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
f numbers. The equations are generalized to calculate
the dimensions of n 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
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