Abstract

In order to establish scattering measurements in material investigations for gravitational-wave detectors, we have built-up devices for measuring the hemispherical scattering distribution of materials which are planned to be used in those detectors as suppressors of scattered light. The measurement benches we have built, a hemispherical goniometer and a direct back-scatterometer, have a maximum background noise of ∼10 4sr 1 BRDF at 1.064 μm wavelength which is the wavelength of the laser-light for our large interferometer for detecting gravitational waves, KAGRA. With these instruments, we have characterized the surface scattering of, e.g., NiP platings, metals, and different carbonaceous coatings, which are supposed to minimize the amount of scattered light in interferometers. The three most important materials for KAGRA’s construction (SiC, “Solblack”, and “VantaBlack”) are presented in this paper. Furthermore, we will try to explain the scattering distributions with the generalized Harvey-Shack model (smooth-surface approximation) which is a common method for surface-scattering calculations. At the end, we give also some valuations about the vacuum compatibility of the materials, which is important for instruments like KAGRA that work under ultra-high vacuum conditions.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

J. Lehman, C. Yung, N. Tomlin, D. Conklin, and M. Stephens, “Carbon nanotube-based black coatings,” Appl. Phys. Rev. 5(1), 011103 (2018).
[Crossref]

2017 (1)

2016 (2)

2014 (1)

G. Volkova, O. Doroshkevych, A. Shylo, T. Zelenyak, V. Burkhovetskiy, I. Danilenko, and T. Konstantinova, “Structural evolution of silicon carbide nanopowders during the sintering process,” J. Ceram. 2014, 723627 (2014).

2013 (1)

2012 (1)

J. E. Harvey, S. Schröder, N. Choi, and A. Duparre, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51, 013402 (2012).
[Crossref]

2011 (2)

S. Zeidler, T. Posch, H. Mutschke, H. Richter, and O. Wehrhan, “Near-infrared absorption properties of oxygen-rich stardust analogs - the influence of coloring metal ions,” Astron. Astrophys. 526, A68 (2011).
[Crossref]

A. Krywonos, J. E. Harvey, and N. Choi, “Linear systems formulation of scattering theory for rough surface with arbitrary incident and scattering angles,” J. Opt. Soc. Am. A,  28, 1121–1139 (2011).
[Crossref]

2010 (3)

K. Lipert, M. Ritschel, A. Leonhardt, Y. Krupskaya, B. Buechner, and R. Klingeler, “Magnetic properties of carbon nanotubes with and without catalyst,” J. Phys.: Conf. Ser. 200, 072061 (2010).

J. E. Harvey, N. Choi, A. Krywonos, S. Schröder, and D. H. Penalver, “Scattering from moderately rough interfaces between two arbitrary media,” Proc. SPIE 7794, 77940 (2010).
[Crossref]

S. Schröder, T. Herffurth, H. Blaschke, and A. Duparre, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, 164–171 (2010).
[Crossref]

2008 (1)

2005 (1)

B. Sun, R. Ramamoorthi, S. G. Narasimhan, and S. K. Nayar, “A practical analytic single scattering model for real time rendering,” ACM Transactions on Graphics 24, 1040–1049 (2005).
[Crossref]

2003 (1)

X. Wu, L. Pan, H. Li, X. Fan, T. Yong Ng, D. Xu, and C. Zhang, “Optical properties of aligned carbon nanotubes,” Phys. Rev. B 68(19), 193401 (2003).
[Crossref]

1997 (2)

F. J. Garcia-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. Lett. 78, 4289–4292 (1997).
[Crossref]

E. Dumont, B. Dugnoille, J. Petitjean, and M. Barigand, “Optical properties of nickel thin films deposited by electroless plating,” Thin Solid Films 301, 149–153 (1997).
[Crossref]

1991 (2)

E. L. Church and P. Z. Takacs, “The optimal estimation of finish parameters,” Proc. SPIE 1530, 71–86 (1991).
[Crossref]

N. S. Goel, I. Rohzenal, and R. L. Thompsen, “A computer graphics based model for scattering from objects of arbitrary shapes in the optical region,” Remote Sens. Environ. 36, 73–104 (1991).
[Crossref]

1958 (1)

J. A. Dillon, R. E. Schlier, and H. E. Farnsworth, “Some surface properties of silicon-carbide crystals,” J. Appl. Phys. 30, 675–679 (1958).
[Crossref]

Abderrazak, H.

