A matrix representation for non-symmetrical optical systems

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Abstract
A matrix representation of non-symmetrical optical systems is introduced. Each component of an optical system containing sphero-symmetrical lenses and cylindrical lenses rotated by arbitrary angles about the optical axis may be represented in the paraxial approximation by a 4*4 unitary matrix. The powers of such lenses and lens systems are matrices instead of scalars. When partitioned matrices are used, the resulting 2*2 matrices are formally identical to the matrices of the normal matrix representation, except that the elements of the matrices are 2*2 matrices instead of scalars.