Abstract

The derived two-dimensional autocorrelation function of speckles in the deep Fresnel region shows that it is related to the scattering of rough surface with the scattered intensity profile acting as the aperture function. We propose the method that is convenient for measuring surface parameters from the normalized autocorrelation function of speckles acquired with a microscopic imaging system. In experiment, a multi-scale behavior of the speckles has been identified, which is compatible with fractal character. With the speckle intensity data, we calculate the normalized autocorrelation function of the speckles and extract the roughness, the lateral correlation length and the roughness exponent of the random surface samples by fitting the expression to the autocorrelation function data. Comparison of the results with an atomic force microscopic measurements shows that our method has a satisfying accuracy.

© 2014 Optical Society of America

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  2. P. Córdoba-Torres, T. J. Mesquita, I. N. Bastos, R. P. Nogueira, “Complex dynamics during metal dissolution: from intrinsic to faceted anomalous scaling,” Phys. Rev. Lett. 102(5), 055504 (2009).
    [CrossRef] [PubMed]
  3. S. Zhang, L. Wu, R. Y. Yue, Z. K. Yan, H. R. Zhan, Y. Xiang, “Effects of Sb-doping on the grain growth of Cu(In, Ga)Se2 thin films fabricated by means of single-target sputtering,” Thin Solid Films 527, 137–140 (2013).
    [CrossRef]
  4. J. G. Goodberlet, H. Kavak, “Patterning sub-50 nm features with near-field embedded-amplitude masks,” Appl. Phys. Lett. 81(7), 1315–1317 (2002).
    [CrossRef]
  5. K. Jang, Y. Ishibashi, D. Iwata, H. Suganuma, T. Yamada, Y. Takemura, “Fabrication of ferromagnetic nanoconstriction using atomic force microscopy nanoscratching,” J. Nanosci. Nanotechnol. 11(12), 10945–10948 (2011).
    [CrossRef] [PubMed]
  6. Ö. F. Farsakoğlu, D. M. Zengin, H. Kocabaş, “Grinding process for beveling and lapping operations in lens manufacturing,” Appl. Opt. 39(10), 1541–1548 (2000).
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. C. F. Cheng, M. Liu, N. Y. Zhang, S. Y. Teng, H. S. Song, Z. Z. Xu, “Speckle intensity correlation in the diffraction region near rough surfaces and simulational experiments for extraction of surface parameters,” Europhys. Lett. 65(6), 779–784 (2004).
    [CrossRef]
  13. G. T. Liang, X. Li, M. N. Zhang, Z. H. Li, C. X. Liu, C. F. Cheng, “Experimental extraction of rough surface parameters from speckles in the deep Fresnel region with a scanning fibre-optic probe,” Eur. Phys. J. D 67, 030498 (2013).
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  19. Y. P. Zhao, I. Wu, C. F. Cheng, U. Block, G. C. Wang, T. M. Lu, “Characterization of random rough surfaces by in-plane light scattering,” J. Appl. Phys. 84(5), 2571–2582 (1998).
    [CrossRef]
  20. C. F. Cheng, C. X. Liu, S. Y. Teng, N. Y. Zhang, M. Liu, “Half-width of intensity profiles of light scattered from self-affine fractal random surfaces and simulational verifications,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 061104 (2002).
    [CrossRef] [PubMed]
  21. M. N. Zhang, Z. H. Li, X. Y. Chen, G. T. Liang, S. Y. Wang, S. Y. Teng, C. F. Cheng, “Evolutions of speckles on rough glass/silver surfaces with film thickness,” Opt. Express 21(7), 8831–8843 (2013).
    [CrossRef] [PubMed]

2013 (3)

G. T. Liang, X. Li, M. N. Zhang, Z. H. Li, C. X. Liu, C. F. Cheng, “Experimental extraction of rough surface parameters from speckles in the deep Fresnel region with a scanning fibre-optic probe,” Eur. Phys. J. D 67, 030498 (2013).