H. Abderrazak and E. S. B. H. Hmida, “Silicon carbide: Synthesis and properties,” in Properties and Applications of Silicon CarbideR. Gerhardt, ed. (InTech, 2011).
[Crossref]

Akutsu, T.

Alleg, S.

S. Alleg, A. Boussaha, W. Tebib, M. Zergoug, and J. J. Sunol, “Microstructure and magnetic properties of nip alloys,” J. Supercond. Nov. Magn. 29, 1001–1011 (2016).
[Crossref]

Ariyama, Y.

Aso, Y.

Barigand, M.

E. Dumont, B. Dugnoille, J. Petitjean, and M. Barigand, “Optical properties of nickel thin films deposited by electroless plating,” Thin Solid Films 301, 149–153 (1997).
[Crossref]

Barrick, D. E.

W. H. Peake and D. E. Barrick, “Scattering from surfaces with different roughness scales; analysis and interpretation,” Electroscience laboratory, The Ohio State University, Columbus, Ohio43212 (1967).

Blaschke, H.

S. Schröder, T. Herffurth, H. Blaschke, and A. Duparre, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, 164–171 (2010).
[Crossref]

Boussaha, A.

S. Alleg, A. Boussaha, W. Tebib, M. Zergoug, and J. J. Sunol, “Microstructure and magnetic properties of nip alloys,” J. Supercond. Nov. Magn. 29, 1001–1011 (2016).
[Crossref]

Buechner, B.

K. Lipert, M. Ritschel, A. Leonhardt, Y. Krupskaya, B. Buechner, and R. Klingeler, “Magnetic properties of carbon nanotubes with and without catalyst,” J. Phys.: Conf. Ser. 200, 072061 (2010).

Burkhovetskiy, V.

G. Volkova, O. Doroshkevych, A. Shylo, T. Zelenyak, V. Burkhovetskiy, I. Danilenko, and T. Konstantinova, “Structural evolution of silicon carbide nanopowders during the sintering process,” J. Ceram. 2014, 723627 (2014).

Butler, J. J.

Chen, D.

Choi, N.

J. E. Harvey, S. Schröder, N. Choi, and A. Duparre, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51, 013402 (2012).
[Crossref]

A. Krywonos, J. E. Harvey, and N. Choi, “Linear systems formulation of scattering theory for rough surface with arbitrary incident and scattering angles,” J. Opt. Soc. Am. A,  28, 1121–1139 (2011).
[Crossref]

J. E. Harvey, N. Choi, A. Krywonos, S. Schröder, and D. H. Penalver, “Scattering from moderately rough interfaces between two arbitrary media,” Proc. SPIE 7794, 77940 (2010).
[Crossref]

Chunnilall, C. J.

Church, E. L.

E. L. Church and P. Z. Takacs, “The optimal estimation of finish parameters,” Proc. SPIE 1530, 71–86 (1991).
[Crossref]

Conklin, D.

J. Lehman, C. Yung, N. Tomlin, D. Conklin, and M. Stephens, “Carbon nanotube-based black coatings,” Appl. Phys. Rev. 5(1), 011103 (2018).
[Crossref]

Danilenko, I.

G. Volkova, O. Doroshkevych, A. Shylo, T. Zelenyak, V. Burkhovetskiy, I. Danilenko, and T. Konstantinova, “Structural evolution of silicon carbide nanopowders during the sintering process,” J. Ceram. 2014, 723627 (2014).

Dillon, J. A.

J. A. Dillon, R. E. Schlier, and H. E. Farnsworth, “Some surface properties of silicon-carbide crystals,” J. Appl. Phys. 30, 675–679 (1958).
[Crossref]

Doroshkevych, O.

G. Volkova, O. Doroshkevych, A. Shylo, T. Zelenyak, V. Burkhovetskiy, I. Danilenko, and T. Konstantinova, “Structural evolution of silicon carbide nanopowders during the sintering process,” J. Ceram. 2014, 723627 (2014).

Dugnoille, B.

