Thin lenses of asymmetric power

Abstract

It is generally supposed that thin systems, including refracting surfaces and thin lenses, have powers that are necessarily symmetric.  In other words they have powers which can be represented assymmetric dioptric power matrices and in the familar spherocylindrical form used in optometry and ophthalmology.  This paper shows that this is not correct and that it is indeed possible for a thin system to have a power that is not symmetric and which cannot be expressed in spherocylindrical form.  Thin systems of asymmetric power are illustratedby means of a thin lens that is modelled with small prisms and is chosen to have a dioptric power ma-trix that is antisymmetric.  Similar models can be devised for a thin system whose dioptric power matrix is any  2 2 ×  matrix.  Thus any power, symmetric, asymmetric or antisymmetric, is possible for a
thin system.  In this sense our understanding of the power of thin systems is now complete.