Abstract

The recently introduced concept of a synthetic acousto-optic hologram [ J. Appl. Phys. 67, 49 ( 1990)] is applied to convert a Gaussian laser beam into a partially coherent anisotropic Gaussian Schell-model (AGSM) beam. Real-time reconfigurability of the coherence properties is achieved by this technique, which features scattering of the laser beam by an electronically synthesized, digitally phase-modulated volume grating that propagates in an acousto-optic Bragg cell. The coherence and intensity distributions of the fields obtained by different types of phase modulation are investigated theoretically. We demonstrate some particularly interesting AGSM sources and fields: a secondary elliptical AGSM source with a circularly symmetric far-field intensity distribution and an AGSM field that retains the eccentricity of its intensity profile in the propagation through any centrosymmetric (paraxial) optical system.

© 1992 Optical Society of America

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  1. A. C. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,”IEEE Trans. Antennas Propag. 15, 187–188 (1967).
    [Crossref]
  2. H. P. Baltes, J. Geist, A. Walther, “Radiometry and coherence,” in Inverse Source Problems in Optics, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1978), pp. 119–154.
    [Crossref]
  3. E. Wolf, E. Collett, “Partially coherent sources which produce the same far-field intensity distribution as a laser,” Opt. Commun. 25, 293–296 (1978).
    [Crossref]
  4. A. T. Friberg, “Radiation from partially coherent sources,” Opt. Eng. 21, 362–369 (1982).
    [Crossref]
  5. A. Gamliel, “Radiation efficiency of planar Gaussian Schell-model sources,” Opt. Commun. 60, 333–338 (1986).
    [Crossref]
  6. A. T. Friberg, “Radiation efficiency of three-dimensional, partially coherent primary sources,” Opt. Eng. 8, 1219–1223 (1986).
  7. N. A. Ansari, M. S. Zubairy, “Second-harmonic generation with a Gaussian Schell-model source,” Opt. Commun. 59, 385–390 (1986).
    [Crossref]
  8. J. Turunen, A. T. Friberg, “Matrix representation of Gaussian Schell-model beams in optical systems,” Opt. Laser Technol. 18, 259–267 (1986).
    [Crossref]
  9. R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).
    [Crossref]
  10. A. T. Friberg, J. Turunen, “Imaging of Gaussian Schell-model sources,” J. Opt. Soc. Am. A 5, 713–720 (1988).
    [Crossref]
  11. F. Gori, R. Grella, “Shape-invariant propagation of poly-chromatic fields,” Opt. Commun. 49, 173–177 (1984).
    [Crossref]
  12. A. Gamliel, G. P. Agrawal, “Spectrum-enhanced spreading of partially coherent beams,” Opt. Commun. 78, 203–207 (1990).
    [Crossref]
  13. P. DeSantis, F. Gori, G. Guattari, C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
    [Crossref]
  14. J. D. Farina, L. M. Narducci, E. Collett, “Generation of highly directional beams from a globally incoherent source,” Opt. Commun. 32, 203–207 (1980).
    [Crossref]
  15. F. Gori, “Collett–Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
    [Crossref]
  16. H. J. Eichler, G. Enterlein, D. Langhans, “Investigation of the spatial coherence of a laser beam by laser-induced grating method,” Appl. Phys. 23, 299–302 (1980).
    [Crossref]
  17. A. Starikov, E. Wolf, “Coherent-mode representation of Gaussian Schell-model sources and their radiation fields,”J. Opt. Soc. Am. 72, 923–927 (1982).
    [Crossref]
  18. J. Deshamps, D. Courjon, J. Bulabois, “Gaussian Schell-model sources: an example and some perspectives,”J. Opt. Soc. Am. 73, 256–261 (1983).
    [Crossref]
  19. Q. He, J. Turunen, A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model sources,” Opt. Commun. 67, 245–250 (1988).
    [Crossref]
  20. W. H. Carter, M. Bertolotti, “An analysis of the far-field coherence and radiant intensity of light scattered from liquid crystals,”J. Opt. Soc. Am. 68, 329–333 (1978).
    [Crossref]
  21. Y. Li, E. Wolf, “Radiation from anisotropic Gaussian Schell-model sources,” Opt. Lett. 7, 256–258 (1982).
    [Crossref] [PubMed]
  22. P. DeSantis, F. Gori, G. Guattari, C. Palma, “Anisotropic Gaussian Schell-model sources,” Opt. Acta 33, 315–326 (1986).
    [Crossref]
  23. S. Lavi, R. Prochaska, E. Keren, “Generalized beam parameters and transformation laws for partially coherent light,” Appl. Opt. 27, 3696–3703 (1986).
    [Crossref]
  24. F. Gori, G. Guattari, “A new type of optical fields,” Opt. Commun. 48, 7–12 (1983).
    [Crossref]
  25. F. Gori, “Directionality and spatial coherence,” Opt. Acta 27, 1025–1034 (1980).
    [Crossref]
  26. J. Turunen, E. Tervonen, A. T. Friberg, “Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings,” J. Appl. Phys. 67, 49–59 (1990).
    [Crossref]
  27. E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
    [Crossref]
  28. L. Mandel, E. Wolf, “Spectral coherence and the concept of cross-spectral purity,”J. Opt. Soc. Am. 66, 529–535 (1976).
    [Crossref]
  29. S. A. Collins, “Lens-system diffraction integral written in terms of matrix optics,”J. Opt. Soc. Am. 60, 1168–1177 (1970).
    [Crossref]
  30. J. Turunen, A. T. Friberg, “Propagation of Gaussian Schell-model beams: a matrix method,” in Optical System Design, Analysis, and Production for Advanced Technology Systems, R. E. Fisher, P. J. Rogers, eds., Proc. Soc. Photo-Opt. Instrum. Eng.655, 60–66 (1986).
    [Crossref]
  31. W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).
  32. H. Dammann, E. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
    [Crossref]
  33. L. P. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
    [Crossref]
  34. J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
    [Crossref]
  35. A. Vasara, J. Turunen, J. Westerholm, M. R. Taghizadeh, “Stepped-phase kinoforms,” in Optics in Complex Systems, F. Lanzl, H.–J. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 298–299 (1990).
    [Crossref]