E. Dumont, B. Dugnoille, J. Petitjean, and M. Barigand, “Optical properties of nickel thin films deposited by electroless plating,” Thin Solid Films 301, 149–153 (1997).
[Crossref]

Dumont, E.

E. Dumont, B. Dugnoille, J. Petitjean, and M. Barigand, “Optical properties of nickel thin films deposited by electroless plating,” Thin Solid Films 301, 149–153 (1997).
[Crossref]

Duparre, A.

J. E. Harvey, S. Schröder, N. Choi, and A. Duparre, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51, 013402 (2012).
[Crossref]

S. Schröder, T. Herffurth, H. Blaschke, and A. Duparre, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, 164–171 (2010).
[Crossref]

Fan, X.

X. Wu, L. Pan, H. Li, X. Fan, T. Yong Ng, D. Xu, and C. Zhang, “Optical properties of aligned carbon nanotubes,” Phys. Rev. B 68(19), 193401 (2003).
[Crossref]

Farnsworth, H. E.

J. A. Dillon, R. E. Schlier, and H. E. Farnsworth, “Some surface properties of silicon-carbide crystals,” J. Appl. Phys. 30, 675–679 (1958).
[Crossref]

Flaminio, R.

Fox, N.

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. Lett. 78, 4289–4292 (1997).
[Crossref]

Georgiev, G. T.

Gibbs, D.

Goel, N. S.

N. S. Goel, I. Rohzenal, and R. L. Thompsen, “A computer graphics based model for scattering from objects of arbitrary shapes in the optical region,” Remote Sens. Environ. 36, 73–104 (1991).
[Crossref]

Hanrahan, P.

H. W. Jensen, S. R. Marschner, M. Levoy, and P. Hanrahan, “A practical model for subsurface light transport,” Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 2001) pp. 511–518.

Harris, O. B.

Harvey, J. E.

J. E. Harvey, S. Schröder, N. Choi, and A. Duparre, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51, 013402 (2012).
[Crossref]

A. Krywonos, J. E. Harvey, and N. Choi, “Linear systems formulation of scattering theory for rough surface with arbitrary incident and scattering angles,” J. Opt. Soc. Am. A,  28, 1121–1139 (2011).
[Crossref]

J. E. Harvey, N. Choi, A. Krywonos, S. Schröder, and D. H. Penalver, “Scattering from moderately rough interfaces between two arbitrary media,” Proc. SPIE 7794, 77940 (2010).
[Crossref]

Herffurth, T.

S. Schröder, T. Herffurth, H. Blaschke, and A. Duparre, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, 164–171 (2010).
[Crossref]

Hirose, E.

Hmida, E. S. B. H.

H. Abderrazak and E. S. B. H. Hmida, “Silicon carbide: Synthesis and properties,” in Properties and Applications of Silicon CarbideR. Gerhardt, ed. (InTech, 2011).
[Crossref]

Howlett, G.

Ikeyama, K.

Jensen, B.

Jensen, H. W.

H. W. Jensen, S. R. Marschner, M. Levoy, and P. Hanrahan, “A practical model for subsurface light transport,” Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 2001) pp. 511–518.

Kimura, N.

Klingeler, R.

K. Lipert, M. Ritschel, A. Leonhardt, Y. Krupskaya, B. Buechner, and R. Klingeler, “Magnetic properties of carbon nanotubes with and without catalyst,” J. Phys.: Conf. Ser. 200, 072061 (2010).

Koike, S.

Kong, J. A.

L. Tsang and J. A. Kong, Scattering of electromagnetic waves - advanced topics(John Wiley and Sons, 2001).

Konstantinova, T.

G. Volkova, O. Doroshkevych, A. Shylo, T. Zelenyak, V. Burkhovetskiy, I. Danilenko, and T. Konstantinova, “Structural evolution of silicon carbide nanopowders during the sintering process,” J. Ceram. 2014, 723627 (2014).

Krupskaya, Y.

K. Lipert, M. Ritschel, A. Leonhardt, Y. Krupskaya, B. Buechner, and R. Klingeler, “Magnetic properties of carbon nanotubes with and without catalyst,” J. Phys.: Conf. Ser. 200, 072061 (2010).

Krywonos, A.

