Page 239 - Modern Optical Engineering The Design of Optical Systems

Optical Materials 219

and a back focal length of
1
bf l
n 2K tan (L 2K )
0
This effect is the basis of the GRIN rod lens and the SELFOC lens.
K is called the Gradient constant, and is a function of wavelength and
material.

10.4 Crystalline Materials

The valuable optical properties of certain natural crystals have been
recognized for years, but in the past the usefulness of these materials
was severely limited by the scarcity of pieces of the size and quality
required for optical applications. However, many crystals are now
available in synthetic form. They are grown under carefully controlled
conditions to a size and clarity otherwise unavailable.
The table of Fig. 10.7 lists the salient characteristics of a number of
useful crystals. The transmission range is indicated in micrometers for
a 2-mm-thick sample; the wavelengths given are the 10 percent trans-
mission points. Indices are given for several wavelengths in the trans-
mission band.
Crystal quartz and calcite are infrequently used because of their
birefringence, which limits their usefulness almost entirely to polariz-
ing prisms and the like. Sapphire is extremely hard and must be
processed with diamond powder. It is used for windows, interference
filter substrates, and occasionally for lens elements. It is slightly bire-
fringent, which limits the angular field over which it can be used. The
halogen salts have good transmission and refraction characteristics,
but their physical properties often leave much to be desired, since they
tend to be soft, fragile, and occasionally hygroscopic.
Germanium and especially silicon are widely used for refracting ele-
ments in infrared devices. They are much like glass in their physical
characteristics, and can be processed with ordinary glass-working
techniques. Both are metallic in appearance, being completely opaque
in the visible. Their extremely high index of refraction is a joy to the
lens designer since the weak curvatures which result from the high
index tend to produce designs of a quality which cannot be duplicated
in comparable glass systems. Special low-reflection coatings are nec-
essary since the surface reflection (per Eq. 10.1 et seq.) is very high,
for example, 36 percent per uncoated germanium surface. Zinc sulfide,
zinc selenide, and AMTIR are also widely used in infrared systems.
Worthy of special mention is calcium fluoride, or fluorite. This mate-
rial has excellent transmission characteristics in both ultraviolet