Abstract

The intensity of scattered light is extremely sensitive to even small changes of illumination wavelength, incident angle, polarization states, or even the measurement position. To obtain light scattering distributions with varied parameters, time-consuming sequential measurement procedures are typically employed. Here, we propose a concept for the measurement of multiple properties at the same time. This is achieved by tailoring orthogonal frequency division multiplexing (OFDM) for light scattering measurement techniques to the required low inter-channel crosstalk performance. The concept is used for a highly-robust roughness and contamination characterization, to derive one-shot roughness information, as well as to characterize color and appearance.

© 2015 Optical Society of America

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References

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2014 (2)

S. Schröder, M. Trost, T. Herffurth, A. von Finck, and A. Duparré, “Light scattering of interference coatings from the IR to the EUV spectral regions,” Adv. Opt. Technol. 3, 113–120 (2014).

A. von Finck, T. Herffurth, S. Schröder, A. Duparré, and S. Sinzinger, “Characterization of optical coatings using a multisource table-top scatterometer,” Appl. Opt. 53(4), A259–A269 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (1)

V. B. Podobedov, C. C. Miller, and M. E. Nadal, “Performance of the NIST goniocolorimeter with a broad-band source and multichannel charged coupled device based spectrometer,” Rev. Sci. Instrum. 83(9), 093108 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (1)

W. Zhang, F. Wang, Z. Wang, and H. Wang, “Measuring of spectral BRDF using fiber optic spectrometer,” Proc. SPIE 7658, 76582P (2010).
[Crossref]

2009 (2)

S. Weinstein, “The history of orthogonal frequency division multiplexing,” IEEE Commun. Mag. 47(11), 26–35 (2009).
[Crossref]

E. Marin and R. Ivanov, “LIA in a nut shell: How can trigonometry help to understand lock-in amplifier operation?” Lat. Am. J. Phys. Educ. 3, 544–546 (2009).

2006 (1)

A. Le Lay and Y. Cornil, “REFLET scatterometer for 3D scattered light measurements to improve design and simulations in the automotive industry,” Proc. SPIE 6198, 619802 (2006).
[Crossref]

2005 (1)

P. Kadkhoda, H. Mädebach, and D. Ristau, “Spectral and angle resolved scatter investigation on optical functional surfaces and particles,” Proc. SPIE 5991, 59910D (2005).
[Crossref]

2003 (2)

T. Rinder and H. Rothe, “Development review of an angle resolved light scatter (ARS) sensor LARISSA,” Proc. SPIE 5189, 116–127 (2003).
[Crossref]

P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424(6950), 852–855 (2003).
[Crossref] [PubMed]

2002 (1)

1999 (2)

T. A. Germer, “Multidetector hemispherical polarized optical scattering instrument,” Proc. SPIE 3784, 304–313 (1999).
[Crossref]

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70(9), 3688–3695 (1999).
[Crossref]

1997 (1)

1996 (1)

1995 (1)

H. Sari, G. Karam, and I. Jeanclaude, “Transmission techniques for digital terrestrial tv broad-casting,” IEEE Commun. Mag. 33(2), 100–109 (1995).
[Crossref]

1994 (2)

C. Amra, “Light scattering from multilayer optics. II. Application to experiment,” J. Opt. Soc. Am. A 11(1), 211–226 (1994).
[Crossref]

H. Rothe, A. Kasper, P. Riedel, O. Specht, and W. Mueller, “Bidirectional reflectance distribution function (BRDF) sensing with fiber optics, programmable laser diodes, and high-resolution CCD arrays,” Proc. SPIE 2260, 83–92 (1994).
[Crossref]

1993 (1)

1992 (1)

1989 (1)

J. C. Stover, J. Rifkin, D. R. Cheever, K. H. Kirchner, and T. F. Schiff, “Comparison of wavelength scaling data to experiment,” Proc. SPIE 967, 44–49 (1989).
[Crossref]

1987 (1)

D. Cheever, F. Cad, K. A. Klicker, and J. C. Stover, “Design review of a unique complete angle-scatter instrument (CASI),” Proc. SPIE 818, 13–20 (1987).
[Crossref]

1978 (1)

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66(1), 51–83 (1978).
[Crossref]

1977 (2)

F. E. Nicodemus, J. C. Richmond, J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” NBS Monograph 160, 1–8 (1977).

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces by differential light scattering,” Opt. Eng. 16(4), 360–374 (1977).
[Crossref]

Al-Jumaily, G. A.

Amra, C.

Asmail, C. C.

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70(9), 3688–3695 (1999).
[Crossref]

Bennett, J. M.

Blaschke, H.

Cad, F.

