Abstract

A generalized bidirectional distribution function (BRDF) that relates the specific intensity of the scattered light from a semi-infinite medium to the specific intensity of the incident light is introduced in the framework of coherence theory. This derivation allows us to obtain from first principles several fundamental properties: First, it is established that the generalized BRDF takes the form of a nonlocal relation between the incident and the scattered specific intensities. This nonlocal structure allows us to account naturally for the lateral shift of a beam. Second, the generalized BRDF is the Fourier transform of the correlation function that describes the memory effect. Third, the Helmholtz principle for specific intensities is derived as a theorem from the reciprocity property of the scattering operator for wave fields. This result allows us to prove Kirchhoff’s law.

© 1998 Optical Society of America

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1998 (1)

1997 (3)

D. Bertilone, “Radiometric coherence tensors for thermal radiation emission from an opaque specular surface,” J. Opt. Soc. Am. A 14, 693–702 (1997).
[CrossRef]

J. LeGall, M. Olivier, J.-J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55, 10105–10114 (1997).
[CrossRef]

T. Chan, Y. Kuga, A. Ishimaru, “Subsurface detection of a buried object using angular correlation function measurement,” Waves Random Media 7, 457–466 (1997).
[CrossRef]

1994 (2)

J. H. Li, A. Z. Genack, “Correlation in laser speckle,” Phys. Rev. E 49, 4530–4533 (1994).
[CrossRef]

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

1993 (2)

1992 (5)

M. E. Knotts, T. R. Michel, K. A. O’Donnell, “Angular correlation functions of polarized intensities from a one-dimensionally rough surface,” J. Opt. Soc. Am. A 9, 1822–1831 (1992).
[CrossRef]

J. J. Greffet, C. Baylard, “Nonspecular astigmatic reflection of a 3D Gaussian beam on an interface,” Opt. Commun. 93, 271–276 (1992).
[CrossRef]

F. Bretenaker, A. L. Floch, L. Dutriaux, “Direct measurement of the optical Goos–Hanchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
[CrossRef] [PubMed]

T. R. Michel, K. A. O’Donnell, “Angular correlation functions of amplitudes scattered from a one-dimensional, perfectly conducting rough surface,” J. Opt. Soc. Am. A 9, 1374–1384 (1992).
[CrossRef]

M. Nieto-Vesperinas, J. A. Sanchez-Gil, “Enhanced long-range correlations of coherent waves reflected from disordered media,” Phys. Rev. B 46, 3112–3115 (1992).
[CrossRef]

1990 (1)

1989 (2)

W. Nasalski, “Modified reflectance and geometrical deformations of Gaussian beams reflected at a dielectric interface,” J. Opt. Soc. Am. A 6, 1447–1454 (1989).
[CrossRef]

R. Berkovits, M. Kaveh, S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[CrossRef]

1988 (5)

I. Freund, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II. Doped silicon: angular variation,” Phys. Rev. B 37, 10803–10813 (1988).
[CrossRef]

P. J. Hesketh, J. N. Zemel, “Polarized spectral emittance from periodic micromachined surfaces. I. Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802 (1988).
[CrossRef]

M. J. Kim, “Verification of reciprocity theorem,” Appl. Opt. 27, 2645–2646 (1988).
[CrossRef] [PubMed]

1987 (1)

1986 (4)

1985 (4)

J. T. Foley, E. Wolf, “Radiometry as a short-wavelength limit of statistical wave theory with globally incoherent sources,” Opt. Commun. 55, 236–241 (1985).
[CrossRef]

F. J. J. Clarke, D. J. Parry, “Helmholtz reciprocity: its validity and application to reflectometry,” Light. Res. Technol. 17, 1–11 (1985).
[CrossRef]

H. J. Eom, “Energy conservation and reciprocity of random rough surface scattering,” Appl. Opt. 24, 1730–1732 (1985).
[CrossRef] [PubMed]

W. H. Venable, “Comments on reciprocity failure,” Appl. Opt. 24, 3943 (1985).
[CrossRef] [PubMed]

1984 (1)

1982 (1)

G. S. Brown, “A stochastic Fourier transform from perfectly conducting randomly rough surfaces,” IEEE Trans. Antennas Propag. AP-30, 1135–1143 (1982).
[CrossRef]

1981 (1)

1978 (2)

E. Wolf, “Coherence and radiometry (R),” J. Opt. Soc. Am. 68, 6–17 (1978).
[CrossRef]

M. Huetz-Aubert, J. Taine, “Rôle de la réflexion ou de la diffusion dans la deuxième loi de Kirchhoff, dite aussi loi de Draper,” Rev. Gen. Therm. 1, 755–764 (1978).

