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[Crossref]

O. G. Cula and K. J. Dana, "3D texture recognition using bidirectional feature histograms," Int. J. Comput. Vis. 59, 33-60 (2004).

[Crossref]

J. Meseth, G. Müller, and R. Klein, "Reflectance field based real-time, high-quality rendering of bidirectional texture functions," Comput. Graphics 28, 105-112 (2004).

[Crossref]

T. M. Elfouhaily and C.-A. Guérin, "A critical survey of approximate scattering wave theories from random rough surfaces," Waves Random Media 14, R1-R40 (2004).

[Crossref]

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[Crossref]

F. Drago and K. Myszkowski, "Validation proposal for global illumination and rendering techniques," Comput. Graphics 25, 511-518 (2001).

[Crossref]

F. Bernardini, I. M. Martin, and H. Rushmeier, "High-quality texture reconstruction from multiple scans," IEEE Trans. Vis. Comput. Graph. 7, 318-332 (2001).

[Crossref]

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[Crossref]

D. Fontani, F. Francini, G. Longobardi, and P. Sansoni, "Optical control of surface finish," Opt. Lasers Eng. 32, 459-472 (2000).

[Crossref]

G. Macelloni, G. Nesti, P. Pampaloni, S. Sigismondi, D. Tarchi, and S. Lolli, "Experimental validation of surface scattering and emission models," IEEE Trans. Geosci. Remote Sens. 38, 459-469 (2000).

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[Crossref]

O. P. Bruno, A. Sei, and M. Caponi, "High-order high-frequency solutions of rough surface scattering problems," Radio Sci. 37, 10.1029/2000 RS002551 (2002).

[Crossref]

M. K. Shepard and B. A. Campbell, "Radar scattering from a self-affine fractal surface: near-nadir regime," Icarus 141, 156-171 (1999).

[Crossref]

O. P. Bruno, A. Sei, and M. Caponi, "High-order high-frequency solutions of rough surface scattering problems," Radio Sci. 37, 10.1029/2000 RS002551 (2002).

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[Crossref]

S. Kaasalainen, J. Piironen, M. Kaasalainen, A. W. Harris, K. Muinonen, and A. Cellino, "Asteroid photometric and polarimetric phase curves: empirical interpretation," Icarus 161, 34-46 (2003).

[Crossref]

A. Ishimaru and J. S. Chen, "Scattering from very rough metallic and dielectric surfaces: a theory based on the modified Kirchhoff approximation," Waves Random Media 1, 25-34 (1991).

[Crossref]

C. Rocchini, P. Cignoni, C. Montani, and R. Scopigno, "Acquiring, stitching, and blending diffuse appearance attributes on 3D models," Visual Comput. 18, 186-204 (2002).

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O. G. Cula and K. J. Dana, "3D texture recognition using bidirectional feature histograms," Int. J. Comput. Vis. 59, 33-60 (2004).

[Crossref]

N. C. Bruce and J. C. Dainty, "Multiple scattering from rough dielectric and metal surfaces using the Kirchhoff approximation," J. Mod. Opt. 38, 1471-1481 (1991).

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[Crossref]

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[Crossref]
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F. Drago and K. Myszkowski, "Validation proposal for global illumination and rendering techniques," Comput. Graphics 25, 511-518 (2001).

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T. M. Elfouhaily and C.-A. Guérin, "A critical survey of approximate scattering wave theories from random rough surfaces," Waves Random Media 14, R1-R40 (2004).

[Crossref]

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[Crossref]

D. Fontani, F. Francini, G. Longobardi, and P. Sansoni, "Optical control of surface finish," Opt. Lasers Eng. 32, 459-472 (2000).

[Crossref]

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. Schirripa-Spagnolo, "Generalized Bessel-Gauss beams," J. Mod. Opt. 43, 1155-1166 (1996).

B. D. Fried and S. D. Conte, The Plasma Dispersion Function: The Hilbert Transform of the Gaussian (Academic, 1961). Note that the function defined in this reference has its real and imaginary parts switched relative to the plasma dispersion function defined in Refs. .

A. K. Fung and R. K. Moore, "Effects of structure size on moon and earth radar returns at various angles," J. Geophys. Res. 69, 1075-1081 (1964).

[Crossref]

A. K. Fung, "Theory of radar scatter from rough surfaces, bistatic and monostatic, with application to lunar radar return," J. Geophys. Res. 69, 1063-1073 (1964).

