Abstract

Antireflective coatings are widely applied on transparent optical components to reduce reflections at surfaces. Nanoporous silica (NP ${{\rm SiO}_{2}}$) thin films with tailored refractive index properties are used as single-layer antireflective coatings providing nearly zero reflectivity. In this work, light scattering properties of nanoporous silica single-layer antireflective coatings are investigated in order to determine their optical quality by means of total scattering and detailed roughness analysis. Scattering and roughness characterization of the samples coated with different film thicknesses were realized to distinguish the influences of nanopores and surface roughness on scattering losses in the visible (VIS) spectral range. No significant correlation of scattering losses with the film thickness is found, showing negligible influence of the nanopores to the overall scattering properties compared with the dominating effect of interface roughness. Moreover, the scattering losses from coated fused silica glass were observed as low as 20 ppm (0.002%). It is confirmed that NP ${{\rm SiO}_{2}}$ single-layer antireflective coatings are suitable to be used in optics demanding extremely low scattering characteristics.

© 2020 Optical Society of America

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References

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    [Crossref]
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2019 (3)

2016 (1)

L. Ghazaryan, E.-B. Kley, A. Tünnermann, and A. Szeghalmi, “Nanoporous SiO2 thin films made by atomic layer deposition and atomic etching,” Nanotechnology 27, 255603 (2016).
[Crossref]

2015 (3)

D. Mahadik, R. Lakshmi, and H. Barshilia, “High performance single layer nano-porous antireflection coatings on glass by sol–gel process for solar energy applications,” Solar Energy Mater. Sol. Cells 140, 61–68 (2015).
[Crossref]

S. Schröder, M. Trost, M. Garrick, A. Duparré, X. Cheng, J. Zhang, and Z. Wang, “Origins of light scattering from thin film coatings,” Thin Solid Films 592, 248–255 (2015).
[Crossref]

N. Mizoshita, M. Ishii, N. Kato, and H. Tanaka, “Hierarchical nanoporous silica films for wear resistant antireflection coatings,” ACS Appl. Mater. Interfaces 7, 19424–19430 (2015).
[Crossref]

2014 (2)

Y.-L. Zhang, C.-X. Zhao, P.-M. Wang, L. Ye, J.-H. Luo, and B. Jiang, “A convenient sol–gel approach to prepare nano-porous silica coatings with very low refractive indices,” Chem. Commun. 50, 13813–13816 (2014).
[Crossref]

A. Eshaghi and M. Mojab, “Fabrication of antireflective antifogging nano-porous silica thin film on glass substrate by layer-by-layer assembly method,” J. Non-Cryst. Solids 405, 148–152 (2014).
[Crossref]

2013 (2)

X. Li, X. Yu, and Y. Han, “Polymer thin films for antireflection coatings,” J. Mater. Chem. C 1, 2266–2285 (2013).
[Crossref]

L. Miao, L. F. Su, S. Tanemura, C. A. Fisher, L. L. Zhao, Q. Liang, and G. Xu, “Cost-effective nanoporous SiO2-TiO2 coatings on glass substrates with antireflective and self-cleaning properties,” Appl. Energy 112, 1198–1205 (2013).
[Crossref]

2011 (2)

2010 (2)

W. Lee, X. Zhang, and R. Briber, “A simple method for creating nanoporous block-copolymer thin films,” Polymer 51, 2376–2382 (2010).
[Crossref]

G. Wicht, R. Ferrini, S. Schüttel, and L. Zuppiroli, “Nanoporous films with low refractive index for large-surface broad-band anti-reflection coatings,” Macromol. Mater. Eng. 295, 628–636 (2010).
[Crossref]

2008 (1)

2006 (1)

M. M. Braun and L. Pilon, “Effective optical properties of non-absorbing nanoporous thin films,” Thin Solid Films 496, 505–514 (2006).
[Crossref]

2003 (1)