1977 (1)

1976 (2)

D. Léger, J. C. Perrin, “Real-time measurement of surface roughness by correlation of speckle pattern,” J. Opt. Soc. Am. 66, 1210–1217 (1976).
[CrossRef]

E. Wolf, “New theory of radiative energy transfer in free electromagnetic fields,” Phys. Rev. D 13, 869–886 (1976).
[CrossRef]

1975 (3)

H. M. Pedersen, “Second-order statistics of light diffracted from Gaussian rough surfaces with applications to the roughness dependence of speckles,” Opt. Acta 22, 523–535 (1975).
[CrossRef]

C. Imbert, Y. Levy, “Déplacement d’un faisceau lumineux par réflexion totale: filtrage des états de polarisation et amplification,” Nouv. Res. Opt. 6, 285–296 (1975).
[CrossRef]

D. Léger, E. Mathieu, J. C. Perrin, “Optical surface roughness determination using speckle correlation techniques,” Appl. Opt. 14, 872–877 (1975).
[CrossRef]

1974 (1)

1973 (1)

1972 (1)

1971 (1)

1970 (1)

1968 (1)

1965 (1)

1955 (1)

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
[CrossRef]

Baylard, C.

J.-J. Greffet, C. Baylard, “Nonspecular reflection from a lossy dielectric,” Opt. Commun. 18, 1129–1131 (1993).

J. J. Greffet, C. Baylard, “Nonspecular astigmatic reflection of a 3D Gaussian beam on an interface,” Opt. Commun. 93, 271–276 (1992).
[CrossRef]

Berkovits, R.

R. Berkovits, M. Kaveh, S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[CrossRef]

Bertilone, D.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bretenaker, F.

F. Bretenaker, A. L. Floch, L. Dutriaux, “Direct measurement of the optical Goos–Hanchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
[CrossRef] [PubMed]

Brown, G. S.

G. S. Brown, “A stochastic Fourier transform from perfectly conducting randomly rough surfaces,” IEEE Trans. Antennas Propag. AP-30, 1135–1143 (1982).
[CrossRef]

Cadilhac, M.

Carminati, R.

Carter, W. H.

Chan, T.

T. Chan, Y. Kuga, A. Ishimaru, “Subsurface detection of a buried object using angular correlation function measurement,” Waves Random Media 7, 457–466 (1997).
[CrossRef]

Clarke, F. J. J.

F. J. J. Clarke, D. J. Parry, “Helmholtz reciprocity: its validity and application to reflectometry,” Light. Res. Technol. 17, 1–11 (1985).
[CrossRef]

Dutriaux, L.

F. Bretenaker, A. L. Floch, L. Dutriaux, “Direct measurement of the optical Goos–Hanchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
[CrossRef] [PubMed]

Eom, H. J.

Falco, F.

Feng, S.

R. Berkovits, M. Kaveh, S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[CrossRef]

I. Freund, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Floch, A. L.

F. Bretenaker, A. L. Floch, L. Dutriaux, “Direct measurement of the optical Goos–Hanchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
[CrossRef] [PubMed]

Foley, J. T.

J. T. Foley, E. Wolf, “Radiometry as a short-wavelength limit of statistical wave theory with globally incoherent sources,” Opt. Commun. 55, 236–241 (1985).
[CrossRef]

Freund, I.

I. Freund, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

Gebhart, B.

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II. Doped silicon: angular variation,” Phys. Rev. B 37, 10803–10813 (1988).
[CrossRef]

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Organ pipes radiant modes of micromachined silicon surfaces,” Nature (London) 352, 549–551 (1986).
[CrossRef]

Genack, A. Z.

J. H. Li, A. Z. Genack, “Correlation in laser speckle,” Phys. Rev. E 49, 4530–4533 (1994).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Greffet, J. J.

J. J. Greffet, C. Baylard, “Nonspecular astigmatic reflection of a 3D Gaussian beam on an interface,” Opt. Commun. 93, 271–276 (1992).
[CrossRef]

Greffet, J.-J.