1990 (2)

A. Gamliel, G. P. Agrawal, “Spectrum-enhanced spreading of partially coherent beams,” Opt. Commun. 78, 203–207 (1990).
[Crossref]

J. Turunen, E. Tervonen, A. T. Friberg, “Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings,” J. Appl. Phys. 67, 49–59 (1990).
[Crossref]

1989 (1)

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
[Crossref]

1988 (2)

Q. He, J. Turunen, A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model sources,” Opt. Commun. 67, 245–250 (1988).
[Crossref]

A. T. Friberg, J. Turunen, “Imaging of Gaussian Schell-model sources,” J. Opt. Soc. Am. A 5, 713–720 (1988).
[Crossref]

1986 (6)

A. Gamliel, “Radiation efficiency of planar Gaussian Schell-model sources,” Opt. Commun. 60, 333–338 (1986).
[Crossref]

A. T. Friberg, “Radiation efficiency of three-dimensional, partially coherent primary sources,” Opt. Eng. 8, 1219–1223 (1986).

N. A. Ansari, M. S. Zubairy, “Second-harmonic generation with a Gaussian Schell-model source,” Opt. Commun. 59, 385–390 (1986).
[Crossref]

J. Turunen, A. T. Friberg, “Matrix representation of Gaussian Schell-model beams in optical systems,” Opt. Laser Technol. 18, 259–267 (1986).
[Crossref]

P. DeSantis, F. Gori, G. Guattari, C. Palma, “Anisotropic Gaussian Schell-model sources,” Opt. Acta 33, 315–326 (1986).
[Crossref]

S. Lavi, R. Prochaska, E. Keren, “Generalized beam parameters and transformation laws for partially coherent light,” Appl. Opt. 27, 3696–3703 (1986).
[Crossref]

1984 (2)

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).
[Crossref]

