Abstract

A far-field setup based on the fast and simultaneous recording of 1 million intensity angle-resolved-light-scattering patterns allows both to reconstruct surface topography and to cancel local defects in this topography. A spectral analysis is performed on measured data and allows to extract roughness and slopes mapping of a surface taking into account the spectral bandpass.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. M. Elson and J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31–47 (1979).
    [CrossRef]
  2. J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, 1999).
  3. C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
    [CrossRef]
  4. C. Amra, “Light scattering from multilayer optics. II. Application to experiment,” J. Opt. Soc. Am. A 11, 211–226 (1994).
    [CrossRef]
  5. 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]
  6. C. Stover, “Scatter, measurements and instrumentation,” in Optical Scattering: Measurement and Analysis, 2nd ed. (SPIE, 1995), Chap. 6.
  7. J. M. Elson, J. P. Rahn, and J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–3219 (1983).
    [CrossRef]
  8. 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]
  9. C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A 10, 365–374 (1993).
    [CrossRef]
  10. C. Amra, C. Grèzes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5503 (1993).
    [CrossRef]
  11. S. Maure, G. Albrand, and C. Amra, “Low-level scattering and localized defects,” Appl. Opt. 35, 5573–5582 (1996).
    [CrossRef]
  12. M. Lequime, M. Zerrad, C. Deumié, and C. Amra, “A goniometric light scattering instrument with high-resolution imaging,” Opt. Commun. 282, 1265–1273 (2009).
    [CrossRef]
  13. C. Amra, M. Zerrad, L. Siozade, G. Georges, and C. Deumié, “Partial polarization of light induced by random defects at surfaces or bulks,” Opt. Express 16, 10372–10383 (2008).
    [CrossRef]
  14. T. A. Germer, C. Asmail, and B. W. Scheer, “Polarization of out of plane scattering from microrough silicon,” Opt. Lett. 22, 1284–1286 (1997).
    [CrossRef]
  15. O. Gilbert, C. Deumié, and C. Amra, “Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks,” Opt. Express 13, 2403–2418 (2005).
    [CrossRef]
  16. M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
    [CrossRef]
  17. M. Zerrad, M. Lequime, C. Deumie, and C. Amra, “CCD-ARS set-up: a comprehensive and fast high-sensitivity characterization tool for optical components,” Proc. SPIE 7718, 77180A (2010).
    [CrossRef]

2011

2010

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
[CrossRef]

M. Zerrad, M. Lequime, C. Deumie, and C. Amra, “CCD-ARS set-up: a comprehensive and fast high-sensitivity characterization tool for optical components,” Proc. SPIE 7718, 77180A (2010).
[CrossRef]

2009

M. Lequime, M. Zerrad, C. Deumié, and C. Amra, “A goniometric light scattering instrument with high-resolution imaging,” Opt. Commun. 282, 1265–1273 (2009).
[CrossRef]

2008

2005

2002

1997

1996

1994

1993

1983

1979

Albrand, G.

Amra, C.

M. Zerrad, M. Lequime, C. Deumie, and C. Amra, “CCD-ARS set-up: a comprehensive and fast high-sensitivity characterization tool for optical components,” Proc. SPIE 7718, 77180A (2010).
[CrossRef]

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
[CrossRef]

M. Lequime, M. Zerrad, C. Deumié, and C. Amra, “A goniometric light scattering instrument with high-resolution imaging,” Opt. Commun. 282, 1265–1273 (2009).
[CrossRef]

C. Amra, M. Zerrad, L. Siozade, G. Georges, and C. Deumié, “Partial polarization of light induced by random defects at surfaces or bulks,” Opt. Express 16, 10372–10383 (2008).
[CrossRef]

O. Gilbert, C. Deumié, and C. Amra, “Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks,” Opt. Express 13, 2403–2418 (2005).
[CrossRef]

S. Maure, G. Albrand, and C. Amra, “Low-level scattering and localized defects,” Appl. Opt. 35, 5573–5582 (1996).
[CrossRef]

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

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

Asmail, C.

Bennett, J. M.

Blaschke, H.

Bruel, L.

Deumie, C.

M. Zerrad, M. Lequime, C. Deumie, and C. Amra, “CCD-ARS set-up: a comprehensive and fast high-sensitivity characterization tool for optical components,” Proc. SPIE 7718, 77180A (2010).
[CrossRef]

Deumié, C.

Duparré, A.

Elson, J. M.

Ferre-Borrull, J.

Georges, G.

Germer, T. A.

Gilbert, O.

Gliech, S.

Grèzes-Besset, C.

Herffurth, T.

Lequime, M.

