title: Shear representations of beam transfer matrices.
abstract: The beam transfer matrix, often called the ABCD matrix, is one of the essential mathematical instruments in optics. It is a unimodular matrix whose determinant is 1. If all the elements are real with three independent parameters, this matrix is a 2 x 2 representation of the group Sp(2). It is shown that a real ABCD matrix can be generated by two shear transformations. It is then noted that, in para-axial lens optics, the lens and translation matrices constitute two shear transformations. It is shown that a system with an arbitrary number of lenses can be reduced to a system consisting of three lenses.
authors: Department of Physics, Middle East Technical University, 06531 Ankara, Turkey. baskal@newton.physics.metu.edu.tr
authors: S
authors: S
authors: Başkal
authors: Y S
authors: YS
authors: Kim