R. Carminati, M. Nieto-Vesperinas, J.-J. Greffet, “Reciprocity of electromagnetic waves,” J. Opt. Soc. Am. A 15, 706–712 (1998).
[CrossRef]

J. LeGall, M. Olivier, J.-J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55, 10105–10114 (1997).
[CrossRef]

J.-J. Greffet, C. Baylard, “Nonspecular reflection from a lossy dielectric,” Opt. Commun. 18, 1129–1131 (1993).

Hesketh, P. J.

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II. Doped silicon: angular variation,” Phys. Rev. B 37, 10803–10813 (1988).
[CrossRef]

P. J. Hesketh, J. N. Zemel, “Polarized spectral emittance from periodic micromachined surfaces. I. Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802 (1988).
[CrossRef]

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Organ pipes radiant modes of micromachined silicon surfaces,” Nature (London) 352, 549–551 (1986).
[CrossRef]

Horowitz, B. R.

Howell, J. R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Hemisphere, Washington, D.C., 1981).

Huetz-Aubert, M.

M. Huetz-Aubert, J. Taine, “Rôle de la réflexion ou de la diffusion dans la deuxième loi de Kirchhoff, dite aussi loi de Draper,” Rev. Gen. Therm. 1, 755–764 (1978).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Hugonin, J. P.

Imbert, C.

C. Imbert, Y. Levy, “Déplacement d’un faisceau lumineux par réflexion totale: filtrage des états de polarisation et amplification,” Nouv. Res. Opt. 6, 285–296 (1975).
[CrossRef]

Ishimaru, A.

T. Chan, Y. Kuga, A. Ishimaru, “Subsurface detection of a buried object using angular correlation function measurement,” Waves Random Media 7, 457–466 (1997).
[CrossRef]

Kane, C.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Kaveh, M.

R. Berkovits, M. Kaveh, S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[CrossRef]

Kim, K.

Kim, M. J.

Knotts, M. E.

Kong, J. A.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Kravtsov, Y. A.

S. M. Rytov, Y. A. Kravtsov, V. I. Tatarskii, Principles of Statistical Radiophysics, Vol. 3: Elements of Random Fields (Springer-Verlag, Berlin, 1989).

Kuga, Y.

T. Chan, Y. Kuga, A. Ishimaru, “Subsurface detection of a buried object using angular correlation function measurement,” Waves Random Media 7, 457–466 (1997).
[CrossRef]

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

LeGall, J.

J. LeGall, M. Olivier, J.-J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55, 10105–10114 (1997).
[CrossRef]

J. LeGall, “Etude experimentale et théorique de la propagation d’ondes de surface sur un réseau. Application à la modification des propriétés radiatives infrarouges de matériaux,” Ph.D. dissertation (Ecole Centrale Paris, Paris, 1996).

Léger, D.

Levy, Y.

C. Imbert, Y. Levy, “Déplacement d’un faisceau lumineux par réflexion totale: filtrage des états de polarisation et amplification,” Nouv. Res. Opt. 6, 285–296 (1975).
[CrossRef]

Li, J. H.

J. H. Li, A. Z. Genack, “Correlation in laser speckle,” Phys. Rev. E 49, 4530–4533 (1994).
[CrossRef]

Mandel, L.

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

Marathay, A. S.

A. S. Marathay, Elements of Optical Coherence Theory (Wiley, New York, 1982).

Marchand, E. W.

Mathieu, E.

Michel, T. R.

Nasalski, W.

Newton, R. G.

R. G. Newton, Scattering Theory of Waves and Particles (Springer-Verlag, New York, 1982).

Nicodemus, F. E.

Nieto-Vesperinas, M.

O’Donnell, K. A.

Ogura, I.

Okayama, H.

Olivier, M.

J. LeGall, M. Olivier, J.-J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55, 10105–10114 (1997).
[CrossRef]

Parry, D. J.

F. J. J. Clarke, D. J. Parry, “Helmholtz reciprocity: its validity and application to reflectometry,” Light. Res. Technol. 17, 1–11 (1985).
[CrossRef]

Pedersen, H. M.

H. M. Pedersen, “Second-order statistics of light diffracted from Gaussian rough surfaces with applications to the roughness dependence of speckles,” Opt. Acta 22, 523–535 (1975).
[CrossRef]

Perrin, J. C.

Petit, R.

Rayleigh, J. W. S.

J. W. S. Rayleigh, Theory of Sound (Macmillan, London, 1896).

Rosenbluh, M.

I. Freund, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

Rytov, S. M.

S. M. Rytov, Y. A. Kravtsov, V. I. Tatarskii, Principles of Statistical Radiophysics, Vol. 3: Elements of Random Fields (Springer-Verlag, Berlin, 1989).

