Shear representations of beam transfer matrices
PHYSICAL REVIEW E, cilt.63, sa.5, 2001 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 63 Sayı: 5
- Basım Tarihi: 2001
- Doi Numarası: 10.1103/physreve.63.056606
- Dergi Adı: PHYSICAL REVIEW E
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Orta Doğu Teknik Üniversitesi Adresli: Hayır
Özet
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.