F. Gori, R. Grella, “Shape-invariant propagation of poly-chromatic fields,” Opt. Commun. 49, 173–177 (1984).
[Crossref]

1983 (2)

1982 (3)

1981 (1)

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
[Crossref]

1980 (4)

F. Gori, “Directionality and spatial coherence,” Opt. Acta 27, 1025–1034 (1980).
[Crossref]

J. D. Farina, L. M. Narducci, E. Collett, “Generation of highly directional beams from a globally incoherent source,” Opt. Commun. 32, 203–207 (1980).
[Crossref]

F. Gori, “Collett–Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[Crossref]

H. J. Eichler, G. Enterlein, D. Langhans, “Investigation of the spatial coherence of a laser beam by laser-induced grating method,” Appl. Phys. 23, 299–302 (1980).
[Crossref]

1979 (1)

P. DeSantis, F. Gori, G. Guattari, C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[Crossref]

1978 (2)

W. H. Carter, M. Bertolotti, “An analysis of the far-field coherence and radiant intensity of light scattered from liquid crystals,”J. Opt. Soc. Am. 68, 329–333 (1978).
[Crossref]

E. Wolf, E. Collett, “Partially coherent sources which produce the same far-field intensity distribution as a laser,” Opt. Commun. 25, 293–296 (1978).
[Crossref]

1976 (1)

1971 (1)

H. Dammann, E. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[Crossref]

1970 (1)

1969 (1)

L. P. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[Crossref]

1967 (1)

A. C. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,”IEEE Trans. Antennas Propag. 15, 187–188 (1967).
[Crossref]

Agrawal, G. P.

A. Gamliel, G. P. Agrawal, “Spectrum-enhanced spreading of partially coherent beams,” Opt. Commun. 78, 203–207 (1990).
[Crossref]

Ansari, N. A.

N. A. Ansari, M. S. Zubairy, “Second-harmonic generation with a Gaussian Schell-model source,” Opt. Commun. 59, 385–390 (1986).
[Crossref]

Baltes, H. P.

H. P. Baltes, J. Geist, A. Walther, “Radiometry and coherence,” in Inverse Source Problems in Optics, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1978), pp. 119–154.
[Crossref]

Bertolotti, M.

Bulabois, J.

Carter, W. H.

Collett, E.

J. D. Farina, L. M. Narducci, E. Collett, “Generation of highly directional beams from a globally incoherent source,” Opt. Commun. 32, 203–207 (1980).
[Crossref]

E. Wolf, E. Collett, “Partially coherent sources which produce the same far-field intensity distribution as a laser,” Opt. Commun. 25, 293–296 (1978).
[Crossref]

Collins, S. A.

Courjon, D.

Dammann, H.

H. Dammann, E. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[Crossref]

Davenport, W. B.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

DeSantis, P.

P. DeSantis, F. Gori, G. Guattari, C. Palma, “Anisotropic Gaussian Schell-model sources,” Opt. Acta 33, 315–326 (1986).
[Crossref]

P. DeSantis, F. Gori, G. Guattari, C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[Crossref]

Deshamps, J.

Eichler, H. J.

H. J. Eichler, G. Enterlein, D. Langhans, “Investigation of the spatial coherence of a laser beam by laser-induced grating method,” Appl. Phys. 23, 299–302 (1980).
[Crossref]

Enterlein, G.

H. J. Eichler, G. Enterlein, D. Langhans, “Investigation of the spatial coherence of a laser beam by laser-induced grating method,” Appl. Phys. 23, 299–302 (1980).
[Crossref]

Farina, J. D.

J. D. Farina, L. M. Narducci, E. Collett, “Generation of highly directional beams from a globally incoherent source,” Opt. Commun. 32, 203–207 (1980).
[Crossref]

Friberg, A. T.

J. Turunen, E. Tervonen, A. T. Friberg, “Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings,” J. Appl. Phys. 67, 49–59 (1990).
[Crossref]

Q. He, J. Turunen, A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model sources,” Opt. Commun. 67, 245–250 (1988).
[Crossref]

A. T. Friberg, J. Turunen, “Imaging of Gaussian Schell-model sources,” J. Opt. Soc. Am. A 5, 713–720 (1988).
[Crossref]

A. T. Friberg, “Radiation efficiency of three-dimensional, partially coherent primary sources,” Opt. Eng. 8, 1219–1223 (1986).