A. Krywonos, J. E. Harvey, and N. Choi, “Linear systems formulation of scattering theory for rough surface with arbitrary incident and scattering angles,” J. Opt. Soc. Am. A,  28, 1121–1139 (2011).
[Crossref]

J. E. Harvey, N. Choi, A. Krywonos, S. Schröder, and D. H. Penalver, “Scattering from moderately rough interfaces between two arbitrary media,” Proc. SPIE 7794, 77940 (2010).
[Crossref]

A. Krywonos, “Predicting surface scatter using a linear systems formulation of non-paraxial scalar diffraction,” Ph.D. thesis (2000).

Lehman, J.

J. Lehman, C. Yung, N. Tomlin, D. Conklin, and M. Stephens, “Carbon nanotube-based black coatings,” Appl. Phys. Rev. 5(1), 011103 (2018).
[Crossref]

Leonhardt, A.

K. Lipert, M. Ritschel, A. Leonhardt, Y. Krupskaya, B. Buechner, and R. Klingeler, “Magnetic properties of carbon nanotubes with and without catalyst,” J. Phys.: Conf. Ser. 200, 072061 (2010).

Levoy, M.

H. W. Jensen, S. R. Marschner, M. Levoy, and P. Hanrahan, “A practical model for subsurface light transport,” Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 2001) pp. 511–518.

Li, H.

X. Wu, L. Pan, H. Li, X. Fan, T. Yong Ng, D. Xu, and C. Zhang, “Optical properties of aligned carbon nanotubes,” Phys. Rev. B 68(19), 193401 (2003).
[Crossref]

Lipert, K.

K. Lipert, M. Ritschel, A. Leonhardt, Y. Krupskaya, B. Buechner, and R. Klingeler, “Magnetic properties of carbon nanotubes with and without catalyst,” J. Phys.: Conf. Ser. 200, 072061 (2010).

Marschner, S. R.

H. W. Jensen, S. R. Marschner, M. Levoy, and P. Hanrahan, “A practical model for subsurface light transport,” Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 2001) pp. 511–518.

Mole, R.

Mutschke, H.

S. Zeidler, T. Posch, H. Mutschke, H. Richter, and O. Wehrhan, “Near-infrared absorption properties of oxygen-rich stardust analogs - the influence of coloring metal ions,” Astron. Astrophys. 526, A68 (2011).
[Crossref]

Narasimhan, S. G.

B. Sun, R. Ramamoorthi, S. G. Narasimhan, and S. K. Nayar, “A practical analytic single scattering model for real time rendering,” ACM Transactions on Graphics 24, 1040–1049 (2005).
[Crossref]

Nayar, S. K.

B. Sun, R. Ramamoorthi, S. G. Narasimhan, and S. K. Nayar, “A practical analytic single scattering model for real time rendering,” ACM Transactions on Graphics 24, 1040–1049 (2005).
[Crossref]

Niwa, Y.

Pan, L.

X. Wu, L. Pan, H. Li, X. Fan, T. Yong Ng, D. Xu, and C. Zhang, “Optical properties of aligned carbon nanotubes,” Phys. Rev. B 68(19), 193401 (2003).
[Crossref]

Parkinson, R.

R. Parkinson, “Properties and applications of electroless nickel,” in Nickel Development Institute Technical Series 37 (Nickel Development Institute, 1997 pp. 1–33.

Peake, W. H.

W. H. Peake and D. E. Barrick, “Scattering from surfaces with different roughness scales; analysis and interpretation,” Electroscience laboratory, The Ohio State University, Columbus, Ohio43212 (1967).

Penalver, D. H.

J. E. Harvey, N. Choi, A. Krywonos, S. Schröder, and D. H. Penalver, “Scattering from moderately rough interfaces between two arbitrary media,” Proc. SPIE 7794, 77940 (2010).
[Crossref]

Pendry, J. B.

F. J. Garcia-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. Lett. 78, 4289–4292 (1997).
[Crossref]

Petitjean, J.

E. Dumont, B. Dugnoille, J. Petitjean, and M. Barigand, “Optical properties of nickel thin films deposited by electroless plating,” Thin Solid Films 301, 149–153 (1997).
[Crossref]

Pitarke, J. M.