Sanchez-Gil, J.

Sanchez-Gil, J. A.

M. Nieto-Vesperinas, J. A. Sanchez-Gil, “Enhanced long-range correlations of coherent waves reflected from disordered media,” Phys. Rev. B 46, 3112–3115 (1992).
[CrossRef]

Saxon, D. S.

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
[CrossRef]

Shin, R. T.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Siegel, R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Hemisphere, Washington, D.C., 1981).

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Stover, J. C.

J. C. Stover, Optical Scattering (McGraw-Hill, New York, 1990).

Taine, J.

M. Huetz-Aubert, J. Taine, “Rôle de la réflexion ou de la diffusion dans la deuxième loi de Kirchhoff, dite aussi loi de Draper,” Rev. Gen. Therm. 1, 755–764 (1978).

Tamir, T.

Tatarskii, V. I.

S. M. Rytov, Y. A. Kravtsov, V. I. Tatarskii, Principles of Statistical Radiophysics, Vol. 3: Elements of Random Fields (Springer-Verlag, Berlin, 1989).

Tsang, L.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Venable, W. H.

von Helmholtz, H.

H. von Helmholtz, Handbuch der Physiologischen Optik (Leopold Voss, Hamburg, 1909).

Walther, A.

Wolf, E.

Zemel, J. N.

P. J. Hesketh, J. N. Zemel, “Polarized spectral emittance from periodic micromachined surfaces. I. Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802 (1988).
[CrossRef]

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II. Doped silicon: angular variation,” Phys. Rev. B 37, 10803–10813 (1988).
[CrossRef]

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Organ pipes radiant modes of micromachined silicon surfaces,” Nature (London) 352, 549–551 (1986).
[CrossRef]

Appl. Opt. (7)

IEEE Trans. Antennas Propag. (1)

G. S. Brown, “A stochastic Fourier transform from perfectly conducting randomly rough surfaces,” IEEE Trans. Antennas Propag. AP-30, 1135–1143 (1982).
[CrossRef]

J. Opt. Soc. Am. (9)

J. Opt. Soc. Am. A (11)

M. Nieto-Vesperinas, J. Sanchez-Gil, “Intensity angular correlations of light multiply scattered from random rough surfaces,” J. Opt. Soc. Am. A 10, 150–157 (1993).
[CrossRef]

M. E. Knotts, T. R. Michel, K. A. O’Donnell, “Angular correlation functions of polarized intensities from a one-dimensionally rough surface,” J. Opt. Soc. Am. A 9, 1822–1831 (1992).
[CrossRef]

R. Carminati, M. Nieto-Vesperinas, J.-J. Greffet, “Reciprocity of electromagnetic waves,” J. Opt. Soc. Am. A 15, 706–712 (1998).
[CrossRef]

D. Bertilone, “Radiometric coherence tensors for thermal radiation emission from an opaque specular surface,” J. Opt. Soc. Am. A 14, 693–702 (1997).
[CrossRef]

T. Tamir, “Nonspecular phenomena in beam fields reflected by multilayered media,” J. Opt. Soc. Am. A 3, 558–565 (1986).
[CrossRef]

M. Nieto-Vesperinas, “Classical radiometry and radiative transfer theory: a short-wavelength limit of a general mapping of cross-spectral densities in second-order coherence theory,” J. Opt. Soc. Am. A 3, 1354–1359 (1986).
[CrossRef]

M. Nieto-Vesperinas, E. Wolf, “Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shape,” J. Opt. Soc. Am. A 3, 2038–2046 (1986).
[CrossRef]

K. Kim, E. Wolf, “Propagation law for Walther’s first generalized radiance function and its short-wavelength limit with quasi-homogeneous sources,” J. Opt. Soc. Am. A 4, 1233–1236 (1987).
[CrossRef]

W. Nasalski, “Modified reflectance and geometrical deformations of Gaussian beams reflected at a dielectric interface,” J. Opt. Soc. Am. A 6, 1447–1454 (1989).
[CrossRef]

F. Falco, T. Tamir, “Improved analysis of nonspecular phenomena in beams reflected from stratified media,” J. Opt. Soc. Am. A 7, 185–190 (1990).
[CrossRef]

T. R. Michel, K. A. O’Donnell, “Angular correlation functions of amplitudes scattered from a one-dimensional, perfectly conducting rough surface,” J. Opt. Soc. Am. A 9, 1374–1384 (1992).
[CrossRef]

