Abstract

Subsurface damage (SSD) in optical components is almost unavoidably caused by mechanical forces involved during grinding and polishing and can be a limiting factor, in particular for applications that require high laser powers or an extreme material strength. In this paper, we report on the characterization of SSD in ground and polished optical surfaces, using different light scattering measurement techniques in the visible and extreme ultraviolet spectral ranges. The materials investigated include fused silica, borosilicate glass, and calcium fluoride. The scattering results are directly linked to classical destructive SSD characterization techniques, based on white light interferometry, optical microscopy, and atomic force microscopy of the substrate topography and cross sections obtained after etching in hydrofluoric acid and fracturing.

© 2013 Optical Society of America

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2013 (1)

2012 (4)

T. Herffurth, S. Schröder, M. Trost, and A. Duparré, “Light scattering to detect imperfections relevant for laser-induced damage,” Proc. SPIE 8530, 85301B (2012).
[CrossRef]

S. Schröder, M. Trost, T. Herffurth, A. von Finck, and A. Duparré, “Sophisticated light scattering techniques from the VUV to the IR regions,” Proc. SPIE 8495, 84950V (2012).
[CrossRef]

M. Trost, S. Schröder, C. C. Lin, A. Duparré, and A. Tünnermann, “Roughness characterization of EUV multilayer coatings and ultra-smooth surfaces by light scattering,” Proc. SPIE 8501, 85010F (2012).
[CrossRef]

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

2011 (6)

S. Schröder, M. Trost, T. Feigl, J. E. Harvey, and A. Duparré, “Efficient specification and charaterization of surface roughness for extreme ultraviolet optics,” Proc. SPIE 7969, 79692C (2011).
[CrossRef]

M. Trost, S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “Roughness characterization of large EUV mirror optics by laser light scattering,” Proc. SPIE 8169, 81690P (2011).
[CrossRef]

J. Wang, Y. Li, J. Han, Q. Xu, and Y. Guo, “Evaluating subsurface damage in optical glasses,” J. Eur. Opt. Soc. 6, 11001 (2011).

J. B. Johnson, D. W. Kim, R. E. Parks, and J. H. Burge, “New approach for pre-polish grinding with low subsurface damage,” Proc. SPIE 8126, 81261E (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, T. Herffurth, H. Blaschke, and A. Duparré, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, C164–C171 (2011).
[CrossRef]

2010 (1)

2009 (4)

2007 (1)

2006 (4)

J. Wang and R. L. Maier, “Surface assessment of CaF2 deep-ultraviolet and vacuum-ultraviolet optical components by the quasi-Brewster angle technique,” Appl. Opt. 45, 5621–5628 (2006).
[CrossRef]

S. Schröder, M. Kamprath, A. Duparré, A. Tünnermann, B. Kühn, and U. Klett, “Bulk scattering properties of synthetic fused silica at 193  nm,” Opt. Express 14, 10537–10549 (2006).
[CrossRef]

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352, 5601–5617 (2006).
[CrossRef]

2005 (3)

J. A. Menapace, P.-J. Davis, W. A. Steele, L. L. Wong, T. I. Suratwala, and P. E. Miller, “MRF applications: measurement of process-dependent subsurface damage in optical materials using the MRF wedge technique,” Proc. SPIE 5991, 599102 (2005).
[CrossRef]

J. A. Randi, J. C. Lambropoulos, and S. D. Jacobs, “Subsurface damage in some single crystalline optical materials,” Appl. Opt. 44, 2241–2249 (2005).
[CrossRef]

C. Amra, C. Deumie, and O. Gilbert, “Elimination of polarized light scattered by surface roughness or bulk heterogeneity,” Opt. Express 13, 10854–10864 (2005).
[CrossRef]

2004 (2)

M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser-induced surface damage,” Proc. SPIE 5273, 264–272 (2004).
[CrossRef]

D. A. Lucca, C. J. Wetteland, A. Misra, M. J. Klopfstein, M. Nastasi, C. J. Maggiore, and J. R. Tesmer, “Assessment of subsurface damage in polished II–VI semiconductors by ion channeling,” Nucl. Instrum. Methods Phys. Res. B 219–220, 611–617 (2004).

2003 (1)

J. Wang, R. L. Maier, and J. H. Bruning, “Surface characterization of optically polished CaF2 crystal by quasi-Brewster angle technique,” Proc. SPIE 5188, 106–114 (2003).

2002 (2)

2000 (1)

J. Steinert, S. Gliech, A. Wuttig, and A. Duparré, “Advanced methods for surface and subsurface defect characterization of optical components,” Proc. SPIE 4099, 290–298 (2000).
[CrossRef]

1999 (1)

1997 (3)

T. A. Germer, “Angular dependence and polarization of out-of-plane optical scattering from particulate contamination, subsurface defects, and surface microroughness,” Appl. Opt. 36, 8798–8805 (1997).
[CrossRef]

J. C. Lambropoulos, S. D. Jacobs, B. Gillman, F. Yang, and J. Ruckman, “Subsurface damage in microgrinding optical glasses,” LLE Rev. 73, 45–49 (1997).