F. J. Garcia-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. Lett. 78, 4289–4292 (1997).
[Crossref]

Posch, T.

S. Zeidler, T. Posch, H. Mutschke, H. Richter, and O. Wehrhan, “Near-infrared absorption properties of oxygen-rich stardust analogs - the influence of coloring metal ions,” Astron. Astrophys. 526, A68 (2011).
[Crossref]

Ramamoorthi, R.

B. Sun, R. Ramamoorthi, S. G. Narasimhan, and S. K. Nayar, “A practical analytic single scattering model for real time rendering,” ACM Transactions on Graphics 24, 1040–1049 (2005).
[Crossref]

Reveles, J. R.

Richter, H.

S. Zeidler, T. Posch, H. Mutschke, H. Richter, and O. Wehrhan, “Near-infrared absorption properties of oxygen-rich stardust analogs - the influence of coloring metal ions,” Astron. Astrophys. 526, A68 (2011).
[Crossref]

Riley, D.

D. Riley and M. Smith, “Controlling light scatter in advanced ligo,” Tech. Rep. T080064-00-D, LIGO Scientific Collaboration (2008).

Ritschel, M.

K. Lipert, M. Ritschel, A. Leonhardt, Y. Krupskaya, B. Buechner, and R. Klingeler, “Magnetic properties of carbon nanotubes with and without catalyst,” J. Phys.: Conf. Ser. 200, 072061 (2010).

Rohzenal, I.

N. S. Goel, I. Rohzenal, and R. L. Thompsen, “A computer graphics based model for scattering from objects of arbitrary shapes in the optical region,” Remote Sens. Environ. 36, 73–104 (1991).
[Crossref]

Saito, Y.

Sakakibara, Y.

Sato, Y.

Schlier, R. E.

J. A. Dillon, R. E. Schlier, and H. E. Farnsworth, “Some surface properties of silicon-carbide crystals,” J. Appl. Phys. 30, 675–679 (1958).
[Crossref]

Schröder, S.

J. E. Harvey, S. Schröder, N. Choi, and A. Duparre, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51, 013402 (2012).
[Crossref]

J. E. Harvey, N. Choi, A. Krywonos, S. Schröder, and D. H. Penalver, “Scattering from moderately rough interfaces between two arbitrary media,” Proc. SPIE 7794, 77940 (2010).
[Crossref]

S. Schröder, T. Herffurth, H. Blaschke, and A. Duparre, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, 164–171 (2010).
[Crossref]

Shang, N.

Shylo, A.

G. Volkova, O. Doroshkevych, A. Shylo, T. Zelenyak, V. Burkhovetskiy, I. Danilenko, and T. Konstantinova, “Structural evolution of silicon carbide nanopowders during the sintering process,” J. Ceram. 2014, 723627 (2014).

Smith, M.

D. Riley and M. Smith, “Controlling light scatter in advanced ligo,” Tech. Rep. T080064-00-D, LIGO Scientific Collaboration (2008).

Stephens, M.

J. Lehman, C. Yung, N. Tomlin, D. Conklin, and M. Stephens, “Carbon nanotube-based black coatings,” Appl. Phys. Rev. 5(1), 011103 (2018).
[Crossref]

Sun, B.

B. Sun, R. Ramamoorthi, S. G. Narasimhan, and S. K. Nayar, “A practical analytic single scattering model for real time rendering,” ACM Transactions on Graphics 24, 1040–1049 (2005).
[Crossref]

Sunol, J. J.

S. Alleg, A. Boussaha, W. Tebib, M. Zergoug, and J. J. Sunol, “Microstructure and magnetic properties of nip alloys,” J. Supercond. Nov. Magn. 29, 1001–1011 (2016).
[Crossref]

Suzuki, T.

Takacs, P. Z.

E. L. Church and P. Z. Takacs, “The optimal estimation of finish parameters,” Proc. SPIE 1530, 71–86 (1991).
[Crossref]

Taylor, R.

Tebib, W.

S. Alleg, A. Boussaha, W. Tebib, M. Zergoug, and J. J. Sunol, “Microstructure and magnetic properties of nip alloys,” J. Supercond. Nov. Magn. 29, 1001–1011 (2016).
[Crossref]

Theocharous, E.