M. Bautista and A. Morales, “Silica antireflective films on glass produced by the sol–gel method,” Solar Energy Materials and Solar Cells 80, 217–225 (2003).
[Crossref]

2002 (1)

2000 (1)

1998 (1)

D. Rönnow, “Interface roughness statistics of thin films from angle resolved light scattering at three wavelengths,” Opt. Eng. 37, 696–704 (1998).
[Crossref]

1994 (2)

1993 (4)

1992 (2)

1991 (1)

E. L. Church and P. Z. Takacs, “Optimal estimation of finish parameters,” Proc. SPIE 1530, 71–85 (1991).
[Crossref]

1988 (2)

1986 (2)

1984 (1)

1983 (1)

1981 (1)

1980 (1)

Achour, S.

Aghaee, M.

L. Ghazaryan, Y. Sekman, S. Schröder, C. Mühlig, I. Stevanovic, R. Botha, M. Aghaee, M. Creatore, A. Tünnermann, and A. Szeghalmi, “On the properties of nanoporous SiO2 films for single layer antireflection coating,” Adv. Eng. Mater. 21, 1801229 (2019).
[Crossref]

Albrand, G.

Amra, C.

G. Soriano, M. Zerrad, and C. Amra, “Anti-scattering effect analyzed with an exact theory of light scattering from rough multilayers,” Opt. Lett. 44, 4455–4458 (2019).
[Crossref]

A. von Finck, T. Herffurth, A. Duparré, S. Schröder, M. Lequime, M. Zerrad, S. Liukaityte, C. Amra, S. Achour, M. Chalony, Q. Kuperman, Y. Cornil, A. Bialek, T. Goodman, C. Greenwell, B. Gur, S. Brinkers, G. Otter, A. Vosteen, J. Stover, R. Vink, A. Deep, and D. Doyle, “International round-robin experiment for angle-resolved light scattering measurement,” Appl. Opt. 58, 6638–6654 (2019).
[Crossref]

C. Amra, “Light scattering from multilayer optics. II. Application to experiment,” J. Opt. Soc. Am. A 11, 211–226 (1994).
[Crossref]

C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
[Crossref]

C. Amra, “From light scattering to the microstructure of thin-film multilayers,” Appl. Opt. 32, 5481–5491 (1993).
[Crossref]

C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A 10, 365–374 (1993).
[Crossref]

C. Amra, C. Grèzes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5503 (1993).
[Crossref]

C. Amra, J. H. Apfel, and E. Pelletier, “Role of interface correlation in light scattering by a multiplayer,” Appl. Opt. 31, 3134–3151 (1992).
[Crossref]

C. Amra, G. Albrand, and P. Roche, “Theory and application of antiscattering single layers: antiscattering antireflection coatings,” Appl. Opt. 25, 2695–2702 (1986).
[Crossref]

Apfel, J. H.

Barshilia, H.

D. Mahadik, R. Lakshmi, and H. Barshilia, “High performance single layer nano-porous antireflection coatings on glass by sol–gel process for solar energy applications,” Solar Energy Mater. Sol. Cells 140, 61–68 (2015).
[Crossref]

Bautista, M.

M. Bautista and A. Morales, “Silica antireflective films on glass produced by the sol–gel method,” Solar Energy Materials and Solar Cells 80, 217–225 (2003).
[Crossref]

Bennett, J. M.

Bialek, A.

Botha, R.

L. Ghazaryan, Y. Sekman, S. Schröder, C. Mühlig, I. Stevanovic, R. Botha, M. Aghaee, M. Creatore, A. Tünnermann, and A. Szeghalmi, “On the properties of nanoporous SiO2 films for single layer antireflection coating,” Adv. Eng. Mater. 21, 1801229 (2019).
[Crossref]

Bousquet, P.

Braun, M. M.

M. M. Braun and L. Pilon, “Effective optical properties of non-absorbing nanoporous thin films,” Thin Solid Films 496, 505–514 (2006).
[Crossref]

Briber, R.