K. Saito, H. Kakiuchida, and A. J. Ikushima, “Investigation of the origin of the Rayleigh scattering in SiO2 glass,” J. Non-Cryst. Solids 222, 329–334 (1997).

1994 (3)

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, and A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

T. Shibata, A. Ono, K. Kurihara, E. Makino, and M. Ikeda, “Cross-section transmission electron microscope observations of diamond-turned single-crystal Si surfaces,” Appl. Phys. Lett. 65, 2553–2555 (1994).
[CrossRef]

C. F. Kranenberg and K. C. Jungling, “Subsurface damage identification in optically transparent materials using a nondestructive method,” Appl. Opt. 33, 4248–4253 (1994).
[CrossRef]

1987 (1)

P. Ostojic and R. McPherson, “A review of indentation fracture theory: its development, principles and limitations,” Int. J. Fract. 33, 297–312 (1987).
[CrossRef]

1984 (1)

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

1979 (1)

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 182125 (1979).
[CrossRef]

1970 (1)

Ambard, C.

Amra, C.

Asmail, C. C.

Baldwin, A.

Bennett, J. M.

Blaschke, H.

Bruning, J. H.

J. Wang, R. L. Maier, and J. H. Bruning, “Surface characterization of optically polished CaF2 crystal by quasi-Brewster angle technique,” Proc. SPIE 5188, 106–114 (2003).

Burge, J. H.

J. B. Johnson, D. W. Kim, R. E. Parks, and J. H. Burge, “New approach for pre-polish grinding with low subsurface damage,” Proc. SPIE 8126, 81261E (2011).
[CrossRef]

Church, E. L.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 182125 (1979).
[CrossRef]

Cormont, P.

Darbois, N.

Davis, P.

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352, 5601–5617 (2006).
[CrossRef]

Davis, P.-J.

J. A. Menapace, P.-J. Davis, W. A. Steele, L. L. Wong, T. I. Suratwala, and P. E. Miller, “MRF applications: measurement of process-dependent subsurface damage in optical materials using the MRF wedge technique,” Proc. SPIE 5991, 599102 (2005).
[CrossRef]

Destribats, J.

Deumie, C.

Duparré, A.

T. Herffurth, S. Schröder, M. Trost, A. Duparré, and A. Tünnermann, “Comprehensive nanostructure and defect analysis using a simple 3D light-scatter sensor,” Appl. Opt. 52, 3279–3287 (2013).
[CrossRef]

T. Herffurth, S. Schröder, M. Trost, and A. Duparré, “Light scattering to detect imperfections relevant for laser-induced damage,” Proc. SPIE 8530, 85301B (2012).
[CrossRef]

M. Trost, S. Schröder, C. C. Lin, A. Duparré, and A. Tünnermann, “Roughness characterization of EUV multilayer coatings and ultra-smooth surfaces by light scattering,” Proc. SPIE 8501, 85010F (2012).
[CrossRef]

S. Schröder, M. Trost, T. Herffurth, A. von Finck, and A. Duparré, “Sophisticated light scattering techniques from the VUV to the IR regions,” Proc. SPIE 8495, 84950V (2012).
[CrossRef]

S. Schröder, M. Trost, T. Feigl, J. E. Harvey, and A. Duparré, “Efficient specification and charaterization of surface roughness for extreme ultraviolet optics,” Proc. SPIE 7969, 79692C (2011).
[CrossRef]

M. Trost, S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “Roughness characterization of large EUV mirror optics by laser light scattering,” Proc. SPIE 8169, 81690P (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, T. Herffurth, H. Blaschke, and A. Duparré, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, C164–C171 (2011).
[CrossRef]

S. Schröder, T. Herffurth, M. Trost, and A. Duparré, “Angle-resolved scattering and reflectance of extreme-ultraviolet multilayer coatings: measurement and analysis,” Appl. Opt. 49, 1503–1512 (2010).
[CrossRef]

S. Schröder, M. Kamprath, A. Duparré, A. Tünnermann, B. Kühn, and U. Klett, “Bulk scattering properties of synthetic fused silica at 193  nm,” Opt. Express 14, 10537–10549 (2006).
[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. Steinert, S. Gliech, A. Wuttig, and A. Duparré, “Advanced methods for surface and subsurface defect characterization of optical components,” Proc. SPIE 4099, 290–298 (2000).
[CrossRef]

Elson, J. M.

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

Evans, R.

Feigl, T.

S. Schröder, M. Trost, T. Feigl, J. E. Harvey, and A. Duparré, “Efficient specification and charaterization of surface roughness for extreme ultraviolet optics,” Proc. SPIE 7969, 79692C (2011).
[CrossRef]

M. Trost, S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “Roughness characterization of large EUV mirror optics by laser light scattering,” Proc. SPIE 8169, 81690P (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]

Feit, M. D.

