Shear representations of beam transfer matrices

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Baskal S., Kim Y.

PHYSICAL REVIEW E, vol.63, no.5, 2001 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 5
  • Publication Date: 2001
  • Doi Number: 10.1103/physreve.63.056606
  • Journal Name: PHYSICAL REVIEW E
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Middle East Technical University Affiliated: No


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.