Correcting the Hyperboloid
The hyperboloid is usually the result of overshooting the paraboloid, or too zealous work in reducing the oblate spheroid. In it, the radius of curvature of the center zone is shorter than that of the edge zone; this is likewise true, of course, of the ellipsoid and the paraboloid, but with the hyperboloid the distance between the intersections of these radii with the axis is greatest.
On the Foucault stand, the shadow boundaries on all three figures will be alike, but the shadow depths will differ (see Fig. 33), the shadows darkening at a rapid rate as the distance between the centers of curvature (ba, Fig. 39) increases.
The treatment to be applied here is similar to that described for correcting the hyperbolic figure that was had from long-stroke grinding (Fig. 23). There, it will be recalled, the edge zones had to be worn back by grinding with short strokes. Now, the knife-edge should be set at the center of curvature of the edge zone, and the figure seen (Fig. 39a is similar) is taken for correction.
The edge glass must be planed down to the level of the depth at the center, and this is done with a short stroke. With this stroke, however, the distribution of the polishing cannot be so controlled as to return the figure to a sphere. Instead, an oblate spheroid is usually the outcome, and that figure can in turn be dealt with as already described.
Occasionally, where the overcorrection is not great, and especially with the molded lap, a knife-edge setting similar to Fig. 39c can be chosen, and the crests, or 70-per-cent zone (explained in the next chapter), planed down smoothly until the overcorrection is brought within the allowable tolerance.
It is quite all right to leave the mirror on the lap overnight if desired, but weights may be dispensed with. Wrap a wet cloth around the disks to prevent evaporation, and the next day you are off to a flying start with perfect contact.
Chapter VI The Paraboloid |
|