J. Turunen, A. T. Friberg, “Matrix representation of Gaussian Schell-model beams in optical systems,” Opt. Laser Technol. 18, 259–267 (1986).
[Crossref]

A. T. Friberg, “Radiation from partially coherent sources,” Opt. Eng. 21, 362–369 (1982).
[Crossref]

J. Turunen, A. T. Friberg, “Propagation of Gaussian Schell-model beams: a matrix method,” in Optical System Design, Analysis, and Production for Advanced Technology Systems, R. E. Fisher, P. J. Rogers, eds., Proc. Soc. Photo-Opt. Instrum. Eng.655, 60–66 (1986).
[Crossref]

Gamliel, A.

A. Gamliel, G. P. Agrawal, “Spectrum-enhanced spreading of partially coherent beams,” Opt. Commun. 78, 203–207 (1990).
[Crossref]

A. Gamliel, “Radiation efficiency of planar Gaussian Schell-model sources,” Opt. Commun. 60, 333–338 (1986).
[Crossref]

Geist, J.

H. P. Baltes, J. Geist, A. Walther, “Radiometry and coherence,” in Inverse Source Problems in Optics, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1978), pp. 119–154.
[Crossref]

Gori, F.

P. DeSantis, F. Gori, G. Guattari, C. Palma, “Anisotropic Gaussian Schell-model sources,” Opt. Acta 33, 315–326 (1986).
[Crossref]

F. Gori, R. Grella, “Shape-invariant propagation of poly-chromatic fields,” Opt. Commun. 49, 173–177 (1984).
[Crossref]

F. Gori, G. Guattari, “A new type of optical fields,” Opt. Commun. 48, 7–12 (1983).
[Crossref]

F. Gori, “Directionality and spatial coherence,” Opt. Acta 27, 1025–1034 (1980).
[Crossref]

F. Gori, “Collett–Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[Crossref]

P. DeSantis, F. Gori, G. Guattari, C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[Crossref]

Görtler, E.

H. Dammann, E. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[Crossref]

Grella, R.

F. Gori, R. Grella, “Shape-invariant propagation of poly-chromatic fields,” Opt. Commun. 49, 173–177 (1984).
[Crossref]

Guattari, G.

P. DeSantis, F. Gori, G. Guattari, C. Palma, “Anisotropic Gaussian Schell-model sources,” Opt. Acta 33, 315–326 (1986).
[Crossref]

F. Gori, G. Guattari, “A new type of optical fields,” Opt. Commun. 48, 7–12 (1983).
[Crossref]

P. DeSantis, F. Gori, G. Guattari, C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[Crossref]

He, Q.

Q. He, J. Turunen, A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model sources,” Opt. Commun. 67, 245–250 (1988).
[Crossref]

Hirsch, P. M.

L. P. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[Crossref]

Jordan, J. A.

L. P. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[Crossref]

Keren, E.

Langhans, D.

H. J. Eichler, G. Enterlein, D. Langhans, “Investigation of the spatial coherence of a laser beam by laser-induced grating method,” Appl. Phys. 23, 299–302 (1980).
[Crossref]

Lavi, S.

Lesem, L. P.

L. P. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[Crossref]

Li, Y.

Mandel, L.

Mukunda, N.

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).
[Crossref]

Narducci, L. M.

J. D. Farina, L. M. Narducci, E. Collett, “Generation of highly directional beams from a globally incoherent source,” Opt. Commun. 32, 203–207 (1980).
[Crossref]

Palma, C.

P. DeSantis, F. Gori, G. Guattari, C. Palma, “Anisotropic Gaussian Schell-model sources,” Opt. Acta 33, 315–326 (1986).
[Crossref]

P. DeSantis, F. Gori, G. Guattari, C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[Crossref]

Prochaska, R.

