Interconverting the matrix and principal meridional representations of dioptric power in general including powers with nonorthogonal and complex principal meridians

The principal meridians of the powers of thick astigmatic systems, like the eye, are not necessarily at right angles. The consequence is a class of ph enomena included in the category commonly described as irregular astigmatis m. The conventional principal meridional representation of power, however, is unsuited to quantitative analysis. This paper presents equations for con verting from the principal meridional form of power to a representation, th e dioptric power matrix, which is amenable to quantitative analysis. It gen eralizes an earlier paper which treated only powers of a conventional form in which the principal meridians are always at right angles. It copes in pa rticular with what are known as asymmetric powers. A routine is also presen ted for converting in the reverse direction, from the power matrix to the p rincipal meridional form of power. The principal meridional form of power t urns out not always to be unique, there being distinct powers (they are asy mmetric) with the same principal powers and meridians. Thus, in general, th e dioptric power matrix is a satisfactory representation of power while the principal meridional representation is not. (C) 2001 The College of Optome trists. Published by Elsevier Science Ltd. All rights reserved.