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Conventional Lens Fabrication and Spherical Surfaces 121

5.2 Generation of Spherical Surfaces
Until recent years, almost all lens optical surfaces were spherical. The
generation of a spherical surface with the correct radius of curvature
was an important step in the production of any lens. Figure 5.3 shows
a diagram depicting the process of generating a spherical surface.
The blank of glass to be generated is mounted on the lower vertical
spindle. The generating tool is mounted on a spindle at an oblique
angle to the vertical spindle. Both spindles are spinning. The generat-
ing tool is hollow with both its outside and inside edges covered with
diamonds. In the diagram, a convex surface is being generated. The
inside-diameter edge W is being used. The outside-diameter edge is
used for concave surfaces, and W is slightly larger than the inside
one. Both of these edge diameters must be greater than one-half the
diameter of the part being generated. One may think in terms of the
points of edge contact forming a cord on a circle of radius of curva-
ture R of the lens. The angle θ between the axis of rotation for the tool
and that of the part being generated can be calculated by

−1
θ= sin (W/2R) (180/π)
where W is the inside diameter in this case and R the desired convex
radius of curvature. In practice, the operators are furnished tables
covering the settings for standard tools and desired curvatures by the
company that manufactures the generator. This method is practical
and has been used for many years.

FIGURE 5.3 Diagram depicting the generation of a spherical surface.