Abstract

The theory of propagation of partially coherent light is well known, but performing numerical calculations still presents a difficulty because of the dimensionality of the problem. We propose using a recently introduced method based on the use of elementary functions [Wald et al. Proc. SPIE6040, 59621G (2005)] to reduce the integrals to two dimensions. We formalize the method, describe its inherent assumptions and approximations, and introduce a sampling criterion for adequate interpolation. We present an analysis of some special cases, such as the Gaussian Schell-model beam, and briefly discuss generalized numerical propagation of two-dimensional field distributions.

© 2009 Optical Society of America

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2008 (1)

2007 (2)

2006 (1)

2005 (1)

M. Wald, M. Burkhardt, A. Pesch, H. Gross, and J. Greif, “Design of a microscopy illumination using a partial coherent light source,” Proc. SPIE 5962, 59621G-1-10 (2005).
[CrossRef]

2004 (2)

2002 (1)

L. E. Vicent and M. A. Alonso, “Generalized radiometry as a tool for the propagation of partially coherent fields,” Opt. Commun. 207, 101-112 (2002).
[CrossRef]

2000 (2)

1999 (2)

1996 (3)

1994 (2)

E. Wolf, “Radiometric model for propagation of coherence,” Opt. Lett. 19, 2024-2026 (1994).
[CrossRef]

A. Aldroubi and M. Unser, “Sampling procedures in function spaces and asymptotic equivalence with Shannon's samping theory,” Numer. Funct. Anal. Optimiz. 15, 1-21 (1994).
[CrossRef]

1992 (1)

1991 (1)

M. J. Bastiaans, “Gabor's signal expansion applied to partially coherent light,” Opt. Commun. 86, 14-18 (1991).
[CrossRef]

1982 (1)

M. J. Bastiaans, “Gabor's signal expansion and degrees of freedom of a signal,” Opt. Acta 29, 1223-1229 (1982).

1981 (1)

M. J. Bastiaans, “A sampling theorem for the complex spectrogram, and Gabor's expansion af a signal in the Gaussian elementary signals,” Opt. Eng. (Bellingham) 20, 594-598 (1981).

1953 (1)

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A 217, 408-432 (1953).
[CrossRef]

Aldroubi, A.

A. Aldroubi and M. Unser, “Sampling procedures in function spaces and asymptotic equivalence with Shannon's samping theory,” Numer. Funct. Anal. Optimiz. 15, 1-21 (1994).
[CrossRef]

Alonso, M. A.

L. E. Vicent and M. A. Alonso, “Generalized radiometry as a tool for the propagation of partially coherent fields,” Opt. Commun. 207, 101-112 (2002).
[CrossRef]

Bastiaans, M. J.

M. J. Bastiaans, “Gabor's signal expansion applied to partially coherent light,” Opt. Commun. 86, 14-18 (1991).
[CrossRef]

M. J. Bastiaans, “Gabor's signal expansion and degrees of freedom of a signal,” Opt. Acta 29, 1223-1229 (1982).

M. J. Bastiaans, “A sampling theorem for the complex spectrogram, and Gabor's expansion af a signal in the Gaussian elementary signals,” Opt. Eng. (Bellingham) 20, 594-598 (1981).

Bengtsson, J.

Berry, R. H.

Born, M.

M. Born and E. Wolf, Principles of Optics 7th ed. (Cambridge U. Press, 1999).

Buck, J.

Y. Lin and J. Buck, “Numerical modelling of the excimer beam,” Proc. SPIE 3677, 700-710 (1999).
[CrossRef]

Burkhardt, M.

M. Wald, M. Burkhardt, A. Pesch, H. Gross, and J. Greif, “Design of a microscopy illumination using a partial coherent light source,” Proc. SPIE 5962, 59621G-1-10 (2005).
[CrossRef]

Dragoman, D.

D. Dragoman, “The Wigner distribution in optics and optoelectronics,” in Progress in Optics, E.Wolf, ed. (North-Holland, Amsterdam, 1995).

Friberg, A. T.

Greif, J.

M. Wald, M. Burkhardt, A. Pesch, H. Gross, and J. Greif, “Design of a microscopy illumination using a partial coherent light source,” Proc. SPIE 5962, 59621G-1-10 (2005).
[CrossRef]

Gross, H.