Thompsen, R. L.

N. S. Goel, I. Rohzenal, and R. L. Thompsen, “A computer graphics based model for scattering from objects of arbitrary shapes in the optical region,” Remote Sens. Environ. 36, 73–104 (1991).
[Crossref]

Tokoku, C.

Tomlin, N.

J. Lehman, C. Yung, N. Tomlin, D. Conklin, and M. Stephens, “Carbon nanotube-based black coatings,” Appl. Phys. Rev. 5(1), 011103 (2018).
[Crossref]

Torii, Y.

Tsang, L.

L. Tsang and J. A. Kong, Scattering of electromagnetic waves - advanced topics(John Wiley and Sons, 2001).

Volkova, G.

G. Volkova, O. Doroshkevych, A. Shylo, T. Zelenyak, V. Burkhovetskiy, I. Danilenko, and T. Konstantinova, “Structural evolution of silicon carbide nanopowders during the sintering process,” J. Ceram. 2014, 723627 (2014).

Wehrhan, O.

S. Zeidler, T. Posch, H. Mutschke, H. Richter, and O. Wehrhan, “Near-infrared absorption properties of oxygen-rich stardust analogs - the influence of coloring metal ions,” Astron. Astrophys. 526, A68 (2011).
[Crossref]

Wu, X.

X. Wu, L. Pan, H. Li, X. Fan, T. Yong Ng, D. Xu, and C. Zhang, “Optical properties of aligned carbon nanotubes,” Phys. Rev. B 68(19), 193401 (2003).
[Crossref]

Xu, D.

X. Wu, L. Pan, H. Li, X. Fan, T. Yong Ng, D. Xu, and C. Zhang, “Optical properties of aligned carbon nanotubes,” Phys. Rev. B 68(19), 193401 (2003).
[Crossref]

Yamamoto, K.

Yong Ng, T.

X. Wu, L. Pan, H. Li, X. Fan, T. Yong Ng, D. Xu, and C. Zhang, “Optical properties of aligned carbon nanotubes,” Phys. Rev. B 68(19), 193401 (2003).
[Crossref]

Yung, C.

J. Lehman, C. Yung, N. Tomlin, D. Conklin, and M. Stephens, “Carbon nanotube-based black coatings,” Appl. Phys. Rev. 5(1), 011103 (2018).
[Crossref]

Zeidler, S.

Zelenyak, T.

G. Volkova, O. Doroshkevych, A. Shylo, T. Zelenyak, V. Burkhovetskiy, I. Danilenko, and T. Konstantinova, “Structural evolution of silicon carbide nanopowders during the sintering process,” J. Ceram. 2014, 723627 (2014).

Zergoug, M.

S. Alleg, A. Boussaha, W. Tebib, M. Zergoug, and J. J. Sunol, “Microstructure and magnetic properties of nip alloys,” J. Supercond. Nov. Magn. 29, 1001–1011 (2016).
[Crossref]

Zhang, C.

X. Wu, L. Pan, H. Li, X. Fan, T. Yong Ng, D. Xu, and C. Zhang, “Optical properties of aligned carbon nanotubes,” Phys. Rev. B 68(19), 193401 (2003).
[Crossref]

ACM Transactions on Graphics (1)

B. Sun, R. Ramamoorthi, S. G. Narasimhan, and S. K. Nayar, “A practical analytic single scattering model for real time rendering,” ACM Transactions on Graphics 24, 1040–1049 (2005).
[Crossref]

Appl. Opt. (2)

S. Schröder, T. Herffurth, H. Blaschke, and A. Duparre, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, 164–171 (2010).
[Crossref]

G. T. Georgiev and J. J. Butler, “Laboratory-based bidirectional reflectance distribution functions of radiometric tarps,” Appl. Opt. 47, 3313–3323 (2008).
[Crossref] [PubMed]

Appl. Phys. Rev. (1)

J. Lehman, C. Yung, N. Tomlin, D. Conklin, and M. Stephens, “Carbon nanotube-based black coatings,” Appl. Phys. Rev. 5(1), 011103 (2018).
[Crossref]

Astron. Astrophys. (1)