L. Wong, T. Suratwala, M. D. Feit, P. E. Miller, and R. Steele, “The effect of HF/NH4F etching on the morphology of surface fractures on fused silica,” J. Non-Cryst. Solids 355, 797–810 (2009).
[CrossRef]

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352, 5601–5617 (2006).
[CrossRef]

M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser-induced surface damage,” Proc. SPIE 5273, 264–272 (2004).
[CrossRef]

Ferre-Borrull, J.

Fiaz, M. A.

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

Frezza, F.

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

Funkenbusch, P. D.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, and A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

Germer, T. A.

Gilbert, O.

Gillman, B.

J. C. Lambropoulos, S. D. Jacobs, B. Gillman, F. Yang, and J. Ruckman, “Subsurface damage in microgrinding optical glasses,” LLE Rev. 73, 45–49 (1997).

Gliech, S.

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. Steinert, S. Gliech, A. Wuttig, and A. Duparré, “Advanced methods for surface and subsurface defect characterization of optical components,” Proc. SPIE 4099, 290–298 (2000).
[CrossRef]

Golini, D.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, and A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

Guo, Y.

J. Wang, Y. Li, J. Han, Q. Xu, and Y. Guo, “Evaluating subsurface damage in optical glasses,” J. Eur. Opt. Soc. 6, 11001 (2011).

Han, J.

J. Wang, Y. Li, J. Han, Q. Xu, and Y. Guo, “Evaluating subsurface damage in optical glasses,” J. Eur. Opt. Soc. 6, 11001 (2011).

Harvey, J. E.

S. Schröder, M. Trost, T. Feigl, J. E. Harvey, and A. Duparré, “Efficient specification and charaterization of surface roughness for extreme ultraviolet optics,” Proc. SPIE 7969, 79692C (2011).
[CrossRef]

Herffurth, T.

Ikeda, M.

T. Shibata, A. Ono, K. Kurihara, E. Makino, and M. Ikeda, “Cross-section transmission electron microscope observations of diamond-turned single-crystal Si surfaces,” Appl. Phys. Lett. 65, 2553–2555 (1994).
[CrossRef]

Ikushima, A. J.

K. Saito, H. Kakiuchida, and A. J. Ikushima, “Investigation of the origin of the Rayleigh scattering in SiO2 glass,” J. Non-Cryst. Solids 222, 329–334 (1997).

Jacobs, S. D.

J. A. Randi, J. C. Lambropoulos, and S. D. Jacobs, “Subsurface damage in some single crystalline optical materials,” Appl. Opt. 44, 2241–2249 (2005).
[CrossRef]

J. C. Lambropoulos, S. D. Jacobs, B. Gillman, F. Yang, and J. Ruckman, “Subsurface damage in microgrinding optical glasses,” LLE Rev. 73, 45–49 (1997).

Jenkinson, H. A.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 182125 (1979).
[CrossRef]

Johnson, J. B.

J. B. Johnson, D. W. Kim, R. E. Parks, and J. H. Burge, “New approach for pre-polish grinding with low subsurface damage,” Proc. SPIE 8126, 81261E (2011).
[CrossRef]

Jungling, K. C.

Kakiuchida, H.

K. Saito, H. Kakiuchida, and A. J. Ikushima, “Investigation of the origin of the Rayleigh scattering in SiO2 glass,” J. Non-Cryst. Solids 222, 329–334 (1997).

Kamprath, M.

Kim, D. W.

J. B. Johnson, D. W. Kim, R. E. Parks, and J. H. Burge, “New approach for pre-polish grinding with low subsurface damage,” Proc. SPIE 8126, 81261E (2011).
[CrossRef]

King, R. J.

Klett, U.

Klopfstein, M. J.

D. A. Lucca, C. J. Wetteland, A. Misra, M. J. Klopfstein, M. Nastasi, C. J. Maggiore, and J. R. Tesmer, “Assessment of subsurface damage in polished II–VI semiconductors by ion channeling,” Nucl. Instrum. Methods Phys. Res. B 219–220, 611–617 (2004).

Kranenberg, C. F.

Kühn, B.

Kuo, C.-H.

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

Kurihara, K.

T. Shibata, A. Ono, K. Kurihara, E. Makino, and M. Ikeda, “Cross-section transmission electron microscope observations of diamond-turned single-crystal Si surfaces,” Appl. Phys. Lett. 65, 2553–2555 (1994).
[CrossRef]

Lambropoulos, J. C.

J. A. Randi, J. C. Lambropoulos, and S. D. Jacobs, “Subsurface damage in some single crystalline optical materials,” Appl. Opt. 44, 2241–2249 (2005).
[CrossRef]

J. C. Lambropoulos, S. D. Jacobs, B. Gillman, F. Yang, and J. Ruckman, “Subsurface damage in microgrinding optical glasses,” LLE Rev. 73, 45–49 (1997).

Legros, P.

Li, Y.

