1.3 Optical Materials

against spatial frequency. Such a graph contains very much information both as to the resolving power of the lens and the contrast in the image of coarse objects. Moreover, in calculating the MTF values, diffraction effects can be taken into account, the result being the most comprehensive representation of lens performance that can be obtained. If the lens is then constructed with dimensions agreeing exactly with the design data, it is possible to measure the MTF experimentally and verify that the lens performance has come up to the theoretical expectations.

1.2.4 System Changes

When working by hand or with a small computer, the designer will have to decide what changes he should make to remove the residual aberrations in his lens. This is often a very difficult problem, and in the following chapters many hints are given as to suitable modifications that should be tried even when using a lens design program. Often a designer will make small trial changes in some of the lens parameters and determine the rate of change, or “coefficient,” of each aberration with respect to each change. The solution of a few simultaneous equations will then indicate some reasonable changes that might be tried, although the extreme nonlinearity of all optical systems makes this procedure not as simple as one would like.

Today there are many programs for use on a high-speed computer in which a large number of aberrations are changed simultaneously by varying several lens parameters, using a least-squares technique. In spite of the enormous amount of computation required in this process, it can be performed remarkably cheaply on today’s personal computers (see Chapter 17). A skew ray trace through a spherical surface would take an experienced human computer using a Marchant mechanical calculator about 500 seconds per ray surface (pre-1955). Today, the time has been reduced using a multiprocessor personal computer to about less than 10 ns or about fifty billion times faster!

1.3 OPTICAL MATERIALS

The most common lens material is, of course, optical glass, but crystals and plastics are frequently used, while mirrors can be made of essentially anything that is capable of being polished. Liquid-filled lenses have often been proposed,

but for many obvious reasons they were practically never used until recently.26,27,28,29 Optical materials in general have been discussed by Kreidl and Rood30 and others.31,32

1.3.1 Optical Glass

There are several well-known manufacturers of optical glass, and their catalogs give an enormous amount of information about the glasses that are available; in particular, the Schott catalog is virtually a textbook of optical glasses and their properties.

Optical glasses are classified roughly as crowns, flints, barium crowns, and so on, but the boundaries of the various classes are not tightly standardized (see Figure 5.5). Optically, glasses differ from one another in respect to refractive index, dispersive power, and partial dispersion ratio, while physically they differ in color, density, thermal properties, chemical stability, bubble content, striae, and ease of polishing.

Glasses vary enormously in cost, over a range of at least 300 to 1 from the densest lanthanum crowns to the most common ordinary plate glass, which is good enough for many simple applications. One of the lens designer’s most difficult problems is how to make a wise choice of glass types, and in doing so he must weigh several factors. A high refractive index leads to weaker surfaces and therefore smaller aberration residuals, but high-index glasses are generally expensive, and they are also dense so that a pound of glass makes fewer lenses. If lens quality is paramount, then of course any glass can be used, but if cost is important the lower-cost glasses must be chosen.

The cost of material in a small lens is likely to be insignificant, but in a large lens it may be a very serious matter, particularly as only a few types are made in large pieces (the so-called “massive optics”), and the price per pound is likely to vary as much as the cube of the weight of the piece. It is perhaps surprising to note that in a lens of 12 in. diameter made of glass having a density of 3.5, each millimeter in thickness adds nearly 0.75 lb to the weight.

The color of glass is largely a matter of impurities, and some manufacturers offer glass with less yellow color at a higher price. This is particularly important if good transmission in the near ultraviolet is required. A trace of yellow color is often insignificant in a very small or a very thin lens and, of course, in aerial camera lenses yellow glass is quite acceptable because the lens will be used with a yellow filter anyway.

It will be found that the cost of glass varies greatly with the form of the pieces, whether in random slabs or thin rolled sheets, whether it is annealed, and whether it has been selected on the basis of low stria content. Some lens makers habitually mold their own blanks, and then it is essential to give these blanks a slow anneal to restore the refractive index to its stable maximum value; this is the value stated by the manufacturer on the melt sheet supplied with the glass.

A most useful feature of modern lens design programs is their inclusion of extensive catalogs of the optical properties of glasses available from the various suppliers as well as many plastics and materials useful in the infrared.

1.3.2 Infrared Materials

Infrared-transmitting materials are a study in themselves, and many articles have appeared in books and journals listing these substances and their properties.33 With few exceptions, they are not generally usable in the visible, however, because of light scatter at the crystal boundaries. An example of an exception is CLEARTRAN™ which is a water-free zinc sulfide material with transmittance from about 0.4 to 12 mm.

1.3.3 Ultraviolet Materials

For the ultraviolet region of the spectrum we have only relatively few materials that include UV-grade fused silica, crystal quartz, calcium fluoride, magnesium fluoride, sapphire, and lithium fluoride, with a few of the lighter glasses when in thin sections. With the advent of integrated circuits, the demand for finer and finer optical resolution to make masks to produce the integrated circuits and to image onto the silicon wafer, significant design and fabrication effort has been expended over the past several decades. Often these optical systems are catadioptric (see Chapter 15), but sometimes they are purely refractive. It should also be realized that these lenses are very, very expensive due to the cost of materials, fabrication, and alignment.34,35,36

1.3.4 Optical Plastics

In spite of the paucity of available types of optical plastics suitable for lens

manufacture, plastics have found extensive application in this field since World War I and particularly since the early 1950s.37,38,39 Since that time hundreds of

millions of plastic lenses have been fitted to inexpensive cameras, and they are now used regularly in eyeglasses and many other applications. Plastic triplets of f/8 aperture were first introduced by the Eastman Kodak Company in 1959, the “crown” material being methyl methacrylate and the “flint” a copolymer of styrene and acrylonitrile. The refractive indices of available optical

plastics are typically very low, so that they fall into the region below the old crown–flint line, along with liquids and a few special titanium flints. The presently available optical plastics are shown in Table 1.3 and properties of frequently used plastic optical materials are provided in Table 1.4.

These refractive index and dispersion data are not highly precise since they depend on such factors as the degree of polymerization and the temperature. The spectral dispersion curves for acrylic, polystyrene, and polycarbonate modeled in the optical design programs CODE V, OSLO, and ZEMAX showed nontrivial differences (up to about 0.005).40 This is an example where the lens designer should take care to be certain the optical material data are adequately valid for the intended purpose.

Table 1.3

Currently Available Plastic Optical Materials