Page 342 - Modern Optical Engineering The Design of Optical Systems

Optical System Layout 321

cladding n 2 1.52, yielding a numerical aperture according to Eq. 13.26
of the order of 0.8. Since the total internal reflection (TIR) occurs at
the core-cladding interface, moisture or contact between the outer sur-
faces does not frustrate the TIR if the cladding is thick enough.
Figure 13.24b shows a flexible gastroscope or sigmoidoscope. An
objective lens forms an image of the object on one end of a coherent
fiber bundle; at the other end the transmitted image is viewed with the
aid of an eyepiece or video camera.
Ordinary photography of a cathode ray tube face is an inefficient
process. The phosphor radiates in all directions and a camera lens
intercepts only a small portion of the radiated light. A tube face com-
posed of a hermetically fused fiber array (Fig. 13.24c) can transmit all
the energy radiated into a cone defined by its NA to a contacted pho-
tographic film with negligible loss. Fused fibers are always clad with
low-index glass to separate the fibers; frequently an absorbing layer or
absorbing fibers are added to prevent contrast reduction by stray light
which is emitted at angles larger than the numerical aperture of the
fibers. Fiber optics are also available as optical conduit, that is, rigid
fused bundles, for efficient transmission of light through labyrinthian
paths, as shown in Fig. 13.24d.
Flexible plastic fibers with diameters on the order of 0.5 in are used
as single fibers in illumination systems.
A tapered, coherent, fused-fiber bundle can be used as either a mag-
nifier or minifier (depending on whether the original object is placed
at the small or large end of the taper). By twisting a coherent bundle
of fibers, either fused or not, an image erector can be made which will
carry out the function of the erector prisms described in Chap. 7. These
are often found in image-intensifier systems such as those used in
night vision goggles.
Hollow glass fibers in diameters from 0.5 to 1.0 mm, internally coated,
are moderately flexible and have been used to transmit radiation in
the 10- m wavelength region. These fibers do a reasonable job of
maintaining the gaussian distribution of the laser light.

Gradient index fibers
The preceding descriptions have dealt with fibers the principal function
of which was to transmit power from one end to the other, with little
or no concern for any coherence; energy incident on one end of the fiber
is effectively homogenized or scrambled and transmitted to the other
end. But if the index of the fiber is made high in the center, gradually
changing to low at the outside, then the ray paths through the fiber will
be curved rather than straight lines. If the index gradient is properly
chosen (i.e., approximately a function of the reciprocal of the square of