Abstract

The complex degree of coherence and the resulting van Cittert–Zernike theorem are employed to analyze the exit of an arbitrary amplitude-division interferometer with two-beam interferences. Considering that the source is a periodic array of spatially incoherent slits and assuming negligible equivalent aberrations and no vignetting, an expression for the complex degree of coherence as a function of the position of an exit point is derived. Formulas for the location, fringe spacing, and fringe localization depth of the multilocalized fringes are given.

© 2000 Optical Society of America

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  1. J W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  2. M. Born, B. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1987).
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    [CrossRef]
  4. P. Hariharan, Optical Interferometry (Academic, Sydney, Australia, 1985).
  5. W. H. Steel, Interferometry (Cambridge U. Press, London, 1985).
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    [CrossRef] [PubMed]
  7. J. M. Simon, S. A. Comastri, “Localization of interference fringes,” Am. J. Phys. 48, 665–668 (1980).
    [CrossRef]
  8. J. M. Simon, S. A. Comastri, “Fringe localization depth,” Appl. Opt. 26, 5125–5129 (1987).
    [CrossRef] [PubMed]
  9. P. Hariharan, W. H. Steel, “Fringe localization depth: a comment,” Appl. Opt. 28, 29–29 (1989).
    [CrossRef] [PubMed]
  10. J. M. Simon, S. A. Comastri, “Interferometers: equivalent sine condition,” Appl. Opt. 27, 4725–4730 (1988).
    [CrossRef] [PubMed]
  11. J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
    [CrossRef]
  12. J. M. Simon, R. M. Echarri, M. C. Simon, M. T. Garea, “Fringe localization in wave-front division interferometers,” Cuaderno de Optica 66E, Ediciones Previas, Laboratorio de Optica, FCEN-UBA (1999), available from the authors at the address on the title page.
  13. J. M. Simon, R. M. Echarri, P. A. Walsh, “Multilocalization of interference fringes in the Mach–Zehnder interferometer,” Cuaderno de Optica 67E, Ediciones Previas, Laboratorio de Optica, FCEN-UBA (1999), available from the authors at the address on the title page.
  14. J. Jahns, A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28, 263–267 (1979).
    [CrossRef]
  15. K. Patorski, “Incoherent superposition of multiple self-imaging: Lau effect and moiré fringe explanation,” Opt. Acta 30, 745–758 (1983).
    [CrossRef]
  16. F. Gori, “Lau effect and coherence theory,” Opt. Commun. 31, 4–8 (1979).
    [CrossRef]
  17. R. Sudol, B. J. Thompson, “Lau effect: theory and experiment,” Appl. Opt. 20, 1107–1116 (1981).
    [CrossRef] [PubMed]
  18. A. W. Lohmann, J. Ojeda-Castaneda, “Spatial periodicities in partially coherent fields,” Opt. Acta 30, 475–479 (1983).
    [CrossRef]
  19. S. A. Comastri, J. M. Simon, R. Blendowske, “Generalized sine condition for image-forming systems with centering errors,” J. Opt. Soc. Am. A 16, 602–612 (1999).
    [CrossRef]
  20. J. M. Simon, S. A. Comastri, “Image-forming systems: matrix formulation of the optical invariant via Fourier optics,” J. Mod. Opt. 43, 2533–2541 (1996).
    [CrossRef]
  21. H. H. Hopkins, “Image formation by a general optical system. 1: General theory,” Appl. Opt. 24, 2491–2505 (1985).
    [CrossRef] [PubMed]
  22. J. M. Simon, S. A. Comastri, C. Tardin, “Multilocalization and the van Cittert–Zernike theorem. 2. Application to the Wollaston prism,” J. Opt. Soc. Am. A 17, 1277–1283 (2000).
    [CrossRef]

2000 (1)

1999 (1)

1998 (1)

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

1996 (1)

J. M. Simon, S. A. Comastri, “Image-forming systems: matrix formulation of the optical invariant via Fourier optics,” J. Mod. Opt. 43, 2533–2541 (1996).
[CrossRef]

1989 (1)

1988 (1)

1987 (1)

1985 (1)

1983 (2)

A. W. Lohmann, J. Ojeda-Castaneda, “Spatial periodicities in partially coherent fields,” Opt. Acta 30, 475–479 (1983).
[CrossRef]

K. Patorski, “Incoherent superposition of multiple self-imaging: Lau effect and moiré fringe explanation,” Opt. Acta 30, 745–758 (1983).
[CrossRef]

1981 (1)

1980 (1)

J. M. Simon, S. A. Comastri, “Localization of interference fringes,” Am. J. Phys. 48, 665–668 (1980).
[CrossRef]

1979 (2)

F. Gori, “Lau effect and coherence theory,” Opt. Commun. 31, 4–8 (1979).
[CrossRef]

J. Jahns, A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28, 263–267 (1979).
[CrossRef]

1978 (1)

1969 (1)

Blendowske, R.

Born, M.

M. Born, B. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1987).

Comastri, S. A.

Echarri, R. M.

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

J. M. Simon, R. M. Echarri, P. A. Walsh, “Multilocalization of interference fringes in the Mach–Zehnder interferometer,” Cuaderno de Optica 67E, Ediciones Previas, Laboratorio de Optica, FCEN-UBA (1999), available from the authors at the address on the title page.

J. M. Simon, R. M. Echarri, M. C. Simon, M. T. Garea, “Fringe localization in wave-front division interferometers,” Cuaderno de Optica 66E, Ediciones Previas, Laboratorio de Optica, FCEN-UBA (1999), available from the authors at the address on the title page.

Garea, M. T.