S. Zhang, L. Wu, R. Y. Yue, Z. K. Yan, H. R. Zhan, Y. Xiang, “Effects of Sb-doping on the grain growth of Cu(In, Ga)Se2 thin films fabricated by means of single-target sputtering,” Thin Solid Films 527, 137–140 (2013).
[CrossRef]

M. N. Zhang, Z. H. Li, X. Y. Chen, G. T. Liang, S. Y. Wang, S. Y. Teng, C. F. Cheng, “Evolutions of speckles on rough glass/silver surfaces with film thickness,” Opt. Express 21(7), 8831–8843 (2013).
[CrossRef] [PubMed]

2011 (1)

K. Jang, Y. Ishibashi, D. Iwata, H. Suganuma, T. Yamada, Y. Takemura, “Fabrication of ferromagnetic nanoconstriction using atomic force microscopy nanoscratching,” J. Nanosci. Nanotechnol. 11(12), 10945–10948 (2011).
[CrossRef] [PubMed]

2009 (1)

P. Córdoba-Torres, T. J. Mesquita, I. N. Bastos, R. P. Nogueira, “Complex dynamics during metal dissolution: from intrinsic to faceted anomalous scaling,” Phys. Rev. Lett. 102(5), 055504 (2009).
[CrossRef] [PubMed]

2007 (1)

R. Cerbino, “Correlations of light in the deep Fresnel region: An extended Van Cittert and Zernike theorem,” Phys. Rev. A 75(5), 053815 (2007).
[CrossRef]

2004 (1)

C. F. Cheng, M. Liu, N. Y. Zhang, S. Y. Teng, H. S. Song, Z. Z. Xu, “Speckle intensity correlation in the diffraction region near rough surfaces and simulational experiments for extraction of surface parameters,” Europhys. Lett. 65(6), 779–784 (2004).
[CrossRef]

2002 (3)

C. F. Cheng, C. X. Liu, S. Y. Teng, N. Y. Zhang, M. Liu, “Half-width of intensity profiles of light scattered from self-affine fractal random surfaces and simulational verifications,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 061104 (2002).
[CrossRef] [PubMed]

J. G. Goodberlet, H. Kavak, “Patterning sub-50 nm features with near-field embedded-amplitude masks,” Appl. Phys. Lett. 81(7), 1315–1317 (2002).
[CrossRef]

D. Brogioli, A. Vailati, M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81(22), 4109–4111 (2002).
[CrossRef]

2001 (1)

2000 (3)

M. Giglio, M. Carpineti, A. Vailati, “Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r),” Phys. Rev. Lett. 85(7), 1416–1419 (2000).
[CrossRef] [PubMed]

Ö. F. Farsakoğlu, D. M. Zengin, H. Kocabaş, “Grinding process for beveling and lapping operations in lens manufacturing,” Appl. Opt. 39(10), 1541–1548 (2000).
[CrossRef] [PubMed]

D. P. Qi, D. L. Liu, S. Y. Teng, N. Y. Zhang, C. F. Cheng, “Morphology analysis atomic force microscope and light scattering study for random scattering screens,” Acta Phys. Sin. 49(7), 1260–1266 (2000).

1998 (1)

Y. P. Zhao, I. Wu, C. F. Cheng, U. Block, G. C. Wang, T. M. Lu, “Characterization of random rough surfaces by in-plane light scattering,” J. Appl. Phys. 84(5), 2571–2582 (1998).
[CrossRef]

Bastos, I. N.

P. Córdoba-Torres, T. J. Mesquita, I. N. Bastos, R. P. Nogueira, “Complex dynamics during metal dissolution: from intrinsic to faceted anomalous scaling,” Phys. Rev. Lett. 102(5), 055504 (2009).
[CrossRef] [PubMed]

Block, U.

Y. P. Zhao, I. Wu, C. F. Cheng, U. Block, G. C. Wang, T. M. Lu, “Characterization of random rough surfaces by in-plane light scattering,” J. Appl. Phys. 84(5), 2571–2582 (1998).
[CrossRef]

Brogioli, D.

D. Brogioli, A. Vailati, M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81(22), 4109–4111 (2002).
[CrossRef]

M. Giglio, M. Carpineti, A. Vailati, D. Brogioli, “Near-field intensity correlations of scattered light,” Appl. Opt. 40(24), 4036–4040 (2001).
[CrossRef] [PubMed]

Carpineti, M.

M. Giglio, M. Carpineti, A. Vailati, D. Brogioli, “Near-field intensity correlations of scattered light,” Appl. Opt. 40(24), 4036–4040 (2001).
[CrossRef] [PubMed]

M. Giglio, M. Carpineti, A. Vailati, “Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r),” Phys. Rev. Lett. 85(7), 1416–1419 (2000).
[CrossRef] [PubMed]

Cerbino, R.