D. Cheever, F. Cad, K. A. Klicker, and J. C. Stover, “Design review of a unique complete angle-scatter instrument (CASI),” Proc. SPIE 818, 13–20 (1987).
[Crossref]

Cheever, D.

D. Cheever, F. Cad, K. A. Klicker, and J. C. Stover, “Design review of a unique complete angle-scatter instrument (CASI),” Proc. SPIE 818, 13–20 (1987).
[Crossref]

Cheever, D. R.

J. C. Stover, J. Rifkin, D. R. Cheever, K. H. Kirchner, and T. F. Schiff, “Comparison of wavelength scaling data to experiment,” Proc. SPIE 967, 44–49 (1989).
[Crossref]

Church, E. L.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces by differential light scattering,” Opt. Eng. 16(4), 360–374 (1977).
[Crossref]

Cornil, Y.

A. Le Lay and Y. Cornil, “REFLET scatterometer for 3D scattered light measurements to improve design and simulations in the automotive industry,” Proc. SPIE 6198, 619802 (2006).
[Crossref]

Deumié, C.

Dumas, P.

Duparré, A.

A. von Finck, T. Herffurth, S. Schröder, A. Duparré, and S. Sinzinger, “Characterization of optical coatings using a multisource table-top scatterometer,” Appl. Opt. 53(4), A259–A269 (2014).
[Crossref] [PubMed]

S. Schröder, M. Trost, T. Herffurth, A. von Finck, and A. Duparré, “Light scattering of interference coatings from the IR to the EUV spectral regions,” Adv. Opt. Technol. 3, 113–120 (2014).

M. Trost, T. Herffurth, D. Schmitz, S. Schröder, A. Duparré, and A. Tünnermann, “Evaluation of subsurface damage by light scattering techniques,” Appl. Opt. 52(26), 6579–6588 (2013).
[Crossref] [PubMed]

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(14), 3279–3287 (2013).
[Crossref] [PubMed]

S. Schröder, T. Herffurth, H. Blaschke, and A. Duparré, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50(9), C164–C171 (2011).
[Crossref] [PubMed]

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(9), C148–C153 (2011).
[Crossref] [PubMed]

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(1), 154–171 (2002).
[Crossref] [PubMed]

Feigl, T.

Ferre-Borrull, J.

Germer, T. A.

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70(9), 3688–3695 (1999).
[Crossref]

T. A. Germer, “Multidetector hemispherical polarized optical scattering instrument,” Proc. SPIE 3784, 304–313 (1999).
[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(33), 8798–8805 (1997).
[Crossref] [PubMed]

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” NBS Monograph 160, 1–8 (1977).

Gliech, S.

Harris, F. J.

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66(1), 51–83 (1978).
[Crossref]

Herffurth, T.

Hsia, J.

F. E. Nicodemus, J. C. Richmond, J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” NBS Monograph 160, 1–8 (1977).

Ivanov, R.

E. Marin and R. Ivanov, “LIA in a nut shell: How can trigonometry help to understand lock-in amplifier operation?” Lat. Am. J. Phys. Educ. 3, 544–546 (2009).

Jacobson, R. D.

Jeanclaude, I.

H. Sari, G. Karam, and I. Jeanclaude, “Transmission techniques for digital terrestrial tv broad-casting,” IEEE Commun. Mag. 33(2), 100–109 (1995).
[Crossref]

Jenkinson, H. A.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces by differential light scattering,” Opt. Eng. 16(4), 360–374 (1977).
[Crossref]

Kadkhoda, P.

P. Kadkhoda, H. Mädebach, and D. Ristau, “Spectral and angle resolved scatter investigation on optical functional surfaces and particles,” Proc. SPIE 5991, 59910D (2005).
[Crossref]

Karam, G.

H. Sari, G. Karam, and I. Jeanclaude, “Transmission techniques for digital terrestrial tv broad-casting,” IEEE Commun. Mag. 33(2), 100–109 (1995).
[Crossref]

Kasper, A.

H. Rothe, A. Kasper, P. Riedel, O. Specht, and W. Mueller, “Bidirectional reflectance distribution function (BRDF) sensing with fiber optics, programmable laser diodes, and high-resolution CCD arrays,” Proc. SPIE 2260, 83–92 (1994).
[Crossref]

Kirchner, K. H.

J. C. Stover, J. Rifkin, D. R. Cheever, K. H. Kirchner, and T. F. Schiff, “Comparison of wavelength scaling data to experiment,” Proc. SPIE 967, 44–49 (1989).
[Crossref]

Klicker, K. A.

D. Cheever, F. Cad, K. A. Klicker, and J. C. Stover, “Design review of a unique complete angle-scatter instrument (CASI),” Proc. SPIE 818, 13–20 (1987).
[Crossref]

Le Lay, A.