Root, W. L.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

Schell, A. C.

A. C. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,”IEEE Trans. Antennas Propag. 15, 187–188 (1967).
[Crossref]

Simon, R.

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).
[Crossref]

Starikov, A.

Sudarshan, E. C. G.

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).
[Crossref]

Taghizadeh, M. R.

A. Vasara, J. Turunen, J. Westerholm, M. R. Taghizadeh, “Stepped-phase kinoforms,” in Optics in Complex Systems, F. Lanzl, H.–J. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 298–299 (1990).
[Crossref]

Tervonen, E.

J. Turunen, E. Tervonen, A. T. Friberg, “Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings,” J. Appl. Phys. 67, 49–59 (1990).
[Crossref]

Turunen, J.

J. Turunen, E. Tervonen, A. T. Friberg, “Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings,” J. Appl. Phys. 67, 49–59 (1990).
[Crossref]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
[Crossref]

A. T. Friberg, J. Turunen, “Imaging of Gaussian Schell-model sources,” J. Opt. Soc. Am. A 5, 713–720 (1988).
[Crossref]

Q. He, J. Turunen, A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model sources,” Opt. Commun. 67, 245–250 (1988).
[Crossref]

J. Turunen, A. T. Friberg, “Matrix representation of Gaussian Schell-model beams in optical systems,” Opt. Laser Technol. 18, 259–267 (1986).
[Crossref]

A. Vasara, J. Turunen, J. Westerholm, M. R. Taghizadeh, “Stepped-phase kinoforms,” in Optics in Complex Systems, F. Lanzl, H.–J. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 298–299 (1990).
[Crossref]

J. Turunen, A. T. Friberg, “Propagation of Gaussian Schell-model beams: a matrix method,” in Optical System Design, Analysis, and Production for Advanced Technology Systems, R. E. Fisher, P. J. Rogers, eds., Proc. Soc. Photo-Opt. Instrum. Eng.655, 60–66 (1986).
[Crossref]

Vasara, A.

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
[Crossref]

A. Vasara, J. Turunen, J. Westerholm, M. R. Taghizadeh, “Stepped-phase kinoforms,” in Optics in Complex Systems, F. Lanzl, H.–J. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 298–299 (1990).
[Crossref]

Walther, A.

H. P. Baltes, J. Geist, A. Walther, “Radiometry and coherence,” in Inverse Source Problems in Optics, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1978), pp. 119–154.
[Crossref]

Westerholm, J.

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
[Crossref]

A. Vasara, J. Turunen, J. Westerholm, M. R. Taghizadeh, “Stepped-phase kinoforms,” in Optics in Complex Systems, F. Lanzl, H.–J. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 298–299 (1990).
[Crossref]

Wolf, E.

Y. Li, E. Wolf, “Radiation from anisotropic Gaussian Schell-model sources,” Opt. Lett. 7, 256–258 (1982).
[Crossref] [PubMed]

A. Starikov, E. Wolf, “Coherent-mode representation of Gaussian Schell-model sources and their radiation fields,”J. Opt. Soc. Am. 72, 923–927 (1982).
[Crossref]

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
[Crossref]

E. Wolf, E. Collett, “Partially coherent sources which produce the same far-field intensity distribution as a laser,” Opt. Commun. 25, 293–296 (1978).
[Crossref]

L. Mandel, E. Wolf, “Spectral coherence and the concept of cross-spectral purity,”J. Opt. Soc. Am. 66, 529–535 (1976).
[Crossref]

Zubairy, M. S.