[Crossref]

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T. Weyrich, H. Pfister, and M. Gross, "Rendering deformable surface reflectance fields," IEEE Trans. Vis. Comput. Graph. 11, 48-58 (2005).

[Crossref]
[PubMed]

T. M. Elfouhaily and C.-A. Guérin, "A critical survey of approximate scattering wave theories from random rough surfaces," Waves Random Media 14, R1-R40 (2004).

[Crossref]

D. D. Duncan, D. V. Hahn, and M. E. Thomas, "Physics-based polarimetric BRDF models," in Optical Diagnostic Methods for Inorganic Materials III, L.M.Hanssen, ed., Proc. SPIE 5192, 129-140 (2003).

J. Dorsey and P. Hanrahan, "Digital materials and virtual weathering," Sci. Am. 282(2), 64-71 (2000).

[Crossref]
[PubMed]

S. Kaasalainen, J. Piironen, M. Kaasalainen, A. W. Harris, K. Muinonen, and A. Cellino, "Asteroid photometric and polarimetric phase curves: empirical interpretation," Icarus 161, 34-46 (2003).

[Crossref]

X. D. He, K. E. Torrance, F. X. Sillion, and D. P. Greenberg, "A comprehensive physical model for light reflection," Comput. Graph. 25, 175-186 (1991).

[Crossref]

O. Korotkova, B. G. Hoover, V. L. Gamiz, and E. Wolf, "Coherence and polarization properties of far-fields generated by quasi-homogeneous electromagnetic sources," J. Opt. Soc. Am. A 22, 2547-2556 (2005).

[Crossref]

B. G. Hoover and V. L. Gamiz, "Diffractive bidirectional reflectance distributions of surfaces with large effective roughness in one dimension," in Laser Radar Techniques for Atmospheric Sensing, U.N.Singh, ed., Proc. SPIE 5575, 137-142 (2004).

A. Ishimaru and J. S. Chen, "Scattering from very rough metallic and dielectric surfaces: a theory based on the modified Kirchhoff approximation," Waves Random Media 1, 25-34 (1991).

[Crossref]

K. Ivanova, M. A. Michalev, and O. I. Yordanov, "Numerical study of scattering by rough surfaces with intermediate and large scale roughness," Radio Sci. 26, 505-510 (1991).

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S. Kaasalainen, J. Piironen, M. Kaasalainen, A. W. Harris, K. Muinonen, and A. Cellino, "Asteroid photometric and polarimetric phase curves: empirical interpretation," Icarus 161, 34-46 (2003).

[Crossref]

M. Kaasalainen, K. Muinonen, and T. Laakso, "Shapes and scattering properties of large irregular bodies from photometric data," Opt. Express 8, 296-301 (2001).

[Crossref]
[PubMed]

S. Kaasalainen, J. Piironen, M. Kaasalainen, A. W. Harris, K. Muinonen, and A. Cellino, "Asteroid photometric and polarimetric phase curves: empirical interpretation," Icarus 161, 34-46 (2003).

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[Crossref]

A. J. Sant, J. C. Dainty, and M.-J. Kim, "Comparison of surface scattering between identical, randomly rough metal and dielectric diffusers," Opt. Lett. 14, 1183-1185 (1989).

[Crossref]
[PubMed]

J. Meseth, G. Müller, and R. Klein, "Reflectance field based real-time, high-quality rendering of bidirectional texture functions," Comput. Graphics 28, 105-112 (2004).

[Crossref]

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[Crossref]

D. Fontani, F. Francini, G. Longobardi, and P. Sansoni, "Optical control of surface finish," Opt. Lasers Eng. 32, 459-472 (2000).

[Crossref]

L. Brainard, W. Lynn, D. Ramer, and W. Shemano, "Optical measurements facility," Air Force Research Laboratory, Materials & Manufacturing Directorate, Rep. AFRL-ML-WP-TR-1999-4142 (1999).

G. Macelloni, G. Nesti, P. Pampaloni, S. Sigismondi, D. Tarchi, and S. Lolli, "Experimental validation of surface scattering and emission models," IEEE Trans. Geosci. Remote Sens. 38, 459-469 (2000).

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[Crossref]

M. S. Gilmore, R. Castaño, T. Mann, R. C. Anderson, E. D. Mjolsness, R. Manduchi, and R. S. Saunders, "Strategies for autonomous rovers at Mars," J. Geophys. Res. 105, 29223-29237 (2000).