W. Lee, X. Zhang, and R. Briber, “A simple method for creating nanoporous block-copolymer thin films,” Polymer 51, 2376–2382 (2010).
[Crossref]

Brinkers, S.

Bruel, L.

Bussemer, P.

Chalony, M.

Cheng, X.

S. Schröder, M. Trost, M. Garrick, A. Duparré, X. Cheng, J. Zhang, and Z. Wang, “Origins of light scattering from thin film coatings,” Thin Solid Films 592, 248–255 (2015).
[Crossref]

Church, E. L.

E. L. Church and P. Z. Takacs, “Optimal estimation of finish parameters,” Proc. SPIE 1530, 71–85 (1991).
[Crossref]

E. L. Church, “Fractal surface finish,” Appl. Opt. 27, 1518–1526 (1988).
[Crossref]

Cornil, Y.

Creatore, M.

L. Ghazaryan, Y. Sekman, S. Schröder, C. Mühlig, I. Stevanovic, R. Botha, M. Aghaee, M. Creatore, A. Tünnermann, and A. Szeghalmi, “On the properties of nanoporous SiO2 films for single layer antireflection coating,” Adv. Eng. Mater. 21, 1801229 (2019).
[Crossref]

Deep, A.

Doyle, D.

Duparré, A.

A. von Finck, T. Herffurth, A. Duparré, S. Schröder, M. Lequime, M. Zerrad, S. Liukaityte, C. Amra, S. Achour, M. Chalony, Q. Kuperman, Y. Cornil, A. Bialek, T. Goodman, C. Greenwell, B. Gur, S. Brinkers, G. Otter, A. Vosteen, J. Stover, R. Vink, A. Deep, and D. Doyle, “International round-robin experiment for angle-resolved light scattering measurement,” Appl. Opt. 58, 6638–6654 (2019).
[Crossref]

S. Schröder, M. Trost, M. Garrick, A. Duparré, X. Cheng, J. Zhang, and Z. Wang, “Origins of light scattering from thin film coatings,” Thin Solid Films 592, 248–255 (2015).
[Crossref]

A. von Finck, M. Hauptvogel, and A. Duparré, “Instrument for close-to-process light scatter measurements of thin film coatings and substrates,” Appl. Opt. 50, C321–C328 (2011).
[Crossref]

M. Trost, S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “Influence of the substrate finish and thin film roughness on the optical performance of Mo/Si multilayers,” Appl. Opt. 50, C148–C153 (2011).
[Crossref]

S. Schröder, A. Duparré, and A. Tünnermann, “Roughness evolution and scatter losses of multilayers for 193 nm optics,” Appl. Opt. 47, C88–C97 (2008).
[Crossref]

A. Duparré, J. Ferre-Borrull, S. Gliech, G. Notni, J. Steinert, and J. M. Bennett, “Surface characterization techniques for determining the root-mean-square roughness and power spectral densities of optical components,” Appl. Opt. 41, 154–171 (2002).
[Crossref]

J. Ferré-Borrull, A. Duparré, and E. Quesnel, “Roughness and light scattering of ion-beam-sputtered fluoride coatings for 193 nm,” Appl. Opt. 39, 5854–5864 (2000).
[Crossref]

A. Duparré and S. Kassam, “Relation between light scattering and the microstructure of optical thin films,” Appl. Opt. 32, 5475–5480 (1993).
[Crossref]

S. Kassam, A. Duparré, K. Hehl, P. Bussemer, and J. Neubert, “Light scattering from the volume of optical thin films: theory and experiment,” Appl. Opt. 31, 1304–1313 (1992).
[Crossref]

A. Duparré and H.-G. Walther, “Surface smoothing and roughening by dielectric thin film deposition,” Appl. Opt. 27, 1393–1395 (1988).
[Crossref]

H.-G. Walther, A. Duparré, and G. Schirmer, “Scattering reduction or enhancement by a dielectric single layer,” Appl. Opt. 25, 4527–4529 (1986).
[Crossref]

Elson, J. M.