R. Cerbino, “Correlations of light in the deep Fresnel region: An extended Van Cittert and Zernike theorem,” Phys. Rev. A 75(5), 053815 (2007).
[CrossRef]

Chen, X. Y.

Cheng, C. F.

M. N. Zhang, Z. H. Li, X. Y. Chen, G. T. Liang, S. Y. Wang, S. Y. Teng, C. F. Cheng, “Evolutions of speckles on rough glass/silver surfaces with film thickness,” Opt. Express 21(7), 8831–8843 (2013).
[CrossRef] [PubMed]

G. T. Liang, X. Li, M. N. Zhang, Z. H. Li, C. X. Liu, C. F. Cheng, “Experimental extraction of rough surface parameters from speckles in the deep Fresnel region with a scanning fibre-optic probe,” Eur. Phys. J. D 67, 030498 (2013).

C. F. Cheng, M. Liu, N. Y. Zhang, S. Y. Teng, H. S. Song, Z. Z. Xu, “Speckle intensity correlation in the diffraction region near rough surfaces and simulational experiments for extraction of surface parameters,” Europhys. Lett. 65(6), 779–784 (2004).
[CrossRef]

C. F. Cheng, C. X. Liu, S. Y. Teng, N. Y. Zhang, M. Liu, “Half-width of intensity profiles of light scattered from self-affine fractal random surfaces and simulational verifications,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 061104 (2002).
[CrossRef] [PubMed]

D. P. Qi, D. L. Liu, S. Y. Teng, N. Y. Zhang, C. F. Cheng, “Morphology analysis atomic force microscope and light scattering study for random scattering screens,” Acta Phys. Sin. 49(7), 1260–1266 (2000).

Y. P. Zhao, I. Wu, C. F. Cheng, U. Block, G. C. Wang, T. M. Lu, “Characterization of random rough surfaces by in-plane light scattering,” J. Appl. Phys. 84(5), 2571–2582 (1998).
[CrossRef]

Córdoba-Torres, P.

P. Córdoba-Torres, T. J. Mesquita, I. N. Bastos, R. P. Nogueira, “Complex dynamics during metal dissolution: from intrinsic to faceted anomalous scaling,” Phys. Rev. Lett. 102(5), 055504 (2009).
[CrossRef] [PubMed]

Farsakoglu, Ö. F.

Giglio, M.

D. Brogioli, A. Vailati, M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81(22), 4109–4111 (2002).
[CrossRef]

M. Giglio, M. Carpineti, A. Vailati, D. Brogioli, “Near-field intensity correlations of scattered light,” Appl. Opt. 40(24), 4036–4040 (2001).
[CrossRef] [PubMed]

M. Giglio, M. Carpineti, A. Vailati, “Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r),” Phys. Rev. Lett. 85(7), 1416–1419 (2000).
[CrossRef] [PubMed]

Goodberlet, J. G.

J. G. Goodberlet, H. Kavak, “Patterning sub-50 nm features with near-field embedded-amplitude masks,” Appl. Phys. Lett. 81(7), 1315–1317 (2002).
[CrossRef]

Ishibashi, Y.

K. Jang, Y. Ishibashi, D. Iwata, H. Suganuma, T. Yamada, Y. Takemura, “Fabrication of ferromagnetic nanoconstriction using atomic force microscopy nanoscratching,” J. Nanosci. Nanotechnol. 11(12), 10945–10948 (2011).
[CrossRef] [PubMed]

Iwata, D.

K. Jang, Y. Ishibashi, D. Iwata, H. Suganuma, T. Yamada, Y. Takemura, “Fabrication of ferromagnetic nanoconstriction using atomic force microscopy nanoscratching,” J. Nanosci. Nanotechnol. 11(12), 10945–10948 (2011).
[CrossRef] [PubMed]

Jang, K.

K. Jang, Y. Ishibashi, D. Iwata, H. Suganuma, T. Yamada, Y. Takemura, “Fabrication of ferromagnetic nanoconstriction using atomic force microscopy nanoscratching,” J. Nanosci. Nanotechnol. 11(12), 10945–10948 (2011).
[CrossRef] [PubMed]

Kavak, H.