M. Zerrad, M. Lequime, C. Deumie, and C. Amra, “CCD-ARS set-up: a comprehensive and fast high-sensitivity characterization tool for optical components,” Proc. SPIE 7718, 77180A (2010).
[CrossRef]

M. Lequime, M. Zerrad, C. Deumié, and C. Amra, “A goniometric light scattering instrument with high-resolution imaging,” Opt. Commun. 282, 1265–1273 (2009).
[CrossRef]

Mattsson, L.

J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, 1999).

Maure, S.

Notni, G.

Rahn, J. P.

Scheer, B. W.

Schröder, S.

Siozade, L.

Soriano, G.

Sorrentini, J.

Steinert, J.

Stover, C.

C. Stover, “Scatter, measurements and instrumentation,” in Optical Scattering: Measurement and Analysis, 2nd ed. (SPIE, 1995), Chap. 6.

Zerrad, M.

M. Zerrad, M. Lequime, C. Deumie, and C. Amra, “CCD-ARS set-up: a comprehensive and fast high-sensitivity characterization tool for optical components,” Proc. SPIE 7718, 77180A (2010).
[CrossRef]

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
[CrossRef]

M. Lequime, M. Zerrad, C. Deumié, and C. Amra, “A goniometric light scattering instrument with high-resolution imaging,” Opt. Commun. 282, 1265–1273 (2009).
[CrossRef]

C. Amra, M. Zerrad, L. Siozade, G. Georges, and C. Deumié, “Partial polarization of light induced by random defects at surfaces or bulks,” Opt. Express 16, 10372–10383 (2008).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

M. Lequime, M. Zerrad, C. Deumié, and C. Amra, “A goniometric light scattering instrument with high-resolution imaging,” Opt. Commun. 282, 1265–1273 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

M. Zerrad, M. Lequime, C. Deumie, and C. Amra, “CCD-ARS set-up: a comprehensive and fast high-sensitivity characterization tool for optical components,” Proc. SPIE 7718, 77180A (2010).
[CrossRef]

Other

J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, 1999).

C. Stover, “Scatter, measurements and instrumentation,” in Optical Scattering: Measurement and Analysis, 2nd ed. (SPIE, 1995), Chap. 6.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1.
Fig. 1.

Spatially and angularly resolved scatterometer.

Fig. 2.
Fig. 2.

Intensity ARS patterns measured at some illumination incidences. The radius is 18 mm for each image.

Fig. 3.
Fig. 3.

Examples of roughness spectra determined from the measurements of Fig. 2.

Fig. 4.
Fig. 4.

Mapping of rms roughness quantified with light scattering in the far field. The measured area is 18 mm (top figure) and 3 mm (zoom, bottom figure). Roughness is given in reference to the median plane.

Fig. 5.
Fig. 5.

Topography histogram of the retrieved surface given in Fig. 4. The abscissa is for the roughness value δij taken by each pixel. The width of the curve is the general roughness (root mean square) of the reconstructed surface.

Fig. 6.
Fig. 6.

Slope topography.

Fig. 7.
Fig. 7.

Slopes histogram.

Fig. 8.
Fig. 8.

Histograms of the spectrum over the pixels, measured for different frequencies.

Fig. 9.
Fig. 9.

Examples of spectra from the polished sample.

Fig. 10.
Fig. 10.

Intrinsic roughness topography for the silicon sample.

Fig. 11.
Fig. 11.

Local defects mapping for the silicon sample.

Fig. 12.
Fig. 12.

Scattering histogram versus local defects.

Equations (19)

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

δ=1Srh2(r)drλ
h^(σ)=14π2rh(r)exp(jσ·r)dr
σ=kcosθ|cosφsinφ
E(σ,σ0)=C(σ,σ0)·h^(σσ0),
E(θ,i)=C(θ,i)·h^(θ,i).
I(σ,σ0)=D(σ,σ0)·γ(σσ0)
γ(σ)=4π2S|h^(σ)|2.
γ(σσ0)=I(σ,σ0)/D(σ,σ0).
δ2=βγ(β)dβ.
β=σσ0.
k(1+sini)β=ksinθksinik(1sini),
i=π20|β|2k.
δ2=σγ(σ)dσ=σ,φσγ(σ,φ)dσdφ=2πσσγ*(σ)dσ
δ2=2πk2θγ*(θ)cosθsinθdθ.
δij2=2πk2θγij*(θ)cosθsinθdθ.
β=(σσ0)x=σ0x
ksiniminβsinimax.
1λsiniminβ1λsinimax2·104nm1β1·101nm1.
sij2=1Sijx,y[(hx)2+(hy)2]dxdy=2πσσ3γij*(σ)dσ.

Metrics