Page 238 - Modern Optical Engineering The Design of Optical Systems

218 Chapter Ten

they can be fabricated with a zero thermal expansion coefficient.
Owens-Illinois CER-VIT was the original material; Corning ULE and
Schott ZERODUR have similar properties. These materials can be tai-
lored to have a zero thermal expansion coefficient (plus or minus about
7
1 10 ) at a given temperature. The zero thermal expansion coeffi-
cient results from the mixture of crystals (with a negative coefficient)
and amorphous glass with a positive coefficient. These materials tend
to be brittle, yellow or brown, and to scatter light, so they are not suit-
able for refracting optics.

Infrared transmitting glasses. A number of special “infrared” glasses are
available. Some of these are much like extremely dense flint glasses,
with index values of 1.8 to 1.9 and transmitting to 4 or 5 m. The
arsenic glasses transmit even further into the infrared. Arsenic-modified
selenium glass transmits from 0.8 to 18 m, but will soften and flow at
70°C. It has the following index values: 2.578 at 1.014 m; 2.481 at 5 m;
2.476 at 10 m; 2.474 at 19 m. Arsenic trisulfide glass transmits from
0.6 to 13 m and is somewhat brittle and soft. Index values: 2.6365 at
0.6 m; 2.4262 at 2 m; 2.4073 at 5 m; 2.3645 at 12 m.

Gradient index glass. As indicated in Chap. 1, if the index of refraction
is not uniform, light rays travel in curved paths rather than in straight
lines. In visualizing this, it often helps to remember that the light rays
curve toward the region of higher index. If the index varies in a con-
trolled way, this property may be advantageously utilized. Glass can
be doped by infusion with other materials, typically by the immersion
of the glass into a bath of molten salts to effect an ion exchange which
produces a changed index. A gradient also can be produced by fusing
together layers of glasses with differing indexes. Several types of index
gradient are useful in optical systems. A radial gradient has an index
which varies with the radial distance from the optical axis. An axial
gradient varies the index with the distance along the axis. A spherical
gradient varies the index as a function of the radial distance from an
axial point. An axial gradient at a spherical surface has an effect on
the aberrations which is quite analogous to that of an aspheric surface.
A radial gradient can produce lens power in a plano-plano element.
For example, a plano element the index of which varies as a function
of the radial distance r according to
2
n (r) n (1 Kr )
0
and has a length L will have a focal length given by
1
f
n 2K sin (L 2K )
0