Caustic coordinates in Platzeck-Gaviola test of conic mirrors.
The centers of curvature of all zones of a spherical mirror coincide at the center of that sphere. In the case of all other conies of revolution, however, the radii of curvature of dif­ ferent zones have different magnitudes; hence their centers of curvature do not coincide but lie along the caustic curve, as shown by Wadsworth. Based on this property Platzeck and Gaviola devised a test to measure the shape of a para­ boloid being figured. What they do is to measure the posi­ tions of the centers of curvature of different regions in the optical surface, then the results are compared with the theo­ retical values. The theoretical positions of these centers of curvature for a paraboloid are computed with two simple formulas given by Schroader, but to our knowledge the ex­ pressions for any conic of revolution have not been given. To derive the expressions for the caustic coordinates (η,ξ) of the centers of curvature of the conic surface (see Fig. 1), we
Conic constant and paraxial radius of curvature measurements for conic surfaces.
From a set of previously derived equations for conic surfaces, we derived another set of equations from which the conic constant k and the paraxial radius of curvature r can be obtained, if at least three values of the longitudinal aberration X and their corresponding angles θ of the normals to the surface are measured. The procedure is useful when the area around the vertex surface cannot be used. Some experimental results are presented.
On the Quantitative Use of the Foucault Knife-Edge Test
The work described in the foregoing paper made the development of a quantitative method of surveying surfaces necessary, that could be used for local measurements and on nonsymmetric surfaces. The theory of the method and the experimental technique are described. The accuracy of the survey is better than 1/20 wave-length with visual subjective observation and could be carried up to 1/100 wave-length with objective photographic measurements. The errors of the Foucault knife-edge test, especially the one produced by parallax, are discussed. Ways of reducing or eliminating them are described.