A. Le Lay and Y. Cornil, “REFLET scatterometer for 3D scattered light measurements to improve design and simulations in the automotive industry,” Proc. SPIE 6198, 619802 (2006).
[Crossref]

Lequime, M.

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” NBS Monograph 160, 1–8 (1977).

Mädebach, H.

P. Kadkhoda, H. Mädebach, and D. Ristau, “Spectral and angle resolved scatter investigation on optical functional surfaces and particles,” Proc. SPIE 5991, 59910D (2005).
[Crossref]

Marin, E.

E. Marin and R. Ivanov, “LIA in a nut shell: How can trigonometry help to understand lock-in amplifier operation?” Lat. Am. J. Phys. Educ. 3, 544–546 (2009).

Mattsson, L.

McNeil, J. R.

Miller, C. C.

V. B. Podobedov, C. C. Miller, and M. E. Nadal, “Performance of the NIST goniocolorimeter with a broad-band source and multichannel charged coupled device based spectrometer,” Rev. Sci. Instrum. 83(9), 093108 (2012).
[Crossref] [PubMed]

Mueller, W.

H. Rothe, A. Kasper, P. Riedel, O. Specht, and W. Mueller, “Bidirectional reflectance distribution function (BRDF) sensing with fiber optics, programmable laser diodes, and high-resolution CCD arrays,” Proc. SPIE 2260, 83–92 (1994).
[Crossref]

Nadal, M. E.

V. B. Podobedov, C. C. Miller, and M. E. Nadal, “Performance of the NIST goniocolorimeter with a broad-band source and multichannel charged coupled device based spectrometer,” Rev. Sci. Instrum. 83(9), 093108 (2012).
[Crossref] [PubMed]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” NBS Monograph 160, 1–8 (1977).

Notni, G.

Podobedov, V. B.

V. B. Podobedov, C. C. Miller, and M. E. Nadal, “Performance of the NIST goniocolorimeter with a broad-band source and multichannel charged coupled device based spectrometer,” Rev. Sci. Instrum. 83(9), 093108 (2012).
[Crossref] [PubMed]

Richier, R.

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” NBS Monograph 160, 1–8 (1977).

Riedel, P.

H. Rothe, A. Kasper, P. Riedel, O. Specht, and W. Mueller, “Bidirectional reflectance distribution function (BRDF) sensing with fiber optics, programmable laser diodes, and high-resolution CCD arrays,” Proc. SPIE 2260, 83–92 (1994).
[Crossref]

Rifkin, J.

J. C. Stover, J. Rifkin, D. R. Cheever, K. H. Kirchner, and T. F. Schiff, “Comparison of wavelength scaling data to experiment,” Proc. SPIE 967, 44–49 (1989).
[Crossref]

Rinder, T.

T. Rinder and H. Rothe, “Development review of an angle resolved light scatter (ARS) sensor LARISSA,” Proc. SPIE 5189, 116–127 (2003).
[Crossref]

Ristau, D.

P. Kadkhoda, H. Mädebach, and D. Ristau, “Spectral and angle resolved scatter investigation on optical functional surfaces and particles,” Proc. SPIE 5991, 59910D (2005).
[Crossref]

Roche, P.

Rothe, H.

T. Rinder and H. Rothe, “Development review of an angle resolved light scatter (ARS) sensor LARISSA,” Proc. SPIE 5189, 116–127 (2003).
[Crossref]

H. Rothe, A. Kasper, P. Riedel, O. Specht, and W. Mueller, “Bidirectional reflectance distribution function (BRDF) sensing with fiber optics, programmable laser diodes, and high-resolution CCD arrays,” Proc. SPIE 2260, 83–92 (1994).
[Crossref]

Sambles, J. R.

P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424(6950), 852–855 (2003).
[Crossref] [PubMed]

Sari, H.

H. Sari, G. Karam, and I. Jeanclaude, “Transmission techniques for digital terrestrial tv broad-casting,” IEEE Commun. Mag. 33(2), 100–109 (1995).
[Crossref]

Schiff, T. F.

J. C. Stover, J. Rifkin, D. R. Cheever, K. H. Kirchner, and T. F. Schiff, “Comparison of wavelength scaling data to experiment,” Proc. SPIE 967, 44–49 (1989).
[Crossref]

Schmitz, D.

Schröder, S.

Sinzinger, S.

Specht, O.

H. Rothe, A. Kasper, P. Riedel, O. Specht, and W. Mueller, “Bidirectional reflectance distribution function (BRDF) sensing with fiber optics, programmable laser diodes, and high-resolution CCD arrays,” Proc. SPIE 2260, 83–92 (1994).
[Crossref]

Steinert, J.

Stover, J. C.