[Crossref]

F. Bernardini, I. M. Martin, and H. Rushmeier, "High-quality texture reconstruction from multiple scans," IEEE Trans. Vis. Comput. Graph. 7, 318-332 (2001).

[Crossref]

S. H. C. P. McCall, "The importance of scatter in stray light analysis," Opt. Photonics News 12(11), 40-47 (2001).

[Crossref]

E. R. Méndez, E. E. Garcia-Guerrero, H. M. Escamilla, A. A. Maradudin, T. A. Leskova, and A. V. Shchegrov, "Photofabrication of random achromatic optical diffusers for uniform illumination," Appl. Opt. 40, 1098-1108 (2001).

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J. Meseth, G. Müller, and R. Klein, "Reflectance field based real-time, high-quality rendering of bidirectional texture functions," Comput. Graphics 28, 105-112 (2004).

[Crossref]

K. Ivanova, M. A. Michalev, and O. I. Yordanov, "Numerical study of scattering by rough surfaces with intermediate and large scale roughness," Radio Sci. 26, 505-510 (1991).

[Crossref]

M. S. Gilmore, R. Castaño, T. Mann, R. C. Anderson, E. D. Mjolsness, R. Manduchi, and R. S. Saunders, "Strategies for autonomous rovers at Mars," J. Geophys. Res. 105, 29223-29237 (2000).

[Crossref]

C. Rocchini, P. Cignoni, C. Montani, and R. Scopigno, "Acquiring, stitching, and blending diffuse appearance attributes on 3D models," Visual Comput. 18, 186-204 (2002).

[Crossref]

A. K. Fung and R. K. Moore, "Effects of structure size on moon and earth radar returns at various angles," J. Geophys. Res. 69, 1075-1081 (1964).

[Crossref]

S. Kaasalainen, J. Piironen, M. Kaasalainen, A. W. Harris, K. Muinonen, and A. Cellino, "Asteroid photometric and polarimetric phase curves: empirical interpretation," Icarus 161, 34-46 (2003).

[Crossref]

M. Kaasalainen, K. Muinonen, and T. Laakso, "Shapes and scattering properties of large irregular bodies from photometric data," Opt. Express 8, 296-301 (2001).

[Crossref]
[PubMed]

J. Meseth, G. Müller, and R. Klein, "Reflectance field based real-time, high-quality rendering of bidirectional texture functions," Comput. Graphics 28, 105-112 (2004).

[Crossref]

F. Drago and K. Myszkowski, "Validation proposal for global illumination and rendering techniques," Comput. Graphics 25, 511-518 (2001).

[Crossref]

G. Macelloni, G. Nesti, P. Pampaloni, S. Sigismondi, D. Tarchi, and S. Lolli, "Experimental validation of surface scattering and emission models," IEEE Trans. Geosci. Remote Sens. 38, 459-469 (2000).

[Crossref]

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G. Macelloni, G. Nesti, P. Pampaloni, S. Sigismondi, D. Tarchi, and S. Lolli, "Experimental validation of surface scattering and emission models," IEEE Trans. Geosci. Remote Sens. 38, 459-469 (2000).

[Crossref]

T. Weyrich, H. Pfister, and M. Gross, "Rendering deformable surface reflectance fields," IEEE Trans. Vis. Comput. Graph. 11, 48-58 (2005).

[Crossref]
[PubMed]

S. Kaasalainen, J. Piironen, M. Kaasalainen, A. W. Harris, K. Muinonen, and A. Cellino, "Asteroid photometric and polarimetric phase curves: empirical interpretation," Icarus 161, 34-46 (2003).

[Crossref]

M. Ashikhmin, S. Premoze, and P. Shirley, "A microfacet-based BRDF generator," in Proceedings of ACM SIGGRAPH 2000 (www.siggraph.org), pp. 65-74.

L. Brainard, W. Lynn, D. Ramer, and W. Shemano, "Optical measurements facility," Air Force Research Laboratory, Materials & Manufacturing Directorate, Rep. AFRL-ML-WP-TR-1999-4142 (1999).

S. O. Rice, "Reflection of electromagnetic waves from slightly rough surfaces," Commun. Pure Appl. Math. 4, 351-378 (1951).

[Crossref]

C. Rocchini, P. Cignoni, C. Montani, and R. Scopigno, "Acquiring, stitching, and blending diffuse appearance attributes on 3D models," Visual Comput. 18, 186-204 (2002).