M. Wald, M. Burkhardt, A. Pesch, H. Gross, and J. Greif, “Design of a microscopy illumination using a partial coherent light source,” Proc. SPIE 5962, 59621G-1-10 (2005).
[CrossRef]

Hobson, M. P.

Hopkins, H. H.

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A 217, 408-432 (1953).
[CrossRef]

Lajunen, H.

Lin, Y.

Y. Lin and J. Buck, “Numerical modelling of the excimer beam,” Proc. SPIE 3677, 700-710 (1999).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Martinsson, P.

Miller, D. A. B.

Pesch, A.

M. Wald, M. Burkhardt, A. Pesch, H. Gross, and J. Greif, “Design of a microscopy illumination using a partial coherent light source,” Proc. SPIE 5962, 59621G-1-10 (2005).
[CrossRef]

Popov, S. Yu.

Rabbini, M.

Rydberg, C.

Saleh, B. E. A.

Torres-Company, V.

Turunen, J.

Unser, M.

M. Unser, “Sampling--50 years after Shannon,” Proc. IEEE 88, 569-587 (2000).
[CrossRef]

A. Aldroubi and M. Unser, “Sampling procedures in function spaces and asymptotic equivalence with Shannon's samping theory,” Numer. Funct. Anal. Optimiz. 15, 1-21 (1994).
[CrossRef]

Vahimaa, P.

Vicent, L. E.

L. E. Vicent and M. A. Alonso, “Generalized radiometry as a tool for the propagation of partially coherent fields,” Opt. Commun. 207, 101-112 (2002).
[CrossRef]

Wald, M.

M. Wald, M. Burkhardt, A. Pesch, H. Gross, and J. Greif, “Design of a microscopy illumination using a partial coherent light source,” Proc. SPIE 5962, 59621G-1-10 (2005).
[CrossRef]

Withington, S.

Wolf, E.

E. Wolf, “Radiometric model for propagation of coherence,” Opt. Lett. 19, 2024-2026 (1994).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarisation of Light (Cambridge U. Press, 2007).

M. Born and E. Wolf, Principles of Optics 7th ed. (Cambridge U. Press, 1999).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Appl. Opt. (3)

J. Opt. Soc. Am. A (5)

Numer. Funct. Anal. Optimiz. (1)

A. Aldroubi and M. Unser, “Sampling procedures in function spaces and asymptotic equivalence with Shannon's samping theory,” Numer. Funct. Anal. Optimiz. 15, 1-21 (1994).
[CrossRef]

Opt. Acta (1)

M. J. Bastiaans, “Gabor's signal expansion and degrees of freedom of a signal,” Opt. Acta 29, 1223-1229 (1982).

Opt. Commun. (2)

L. E. Vicent and M. A. Alonso, “Generalized radiometry as a tool for the propagation of partially coherent fields,” Opt. Commun. 207, 101-112 (2002).
[CrossRef]

M. J. Bastiaans, “Gabor's signal expansion applied to partially coherent light,” Opt. Commun. 86, 14-18 (1991).
[CrossRef]

Opt. Eng. (Bellingham) (1)

M. J. Bastiaans, “A sampling theorem for the complex spectrogram, and Gabor's expansion af a signal in the Gaussian elementary signals,” Opt. Eng. (Bellingham) 20, 594-598 (1981).

Opt. Express (4)

Opt. Lett. (1)

Proc. IEEE (1)

M. Unser, “Sampling--50 years after Shannon,” Proc. IEEE 88, 569-587 (2000).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A 217, 408-432 (1953).
[CrossRef]

Proc. SPIE (2)

Y. Lin and J. Buck, “Numerical modelling of the excimer beam,” Proc. SPIE 3677, 700-710 (1999).
[CrossRef]

M. Wald, M. Burkhardt, A. Pesch, H. Gross, and J. Greif, “Design of a microscopy illumination using a partial coherent light source,” Proc. SPIE 5962, 59621G-1-10 (2005).
[CrossRef]

Other (4)

D. Dragoman, “The Wigner distribution in optics and optoelectronics,” in Progress in Optics, E.Wolf, ed. (North-Holland, Amsterdam, 1995).

E. Wolf, Introduction to the Theory of Coherence and Polarisation of Light (Cambridge U. Press, 2007).

M. Born and E. Wolf, Principles of Optics 7th ed. (Cambridge U. Press, 1999).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

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