S. Zeidler, T. Posch, H. Mutschke, H. Richter, and O. Wehrhan, “Near-infrared absorption properties of oxygen-rich stardust analogs - the influence of coloring metal ions,” Astron. Astrophys. 526, A68 (2011).
[Crossref]

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J. A. Dillon, R. E. Schlier, and H. E. Farnsworth, “Some surface properties of silicon-carbide crystals,” J. Appl. Phys. 30, 675–679 (1958).
[Crossref]

J. Ceram. (1)

G. Volkova, O. Doroshkevych, A. Shylo, T. Zelenyak, V. Burkhovetskiy, I. Danilenko, and T. Konstantinova, “Structural evolution of silicon carbide nanopowders during the sintering process,” J. Ceram. 2014, 723627 (2014).

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

J. Phys.: Conf. Ser. (1)

K. Lipert, M. Ritschel, A. Leonhardt, Y. Krupskaya, B. Buechner, and R. Klingeler, “Magnetic properties of carbon nanotubes with and without catalyst,” J. Phys.: Conf. Ser. 200, 072061 (2010).

J. Supercond. Nov. Magn. (1)

S. Alleg, A. Boussaha, W. Tebib, M. Zergoug, and J. J. Sunol, “Microstructure and magnetic properties of nip alloys,” J. Supercond. Nov. Magn. 29, 1001–1011 (2016).
[Crossref]

Opt. Eng. (1)

J. E. Harvey, S. Schröder, N. Choi, and A. Duparre, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51, 013402 (2012).
[Crossref]

Opt. Express (2)

Opt. Mater. Express (1)

Phys. Rev. B (1)

X. Wu, L. Pan, H. Li, X. Fan, T. Yong Ng, D. Xu, and C. Zhang, “Optical properties of aligned carbon nanotubes,” Phys. Rev. B 68(19), 193401 (2003).
[Crossref]

Phys. Rev. Lett. (1)

F. J. Garcia-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. Lett. 78, 4289–4292 (1997).
[Crossref]

Proc. SPIE (2)

E. L. Church and P. Z. Takacs, “The optimal estimation of finish parameters,” Proc. SPIE 1530, 71–86 (1991).
[Crossref]

J. E. Harvey, N. Choi, A. Krywonos, S. Schröder, and D. H. Penalver, “Scattering from moderately rough interfaces between two arbitrary media,” Proc. SPIE 7794, 77940 (2010).
[Crossref]

Remote Sens. Environ. (1)

N. S. Goel, I. Rohzenal, and R. L. Thompsen, “A computer graphics based model for scattering from objects of arbitrary shapes in the optical region,” Remote Sens. Environ. 36, 73–104 (1991).
[Crossref]

Thin Solid Films (1)

E. Dumont, B. Dugnoille, J. Petitjean, and M. Barigand, “Optical properties of nickel thin films deposited by electroless plating,” Thin Solid Films 301, 149–153 (1997).
[Crossref]

Other (8)

D. Riley and M. Smith, “Controlling light scatter in advanced ligo,” Tech. Rep. T080064-00-D, LIGO Scientific Collaboration (2008).

H. Abderrazak and E. S. B. H. Hmida, “Silicon carbide: Synthesis and properties,” in Properties and Applications of Silicon CarbideR. Gerhardt, ed. (InTech, 2011).
[Crossref]

H. W. Jensen, S. R. Marschner, M. Levoy, and P. Hanrahan, “A practical model for subsurface light transport,” Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 2001) pp. 511–518.

W. H. Peake and D. E. Barrick, “Scattering from surfaces with different roughness scales; analysis and interpretation,” Electroscience laboratory, The Ohio State University, Columbus, Ohio43212 (1967).

L. Tsang and J. A. Kong, Scattering of electromagnetic waves - advanced topics(John Wiley and Sons, 2001).

D. Beckett, Y. Liu, and D. Hawthorne, “Investigation of the blackening process of electroless nickel-phosphorous coatings and their properties,” Products Finishing (2011). https://www.pfonline.com/articles/investigation-of-theblackening-process-of-electroless-nickel-phosphorous-coatings-and-their-properties

R. Parkinson, “Properties and applications of electroless nickel,” in Nickel Development Institute Technical Series 37 (Nickel Development Institute, 1997 pp. 1–33.

