Abstract

A new approach to the representation of nonsymmetrical optical systems by matrices is introduced. In the paraxial approximation each component of an optical system is represented by a 4 × 4 unitary matrix, and the product of those matrices yields the transfer matrix of the system. The transfer matrix that represents the propagation between two arbitrary planes through the system containing two independently rotated cylindrical lenses is decomposed into the product of three matrices. The eigenvalues of the submatrices in this factorized form determine the focal lengths of the equivalent system and the localization of the foci of the system with respect to these arbitrarily chosen planes.

© 1983 Optical Society of America

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  1. H. H. Arsenault, "A matrix representation for non-symmetrical optical systems," J. Opt. (Paris) 11, 87–91 (1980).
  2. S. A. Collins, "Lens-system diffraction integral written in terms of matrix optics," J. Opt. Soc. Am. 60, 1168–1177 (1970).
  3. H. H. Arsenault, "The rotation of light fans by cylindrical lens," Opt. Commun. 31, 275–278 (1979).
  4. H. Braunecker, O. Bryngdahl, and B. Schnell, "Optical system for image rotation and magnification," J. Opt. Soc. Am. 70, 137–141 (1980).
  5. J. Shamir, "Cylindrical lens systems described by operator algebra," Appl. Opt. 18, 4195–4202 (1979).
  6. H. H. Arsenault and B. Macukow, "Factorization of the transfer matrix for symmetrical optical systems," J. Opt. Soc. Am. 73, 1350–1359 (1983).
  7. H. H. Arsenault, "Generalization of the principal plane concept in matrix optics," Am. J. Phys. 48, 397–399 (1980).
  8. See, for example, G. Strang, Linear Algebra and Its Applications (Academic, New York, 1976), Chap. 1.
  9. S. A. Rodionov, "Matrix technique of Gaussian optics near an arbitrary ray," Opt. Spectrosc. 50, 531–535 (1981).
  10. J. A. Arnaud, "Nonorthogonal optical waveguides and resonators," Bell Syst. Tech. J. 49, 2311–2348 (1970).

1983 (1)

1981 (1)

S. A. Rodionov, "Matrix technique of Gaussian optics near an arbitrary ray," Opt. Spectrosc. 50, 531–535 (1981).

1980 (3)

H. H. Arsenault, "Generalization of the principal plane concept in matrix optics," Am. J. Phys. 48, 397–399 (1980).

H. H. Arsenault, "A matrix representation for non-symmetrical optical systems," J. Opt. (Paris) 11, 87–91 (1980).

H. Braunecker, O. Bryngdahl, and B. Schnell, "Optical system for image rotation and magnification," J. Opt. Soc. Am. 70, 137–141 (1980).

1979 (2)

J. Shamir, "Cylindrical lens systems described by operator algebra," Appl. Opt. 18, 4195–4202 (1979).

H. H. Arsenault, "The rotation of light fans by cylindrical lens," Opt. Commun. 31, 275–278 (1979).

1970 (2)

S. A. Collins, "Lens-system diffraction integral written in terms of matrix optics," J. Opt. Soc. Am. 60, 1168–1177 (1970).

J. A. Arnaud, "Nonorthogonal optical waveguides and resonators," Bell Syst. Tech. J. 49, 2311–2348 (1970).

Arnaud, J. A.

J. A. Arnaud, "Nonorthogonal optical waveguides and resonators," Bell Syst. Tech. J. 49, 2311–2348 (1970).

Arsenault, H. H.

H. H. Arsenault and B. Macukow, "Factorization of the transfer matrix for symmetrical optical systems," J. Opt. Soc. Am. 73, 1350–1359 (1983).

H. H. Arsenault, "A matrix representation for non-symmetrical optical systems," J. Opt. (Paris) 11, 87–91 (1980).

H. H. Arsenault, "Generalization of the principal plane concept in matrix optics," Am. J. Phys. 48, 397–399 (1980).

H. H. Arsenault, "The rotation of light fans by cylindrical lens," Opt. Commun. 31, 275–278 (1979).

Braunecker, H.

Bryngdahl, O.

Collins, S. A.

Macukow, B.

Rodionov, S. A.

S. A. Rodionov, "Matrix technique of Gaussian optics near an arbitrary ray," Opt. Spectrosc. 50, 531–535 (1981).

Schnell, B.

Shamir, J.

Strang, G.

See, for example, G. Strang, Linear Algebra and Its Applications (Academic, New York, 1976), Chap. 1.

Am. J. Phys. (1)

H. H. Arsenault, "Generalization of the principal plane concept in matrix optics," Am. J. Phys. 48, 397–399 (1980).

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

J. A. Arnaud, "Nonorthogonal optical waveguides and resonators," Bell Syst. Tech. J. 49, 2311–2348 (1970).

J. Opt. (1)

H. H. Arsenault, "A matrix representation for non-symmetrical optical systems," J. Opt. (Paris) 11, 87–91 (1980).

J. Opt. Soc. Am. (3)

Opt. Commun. (1)

H. H. Arsenault, "The rotation of light fans by cylindrical lens," Opt. Commun. 31, 275–278 (1979).

Opt. Spectrosc. (1)

S. A. Rodionov, "Matrix technique of Gaussian optics near an arbitrary ray," Opt. Spectrosc. 50, 531–535 (1981).

Other (1)

See, for example, G. Strang, Linear Algebra and Its Applications (Academic, New York, 1976), Chap. 1.

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