[Crossref]

F. Bernardini, I. M. Martin, and H. Rushmeier, "High-quality texture reconstruction from multiple scans," IEEE Trans. Vis. Comput. Graph. 7, 318-332 (2001).

[Crossref]

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, corrected and enlarged ed. (Academic, 1980), 6.623(2).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, corrected and enlarged ed. (Academic, 1980), 6.631(4).

M. Saillard and A. Sentenac, "Rigorous solutions for electromagnetic scattering from rough surfaces," Waves Random Media 11, R103-R137 (2001).

[Crossref]

D. Fontani, F. Francini, G. Longobardi, and P. Sansoni, "Optical control of surface finish," Opt. Lasers Eng. 32, 459-472 (2000).

[Crossref]

M.-J. Kim, J. C. Dainty, A. T. Friberg, and A. J. Sant, "Experimental study of enhanced backscattering from one- and two-dimensional random rough surfaces," J. Opt. Soc. Am. A 7, 569-577 (1990).

[Crossref]

A. J. Sant, J. C. Dainty, and M.-J. Kim, "Comparison of surface scattering between identical, randomly rough metal and dielectric diffusers," Opt. Lett. 14, 1183-1185 (1989).

[Crossref]
[PubMed]

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. Schirripa-Spagnolo, "Generalized Bessel-Gauss beams," J. Mod. Opt. 43, 1155-1166 (1996).

M. S. Gilmore, R. Castaño, T. Mann, R. C. Anderson, E. D. Mjolsness, R. Manduchi, and R. S. Saunders, "Strategies for autonomous rovers at Mars," J. Geophys. Res. 105, 29223-29237 (2000).

[Crossref]

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. Schirripa-Spagnolo, "Generalized Bessel-Gauss beams," J. Mod. Opt. 43, 1155-1166 (1996).

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. Schirripa-Spagnolo, "Generalized Bessel-Gauss beams," J. Mod. Opt. 43, 1155-1166 (1996).

C. Rocchini, P. Cignoni, C. Montani, and R. Scopigno, "Acquiring, stitching, and blending diffuse appearance attributes on 3D models," Visual Comput. 18, 186-204 (2002).

[Crossref]

O. P. Bruno, A. Sei, and M. Caponi, "High-order high-frequency solutions of rough surface scattering problems," Radio Sci. 37, 10.1029/2000 RS002551 (2002).

[Crossref]

Derivatives of the delta function are considered in T. B. A. Senior and J. L. Volakis, Approximate Boundary Conditions in Electromagnetics (IEEE Press, 1995).

M. Saillard and A. Sentenac, "Rigorous solutions for electromagnetic scattering from rough surfaces," Waves Random Media 11, R103-R137 (2001).

[Crossref]

L. Brainard, W. Lynn, D. Ramer, and W. Shemano, "Optical measurements facility," Air Force Research Laboratory, Materials & Manufacturing Directorate, Rep. AFRL-ML-WP-TR-1999-4142 (1999).

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[Crossref]

M. Ashikhmin, S. Premoze, and P. Shirley, "A microfacet-based BRDF generator," in Proceedings of ACM SIGGRAPH 2000 (www.siggraph.org), pp. 65-74.

G. Macelloni, G. Nesti, P. Pampaloni, S. Sigismondi, D. Tarchi, and S. Lolli, "Experimental validation of surface scattering and emission models," IEEE Trans. Geosci. Remote Sens. 38, 459-469 (2000).

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W. C. Snyder and Z. Wan, "BRDF models to predict spectral reflectance and emissivity in the thermal infrared," IEEE Trans. Geosci. Remote Sens. 36, 214-225 (1998).

[Crossref]

W. C. Snyder, "Reciprocity of the bidirectional reflectance distribution function (BRDF) in measurements and models of structured surfaces," IEEE Trans. Geosci. Remote Sens. 36, 685-691 (1998).

[Crossref]

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[Crossref]

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G. Macelloni, G. Nesti, P. Pampaloni, S. Sigismondi, D. Tarchi, and S. Lolli, "Experimental validation of surface scattering and emission models," IEEE Trans. Geosci. Remote Sens. 38, 459-469 (2000).

[Crossref]

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D. D. Duncan, D. V. Hahn, and M. E. Thomas, "Physics-based polarimetric BRDF models," in Optical Diagnostic Methods for Inorganic Materials III, L.M.Hanssen, ed., Proc. SPIE 5192, 129-140 (2003).

