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Mathematical apparatus of expanded 3 × 3 matrices to describe noncentered optical systems

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A simple mathematical apparatus is proposed to describe noncentered optical systems. The apparatus can be used to describe optical systems with isotropic elements or anisotropic elements with coincident principal directions. The approach proposed permits substantial expansion of the circle of problems that can be solved effectively within the framework of the geometric optics representations.

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Literature cited

  1. 1.

    E. O'Neil, Introduction to Statistical Optics [Russian translation], Mir, Moscow (1966).

  2. 2.

    A. Gerard and J. M. Birch, Introduction to Matrix Optics [Russian translation], Mir, Moscow (1978).

  3. 3.

    B. Magukov and H. H. Arsenault, J. Opt. Soc. Am.,73, No. 10, 1360–1366 (1983).

  4. 4.

    S. A. Rodionov, Opt. Spektrosk.,50, No. 5, 969–976 (1981).

  5. 5.

    Yu. A. Kravtsov and Yu. I. Orlov, Geometric Optics of Inhomogeneous Media [in Russian], Nauka, Moscow (1980).

  6. 6.

    M. M. Gorshkov, Ellipsometry [in Russian], Sovetskoe Radio, Moscow (1974).

  7. 7.

    O. N. Litvinenko, Principles of Radio Optics [in Russian], Tekhnika, Kiev (1974).

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 106–109, June, 1988.

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Volkov, V.M. Mathematical apparatus of expanded 3 × 3 matrices to describe noncentered optical systems. Soviet Physics Journal 31, 517–519 (1988). https://doi.org/10.1007/BF00897621

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  • Optical System
  • Principal Direction
  • Geometric Optic
  • Isotropic Element
  • Mathematical Apparatus