J. Wang, Y. Li, J. Han, Q. Xu, and Y. Guo, “Evaluating subsurface damage in optical glasses,” J. Eur. Opt. Soc. 6, 11001 (2011).

Lin, C. C.

M. Trost, S. Schröder, C. C. Lin, A. Duparré, and A. Tünnermann, “Roughness characterization of EUV multilayer coatings and ultra-smooth surfaces by light scattering,” Proc. SPIE 8501, 85010F (2012).
[CrossRef]

Lindquist, A.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, and A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

Lucca, D. A.

D. A. Lucca, C. J. Wetteland, A. Misra, M. J. Klopfstein, M. Nastasi, C. J. Maggiore, and J. R. Tesmer, “Assessment of subsurface damage in polished II–VI semiconductors by ion channeling,” Nucl. Instrum. Methods Phys. Res. B 219–220, 611–617 (2004).

Luitot, C.

Maggiore, C. J.

D. A. Lucca, C. J. Wetteland, A. Misra, M. J. Klopfstein, M. Nastasi, C. J. Maggiore, and J. R. Tesmer, “Assessment of subsurface damage in polished II–VI semiconductors by ion channeling,” Nucl. Instrum. Methods Phys. Res. B 219–220, 611–617 (2004).

Maier, R. L.

J. Wang and R. L. Maier, “Surface assessment of CaF2 deep-ultraviolet and vacuum-ultraviolet optical components by the quasi-Brewster angle technique,” Appl. Opt. 45, 5621–5628 (2006).
[CrossRef]

J. Wang, R. L. Maier, and J. H. Bruning, “Surface characterization of optically polished CaF2 crystal by quasi-Brewster angle technique,” Proc. SPIE 5188, 106–114 (2003).

Makino, E.

T. Shibata, A. Ono, K. Kurihara, E. Makino, and M. Ikeda, “Cross-section transmission electron microscope observations of diamond-turned single-crystal Si surfaces,” Appl. Phys. Lett. 65, 2553–2555 (1994).
[CrossRef]

McPherson, R.

P. Ostojic and R. McPherson, “A review of indentation fracture theory: its development, principles and limitations,” Int. J. Fract. 33, 297–312 (1987).
[CrossRef]

Meier, S. R.

R. G. Priest and S. R. Meier, “Polarimetric microfacet scattering theory with applications to absorptive and reflective surfaces,” Opt. Eng. 41, 988–993 (2002).
[CrossRef]

Menapace, J.

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352, 5601–5617 (2006).
[CrossRef]

Menapace, J. A.

J. A. Menapace, P.-J. Davis, W. A. Steele, L. L. Wong, T. I. Suratwala, and P. E. Miller, “MRF applications: measurement of process-dependent subsurface damage in optical materials using the MRF wedge technique,” Proc. SPIE 5991, 599102 (2005).
[CrossRef]

Miller, P.

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352, 5601–5617 (2006).
[CrossRef]

Miller, P. E.

L. Wong, T. Suratwala, M. D. Feit, P. E. Miller, and R. Steele, “The effect of HF/NH4F etching on the morphology of surface fractures on fused silica,” J. Non-Cryst. Solids 355, 797–810 (2009).
[CrossRef]

J. A. Menapace, P.-J. Davis, W. A. Steele, L. L. Wong, T. I. Suratwala, and P. E. Miller, “MRF applications: measurement of process-dependent subsurface damage in optical materials using the MRF wedge technique,” Proc. SPIE 5991, 599102 (2005).
[CrossRef]

Misra, A.

D. A. Lucca, C. J. Wetteland, A. Misra, M. J. Klopfstein, M. Nastasi, C. J. Maggiore, and J. R. Tesmer, “Assessment of subsurface damage in polished II–VI semiconductors by ion channeling,” Nucl. Instrum. Methods Phys. Res. B 219–220, 611–617 (2004).

Moghaddam, M.

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

Morantz, P.

Moyer, P. J.

Mullany, B. A.

Nastasi, M.

D. A. Lucca, C. J. Wetteland, A. Misra, M. J. Klopfstein, M. Nastasi, C. J. Maggiore, and J. R. Tesmer, “Assessment of subsurface damage in polished II–VI semiconductors by ion channeling,” Nucl. Instrum. Methods Phys. Res. B 219–220, 611–617 (2004).

Neauport, J.

Notni, G.

Ono, A.

T. Shibata, A. Ono, K. Kurihara, E. Makino, and M. Ikeda, “Cross-section transmission electron microscope observations of diamond-turned single-crystal Si surfaces,” Appl. Phys. Lett. 65, 2553–2555 (1994).
[CrossRef]

Ostojic, P.

P. Ostojic and R. McPherson, “A review of indentation fracture theory: its development, principles and limitations,” Int. J. Fract. 33, 297–312 (1987).
[CrossRef]

Pajewski, L.

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

Parker, W. C.

Parks, R. E.

J. B. Johnson, D. W. Kim, R. E. Parks, and J. H. Burge, “New approach for pre-polish grinding with low subsurface damage,” Proc. SPIE 8126, 81261E (2011).
[CrossRef]

Ponti, C.