Eshaghi, A.

A. Eshaghi and M. Mojab, “Fabrication of antireflective antifogging nano-porous silica thin film on glass substrate by layer-by-layer assembly method,” J. Non-Cryst. Solids 405, 148–152 (2014).
[Crossref]

Feigl, T.

Ferre-Borrull, J.

Ferré-Borrull, J.

Ferrini, R.

G. Wicht, R. Ferrini, S. Schüttel, and L. Zuppiroli, “Nanoporous films with low refractive index for large-surface broad-band anti-reflection coatings,” Macromol. Mater. Eng. 295, 628–636 (2010).
[Crossref]

Fisher, C. A.

L. Miao, L. F. Su, S. Tanemura, C. A. Fisher, L. L. Zhao, Q. Liang, and G. Xu, “Cost-effective nanoporous SiO2-TiO2 coatings on glass substrates with antireflective and self-cleaning properties,” Appl. Energy 112, 1198–1205 (2013).
[Crossref]

Flory, F.

Garrick, M.

S. Schröder, M. Trost, M. Garrick, A. Duparré, X. Cheng, J. Zhang, and Z. Wang, “Origins of light scattering from thin film coatings,” Thin Solid Films 592, 248–255 (2015).
[Crossref]

Ghazaryan, L.

L. Ghazaryan, Y. Sekman, S. Schröder, C. Mühlig, I. Stevanovic, R. Botha, M. Aghaee, M. Creatore, A. Tünnermann, and A. Szeghalmi, “On the properties of nanoporous SiO2 films for single layer antireflection coating,” Adv. Eng. Mater. 21, 1801229 (2019).
[Crossref]

L. Ghazaryan, E.-B. Kley, A. Tünnermann, and A. Szeghalmi, “Nanoporous SiO2 thin films made by atomic layer deposition and atomic etching,” Nanotechnology 27, 255603 (2016).
[Crossref]

Gliech, S.

Goodman, T.

Greenwell, C.

Grèzes-Besset, C.

Gur, B.

Han, Y.

X. Li, X. Yu, and Y. Han, “Polymer thin films for antireflection coatings,” J. Mater. Chem. C 1, 2266–2285 (2013).
[Crossref]

Hauptvogel, M.

Hehl, K.

Herffurth, T.

Ishii, M.

N. Mizoshita, M. Ishii, N. Kato, and H. Tanaka, “Hierarchical nanoporous silica films for wear resistant antireflection coatings,” ACS Appl. Mater. Interfaces 7, 19424–19430 (2015).
[Crossref]

Jiang, B.

Y.-L. Zhang, C.-X. Zhao, P.-M. Wang, L. Ye, J.-H. Luo, and B. Jiang, “A convenient sol–gel approach to prepare nano-porous silica coatings with very low refractive indices,” Chem. Commun. 50, 13813–13816 (2014).
[Crossref]

Kassam, S.

Kato, N.

N. Mizoshita, M. Ishii, N. Kato, and H. Tanaka, “Hierarchical nanoporous silica films for wear resistant antireflection coatings,” ACS Appl. Mater. Interfaces 7, 19424–19430 (2015).
[Crossref]

Kley, E.-B.

L. Ghazaryan, E.-B. Kley, A. Tünnermann, and A. Szeghalmi, “Nanoporous SiO2 thin films made by atomic layer deposition and atomic etching,” Nanotechnology 27, 255603 (2016).
[Crossref]

Kuperman, Q.

Lakshmi, R.

D. Mahadik, R. Lakshmi, and H. Barshilia, “High performance single layer nano-porous antireflection coatings on glass by sol–gel process for solar energy applications,” Solar Energy Mater. Sol. Cells 140, 61–68 (2015).
[Crossref]

Lee, W.

