented, or “coherent,” bundle of fibers in transmitting
an image from one end of the fiber to the other. If the bundle is con-
strained at both ends so that each fiber occupies the same relative
position at each end, then the fiber rope may literally be tied in knots
without affecting its image-transmitting properties. Fiber bundles with
lengths of many feet are obtainable with surprisingly high transmissions.

Figure 13.23 The path of skew
(nonmeridional) rays through a
reflecting cylinder is a sort of
helix. The amount of rotation a
ray undergoes in traversing a
given length depends on its
entrance position.