1.1.5 Establishing Tolerances

It is essential for the lens designer to assign a tolerance to every dimension of a lens, for if he does not do so somebody else will, and that person’s tolerances may be completely incorrect. If tolerances are set too loose a poor lens may result, and if too tight the cost of manufacture will be unjustifiably increased. This remark applies to radii, thicknesses, airspaces, surface quality, glass index and dispersion, lens diameters, and perfection of centering. These tolerances are generally found by applying a small error to each parameter, and tracing sufficient rays through the altered lens to determine the effects of the error.

Knowledge of the tolerances on glass index and dispersion may make the difference between being able to use a stock of glass on hand, or the necessity of ordering glass with an unusually tight tolerance, which may seriously delay production and raise the cost of the lens. When making a single high-quality lens, it is customary to design with catalog indices, then order the glass, and then redesign the lens to make use of the actual glass received from the manufacturer. On the other hand, when designing a high-production lens, it is necessary to adapt the design to the normal factory variation of about 0.0005 in refractive index and 0.5% in V value.20

Matching thicknesses in assembly is a possible though expensive way to increase the manufacturing tolerances on individual elements. For instance, in a Double-Gauss lens of the type shown in Figure 1.3, the designer may determine permissible thickness tolerances for the two cemented doublets in the following form:

each single element: 0.2 mm each cemented doublet: 0.1 mm

the sum of both doublets: 0.02 mm

Clearly such a matching scheme requires that a large number of lenses be available for assembly, with a range of thicknesses. If every lens is made on the thick side no assemblies will be possible.

Figure 1.3 A typical Double-Gauss lens.

Very often the most important tolerances to specify are those for surface tilt and lens element decentration. A knowledge of these can have a great effect on the design of the mounting and on the manufacturability of the system. A decentered lens generally shows coma on the axis, whereas a tilted element often leads to a tilted field. Some surfaces are affected very little by a small tilt, whereas others may be extremely sensitive in this regard. A table of tilt coefficients should be in the hands of the optical engineers before they begin work on the mount design.

The subject of optical tolerancing is almost a study in itself, and the setting of realistic tolerances is far from being an obvious or simple matter. Table 1.1 presents the generally accepted tolerances for a variety of optical element attributes at three production levels, namely commercial quality, precision quality, and manufacturing limits. Tolerances for injection molded polymer optics are given in Table 1.2.21

Table 1.1

Optics Manufacturing Tolerances for Glass

Source: Reprinted by permission of Optimax Systems, Inc.