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

Priest, R. G.

R. G. Priest and S. R. Meier, “Polarimetric microfacet scattering theory with applications to absorptive and reflective surfaces,” Opt. Eng. 41, 988–993 (2002).
[CrossRef]

Quesnel, D. J.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, and A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

Randi, J. A.

Randles, M. H.

Rondeau, O.

Rubenchik, A. M.

M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser-induced surface damage,” Proc. SPIE 5273, 264–272 (2004).
[CrossRef]

Ruckman, J.

J. C. Lambropoulos, S. D. Jacobs, B. Gillman, F. Yang, and J. Ruckman, “Subsurface damage in microgrinding optical glasses,” LLE Rev. 73, 45–49 (1997).

Saito, K.

K. Saito, H. Kakiuchida, and A. J. Ikushima, “Investigation of the origin of the Rayleigh scattering in SiO2 glass,” J. Non-Cryst. Solids 222, 329–334 (1997).

Schettini, G.

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

Schröder, S.

T. Herffurth, S. Schröder, M. Trost, A. Duparré, and A. Tünnermann, “Comprehensive nanostructure and defect analysis using a simple 3D light-scatter sensor,” Appl. Opt. 52, 3279–3287 (2013).
[CrossRef]

T. Herffurth, S. Schröder, M. Trost, and A. Duparré, “Light scattering to detect imperfections relevant for laser-induced damage,” Proc. SPIE 8530, 85301B (2012).
[CrossRef]

M. Trost, S. Schröder, C. C. Lin, A. Duparré, and A. Tünnermann, “Roughness characterization of EUV multilayer coatings and ultra-smooth surfaces by light scattering,” Proc. SPIE 8501, 85010F (2012).
[CrossRef]

S. Schröder, M. Trost, T. Herffurth, A. von Finck, and A. Duparré, “Sophisticated light scattering techniques from the VUV to the IR regions,” Proc. SPIE 8495, 84950V (2012).
[CrossRef]

S. Schröder, M. Trost, T. Feigl, J. E. Harvey, and A. Duparré, “Efficient specification and charaterization of surface roughness for extreme ultraviolet optics,” Proc. SPIE 7969, 79692C (2011).
[CrossRef]

M. Trost, S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “Roughness characterization of large EUV mirror optics by laser light scattering,” Proc. SPIE 8169, 81690P (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, T. Herffurth, H. Blaschke, and A. Duparré, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, C164–C171 (2011).
[CrossRef]

S. Schröder, T. Herffurth, M. Trost, and A. Duparré, “Angle-resolved scattering and reflectance of extreme-ultraviolet multilayer coatings: measurement and analysis,” Appl. Opt. 49, 1503–1512 (2010).
[CrossRef]

S. Schröder, M. Kamprath, A. Duparré, A. Tünnermann, B. Kühn, and U. Klett, “Bulk scattering properties of synthetic fused silica at 193  nm,” Opt. Express 14, 10537–10549 (2006).
[CrossRef]

Shibata, T.

T. Shibata, A. Ono, K. Kurihara, E. Makino, and M. Ikeda, “Cross-section transmission electron microscope observations of diamond-turned single-crystal Si surfaces,” Appl. Phys. Lett. 65, 2553–2555 (1994).
[CrossRef]

Shore, P.

Steele, R.

L. Wong, T. Suratwala, M. D. Feit, P. E. Miller, and R. Steele, “The effect of HF/NH4F etching on the morphology of surface fractures on fused silica,” J. Non-Cryst. Solids 355, 797–810 (2009).
[CrossRef]

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352, 5601–5617 (2006).
[CrossRef]

Steele, W. A.

J. A. Menapace, P.-J. Davis, W. A. Steele, L. L. Wong, T. I. Suratwala, and P. E. Miller, “MRF applications: measurement of process-dependent subsurface damage in optical materials using the MRF wedge technique,” Proc. SPIE 5991, 599102 (2005).
[CrossRef]

Steinert, J.

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. Steinert, S. Gliech, A. Wuttig, and A. Duparré, “Advanced methods for surface and subsurface defect characterization of optical components,” Proc. SPIE 4099, 290–298 (2000).
[CrossRef]

Stover, J. C.

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

Suratwala, T.

L. Wong, T. Suratwala, M. D. Feit, P. E. Miller, and R. Steele, “The effect of HF/NH4F etching on the morphology of surface fractures on fused silica,” J. Non-Cryst. Solids 355, 797–810 (2009).
[CrossRef]

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352, 5601–5617 (2006).
[CrossRef]

Suratwala, T. I.

J. A. Menapace, P.-J. Davis, W. A. Steele, L. L. Wong, T. I. Suratwala, and P. E. Miller, “MRF applications: measurement of process-dependent subsurface damage in optical materials using the MRF wedge technique,” Proc. SPIE 5991, 599102 (2005).
[CrossRef]

Tesmer, J. R.