W. Lee, X. Zhang, and R. Briber, “A simple method for creating nanoporous block-copolymer thin films,” Polymer 51, 2376–2382 (2010).
[Crossref]

Lequime, M.

Li, X.

X. Li, X. Yu, and Y. Han, “Polymer thin films for antireflection coatings,” J. Mater. Chem. C 1, 2266–2285 (2013).
[Crossref]

Liang, Q.

L. Miao, L. F. Su, S. Tanemura, C. A. Fisher, L. L. Zhao, Q. Liang, and G. Xu, “Cost-effective nanoporous SiO2-TiO2 coatings on glass substrates with antireflective and self-cleaning properties,” Appl. Energy 112, 1198–1205 (2013).
[Crossref]

Liukaityte, S.

Luo, J.-H.

Y.-L. Zhang, C.-X. Zhao, P.-M. Wang, L. Ye, J.-H. Luo, and B. Jiang, “A convenient sol–gel approach to prepare nano-porous silica coatings with very low refractive indices,” Chem. Commun. 50, 13813–13816 (2014).
[Crossref]

Mahadik, D.

D. Mahadik, R. Lakshmi, and H. Barshilia, “High performance single layer nano-porous antireflection coatings on glass by sol–gel process for solar energy applications,” Solar Energy Mater. Sol. Cells 140, 61–68 (2015).
[Crossref]

Miao, L.

L. Miao, L. F. Su, S. Tanemura, C. A. Fisher, L. L. Zhao, Q. Liang, and G. Xu, “Cost-effective nanoporous SiO2-TiO2 coatings on glass substrates with antireflective and self-cleaning properties,” Appl. Energy 112, 1198–1205 (2013).
[Crossref]

Mizoshita, N.

N. Mizoshita, M. Ishii, N. Kato, and H. Tanaka, “Hierarchical nanoporous silica films for wear resistant antireflection coatings,” ACS Appl. Mater. Interfaces 7, 19424–19430 (2015).
[Crossref]

Mojab, M.

A. Eshaghi and M. Mojab, “Fabrication of antireflective antifogging nano-porous silica thin film on glass substrate by layer-by-layer assembly method,” J. Non-Cryst. Solids 405, 148–152 (2014).
[Crossref]

Morales, A.

M. Bautista and A. Morales, “Silica antireflective films on glass produced by the sol–gel method,” Solar Energy Materials and Solar Cells 80, 217–225 (2003).
[Crossref]

Mühlig, C.

L. Ghazaryan, Y. Sekman, S. Schröder, C. Mühlig, I. Stevanovic, R. Botha, M. Aghaee, M. Creatore, A. Tünnermann, and A. Szeghalmi, “On the properties of nanoporous SiO2 films for single layer antireflection coating,” Adv. Eng. Mater. 21, 1801229 (2019).
[Crossref]

Neubert, J.

Notni, G.

Otter, G.

Pelletier, E.

Pilon, L.

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Sekman, Y.

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Steinert, J.

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L. Ghazaryan, Y. Sekman, S. Schröder, C. Mühlig, I. Stevanovic, R. Botha, M. Aghaee, M. Creatore, A. Tünnermann, and A. Szeghalmi, “On the properties of nanoporous SiO2 films for single layer antireflection coating,” Adv. Eng. Mater. 21, 1801229 (2019).
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Stover, J.

Su, L. F.

L. Miao, L. F. Su, S. Tanemura, C. A. Fisher, L. L. Zhao, Q. Liang, and G. Xu, “Cost-effective nanoporous SiO2-TiO2 coatings on glass substrates with antireflective and self-cleaning properties,” Appl. Energy 112, 1198–1205 (2013).
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Szeghalmi, A.