N. A. Ansari, M. S. Zubairy, “Second-harmonic generation with a Gaussian Schell-model source,” Opt. Commun. 59, 385–390 (1986).
[Crossref]

Appl. Opt. (1)

Appl. Phys. (1)

H. J. Eichler, G. Enterlein, D. Langhans, “Investigation of the spatial coherence of a laser beam by laser-induced grating method,” Appl. Phys. 23, 299–302 (1980).
[Crossref]

IBM J. Res. Dev. (1)

L. P. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[Crossref]

IEEE Trans. Antennas Propag. (1)

A. C. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,”IEEE Trans. Antennas Propag. 15, 187–188 (1967).
[Crossref]

J. Appl. Phys. (1)

J. Turunen, E. Tervonen, A. T. Friberg, “Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings,” J. Appl. Phys. 67, 49–59 (1990).
[Crossref]

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (1)

Opt. Acta (2)

P. DeSantis, F. Gori, G. Guattari, C. Palma, “Anisotropic Gaussian Schell-model sources,” Opt. Acta 33, 315–326 (1986).
[Crossref]

F. Gori, “Directionality and spatial coherence,” Opt. Acta 27, 1025–1034 (1980).
[Crossref]

Opt. Commun. (12)

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
[Crossref]

F. Gori, G. Guattari, “A new type of optical fields,” Opt. Commun. 48, 7–12 (1983).
[Crossref]

H. Dammann, E. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[Crossref]

F. Gori, R. Grella, “Shape-invariant propagation of poly-chromatic fields,” Opt. Commun. 49, 173–177 (1984).
[Crossref]

A. Gamliel, G. P. Agrawal, “Spectrum-enhanced spreading of partially coherent beams,” Opt. Commun. 78, 203–207 (1990).
[Crossref]

P. DeSantis, F. Gori, G. Guattari, C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[Crossref]

J. D. Farina, L. M. Narducci, E. Collett, “Generation of highly directional beams from a globally incoherent source,” Opt. Commun. 32, 203–207 (1980).
[Crossref]

F. Gori, “Collett–Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[Crossref]

Q. He, J. Turunen, A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model sources,” Opt. Commun. 67, 245–250 (1988).
[Crossref]

E. Wolf, E. Collett, “Partially coherent sources which produce the same far-field intensity distribution as a laser,” Opt. Commun. 25, 293–296 (1978).
[Crossref]

A. Gamliel, “Radiation efficiency of planar Gaussian Schell-model sources,” Opt. Commun. 60, 333–338 (1986).
[Crossref]

N. A. Ansari, M. S. Zubairy, “Second-harmonic generation with a Gaussian Schell-model source,” Opt. Commun. 59, 385–390 (1986).
[Crossref]

Opt. Eng. (3)

A. T. Friberg, “Radiation efficiency of three-dimensional, partially coherent primary sources,” Opt. Eng. 8, 1219–1223 (1986).

A. T. Friberg, “Radiation from partially coherent sources,” Opt. Eng. 21, 362–369 (1982).
[Crossref]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
[Crossref]

Opt. Laser Technol. (1)

J. Turunen, A. T. Friberg, “Matrix representation of Gaussian Schell-model beams in optical systems,” Opt. Laser Technol. 18, 259–267 (1986).
[Crossref]

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Phys. Rev. A (1)

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).
[Crossref]

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[Crossref]

A. Vasara, J. Turunen, J. Westerholm, M. R. Taghizadeh, “Stepped-phase kinoforms,” in Optics in Complex Systems, F. Lanzl, H.–J. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 298–299 (1990).
[Crossref]

J. Turunen, A. T. Friberg, “Propagation of Gaussian Schell-model beams: a matrix method,” in Optical System Design, Analysis, and Production for Advanced Technology Systems, R. E. Fisher, P. J. Rogers, eds., Proc. Soc. Photo-Opt. Instrum. Eng.655, 60–66 (1986).
[Crossref]

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

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Figures (9)

Fig. 1
Fig. 1

Generation of GSM beams with periodic scatterers. In a, c, and e, Δ = 1; and in b, d, and f, Δ = 3. a, b, Degree of coherence |μx; z0)|, Δx = x1x2, across the secondary source produced by a periodic (solid curves, period Λ) and a nonperiodic (dashed curve) scatterer. c,d, Optical intensity distribution I(u, zF) in the Fourier plane: solid curves, periodic scatterer; dashed curves, nonperiodic scatterer; dotted curves, a single diffraction order. e,f, Degree of spatial coherence |μ(0,u;zF)| in the Fourier plane: solid curves, periodic scatterer; dashed curves, nonperiodic scatterer.