D. A. Lucca, C. J. Wetteland, A. Misra, M. J. Klopfstein, M. Nastasi, C. J. Maggiore, and J. R. Tesmer, “Assessment of subsurface damage in polished II–VI semiconductors by ion channeling,” Nucl. Instrum. Methods Phys. Res. B 219–220, 611–617 (2004).

Tonnellier, X.

Trost, M.

T. Herffurth, S. Schröder, M. Trost, A. Duparré, and A. Tünnermann, “Comprehensive nanostructure and defect analysis using a simple 3D light-scatter sensor,” Appl. Opt. 52, 3279–3287 (2013).
[CrossRef]

T. Herffurth, S. Schröder, M. Trost, and A. Duparré, “Light scattering to detect imperfections relevant for laser-induced damage,” Proc. SPIE 8530, 85301B (2012).
[CrossRef]

M. Trost, S. Schröder, C. C. Lin, A. Duparré, and A. Tünnermann, “Roughness characterization of EUV multilayer coatings and ultra-smooth surfaces by light scattering,” Proc. SPIE 8501, 85010F (2012).
[CrossRef]

S. Schröder, M. Trost, T. Herffurth, A. von Finck, and A. Duparré, “Sophisticated light scattering techniques from the VUV to the IR regions,” Proc. SPIE 8495, 84950V (2012).
[CrossRef]

S. Schröder, M. Trost, T. Feigl, J. E. Harvey, and A. Duparré, “Efficient specification and charaterization of surface roughness for extreme ultraviolet optics,” Proc. SPIE 7969, 79692C (2011).
[CrossRef]

M. Trost, S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “Roughness characterization of large EUV mirror optics by laser light scattering,” Proc. SPIE 8169, 81690P (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, T. Herffurth, M. Trost, and A. Duparré, “Angle-resolved scattering and reflectance of extreme-ultraviolet multilayer coatings: measurement and analysis,” Appl. Opt. 49, 1503–1512 (2010).
[CrossRef]

Tünnermann, A.

von Finck, A.

S. Schröder, M. Trost, T. Herffurth, A. von Finck, and A. Duparré, “Sophisticated light scattering techniques from the VUV to the IR regions,” Proc. SPIE 8495, 84950V (2012).
[CrossRef]

Walker, D. D.

Walmer, D.

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352, 5601–5617 (2006).
[CrossRef]

Wang, J.

J. Wang, Y. Li, J. Han, Q. Xu, and Y. Guo, “Evaluating subsurface damage in optical glasses,” J. Eur. Opt. Soc. 6, 11001 (2011).

J. Wang and R. L. Maier, “Surface assessment of CaF2 deep-ultraviolet and vacuum-ultraviolet optical components by the quasi-Brewster angle technique,” Appl. Opt. 45, 5621–5628 (2006).
[CrossRef]

J. Wang, R. L. Maier, and J. H. Bruning, “Surface characterization of optically polished CaF2 crystal by quasi-Brewster angle technique,” Proc. SPIE 5188, 106–114 (2003).

Wetteland, C. J.

D. A. Lucca, C. J. Wetteland, A. Misra, M. J. Klopfstein, M. Nastasi, C. J. Maggiore, and J. R. Tesmer, “Assessment of subsurface damage in polished II–VI semiconductors by ion channeling,” Nucl. Instrum. Methods Phys. Res. B 219–220, 611–617 (2004).

Williams, W. B.

Wong, L.

L. Wong, T. Suratwala, M. D. Feit, P. E. Miller, and R. Steele, “The effect of HF/NH4F etching on the morphology of surface fractures on fused silica,” J. Non-Cryst. Solids 355, 797–810 (2009).
[CrossRef]

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352, 5601–5617 (2006).
[CrossRef]

Wong, L. L.

J. A. Menapace, P.-J. Davis, W. A. Steele, L. L. Wong, T. I. Suratwala, and P. E. Miller, “MRF applications: measurement of process-dependent subsurface damage in optical materials using the MRF wedge technique,” Proc. SPIE 5991, 599102 (2005).
[CrossRef]

Wuttig, A.

J. Steinert, S. Gliech, A. Wuttig, and A. Duparré, “Advanced methods for surface and subsurface defect characterization of optical components,” Proc. SPIE 4099, 290–298 (2000).
[CrossRef]

Xu, Q.

J. Wang, Y. Li, J. Han, Q. Xu, and Y. Guo, “Evaluating subsurface damage in optical glasses,” J. Eur. Opt. Soc. 6, 11001 (2011).

Yang, F.

J. C. Lambropoulos, S. D. Jacobs, B. Gillman, F. Yang, and J. Ruckman, “Subsurface damage in microgrinding optical glasses,” LLE Rev. 73, 45–49 (1997).