L. Ghazaryan, Y. Sekman, S. Schröder, C. Mühlig, I. Stevanovic, R. Botha, M. Aghaee, M. Creatore, A. Tünnermann, and A. Szeghalmi, “On the properties of nanoporous SiO2 films for single layer antireflection coating,” Adv. Eng. Mater. 21, 1801229 (2019).
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L. Miao, L. F. Su, S. Tanemura, C. A. Fisher, L. L. Zhao, Q. Liang, and G. Xu, “Cost-effective nanoporous SiO2-TiO2 coatings on glass substrates with antireflective and self-cleaning properties,” Appl. Energy 112, 1198–1205 (2013).
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S. Schröder, M. Trost, M. Garrick, A. Duparré, X. Cheng, J. Zhang, and Z. Wang, “Origins of light scattering from thin film coatings,” Thin Solid Films 592, 248–255 (2015).
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M. Trost, S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “Influence of the substrate finish and thin film roughness on the optical performance of Mo/Si multilayers,” Appl. Opt. 50, C148–C153 (2011).
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L. Ghazaryan, Y. Sekman, S. Schröder, C. Mühlig, I. Stevanovic, R. Botha, M. Aghaee, M. Creatore, A. Tünnermann, and A. Szeghalmi, “On the properties of nanoporous SiO2 films for single layer antireflection coating,” Adv. Eng. Mater. 21, 1801229 (2019).
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L. Ghazaryan, E.-B. Kley, A. Tünnermann, and A. Szeghalmi, “Nanoporous SiO2 thin films made by atomic layer deposition and atomic etching,” Nanotechnology 27, 255603 (2016).
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M. Trost, S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “Influence of the substrate finish and thin film roughness on the optical performance of Mo/Si multilayers,” Appl. Opt. 50, C148–C153 (2011).
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S. Schröder, M. Trost, M. Garrick, A. Duparré, X. Cheng, J. Zhang, and Z. Wang, “Origins of light scattering from thin film coatings,” Thin Solid Films 592, 248–255 (2015).
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G. Wicht, R. Ferrini, S. Schüttel, and L. Zuppiroli, “Nanoporous films with low refractive index for large-surface broad-band anti-reflection coatings,” Macromol. Mater. Eng. 295, 628–636 (2010).
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Xu, G.

L. Miao, L. F. Su, S. Tanemura, C. A. Fisher, L. L. Zhao, Q. Liang, and G. Xu, “Cost-effective nanoporous SiO2-TiO2 coatings on glass substrates with antireflective and self-cleaning properties,” Appl. Energy 112, 1198–1205 (2013).
[Crossref]

Ye, L.

Y.-L. Zhang, C.-X. Zhao, P.-M. Wang, L. Ye, J.-H. Luo, and B. Jiang, “A convenient sol–gel approach to prepare nano-porous silica coatings with very low refractive indices,” Chem. Commun. 50, 13813–13816 (2014).
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X. Li, X. Yu, and Y. Han, “Polymer thin films for antireflection coatings,” J. Mater. Chem. C 1, 2266–2285 (2013).
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Zhang, J.

S. Schröder, M. Trost, M. Garrick, A. Duparré, X. Cheng, J. Zhang, and Z. Wang, “Origins of light scattering from thin film coatings,” Thin Solid Films 592, 248–255 (2015).
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Zhang, X.

W. Lee, X. Zhang, and R. Briber, “A simple method for creating nanoporous block-copolymer thin films,” Polymer 51, 2376–2382 (2010).
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Zhang, Y.-L.

Y.-L. Zhang, C.-X. Zhao, P.-M. Wang, L. Ye, J.-H. Luo, and B. Jiang, “A convenient sol–gel approach to prepare nano-porous silica coatings with very low refractive indices,” Chem. Commun. 50, 13813–13816 (2014).
[Crossref]

Zhao, C.-X.

Y.-L. Zhang, C.-X. Zhao, P.-M. Wang, L. Ye, J.-H. Luo, and B. Jiang, “A convenient sol–gel approach to prepare nano-porous silica coatings with very low refractive indices,” Chem. Commun. 50, 13813–13816 (2014).
[Crossref]

Zhao, L. L.