A. Krywonos, “Predicting surface scatter using a linear systems formulation of non-paraxial scalar diffraction,” Ph.D. thesis (2000).

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Figures (14)

Fig. 1
Fig. 1 Sketch of the hemispherical scatterometer and the description of its basic elements. The triangular shape has been chosen to provide additional traps for stray-light and to further reduce the background scattering-noise.
Fig. 2
Fig. 2 Sketch of the back-scatterometer and the description of its basic elements. The sample holder is rotatable for changing the AOI. The beam dump in the upper part of the device is one of the key-parts and has been designed as a light-trap.
Fig. 3
Fig. 3 Image of the surface characteristics of the SiC1 (left) and SiC2 (right) samples taken from the metrology measurements by the “NewView8000” instrument from ZYGO.
Fig. 4
Fig. 4 Comparison of the scattering probabilities along the plane of incidence of the two SiC samples at three different AOIs. The black dots mark the results of the back-scattering measurements at the respective AOI.
Fig. 5
Fig. 5 Results of the reflectance measurements on both SiC samples and the comparison with the integrated scattering around the specular peak.
Fig. 6
Fig. 6 Scattering probability of the Solblack sample showing the hemispherical scattering along the plane of incidence at 0, 20, 40, and 60°AOI. The black dots mark the results of the back-scattering measurements at the respective AOI.
Fig. 7
Fig. 7 Surface structure as measured by Zygo’s NewView instrument on a Solblack sample. The surface seems relatively smooth but there are many 1 μm deep, steep structures visible as well.
Fig. 8
Fig. 8 Reflectance of the Solblack sample: measured (from [9]) and calculated from the scattering data. Additionally, the theoretical reflectance according to the Fresnel-formula is given (for p-polarization from [9], and for s- and p-polarization from the model calculations treated in section 4.2.).
Fig. 9
Fig. 9 Scattering probability of the VantaBlack sample showing the hemispherical scattering along the plane of incidence at 0, 20, 40, and 60°AOI.
Fig. 10
Fig. 10 PSD data (one-dimensional) taken from the surface maps with the aid of Zygo’s MetroPro software for both SiC samples and the fits calculated according to those data.
Fig. 11
Fig. 11 Comparison of the scattering probability both measured and calculated (see text) for SiC. The graph includes the data for three different AOIs at s- and p-polarization.
Fig. 12
Fig. 12 PSD data (one-dimensional) taken from the surface maps with the aid of Zygo’s MetroPro software for the Solblack sample and the fit calculated according to the data.
Fig. 13
Fig. 13 Comparison of the scattering probability both measured and calculated (see text) for Solblack. The graph includes the data for three different AOIs at s- and p-polarization.
Fig. 14
Fig. 14 Comparison of the scattering probability both measured and calculated (see text) for VantaBlack. The graph includes the data for three different AOIs at s- and p-polarization.

Tables (5)

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Table 1 Table showing the surface parameters that have been obtained with metrology measurements on a Zygo-NewView 8000 instrument.

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Table 2 Parameters used for the ABC-model to fit the measured PSD of the SiC samples.

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Table 3 Parameters used for the ABC-model to fit the measured PSD of the Solblack sample.

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Table 4 Parameters used for the quasi-constant ABC-model of the VantaBlack sample.

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Table 5 Dielectric index ε eff used to fit the scattering probability curves of the VantaBlack sample.

Equations (8)

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

BRDF hsc = I PC n PC P laser Δ Ω cos  θ .
BRDF bsc = I PC n PC P laser / 4 Δ Ω cos  θ .
BRDF m ( θ in , θ sc , ϕ sc ) = 4 π 2 λ 4 ( cos  θ in + cos  θ sc ) 2 Q PSD ( f x , f y ) ,
f x = sin  ( θ sc ) cos  ( ϕ sc ) sin  ( θ in ) λ , f y = sin  ( θ sc ) sin  ( ϕ sc ) λ ,
PSD 1 D = A [ 1 + ( B f ) 2 ] C / 2
f = f x 2 + f y 2 .
PSD 2 D = K A B [ 1 + ( B f ) 2 ] ( C + 1 ) / 2
K = 1 2 π Γ [ ( C + 1 ) / 2 ] Γ ( C / 2 ) .

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