Zavada, J. M.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 182125 (1979).
[CrossRef]

Zhou, Y.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, and A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

Appl. Opt. (11)

C. F. Kranenberg and K. C. Jungling, “Subsurface damage identification in optically transparent materials using a nondestructive method,” Appl. Opt. 33, 4248–4253 (1994).
[CrossRef]

T. A. Germer, “Angular dependence and polarization of out-of-plane optical scattering from particulate contamination, subsurface defects, and surface microroughness,” Appl. Opt. 36, 8798–8805 (1997).
[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. A. Randi, J. C. Lambropoulos, and S. D. Jacobs, “Subsurface damage in some single crystalline optical materials,” Appl. Opt. 44, 2241–2249 (2005).
[CrossRef]

J. Wang and R. L. Maier, “Surface assessment of CaF2 deep-ultraviolet and vacuum-ultraviolet optical components by the quasi-Brewster angle technique,” Appl. Opt. 45, 5621–5628 (2006).
[CrossRef]

J. M. Bennett and R. J. King, “Effect of polishing technique on the roughness and residual surface film on fused quartz optical flats,” Appl. Opt. 9, 236–238 (1970).
[CrossRef]

W. B. Williams, B. A. Mullany, W. C. Parker, P. J. Moyer, and M. H. Randles, “Using quantum dots to tag subsurface damage in lapped and polished glass samples,” Appl. Opt. 48, 5155–5163 (2009).
[CrossRef]

S. Schröder, T. Herffurth, M. Trost, and A. Duparré, “Angle-resolved scattering and reflectance of extreme-ultraviolet multilayer coatings: measurement and analysis,” Appl. Opt. 49, 1503–1512 (2010).
[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, T. Herffurth, H. Blaschke, and A. Duparré, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, C164–C171 (2011).
[CrossRef]

T. Herffurth, S. Schröder, M. Trost, A. Duparré, and A. Tünnermann, “Comprehensive nanostructure and defect analysis using a simple 3D light-scatter sensor,” Appl. Opt. 52, 3279–3287 (2013).
[CrossRef]

Appl. Phys. Lett. (1)

T. Shibata, A. Ono, K. Kurihara, E. Makino, and M. Ikeda, “Cross-section transmission electron microscope observations of diamond-turned single-crystal Si surfaces,” Appl. Phys. Lett. 65, 2553–2555 (1994).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

Int. J. Fract. (1)

P. Ostojic and R. McPherson, “A review of indentation fracture theory: its development, principles and limitations,” Int. J. Fract. 33, 297–312 (1987).
[CrossRef]

J. Am. Ceram. Soc. (1)

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, and A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

J. Eur. Opt. Soc. (1)

J. Wang, Y. Li, J. Han, Q. Xu, and Y. Guo, “Evaluating subsurface damage in optical glasses,” J. Eur. Opt. Soc. 6, 11001 (2011).

J. Non-Cryst. Solids (3)

L. Wong, T. Suratwala, M. D. Feit, P. E. Miller, and R. Steele, “The effect of HF/NH4F etching on the morphology of surface fractures on fused silica,” J. Non-Cryst. Solids 355, 797–810 (2009).
[CrossRef]

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352, 5601–5617 (2006).
[CrossRef]

K. Saito, H. Kakiuchida, and A. J. Ikushima, “Investigation of the origin of the Rayleigh scattering in SiO2 glass,” J. Non-Cryst. Solids 222, 329–334 (1997).

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

LLE Rev. (1)

J. C. Lambropoulos, S. D. Jacobs, B. Gillman, F. Yang, and J. Ruckman, “Subsurface damage in microgrinding optical glasses,” LLE Rev. 73, 45–49 (1997).

Nucl. Instrum. Methods Phys. Res. B (1)

D. A. Lucca, C. J. Wetteland, A. Misra, M. J. Klopfstein, M. Nastasi, C. J. Maggiore, and J. R. Tesmer, “Assessment of subsurface damage in polished II–VI semiconductors by ion channeling,” Nucl. Instrum. Methods Phys. Res. B 219–220, 611–617 (2004).

Opt. Eng. (2)

R. G. Priest and S. R. Meier, “Polarimetric microfacet scattering theory with applications to absorptive and reflective surfaces,” Opt. Eng. 41, 988–993 (2002).
[CrossRef]

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 182125 (1979).
[CrossRef]

Opt. Express (5)

Phys. Rev. B (1)

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

Proc. SPIE (10)

M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser-induced surface damage,” Proc. SPIE 5273, 264–272 (2004).
[CrossRef]

J. Wang, R. L. Maier, and J. H. Bruning, “Surface characterization of optically polished CaF2 crystal by quasi-Brewster angle technique,” Proc. SPIE 5188, 106–114 (2003).