L. Miao, L. F. Su, S. Tanemura, C. A. Fisher, L. L. Zhao, Q. Liang, and G. Xu, “Cost-effective nanoporous SiO2-TiO2 coatings on glass substrates with antireflective and self-cleaning properties,” Appl. Energy 112, 1198–1205 (2013).
[Crossref]

Zuppiroli, L.

G. Wicht, R. Ferrini, S. Schüttel, and L. Zuppiroli, “Nanoporous films with low refractive index for large-surface broad-band anti-reflection coatings,” Macromol. Mater. Eng. 295, 628–636 (2010).
[Crossref]

ACS Appl. Mater. Interfaces (1)

N. Mizoshita, M. Ishii, N. Kato, and H. Tanaka, “Hierarchical nanoporous silica films for wear resistant antireflection coatings,” ACS Appl. Mater. Interfaces 7, 19424–19430 (2015).
[Crossref]

Adv. Eng. Mater. (1)

L. Ghazaryan, Y. Sekman, S. Schröder, C. Mühlig, I. Stevanovic, R. Botha, M. Aghaee, M. Creatore, A. Tünnermann, and A. Szeghalmi, “On the properties of nanoporous SiO2 films for single layer antireflection coating,” Adv. Eng. Mater. 21, 1801229 (2019).
[Crossref]

Appl. Energy (1)

L. Miao, L. F. Su, S. Tanemura, C. A. Fisher, L. L. Zhao, Q. Liang, and G. Xu, “Cost-effective nanoporous SiO2-TiO2 coatings on glass substrates with antireflective and self-cleaning properties,” Appl. Energy 112, 1198–1205 (2013).
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S. Schröder, A. Duparré, and A. Tünnermann, “Roughness evolution and scatter losses of multilayers for 193 nm optics,” Appl. Opt. 47, C88–C97 (2008).
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M. Trost, S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “Influence of the substrate finish and thin film roughness on the optical performance of Mo/Si multilayers,” Appl. Opt. 50, C148–C153 (2011).
[Crossref]

A. von Finck, M. Hauptvogel, and A. Duparré, “Instrument for close-to-process light scatter measurements of thin film coatings and substrates,” Appl. Opt. 50, C321–C328 (2011).
[Crossref]

A. von Finck, T. Herffurth, A. Duparré, S. Schröder, M. Lequime, M. Zerrad, S. Liukaityte, C. Amra, S. Achour, M. Chalony, Q. Kuperman, Y. Cornil, A. Bialek, T. Goodman, C. Greenwell, B. Gur, S. Brinkers, G. Otter, A. Vosteen, J. Stover, R. Vink, A. Deep, and D. Doyle, “International round-robin experiment for angle-resolved light scattering measurement,” Appl. Opt. 58, 6638–6654 (2019).
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Y.-L. Zhang, C.-X. Zhao, P.-M. Wang, L. Ye, J.-H. Luo, and B. Jiang, “A convenient sol–gel approach to prepare nano-porous silica coatings with very low refractive indices,” Chem. Commun. 50, 13813–13816 (2014).
[Crossref]

J. Mater. Chem. C (1)

X. Li, X. Yu, and Y. Han, “Polymer thin films for antireflection coatings,” J. Mater. Chem. C 1, 2266–2285 (2013).
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A. Eshaghi and M. Mojab, “Fabrication of antireflective antifogging nano-porous silica thin film on glass substrate by layer-by-layer assembly method,” J. Non-Cryst. Solids 405, 148–152 (2014).
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Macromol. Mater. Eng. (1)

G. Wicht, R. Ferrini, S. Schüttel, and L. Zuppiroli, “Nanoporous films with low refractive index for large-surface broad-band anti-reflection coatings,” Macromol. Mater. Eng. 295, 628–636 (2010).
[Crossref]

Nanotechnology (1)

L. Ghazaryan, E.-B. Kley, A. Tünnermann, and A. Szeghalmi, “Nanoporous SiO2 thin films made by atomic layer deposition and atomic etching,” Nanotechnology 27, 255603 (2016).
[Crossref]

