GEOMETRY OF THE HALF-SYMMETRIC IMAGE.

Herzberger defined the half-symmetric image as the image formed when the manifold of diapoints degenerates into a curve on the meridian plane. The caustic associated with the half-symmetric image is here analyzed in terms of the W and the C// plus or minus functions discussed in an earlier paper. It is shown that two cases are obtained. In one, an aberration pattern is produced which resembles coma. In the other, an object point is imaged as a curve on the meridian plane and thus resembles astigmatism. However, true coma and true astigmatism both belong to the more general deformation error in which the diapont manifold covers a region of the meridian plane.