J. G. Goodberlet, H. Kavak, “Patterning sub-50 nm features with near-field embedded-amplitude masks,” Appl. Phys. Lett. 81(7), 1315–1317 (2002).
[CrossRef]

Kocabas, H.

Li, X.

G. T. Liang, X. Li, M. N. Zhang, Z. H. Li, C. X. Liu, C. F. Cheng, “Experimental extraction of rough surface parameters from speckles in the deep Fresnel region with a scanning fibre-optic probe,” Eur. Phys. J. D 67, 030498 (2013).

Li, Z. H.

G. T. Liang, X. Li, M. N. Zhang, Z. H. Li, C. X. Liu, C. F. Cheng, “Experimental extraction of rough surface parameters from speckles in the deep Fresnel region with a scanning fibre-optic probe,” Eur. Phys. J. D 67, 030498 (2013).

M. N. Zhang, Z. H. Li, X. Y. Chen, G. T. Liang, S. Y. Wang, S. Y. Teng, C. F. Cheng, “Evolutions of speckles on rough glass/silver surfaces with film thickness,” Opt. Express 21(7), 8831–8843 (2013).
[CrossRef] [PubMed]

Liang, G. T.

M. N. Zhang, Z. H. Li, X. Y. Chen, G. T. Liang, S. Y. Wang, S. Y. Teng, C. F. Cheng, “Evolutions of speckles on rough glass/silver surfaces with film thickness,” Opt. Express 21(7), 8831–8843 (2013).
[CrossRef] [PubMed]

G. T. Liang, X. Li, M. N. Zhang, Z. H. Li, C. X. Liu, C. F. Cheng, “Experimental extraction of rough surface parameters from speckles in the deep Fresnel region with a scanning fibre-optic probe,” Eur. Phys. J. D 67, 030498 (2013).

Liu, C. X.

G. T. Liang, X. Li, M. N. Zhang, Z. H. Li, C. X. Liu, C. F. Cheng, “Experimental extraction of rough surface parameters from speckles in the deep Fresnel region with a scanning fibre-optic probe,” Eur. Phys. J. D 67, 030498 (2013).

C. F. Cheng, C. X. Liu, S. Y. Teng, N. Y. Zhang, M. Liu, “Half-width of intensity profiles of light scattered from self-affine fractal random surfaces and simulational verifications,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 061104 (2002).
[CrossRef] [PubMed]

Liu, D. L.

D. P. Qi, D. L. Liu, S. Y. Teng, N. Y. Zhang, C. F. Cheng, “Morphology analysis atomic force microscope and light scattering study for random scattering screens,” Acta Phys. Sin. 49(7), 1260–1266 (2000).

Liu, M.

C. F. Cheng, M. Liu, N. Y. Zhang, S. Y. Teng, H. S. Song, Z. Z. Xu, “Speckle intensity correlation in the diffraction region near rough surfaces and simulational experiments for extraction of surface parameters,” Europhys. Lett. 65(6), 779–784 (2004).
[CrossRef]

C. F. Cheng, C. X. Liu, S. Y. Teng, N. Y. Zhang, M. Liu, “Half-width of intensity profiles of light scattered from self-affine fractal random surfaces and simulational verifications,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 061104 (2002).
[CrossRef] [PubMed]

Lu, T. M.

Y. P. Zhao, I. Wu, C. F. Cheng, U. Block, G. C. Wang, T. M. Lu, “Characterization of random rough surfaces by in-plane light scattering,” J. Appl. Phys. 84(5), 2571–2582 (1998).
[CrossRef]

Mesquita, T. J.

P. Córdoba-Torres, T. J. Mesquita, I. N. Bastos, R. P. Nogueira, “Complex dynamics during metal dissolution: from intrinsic to faceted anomalous scaling,” Phys. Rev. Lett. 102(5), 055504 (2009).
[CrossRef] [PubMed]

Nogueira, R. P.

P. Córdoba-Torres, T. J. Mesquita, I. N. Bastos, R. P. Nogueira, “Complex dynamics during metal dissolution: from intrinsic to faceted anomalous scaling,” Phys. Rev. Lett. 102(5), 055504 (2009).
[CrossRef] [PubMed]

Qi, D. P.

D. P. Qi, D. L. Liu, S. Y. Teng, N. Y. Zhang, C. F. Cheng, “Morphology analysis atomic force microscope and light scattering study for random scattering screens,” Acta Phys. Sin. 49(7), 1260–1266 (2000).