J. C. Stover, J. Rifkin, D. R. Cheever, K. H. Kirchner, and T. F. Schiff, “Comparison of wavelength scaling data to experiment,” Proc. SPIE 967, 44–49 (1989).
[Crossref]

D. Cheever, F. Cad, K. A. Klicker, and J. C. Stover, “Design review of a unique complete angle-scatter instrument (CASI),” Proc. SPIE 818, 13–20 (1987).
[Crossref]

Torricini, D.

Trost, M.

Tünnermann, A.

von Finck, A.

S. Schröder, M. Trost, T. Herffurth, A. von Finck, and A. Duparré, “Light scattering of interference coatings from the IR to the EUV spectral regions,” Adv. Opt. Technol. 3, 113–120 (2014).

A. von Finck, T. Herffurth, S. Schröder, A. Duparré, and S. Sinzinger, “Characterization of optical coatings using a multisource table-top scatterometer,” Appl. Opt. 53(4), A259–A269 (2014).
[Crossref] [PubMed]

Vukusic, P.

P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424(6950), 852–855 (2003).
[Crossref] [PubMed]

Wang, F.

W. Zhang, F. Wang, Z. Wang, and H. Wang, “Measuring of spectral BRDF using fiber optic spectrometer,” Proc. SPIE 7658, 76582P (2010).
[Crossref]

Wang, H.

W. Zhang, F. Wang, Z. Wang, and H. Wang, “Measuring of spectral BRDF using fiber optic spectrometer,” Proc. SPIE 7658, 76582P (2010).
[Crossref]

Wang, Z.

W. Zhang, F. Wang, Z. Wang, and H. Wang, “Measuring of spectral BRDF using fiber optic spectrometer,” Proc. SPIE 7658, 76582P (2010).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Light scattering geometry and definitions: 1 - sample, 2 - incident beam, 3 - reflected beam, 4 - transmitted beam, θi - angle of incidence, φi - azimuthal angle of incidence, θs - polar scattering angle, φs - azimuthal scattering angle, ΔΩs - solid angle, X / Y - sample coordinates.
Fig. 2
Fig. 2 (a) Proposed set-up for multiplexed light scattering measurements. (b) Selected ARS examples.
Fig. 3
Fig. 3 Transfer functions of analog and digital low-pass filters for τ = 50 ms.
Fig. 4
Fig. 4 Crosstalk from channel 2 into channel 1 as a function of the modulation frequency of channel 2.
Fig. 5
Fig. 5 Signal noise and signal distortion as a function of the signal ratio A2/A1 and for different demodulation parameters.
Fig. 6
Fig. 6 Schematic and photograph of the multichannel table-top scatterometer AlbatrossTT [7].
Fig. 7
Fig. 7 (a) Parallel ARS measurements at a polished aluminum surface with a nickel coating compared to conventional sequential ARS measurements. (b) The corresponding PSD functions indicate a non-topographic light scattering source, probably contamination.
Fig. 8
Fig. 8 Roughness characterization of a silicon substrate with two parallel wavelength channels.
Fig. 9
Fig. 9 Parallel BRDF measurements performed on a butterfly wing at three wavelengths in the reflection hemisphere (top). The measurements were combined to a single RGB color plot (bottom). Bottom left show a focus variation microscope measurement of the topography.

Equations (10)

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ARS( θ i , φ i , θ s , φ s ,X,Y,λ,p )= Δ P s ( θ i , φ i , θ s , φ s ,X,Y,λ,p ) P i Δ Ω s .
BSDF( θ i , φ i , θ s , φ s ,X,Y,λ,p )= ARS( θ i , φ i , θ s , φ s ,X,Y,λ,p ) cos θ s .
PSD( f x , f y )= λ 4 16 π 2 cos θ i cos 2 θ s Q ARS( φ s , θ s ),
U(t)= 4 π A 1 i=1 cos( (2i1) ω 1 t ) 2i1 + 4 π A 2 j=1 cos( (2j1) ω 2 t ) 2j1 .
X 1 (t)=U(t)cos( ω 1 t) = 2 π A 1 + 2 π A 1 cos(2 ω 1 t)+ 2 π A 1 i=2 cos(2i ω 1 t)+cos( (2i2) ω 1 t ) 2i1 . + 2 π A 2 j=1 cos( ((2j1) ω 2 ω 1 )t )+cos( ((2j1) ω 2 + ω 1 )t ) 2j1
V 1 (t)= 1 { { X 1 (t) }H(ω) }2 A 1 /π,
| H(ω) |=1/ 1+ ( ωτ ) 2 ,
| H rect,N (ω) |= ( sin(ωτ) ωτ ) N
ω 2 = ω 1 +Mπ/τforM{±1,±2,...}, ζ 2 = ζ 1 +M/(2τ)forM{±1,±2,...},
10 DR el < A 2 / A 1 < 10 DR el

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