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

J. M. Simon, R. M. Echarri, M. C. Simon, M. T. Garea, “Fringe localization in wave-front division interferometers,” Cuaderno de Optica 66E, Ediciones Previas, Laboratorio de Optica, FCEN-UBA (1999), available from the authors at the address on the title page.

Goodman, J W.

J W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gori, F.

F. Gori, “Lau effect and coherence theory,” Opt. Commun. 31, 4–8 (1979).
[CrossRef]

Hariharan, P.

Hopkins, H. H.

Jahns, J.

J. Jahns, A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28, 263–267 (1979).
[CrossRef]

Lohmann, A. W.

A. W. Lohmann, J. Ojeda-Castaneda, “Spatial periodicities in partially coherent fields,” Opt. Acta 30, 475–479 (1983).
[CrossRef]

J. Jahns, A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28, 263–267 (1979).
[CrossRef]

Ojeda-Castaneda, J.

A. W. Lohmann, J. Ojeda-Castaneda, “Spatial periodicities in partially coherent fields,” Opt. Acta 30, 475–479 (1983).
[CrossRef]

Patorski, K.

K. Patorski, “Incoherent superposition of multiple self-imaging: Lau effect and moiré fringe explanation,” Opt. Acta 30, 745–758 (1983).
[CrossRef]

Simon, J. M.

J. M. Simon, S. A. Comastri, C. Tardin, “Multilocalization and the van Cittert–Zernike theorem. 2. Application to the Wollaston prism,” J. Opt. Soc. Am. A 17, 1277–1283 (2000).
[CrossRef]

S. A. Comastri, J. M. Simon, R. Blendowske, “Generalized sine condition for image-forming systems with centering errors,” J. Opt. Soc. Am. A 16, 602–612 (1999).
[CrossRef]

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

J. M. Simon, S. A. Comastri, “Image-forming systems: matrix formulation of the optical invariant via Fourier optics,” J. Mod. Opt. 43, 2533–2541 (1996).
[CrossRef]

J. M. Simon, S. A. Comastri, “Interferometers: equivalent sine condition,” Appl. Opt. 27, 4725–4730 (1988).
[CrossRef] [PubMed]

J. M. Simon, S. A. Comastri, “Fringe localization depth,” Appl. Opt. 26, 5125–5129 (1987).
[CrossRef] [PubMed]

J. M. Simon, S. A. Comastri, “Localization of interference fringes,” Am. J. Phys. 48, 665–668 (1980).
[CrossRef]

J. M. Simon, R. M. Echarri, P. A. Walsh, “Multilocalization of interference fringes in the Mach–Zehnder interferometer,” Cuaderno de Optica 67E, Ediciones Previas, Laboratorio de Optica, FCEN-UBA (1999), available from the authors at the address on the title page.

J. M. Simon, R. M. Echarri, M. C. Simon, M. T. Garea, “Fringe localization in wave-front division interferometers,” Cuaderno de Optica 66E, Ediciones Previas, Laboratorio de Optica, FCEN-UBA (1999), available from the authors at the address on the title page.

Simon, M. C.

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

J. M. Simon, R. M. Echarri, M. C. Simon, M. T. Garea, “Fringe localization in wave-front division interferometers,” Cuaderno de Optica 66E, Ediciones Previas, Laboratorio de Optica, FCEN-UBA (1999), available from the authors at the address on the title page.

Steel, W. H.

Sudol, R.

Tardin, C.

Thompson, B. J.

Walsh, P. A.

J. M. Simon, R. M. Echarri, P. A. Walsh, “Multilocalization of interference fringes in the Mach–Zehnder interferometer,” Cuaderno de Optica 67E, Ediciones Previas, Laboratorio de Optica, FCEN-UBA (1999), available from the authors at the address on the title page.

Wolf, B.

M. Born, B. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1987).

Wyant, J. C.

Am. J. Phys. (1)

J. M. Simon, S. A. Comastri, “Localization of interference fringes,” Am. J. Phys. 48, 665–668 (1980).
[CrossRef]

Appl. Opt. (6)

J. Mod. Opt. (2)

J. M. Simon, S. A. Comastri, “Image-forming systems: matrix formulation of the optical invariant via Fourier optics,” J. Mod. Opt. 43, 2533–2541 (1996).
[CrossRef]

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Acta (2)

A. W. Lohmann, J. Ojeda-Castaneda, “Spatial periodicities in partially coherent fields,” Opt. Acta 30, 475–479 (1983).
[CrossRef]

K. Patorski, “Incoherent superposition of multiple self-imaging: Lau effect and moiré fringe explanation,” Opt. Acta 30, 745–758 (1983).
[CrossRef]

Opt. Commun. (2)

F. Gori, “Lau effect and coherence theory,” Opt. Commun. 31, 4–8 (1979).
[CrossRef]

J. Jahns, A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28, 263–267 (1979).
[CrossRef]

Other (6)

J. M. Simon, R. M. Echarri, M. C. Simon, M. T. Garea, “Fringe localization in wave-front division interferometers,” Cuaderno de Optica 66E, Ediciones Previas, Laboratorio de Optica, FCEN-UBA (1999), available from the authors at the address on the title page.

J. M. Simon, R. M. Echarri, P. A. Walsh, “Multilocalization of interference fringes in the Mach–Zehnder interferometer,” Cuaderno de Optica 67E, Ediciones Previas, Laboratorio de Optica, FCEN-UBA (1999), available from the authors at the address on the title page.

J W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

M. Born, B. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1987).

P. Hariharan, Optical Interferometry (Academic, Sydney, Australia, 1985).

W. H. Steel, Interferometry (Cambridge U. Press, London, 1985).

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