Fig. 2
Fig. 2

Coding techniques of phase-only holograms. a, Continuous piecewise linear design. b, Cellular stepped-phase design (kinoform). c, Binary design (Dammann grating).

Fig. 3
Fig. 3

Optimized, high-efficiency, piecewise linear synthetic hologram with Δ = 7 (solid curves) compared with an ideal non-periodic scatterer (dashed curves): a, near-field coherence profiles; b, far-field intensity distributions; c, far-field coherence profiles.

Fig. 4
Fig. 4

Optimized binary hologram with Δ = 7.35 (solid curves) compared with an ideal nonperiodic scatterer (dashed curves): a, near-field coherence profiles; b, far-field intensity distributions; c, far-field coherence profiles.

Fig. 5
Fig. 5

Low-pass spatial filter (dotted vertical lines) applied in the Fourier plane of a four-level cellular grating with Δ = 7. a, Fourier-plane optical intensity distribution (solid curve). b, Filtered (solid curve) and unfiltered (dotted curve) coherence profiles across the secondary source. The results for an ideal nonperiodic scatterer are shown for comparison (dashed curves).

Fig. 6
Fig. 6

The experimental setup. AOD, acousto-optic deflector; C, fixed-frequency generator; H, hologram waveform generator; M, phase modulator; A, amplifier; L1–L3, spherical lenses; C1, C2, cylindrical lenses; F, spatial filter; V, V-shaped aperture; CCD, charged-coupled-device detector array.

Fig. 7
Fig. 7

Experimental results: an elliptic GSM source that radiates a symmetric far-field intensity profile. a, The measured Fourier-plane intensity profiles in the x (solid curve) and y (dotted curve) directions; the dashed curve is the calculated profile in the x direction. b, Unfiltered (open circles) and filtered (filled circles) spatial coherence profiles across the secondary source.

Fig. 8
Fig. 8

Experimental results: a bladelike AGSM beam. a, The measured Fourier-plane intensity profiles in x (solid line) and y (dotted line) directions; dashed line is the calculated profile in the x direction. b, Unfiltered (circles) and filtered (dots) spatial coherence profiles across the secondary source.

Fig. 9
Fig. 9

Control of GSM beam divergence by varying the period of a continuous-phase acousto-optic hologram from ΛH = 10 mm to ΛH = 2.0 mm.

Equations (35)