Song, H. S.

C. F. Cheng, M. Liu, N. Y. Zhang, S. Y. Teng, H. S. Song, Z. Z. Xu, “Speckle intensity correlation in the diffraction region near rough surfaces and simulational experiments for extraction of surface parameters,” Europhys. Lett. 65(6), 779–784 (2004).
[CrossRef]

Suganuma, H.

K. Jang, Y. Ishibashi, D. Iwata, H. Suganuma, T. Yamada, Y. Takemura, “Fabrication of ferromagnetic nanoconstriction using atomic force microscopy nanoscratching,” J. Nanosci. Nanotechnol. 11(12), 10945–10948 (2011).
[CrossRef] [PubMed]

Takemura, Y.

K. Jang, Y. Ishibashi, D. Iwata, H. Suganuma, T. Yamada, Y. Takemura, “Fabrication of ferromagnetic nanoconstriction using atomic force microscopy nanoscratching,” J. Nanosci. Nanotechnol. 11(12), 10945–10948 (2011).
[CrossRef] [PubMed]

Teng, S. Y.

M. N. Zhang, Z. H. Li, X. Y. Chen, G. T. Liang, S. Y. Wang, S. Y. Teng, C. F. Cheng, “Evolutions of speckles on rough glass/silver surfaces with film thickness,” Opt. Express 21(7), 8831–8843 (2013).
[CrossRef] [PubMed]

C. F. Cheng, M. Liu, N. Y. Zhang, S. Y. Teng, H. S. Song, Z. Z. Xu, “Speckle intensity correlation in the diffraction region near rough surfaces and simulational experiments for extraction of surface parameters,” Europhys. Lett. 65(6), 779–784 (2004).
[CrossRef]

C. F. Cheng, C. X. Liu, S. Y. Teng, N. Y. Zhang, M. Liu, “Half-width of intensity profiles of light scattered from self-affine fractal random surfaces and simulational verifications,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 061104 (2002).
[CrossRef] [PubMed]

D. P. Qi, D. L. Liu, S. Y. Teng, N. Y. Zhang, C. F. Cheng, “Morphology analysis atomic force microscope and light scattering study for random scattering screens,” Acta Phys. Sin. 49(7), 1260–1266 (2000).

Vailati, A.

D. Brogioli, A. Vailati, M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81(22), 4109–4111 (2002).
[CrossRef]

M. Giglio, M. Carpineti, A. Vailati, D. Brogioli, “Near-field intensity correlations of scattered light,” Appl. Opt. 40(24), 4036–4040 (2001).
[CrossRef] [PubMed]

M. Giglio, M. Carpineti, A. Vailati, “Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r),” Phys. Rev. Lett. 85(7), 1416–1419 (2000).
[CrossRef] [PubMed]

Wang, G. C.

Y. P. Zhao, I. Wu, C. F. Cheng, U. Block, G. C. Wang, T. M. Lu, “Characterization of random rough surfaces by in-plane light scattering,” J. Appl. Phys. 84(5), 2571–2582 (1998).
[CrossRef]

Wang, S. Y.

Wu, I.

Y. P. Zhao, I. Wu, C. F. Cheng, U. Block, G. C. Wang, T. M. Lu, “Characterization of random rough surfaces by in-plane light scattering,” J. Appl. Phys. 84(5), 2571–2582 (1998).
[CrossRef]

Wu, L.

S. Zhang, L. Wu, R. Y. Yue, Z. K. Yan, H. R. Zhan, Y. Xiang, “Effects of Sb-doping on the grain growth of Cu(In, Ga)Se2 thin films fabricated by means of single-target sputtering,” Thin Solid Films 527, 137–140 (2013).
[CrossRef]

Xiang, Y.

S. Zhang, L. Wu, R. Y. Yue, Z. K. Yan, H. R. Zhan, Y. Xiang, “Effects of Sb-doping on the grain growth of Cu(In, Ga)Se2 thin films fabricated by means of single-target sputtering,” Thin Solid Films 527, 137–140 (2013).
[CrossRef]

Xu, Z. Z.

C. F. Cheng, M. Liu, N. Y. Zhang, S. Y. Teng, H. S. Song, Z. Z. Xu, “Speckle intensity correlation in the diffraction region near rough surfaces and simulational experiments for extraction of surface parameters,” Europhys. Lett. 65(6), 779–784 (2004).
[CrossRef]

Yamada, T.

