Lens Effectivity in Terms of Dioptric Power Matrices

An effective dioptric power matrix is defined. The effective dioptric power matrix can be calculated directly from the lens dioptric power matrix, its trace, and its determinant, without using the sphere, cylinder, and axis parameters of the lens. This greatly simplifies any calculations in which dioptric power matrices are obtained in intermediate steps, including separated obliquely crossed spherocylindrical lens calculations. The generalization of the effective dioptric power matrix to a reduced vergence matrix is also discussed.