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t ( x ) = - A ( f ) exp ( i 2 π f x ) d f
W ( x 1 , x 2 ; z 0 ) = W 0 ( x 1 , x 2 ; z 0 ) - A * ( f 1 ) A ( f 2 ) × exp [ - i 2 π ( f 1 x 1 - f 2 x 2 ) ] d f 1 d f 2 ,
A * ( f 1 ) A ( f 2 ) = P ( f 1 ) δ ( f 1 - f 2 ) .
P ( f ) = - C ( x ) exp ( i 2 π f x ) d x ,
W ( x 1 , x 2 ; z 0 ) = [ I ( x 1 , z 0 ) I ( x 2 , z 0 ) ] 1 / 2 μ ( x 1 , x 2 ; z 0 ) ,
I ( x , z 0 ) = U ( x , z 0 ) 2 = U 0 ( x , z 0 ) 2 P ,
μ ( x 1 , x 2 ; z 0 ) = P - 1 exp { - i [ φ 0 ( x 1 , z 0 ) - φ 0 ( x 2 , z 0 ) ] } × - P ( f ) exp [ - i 2 π f ( x 1 - x 2 ) ] d f ,
P = - P ( f ) d f = C ( 0 ) = t 2
W ( u 1 , u 2 ; z ) = ( λ B ) - 1 - W ( x 1 , x 2 ; z 0 ) × exp { - i π [ D ( u 1 2 - u 2 2 ) - 2 ( u 1 x 1 - u 2 x 2 ) + A ( x 1 2 - x 2 2 ) ] / λ B } d x 1 d x 2 .
W ( u 1 , u 2 ; z ) = ( λ B ) - 1 exp [ - i π D ( u 1 2 - u 2 2 ) / λ B ] × - U 0 * ( x 1 , z 0 ) U 0 ( x 2 , z 0 ) exp [ - i π A ( x 1 2 - x 2 2 ) / λ B ] × - P ( f ) exp { i 2 π [ ( u 1 / λ B - f ) x 1 - ( u 2 / λ B - f ) x 2 ] } × d f d x 1 d x 2 ,
P ( f ) = ( 2 / π ) 1 / 2 δ - 1 exp ( - 2 f 2 / δ 2 ) .
I ( x , z 0 ) = I 0 exp [ - 2 x 2 / w 2 ( z 0 ) ]
μ ( x 1 , x 2 ; z 0 ) = exp [ - ( x 1 - x 2 ) 2 / 2 σ 2 ( z 0 ) ] ,
W ( u 1 , u 2 ; z ) = [ I ( u 1 , z ) I ( u 2 , z ) ] 1 / 2 μ ( u 1 , u 2 ; z ) ,
I ( u , z ) = I 0 [ w ( z 0 ) / w ( z ) ] 2 exp [ - 2 u 2 / w 2 ( z ) ] ,
μ ( u 1 , u 2 ; z ) = exp [ - ( u 1 - u 2 ) 2 / 2 σ 2 ( z ) ] × exp [ - i k ( u 1 2 - u 2 2 ) / 2 R ( z ) ] .
w ( z ) = w ( z 0 ) ( A 2 + B 2 b 0 - 2 ) 1 / 2 ,
σ ( z ) = α w ( z ) ,
R ( z ) = ( A 2 + B 2 b 0 - 2 ) / ( A C + B D b 0 - 1 ) ,
w ( z F ) = F λ / π w ( z 0 ) β
w ( z F ) = w ¯ ( z F ) { 1 + [ π δ w ( z 0 ) ] 2 } 1 / 2 ,
σ ( z F ) = w ¯ ( z F ) { 1 + [ π δ w ( z 0 ) ] - 2 } 1 / 2 ,
w x ( z 0 ) β x = w y ( z 0 ) β y ,
w x 2 ( z 0 ) β x = w y 2 ( z 0 ) β y ,
exp ( i φ ( x ) ] = m = - G m exp ( i 2 π m x / Λ ) .
P S ( f ) = m = - P m δ ( f - m / Λ ) ,
μ ( x 1 , x 2 ; z 0 ) = m = - P m exp [ - i 2 π m ( x 1 - x 2 ) / Λ ] .
W ( u 1 , u 2 ; z F ) = I 0 [ π w 2 ( z 0 ) / λ F ] m = - P m × exp { - π 2 w 2 ( z 0 ) [ ( u 1 / λ F - m / Λ ) 2 + ( u 2 / λ F - m / Λ ) 2 ] } .
I ( u , z F ) = I 0 [ w ( z 0 ) / w ¯ ( z F ) ] × m = - P m exp [ - 2 ( u - m u 0 ) 2 / w ¯ 2 ( z F ) ] ,
μ ( u 1 , u 2 ; z F ) = m = - P m exp { - [ ( u 1 - m u 0 ) 2 + ( u 2 - m u 0 ) 2 ] / w ¯ 2 ( z F ) } × { n = - P n exp [ - 2 ( u 1 - n u 0 ) 2 / w ¯ 2 ( z F ) ] } 1 / 2 × { q = - P q exp [ - 2 ( u 2 - q u 0 ) 2 / w ¯ 2 ( z F ) ] } - 1 / 2 .
P ^ m = exp ( - 2 m 2 / Δ 2 ) [ n = - exp ( - 2 n 2 / Δ 2 ) ] - 1
P m = | Λ - 1 0 Λ exp { i [ φ ( x ) - 2 π m x / Λ ] } d x | 2 .
M f = m = - N N ( P m - η P ^ m ) 2 .
Λ H = π Δ ( E 2 - 1 ) - 1 / 2 w x ( z 0 ) .
Λ H = π Δ ( E 4 - 1 ) - 1 / 2 w x ( z 0 ) .

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