Opt. Eng. (1)

D. Rönnow, “Interface roughness statistics of thin films from angle resolved light scattering at three wavelengths,” Opt. Eng. 37, 696–704 (1998).
[Crossref]

Opt. Lett. (1)

Polymer (1)

W. Lee, X. Zhang, and R. Briber, “A simple method for creating nanoporous block-copolymer thin films,” Polymer 51, 2376–2382 (2010).
[Crossref]

Proc. SPIE (1)

E. L. Church and P. Z. Takacs, “Optimal estimation of finish parameters,” Proc. SPIE 1530, 71–85 (1991).
[Crossref]

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D. Mahadik, R. Lakshmi, and H. Barshilia, “High performance single layer nano-porous antireflection coatings on glass by sol–gel process for solar energy applications,” Solar Energy Mater. Sol. Cells 140, 61–68 (2015).
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Thin Solid Films (2)

S. Schröder, M. Trost, M. Garrick, A. Duparré, X. Cheng, J. Zhang, and Z. Wang, “Origins of light scattering from thin film coatings,” Thin Solid Films 592, 248–255 (2015).
[Crossref]

M. M. Braun and L. Pilon, “Effective optical properties of non-absorbing nanoporous thin films,” Thin Solid Films 496, 505–514 (2006).
[Crossref]

Other (2)

“Optics and optical instruments-test methods for radiation scattered by optical components,” (International Organization for Standardization, 2002).

J. Stover, Optical Scattering: Measurement and Analysis, 3rd ed. (SPIE, 2012).

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Figures (6)

Fig. 1.
Fig. 1. ARS measurement geometry (${\theta_i}$, angle of incidence; ${\theta_s}$, polar scattering angle; ${\phi_s}$, azimuthal scattering angle).
Fig. 2.
Fig. 2. Roughness evolution of thin film coating on substrate.
Fig. 3.
Fig. 3. TS/R versus coating thickness.
Fig. 4.
Fig. 4. Master PSDs of all samples with corresponding substrate and coating model fits (color online).
Fig. 5.
Fig. 5. Wavelength averaged TS/R values with respect to their relevant roughness in VIS.
Fig. 6.
Fig. 6. Comparison of the ARS diagrams of the coating on fused silica and on Si substrates at 532 nm ($-{90^\circ}\lt {\theta_s}\lt 90^\circ$, backscattering angles; ${90^\circ}\lt {\theta_s}\lt 270^\circ$, forward-scattering angles) (color online).

Tables (1)

Tables Icon

Table 1. TS Values of the Coatings on Fused Silica (FS) and Si Substrates

Equations (11)

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

P S D ( f x , f y ) = lim L 1 L 2 | L / 2 L / 2 L / 2 L / 2 h ( x , y ) × exp [ 2 π i ( f x x + f y y ) ] d x d y | 2 ,
σ = 2 π f min f max P S D 2 D ( f ) d f .
A R S ( θ s , ϕ s ) = Δ P s ( θ s , ϕ s ) P i Δ Ω s = B S D F ( θ s , ϕ s ) cos θ s .
T S b = P s P i = 0 2 π 2 85 A R S ( θ s , ϕ s ) sin θ s d θ s d ϕ s .
A R S ( θ s , ϕ s ) = 16 π 2 λ 4 cos θ i cos 2 θ s Q P S D ( f x , f y ) ,
f x = sin θ s cos ϕ s sin θ i λ ,
f y = sin θ s sin ϕ s λ .
T I S = P s R P i = T S R ( 4 π σ cos θ i λ ) 2 .
A R S ( θ s ) = 1 λ 4 i = 0 N j = 0 N C i C j P S D ij ( f x , f y ) ,
P S D f r a c t a l ( f ) = K f η + 1 ,
P S D ABC ( f ) = A ( 1 + B 2 f 2 ) C + 1 2 .

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