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[CrossRef]

Nature (London) (1)

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Organ pipes radiant modes of micromachined silicon surfaces,” Nature (London) 352, 549–551 (1986).
[CrossRef]

Nouv. Res. Opt. (1)

C. Imbert, Y. Levy, “Déplacement d’un faisceau lumineux par réflexion totale: filtrage des états de polarisation et amplification,” Nouv. Res. Opt. 6, 285–296 (1975).
[CrossRef]

Opt. Acta (1)

H. M. Pedersen, “Second-order statistics of light diffracted from Gaussian rough surfaces with applications to the roughness dependence of speckles,” Opt. Acta 22, 523–535 (1975).
[CrossRef]

Opt. Commun. (3)

J.-J. Greffet, C. Baylard, “Nonspecular reflection from a lossy dielectric,” Opt. Commun. 18, 1129–1131 (1993).

J. J. Greffet, C. Baylard, “Nonspecular astigmatic reflection of a 3D Gaussian beam on an interface,” Opt. Commun. 93, 271–276 (1992).
[CrossRef]

J. T. Foley, E. Wolf, “Radiometry as a short-wavelength limit of statistical wave theory with globally incoherent sources,” Opt. Commun. 55, 236–241 (1985).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
[CrossRef]

Phys. Rev. B (5)

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II. Doped silicon: angular variation,” Phys. Rev. B 37, 10803–10813 (1988).
[CrossRef]

P. J. Hesketh, J. N. Zemel, “Polarized spectral emittance from periodic micromachined surfaces. I. Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802 (1988).
[CrossRef]

J. LeGall, M. Olivier, J.-J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55, 10105–10114 (1997).
[CrossRef]

R. Berkovits, M. Kaveh, S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[CrossRef]

M. Nieto-Vesperinas, J. A. Sanchez-Gil, “Enhanced long-range correlations of coherent waves reflected from disordered media,” Phys. Rev. B 46, 3112–3115 (1992).
[CrossRef]

Phys. Rev. D (1)

E. Wolf, “New theory of radiative energy transfer in free electromagnetic fields,” Phys. Rev. D 13, 869–886 (1976).
[CrossRef]

Phys. Rev. E (1)

J. H. Li, A. Z. Genack, “Correlation in laser speckle,” Phys. Rev. E 49, 4530–4533 (1994).
[CrossRef]

Phys. Rev. Lett. (3)

F. Bretenaker, A. L. Floch, L. Dutriaux, “Direct measurement of the optical Goos–Hanchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
[CrossRef] [PubMed]

I. Freund, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Rev. Gen. Therm. (1)

M. Huetz-Aubert, J. Taine, “Rôle de la réflexion ou de la diffusion dans la deuxième loi de Kirchhoff, dite aussi loi de Draper,” Rev. Gen. Therm. 1, 755–764 (1978).

Waves Random Media (1)

T. Chan, Y. Kuga, A. Ishimaru, “Subsurface detection of a buried object using angular correlation function measurement,” Waves Random Media 7, 457–466 (1997).
[CrossRef]

Other (13)

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

S. M. Rytov, Y. A. Kravtsov, V. I. Tatarskii, Principles of Statistical Radiophysics, Vol. 3: Elements of Random Fields (Springer-Verlag, Berlin, 1989).

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Hemisphere, Washington, D.C., 1981).

A. S. Marathay, Elements of Optical Coherence Theory (Wiley, New York, 1982).

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

J. LeGall, “Etude experimentale et théorique de la propagation d’ondes de surface sur un réseau. Application à la modification des propriétés radiatives infrarouges de matériaux,” Ph.D. dissertation (Ecole Centrale Paris, Paris, 1996).

R. G. Newton, Scattering Theory of Waves and Particles (Springer-Verlag, New York, 1982).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

H. von Helmholtz, Handbuch der Physiologischen Optik (Leopold Voss, Hamburg, 1909).

J. C. Stover, Optical Scattering (McGraw-Hill, New York, 1990).

J. W. S. Rayleigh, Theory of Sound (Macmillan, London, 1896).

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Figures (2)

Fig. 1
Fig. 1

Scattering geometry.

Fig. 2
Fig. 2

Comparison of (a) volume scattering and (b) surface scattering. For volume scattering, light migrates over distances of the order of several mean free paths.