W. J. Thompson, "Numerous neat algorithms for the Voight profile function," Comput. Phys. 7, 627-631 (1993).

P. A. Smith, D. A. van Veldhuizen, and K. S. Keppler, "Modeling and simulation tools for high-energy laser safety applications," in Enabling Technology for Simulation Science V, A.F.Sisti and D.A.Trevisani, eds., Proc. SPIE 4367, 478-485 (2001).

Derivatives of the delta function are considered in T. B. A. Senior and J. L. Volakis, Approximate Boundary Conditions in Electromagnetics (IEEE Press, 1995).

W. C. Snyder and Z. Wan, "BRDF models to predict spectral reflectance and emissivity in the thermal infrared," IEEE Trans. Geosci. Remote Sens. 36, 214-225 (1998).

[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

X. D. He, K. E. Torrance, F. X. Sillion, and D. P. Greenberg, "A comprehensive physical model for light reflection," Comput. Graph. 25, 175-186 (1991).

[Crossref]

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S. Kaasalainen, J. Piironen, M. Kaasalainen, A. W. Harris, K. Muinonen, and A. Cellino, "Asteroid photometric and polarimetric phase curves: empirical interpretation," Icarus 161, 34-46 (2003).

[Crossref]

M. K. Shepard and B. A. Campbell, "Radar scattering from a self-affine fractal surface: near-nadir regime," Icarus 141, 156-171 (1999).

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[Crossref]

G. Macelloni, G. Nesti, P. Pampaloni, S. Sigismondi, D. Tarchi, and S. Lolli, "Experimental validation of surface scattering and emission models," IEEE Trans. Geosci. Remote Sens. 38, 459-469 (2000).

[Crossref]

W. C. Snyder and Z. Wan, "BRDF models to predict spectral reflectance and emissivity in the thermal infrared," IEEE Trans. Geosci. Remote Sens. 36, 214-225 (1998).

[Crossref]

W. C. Snyder, "Reciprocity of the bidirectional reflectance distribution function (BRDF) in measurements and models of structured surfaces," IEEE Trans. Geosci. Remote Sens. 36, 685-691 (1998).

[Crossref]

F. Bernardini, I. M. Martin, and H. Rushmeier, "High-quality texture reconstruction from multiple scans," IEEE Trans. Vis. Comput. Graph. 7, 318-332 (2001).

[Crossref]

T. Weyrich, H. Pfister, and M. Gross, "Rendering deformable surface reflectance fields," IEEE Trans. Vis. Comput. Graph. 11, 48-58 (2005).

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[Crossref]

O. Korotkova, B. G. Hoover, V. L. Gamiz, and E. Wolf, "Coherence and polarization properties of far-fields generated by quasi-homogeneous electromagnetic sources," J. Opt. Soc. Am. A 22, 2547-2556 (2005).

[Crossref]

K. A. O'Donnell and E. R. Méndez, "Experimental study of scattering from characterized random surfaces," J. Opt. Soc. Am. A 4, 1194-1205 (1987).

[Crossref]

M.-J. Kim, J. C. Dainty, A. T. Friberg, and A. J. Sant, "Experimental study of enhanced backscattering from one- and two-dimensional random rough surfaces," J. Opt. Soc. Am. A 7, 569-577 (1990).

[Crossref]

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[Crossref]

G. S. Agarwal, "Scattering from rough surfaces," Opt. Commun. 14, 161-166 (1975).

[Crossref]

E. Wolf and W. H. Carter, "Angular distribution of radiant intensity from sources of different degrees of spatial coherence," Opt. Commun. 13, 205-209 (1975).

[Crossref]

H. P. Baltes, B. Steinle, and G. Antes, "Spectral coherence and the radiant intensity from statistically homogeneous and isotropic planar sources," Opt. Commun. 18, 242-246 (1976).

[Crossref]

A review of theory and measurements in the small-roughness regime is provided in J. M. Elson and J. M. Bennett, "Vector scattering theory," Opt. Eng. (Bellingham) 18, 116-124 (1979).

J. C. Leader, "Similarities and distinctions between coherence theory relations and laser scattering phenomena," Opt. Eng. (Bellingham) 19, 593-601 (1980).

D. Fontani, F. Francini, G. Longobardi, and P. Sansoni, "Optical control of surface finish," Opt. Lasers Eng. 32, 459-472 (2000).

[Crossref]

F. Gori, "Matrix treatment for partially polarized, partially coherent beams," Opt. Lett. 23, 241-243 (1998).

[Crossref]

A. J. Sant, J. C. Dainty, and M.-J. Kim, "Comparison of surface scattering between identical, randomly rough metal and dielectric diffusers," Opt. Lett. 14, 1183-1185 (1989).