J. A. Menapace, P.-J. Davis, W. A. Steele, L. L. Wong, T. I. Suratwala, and P. E. Miller, “MRF applications: measurement of process-dependent subsurface damage in optical materials using the MRF wedge technique,” Proc. SPIE 5991, 599102 (2005).
[CrossRef]

J. Steinert, S. Gliech, A. Wuttig, and A. Duparré, “Advanced methods for surface and subsurface defect characterization of optical components,” Proc. SPIE 4099, 290–298 (2000).
[CrossRef]

T. Herffurth, S. Schröder, M. Trost, and A. Duparré, “Light scattering to detect imperfections relevant for laser-induced damage,” Proc. SPIE 8530, 85301B (2012).
[CrossRef]

J. B. Johnson, D. W. Kim, R. E. Parks, and J. H. Burge, “New approach for pre-polish grinding with low subsurface damage,” Proc. SPIE 8126, 81261E (2011).
[CrossRef]

M. Trost, S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “Roughness characterization of large EUV mirror optics by laser light scattering,” Proc. SPIE 8169, 81690P (2011).
[CrossRef]

S. Schröder, M. Trost, T. Feigl, J. E. Harvey, and A. Duparré, “Efficient specification and charaterization of surface roughness for extreme ultraviolet optics,” Proc. SPIE 7969, 79692C (2011).
[CrossRef]

S. Schröder, M. Trost, T. Herffurth, A. von Finck, and A. Duparré, “Sophisticated light scattering techniques from the VUV to the IR regions,” Proc. SPIE 8495, 84950V (2012).
[CrossRef]

M. Trost, S. Schröder, C. C. Lin, A. Duparré, and A. Tünnermann, “Roughness characterization of EUV multilayer coatings and ultra-smooth surfaces by light scattering,” Proc. SPIE 8501, 85010F (2012).
[CrossRef]

Other (3)

“A guide to reflectance coatings and materials,” (Labsphere, Inc.), http://www.labsphere.com .

Center of X-ray Optics, http://henke.lbl.gov/optical_constants/getdb2.html .

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

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Figures (11)

Fig. 1.
Fig. 1.

Schematic showing different light scattering mechanisms in a transparent substrate. Shown are scattering from surface roughness at the (1) front and (2) rear sides, (3) bulk scattering, and (4) SSD.

Fig. 2.
Fig. 2.

Basic geometry for the definitions of specular quantities and scattering.

Fig. 3.
Fig. 3.

Optical factor for surface roughness and SSD for fused silica at a wavelength of 395 nm. In the top row the incidence angle is 55.78° (Brewster angle). In the bottom row the incidence angle is 30°. The direction of the specular reflection is indicated by a white cross. Right: plot of the optical factor (solid line) and spatial frequency (dashed line) along the red-dashed circle in the corresponding 3D plots.

Fig. 4.
Fig. 4.

Cross-sectional images of ground glasses. (a) Schematic showing the sample preparation, (b) inclusions close to the surface, (c) chip-like fracture, (d) lateral crack, (e) radial cracks, and (f) Hertzian crack.

Fig. 5.
Fig. 5.

Degree of linear polarization of ground glasses.

Fig. 6.
Fig. 6.

PSD of sample BK7-1 before and after deposition of a 350 nm thick Si layer.

Fig. 7.
Fig. 7.

ARS measurements according to the measurement scheme shown in Fig. 3 of ground glasses for an incidence angle of 30°.

Fig. 8.
Fig. 8.

Roughness analysis of etched fused silica substrate. Left: roughness evolution as a function of etching depth (measurement area: 618 μm × 461 μm ). Right: schematic showing the etching process and corresponding topography measurements from white light interferometry.

Fig. 9.
Fig. 9.

ARS measurements of fused silica after etching according to the measurement scheme shown in Fig. 3. As the incidence angle, the Brewster angle 55.78° was used.

Fig. 10.
Fig. 10.

SSD characterization of CaF 2 . Left: ARS measurements according to measurement scheme shown in Fig. 3. As the incidence angle, the Brewster angle for CaF 2 (55.26°) at 395 nm was chosen. Right: atomic force microscopy (AFM) measurements of the surface topography (measurement area: 10 μm × 10 μm ) and corresponding rms-roughness values.

Fig. 11.
Fig. 11.

ARS measurements and simulations of two differently polished CaF 2 substrates at 13.5 nm.

Tables (1)

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Table 1. Roughness and SSD Depth of Ground Surfacesa

Equations (4)

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ARS ( θ n , φ n ) = Δ P s ( θ n , φ n ) Δ Ω s P i = 16 π 2 λ 4 cos θ i cos 2 θ n Q Surface PSD ( f ) ,
ζ ( θ n ) = ARS ( θ n ) ARS ( θ n ) ARS ( θ n ) + ARS ( θ n ) ,
Q pp Surface = | ( n 2 1 ) ( n 2 sin 2 θ n n 2 sin 2 θ i cos φ n n 2 sin θ i sin θ n ) ( n 2 cos θ i + n 2 sin 2 θ i ) ( n 2 cos θ n + n 2 sin 2 θ n ) | 2
Q pp SSD = | ( n 2 sin 2 θ n n 2 sin 2 θ i cos φ n sin θ i sin θ n ) ( n 2 cos θ i + n 2 sin 2 θ i ) ( n 2 cos θ n + n 2 sin 2 θ n ) | 2

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