We present calculations with an exact ray trace to determine the dimensions that define one or two Hindle spheres, since the paraxial theory is incongruent for convex hyperboloid mirrors with small <i>f</i> numbers. The equations are generalized to calculate the dimensions of <i>n</i> Hindle spheres, since in this way it is possible to reduce the dimensions of the spheres more. Actual calculations are done for the secondary mirrors of the Benemerita Universidad Autonoma de Puebla and Large Milimetric Telescopes; experimental results are shown for the latter.
© 1999 Optical Society of America
(080.0080) Geometric optics : Geometric optics
(110.6770) Imaging systems : Telescopes
(120.4800) Instrumentation, measurement, and metrology : Optical standards and testing
(230.4040) Optical devices : Mirrors
(350.1260) Other areas of optics : Astronomical optics
María E. Percino-Zacarias and Alberto Cordero-Dávila, "n-Hindle-Sphere Arrangement with an Exact Ray Trace for Testing Hyperboloid Convex Mirrors," Appl. Opt. 38, 6050-6054 (1999)