K. Jang, Y. Ishibashi, D. Iwata, H. Suganuma, T. Yamada, Y. Takemura, “Fabrication of ferromagnetic nanoconstriction using atomic force microscopy nanoscratching,” J. Nanosci. Nanotechnol. 11(12), 10945–10948 (2011).
[CrossRef] [PubMed]

Yan, Z. K.

S. Zhang, L. Wu, R. Y. Yue, Z. K. Yan, H. R. Zhan, Y. Xiang, “Effects of Sb-doping on the grain growth of Cu(In, Ga)Se2 thin films fabricated by means of single-target sputtering,” Thin Solid Films 527, 137–140 (2013).
[CrossRef]

Yue, R. Y.

S. Zhang, L. Wu, R. Y. Yue, Z. K. Yan, H. R. Zhan, Y. Xiang, “Effects of Sb-doping on the grain growth of Cu(In, Ga)Se2 thin films fabricated by means of single-target sputtering,” Thin Solid Films 527, 137–140 (2013).
[CrossRef]

Zengin, D. M.

Zhan, H. R.

S. Zhang, L. Wu, R. Y. Yue, Z. K. Yan, H. R. Zhan, Y. Xiang, “Effects of Sb-doping on the grain growth of Cu(In, Ga)Se2 thin films fabricated by means of single-target sputtering,” Thin Solid Films 527, 137–140 (2013).
[CrossRef]

Zhang, M. N.

M. N. Zhang, Z. H. Li, X. Y. Chen, G. T. Liang, S. Y. Wang, S. Y. Teng, C. F. Cheng, “Evolutions of speckles on rough glass/silver surfaces with film thickness,” Opt. Express 21(7), 8831–8843 (2013).
[CrossRef] [PubMed]

G. T. Liang, X. Li, M. N. Zhang, Z. H. Li, C. X. Liu, C. F. Cheng, “Experimental extraction of rough surface parameters from speckles in the deep Fresnel region with a scanning fibre-optic probe,” Eur. Phys. J. D 67, 030498 (2013).

Zhang, N. Y.

C. F. Cheng, M. Liu, N. Y. Zhang, S. Y. Teng, H. S. Song, Z. Z. Xu, “Speckle intensity correlation in the diffraction region near rough surfaces and simulational experiments for extraction of surface parameters,” Europhys. Lett. 65(6), 779–784 (2004).
[CrossRef]

C. F. Cheng, C. X. Liu, S. Y. Teng, N. Y. Zhang, M. Liu, “Half-width of intensity profiles of light scattered from self-affine fractal random surfaces and simulational verifications,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 061104 (2002).
[CrossRef] [PubMed]

D. P. Qi, D. L. Liu, S. Y. Teng, N. Y. Zhang, C. F. Cheng, “Morphology analysis atomic force microscope and light scattering study for random scattering screens,” Acta Phys. Sin. 49(7), 1260–1266 (2000).

Zhang, S.

S. Zhang, L. Wu, R. Y. Yue, Z. K. Yan, H. R. Zhan, Y. Xiang, “Effects of Sb-doping on the grain growth of Cu(In, Ga)Se2 thin films fabricated by means of single-target sputtering,” Thin Solid Films 527, 137–140 (2013).
[CrossRef]

Zhao, Y. P.

Y. P. Zhao, I. Wu, C. F. Cheng, U. Block, G. C. Wang, T. M. Lu, “Characterization of random rough surfaces by in-plane light scattering,” J. Appl. Phys. 84(5), 2571–2582 (1998).
[CrossRef]

Acta Phys. Sin. (1)

D. P. Qi, D. L. Liu, S. Y. Teng, N. Y. Zhang, C. F. Cheng, “Morphology analysis atomic force microscope and light scattering study for random scattering screens,” Acta Phys. Sin. 49(7), 1260–1266 (2000).

