Abstract

The Herschel condition is the axial counterpart to the sine condition; its satisfaction guarantees that spherical aberration not change for small axial displacements of the object. The more general case would be a system that is corrected for spherical aberration for all conjugate distances. Wynne has shown that four separate conditions must be met for this to be possible. For an optical system of thin elements in contact, one of the conditions requires a certain amount of Petzval curvature—a surprising result with no obvious relationship to the imaging of axial points. This turns out to be difficult to achieve in a thin system except in a catadioptric design. Then the Petzval curvature and the net power can be controlled completely independently. The simplest conventional-type example of a system with correction for third-order spherical aberration for all conjugates is a particular single element aspheric Mangin mirror. More exotic, but simpler still, is a single reflective surface with a binary optics diffractive overlay. This is discussed, as well as one application—its use in a zoom laser beam expander.

© 1991 Optical Society of America