Shear representations of beam transfer matrices

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Baskal S., Kim Y.

PHYSICAL REVIEW E, cilt.63, sa.5, 2001 (SCI İndekslerine Giren Dergi) identifier identifier identifier


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.