Appl. Opt. (2)

Appl. Phys. Lett. (2)

D. Brogioli, A. Vailati, M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81(22), 4109–4111 (2002).
[CrossRef]

J. G. Goodberlet, H. Kavak, “Patterning sub-50 nm features with near-field embedded-amplitude masks,” Appl. Phys. Lett. 81(7), 1315–1317 (2002).
[CrossRef]

Eur. Phys. J. D (1)

G. T. Liang, X. Li, M. N. Zhang, Z. H. Li, C. X. Liu, C. F. Cheng, “Experimental extraction of rough surface parameters from speckles in the deep Fresnel region with a scanning fibre-optic probe,” Eur. Phys. J. D 67, 030498 (2013).

Europhys. Lett. (1)

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[CrossRef] [PubMed]

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Phys. Rev. A (1)

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[CrossRef]

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[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic diagram for generating and observing the speckle fields in deep Fresnel region. (b) Diagram of the equivalent aperture contributing to the intensity of the point x = 0.

Fig. 2
Fig. 2

The scattered intensity profiles produced by random surfaces with different parameters.

Fig. 3
Fig. 3

Diagram of the optical setup for collecting the speckle fields in deep Fresnel region.

Fig. 4
Fig. 4

AFM images of three random surfaces labeled as No.1, No. 2 and No. 3, respectively.

Fig. 5
Fig. 5

Speckle patterns for the samples No.1, No.2 and No.3, respectively.

Fig. 6
Fig. 6

The curves of the normalized autocorrelation function produced by the samples No.1, No.2 and No.3, respectively, and the extracted values of surface parameters.

Fig. 7
Fig. 7

The curves of 1 γ I ( ρ ) vs. ρ produced by the samples No.1, No.2 and No.3, respectively, and the extracted fractal exponent α I of the speckle patterns. The insets show the probability density function curves of speckles for three samples.

Equations (15)

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U(x,y)= exp[ik(n1)h( x 0 , y 0 )] exp(ikr) r cosθd x 0 d y 0 ,
R I ( x 1 , y 1 ; x 2 , y 2 )=<I( x 1 , y 1 )I( x 2 , y 2 )>,
γ I ( x 1 , y 1 ; x 2 , y 2 )=[ R I ( x 1 , y 1 ; x 2 , y 2 )<I > 2 ]/<I > 2 ,
R I ( x 1 , y 1 ; x 2 , y 2 )=<I > 2 +|<U( x 1 , y 1 ) U ( x 2 , y 2 )> | 2 ,
γ I ( x 1 , y 1 ; x 2 , y 2 )= | <U( x 1 , y 1 ) U ( x 2 , y 2 )> | 2 /<I > 2 ,
R U ( x 1 , y 1 ; x 2 , y 2 )=<U( x 1 , y 1 ) U ( x 2 , y 2 )>,
<exp{ik(n1)[h( x 01 , y 01 )-h( x 02 , y 02 )]}> = p j [h( x 01 , y 01 ),h( x 02 , y 02 )]exp{ik(n1)[h( x 01 , y 01 )-h( x 02 , y 02 )]}d x 01 d y 01 d x 02 d y 02 ,
<exp{ik(n1)[h( x 01 , y 01 )-h( x 02 , y 02 )]}>=exp{-[k(n 1)] 2 [ w 2 - R h ( x 01 , y 01 ; x 02 , y 02 )]},
R U ( x 1 , y 1 ; x 2 , y 2 )= R U (Δx,Δy)= λ z 2 exp{-[k(n1 )] 2 [ w 2 - R h (Δ x 0 ,Δ y 0 )]} ×exp[i2π k p x 0 x)]exp[i2π k q y 0 y)]dΔ x 0 dΔ y 0 d k p dk,
I( k || )= exp{ [k(n1)] 2 [ w 2 R h (ρ)]}exp(i k || ρ) d 2 ρ =F T 1 [F(Δ x 0 ,Δ y 0 )],
γ I (Δx,Δy)=exp{-2[2π(n1)/λ ] 2 [ w 2 - R h (Δx,Δy)]},
R h (ρ)=<h( r 0 )h( r 0 +ρ)>= w 2 exp[ (ρ/ξ) 2α ],
H I x y ) = 2 σ I 2 [1 γ I x y )] ,
H I x y )= 2 σ I 2 {1 exp{-2[2 π ( n -1) / λ ] 2 [ w 2 - R h x , Δ y )]}} = 4 σ I 2 [2 π ( n -1) / λ ] 2 w 2 ( ρ / ξ ) 2 α ,
γ I ( ρ ) = exp[ ( ρ / ξ I ) 2 α I ] ,

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