Equations (69)

Equations on this page are rendered with MathJax. Learn more.

dQν=Iν(r, s)dA cos θdΩ.
Jν(s)=Iν(r, s)cos θdA.
Iνr(r, s)=ρ(r, s, S)Iνinc(r, S)cos θdΩ.
u(r)=a(s)exp[iks·r]ds,
u(r, z)=[a(s)exp(ikszz)]exp[iks·r]ds,
a(s)=k2π2u(r)exp[-iks·r]dr,
a(s)exp(iszz)=k2π2u(r, z)exp[-iks·r]dr.
u(r)=-i2πk|sz|a(s) exp(ikr)r,wheres=r/r.
Jν(s)dΩ=|u(r)|2r2dΩ=4π2k2sz2|a(s)|2dΩ,
Jν(s)=sz2k2π2drur+r2, z
×u*r-r2, zexp[-iks·r]dr.
Iν(r, s)=|sz|k2π2ur+r2, z
×u*r-r2, zexp(-iks·r)dr.
Iν(r, s)=|sz|as+s2a*s-s2
×exp(iks·r)ds.
Iν(r, s)=|sz|as+s2a*s-s2
×exp(iks·r)ds.
u*r-r2ur+r2=S(r)g(r).
a*s-s2as+s2=k4S˜(ks)g˜(ks).
Iν(r, s)=k2|sz|S(r)g˜(ks).
u(r)=A(s)exp(iks·r)dΩ.
Ar(s)=R(s, S)Ainc(S)dΩ,
R(s, S)=R(-S,-s).
ar(s)=r(s, S)ainc(S)dS,
szr(s, S)=-Szr(-S,-s).
Iνr(r, s)=|sz|ar*s-s2ars+s2
×exp(iks·r)ds,
Iνr(r, s)=|sz|r*s-s2, s1
×rs+s2, s2ain*(s1)ain(s2)
×exp(iks·r)dsds1ds2.
ain * S-S2ainS+S2
=1λ21|Sz|dr exp[-ikS·r]Iνin(r, S).
Iνr(r, s)=ρ(s, S, r, r)Iνinc(r, S)|Sz|dΩdr.
ρ(s, S, r, r)
=szSzk2π2dsdS exp[ik(s·r-S·r)]
×Cs-s2, S-S2, s+s2, S+S2.
Cs-s2, S-S2, s+s2, S+S2
=Szszk2π2drdrρ(s, S, r, r)
×exp[-ik(s·r-S·r)].
Cs-s2, S-S2, s+s2, S+S2
=Szszk2π2dR exp[-ik(s-S)·R]
×dvρ(s, S, v, R)
×exp-ik (s+S)2·v.
ρ(s, S, r-r)
=szSzk2π2dS exp[ikS·(r-r)]×Cs-S2, S-S2, s+S2, S+S2.
r(s, s)=exp[iΦ(s)]δ(s-s).
Φs-S2=Φ(s)-Φ·S2.
ρ(s, s, r)=δ(s-s) exp[ikS·(r+Φ)]dS.
ρ(s, s, r)=δ(s-s)δ(r+Φ).
ρ(s, S)=szSzr*(s, S)r(s, S)¯.
ρ(s, S)=|r(S, S)|2δ(s-S).
ρ(s, S)=ρ(-S,-s).
ρ(s, S, r, r)=ρ(-S,-s, r, r).
Iνe(r, s)=ν(r, s)Iν°(T).
Iν°(T)=ν(r, s)Iν°(T)+ρν(r, s, s)Iν°(T)szdΩ.
1=ν(r, s)+ρν(r, s, s)szdΩ=ν(r, s)+ρν(r, s, h).
1=αν(r, s)+ρν(r, s, s)szdΩ=αν(r, s)+ρν(r, h, s).
ρν(r, h, s)=ρν(r, s, h).
Iν(r, s)=|sz|k2π2dr exp(-iks·r)
×ds1ds2a(s1)a*(s2)
×exp{ik[s1(r+r/2)-s2(r-r/2)]}.
Iν(r, s)=|sz|k2π2dSdr 
×exp[-ik(S-s)·r]
×dsa(S+s/2)a*(S-s/2)
×exp[ik(s·r)].
dr exp[ik(s·r)]=2πk2δ(s),
Iνr(r, s)=|sz|dS exp(ikS·r)Iνinc(S, S)×Cs-S2, S-S2, s+S2, S+S2dΩ.
Iνr(r, s)
=szSzr*(s, S)r(s, S)¯Iνinc(r, S)|Sz|dΩ.

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