[Crossref]
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[Crossref]

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[Crossref]

K. Ivanova, M. A. Michalev, and O. I. Yordanov, "Numerical study of scattering by rough surfaces with intermediate and large scale roughness," Radio Sci. 26, 505-510 (1991).

[Crossref]

O. P. Bruno, A. Sei, and M. Caponi, "High-order high-frequency solutions of rough surface scattering problems," Radio Sci. 37, 10.1029/2000 RS002551 (2002).

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[Crossref]

A. Ishimaru and J. S. Chen, "Scattering from very rough metallic and dielectric surfaces: a theory based on the modified Kirchhoff approximation," Waves Random Media 1, 25-34 (1991).

[Crossref]

M. Saillard and A. Sentenac, "Rigorous solutions for electromagnetic scattering from rough surfaces," Waves Random Media 11, R103-R137 (2001).

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T. M. Elfouhaily and C.-A. Guérin, "A critical survey of approximate scattering wave theories from random rough surfaces," Waves Random Media 14, R1-R40 (2004).

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P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

J. Stover, Optical Scattering: Measurement and Analysis (McGraw-Hill, 1990).

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger/IOP, 1991).

M. Ashikhmin, S. Premoze, and P. Shirley, "A microfacet-based BRDF generator," in Proceedings of ACM SIGGRAPH 2000 (www.siggraph.org), pp. 65-74.

S. Silver, "Scattering and diffraction," in Microwave Antenna Theory and Design, S.Silver, ed. (McGraw-Hill, 1949), Chap. 5.

P. A. Smith, D. A. van Veldhuizen, and K. S. Keppler, "Modeling and simulation tools for high-energy laser safety applications," in Enabling Technology for Simulation Science V, A.F.Sisti and D.A.Trevisani, eds., Proc. SPIE 4367, 478-485 (2001).

O. Steinvall and T. Carlsson, "Three-dimensional laser radar modelling," inLaser Radar Technology and Applications VI, G.W.Kamerman, ed., Proc. SPIE 4377, 23-24 (2001).

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A review of the radiometric units and notation used in this paper is provided in E. L. Dereniak and D. G. Crowe, Optical Radiation Detectors (Wiley, 1984).

D. D. Duncan, D. V. Hahn, and M. E. Thomas, "Physics-based polarimetric BRDF models," in Optical Diagnostic Methods for Inorganic Materials III, L.M.Hanssen, ed., Proc. SPIE 5192, 129-140 (2003).

B. G. Hoover and V. L. Gamiz, "Diffractive bidirectional reflectance distributions of surfaces with large effective roughness in one dimension," in Laser Radar Techniques for Atmospheric Sensing, U.N.Singh, ed., Proc. SPIE 5575, 137-142 (2004).

J. W. Goodman, Statistical Optics (Wiley, 1985), Chap. 5.

x and Deltax represent two-dimensional vectors in the plane of the average surface, i.e., x=xx̂+yŷ.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chap. 5.7.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), Chap. 2.

See Ref. and references therein.

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I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, corrected and enlarged ed. (Academic, 1980), 6.631(4).

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It is possible to dispense with the quasi-monochromatic conditions by using the cross-spectral density W(x1,x2,nu)=∫Gamma(x1,x2,tau)exp(2pijnutau)dtau rather than the coherence function, thus proceeding in the space-frequency rather than the space-time domain. Under the quasi-monochromatic conditions these two approaches are essentially equivalent.

Some authors use the symbol µ to represent the normalized mutual intensity function. We reserve µ for the analogous correlation function in the space-frequency domain.

The meanings of the terms "high frequency" and "low frequency" in coherence theory are unfortunately essentially opposite their meanings in scattering theory. Use of these terms in this context is therefore avoided.

Derivatives of the delta function are considered in T. B. A. Senior and J. L. Volakis, Approximate Boundary Conditions in Electromagnetics (IEEE Press, 1995).

E. W. Weisstein, "Erf," from MathWorld-A Wolfram Web Resource, http://mathworld.wolfram.com/Erf.html.

L. Brainard, W. Lynn, D. Ramer, and W. Shemano, "Optical measurements facility," Air Force Research Laboratory, Materials & Manufacturing Directorate, Rep. AFRL-ML-WP-TR-1999-4142 (1999).