Abstract

The near-field optical images have been traditionally analyzed by Fourier analysis and, recently, by wavelet analysis. Those data are nonstationary, which means that their spectral content varies with time, owing to the scanning-probe recording process; therefore time–frequency representations are, potentially, powerful tools for local characteristics extraction or shape separation, since they distribute the energy of the analyzed signal over the time and frequency variables and faithfully depict the signal local behavior. In this study we show that Cohen’s class time–frequency distributions and their modified version by the reassignment method are appropriate tools for the analysis of near-field optical data. We demonstrate this by using these tools first on simulated data and second on experimental near-field optical images. Within this context we observe that time–frequency analysis allows one to easily characterize local frequencies, which involves a possible separation of relevant optical signal from artifacts.

© 2000 Optical Society of America

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  1. D. Courjon, F. Baida, C. Bainier, D. Van Labeke, D. Barchiesi, “Near field instrumentation,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO ASI Series E: Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 59–78.
  2. J. L. Kann, T. D. Milster, F. F. Froehlich, R. W. Ziolkowski, J. B. Judkins, “Linear behavior of near-field optical system,” J. Opt. Soc. Am. A 12, 1677–1682 (1995).
    [CrossRef]
  3. R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of transfer function,” Opt. Commun. 116, 316–321 (1995); erratum, 120, 371 (1995).
    [CrossRef]
  4. D. Barchiesi, “Pseudo modulation transfer function in reflection scanning near-field optical microscopy,” Opt. Commun. 154, 167–172 (1998).
    [CrossRef]
  5. S. I. Bozhevolnyi, “Topographical artifacts and optical resolution in near-field optical microscopy,” J. Opt. Soc. Am. B 14, 2254–2259 (1997).
    [CrossRef]
  6. S. Davy, D. Barchiesi, M. Spajer, D. Courjon, “Spectroscopic study of resonant dielectric structures in near-field,” Eur. Phys. J. (Appl. Phys.) 5, 277–281 (1999).
    [CrossRef]
  7. B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
    [CrossRef]
  8. C. Girard, D. Courjon, “The role of scanning mode in near-field optical microscopy,” Surf. Sci. 382, 9–18 (1997).
    [CrossRef]
  9. D. Barchiesi, T. Gharbi, “Local spectral information in the near field with wavelet analysis and entropy,” Appl. Opt. 38, 6587–6596 (1999).
    [CrossRef]
  10. D. Barchiesi, “Application of Fourier algorithm to near field optical images: local resolution estimation,” Microsc. Microanal. Microstruct. 8, 1–10 (1997).
    [CrossRef]
  11. D. Barchiesi, “Characterization of R-SNOM and STOM/PSTM working in preliminary approach constant height mode,” J. Microsc. (Oxford) 194, 299–306 (1999).
    [CrossRef]
  12. T. Gharbi, D. Barchiesi, “Local signal processing to evaluate resolution in SNOM images, using 1D wavelets,” Opt. Commun. 177, 85–93 (2000).
    [CrossRef]
  13. D. Barchiesi, T. Gharbi, “Wavelet analysis of near-field data and the resolution problem,” Eur. Phys. J. (Appl. Phys.) 5, 297–301 (1999).
    [CrossRef]
  14. L. Cohen, “Time–frequency distribution—a review,” Proc. IEEE 77, 941–981 (1989).
    [CrossRef]
  15. T. A. C. M. Claasen, W. F. G. Mecklenbräuker, “The Wigner distribution—a tool for time–frequency signal analysis,” Philips J. Res. 35, 217–250 (1980).
  16. F. Auger, P. Flandrin, “Improving the readability of time frequency and time-scale representations by the reassignment method,” IEEE Trans. Signal Process. 43, 1068–1089 (1995).
    [CrossRef]
  17. D. Barchiesi, “A 3-D multilayer model of scattering by nanostructures. Application to the optimisation of thin coated nano-sources,” Opt. Commun. 126, 7–13 (1996).
    [CrossRef]
  18. D. Van Labeke, D. Barchiesi, “Scanning tunneling optical microscopy: a theoretical macroscopic approach,” J. Opt. Soc. Am. A 9, 732–739 (1992).
    [CrossRef]
  19. D. Barchiesi, O. Bergossi, C. Pieralli, M. Spajer, “Reflection scanning near-field optical microscopy (R-SNOM) in constant height mode with a dielectric probe: image interpretation and resolution for high topographic variations,” Ultramicroscopy 71, 361–370 (1998).
    [CrossRef]
  20. D. Barchiesi, O. Bergossi, M. Spajer, C. Pieralli, “Image resolution in reflection scanning near-field optical microscopy using shear-force feedback: characterization with a spline and Fourier spectrum,” Appl. Opt. 36, 2171–2177 (1997).
    [CrossRef] [PubMed]
  21. O. Bergossi, M. Spajer, “Scanning local probe interferometer and reflectometer: application to very low relief objects,” in Interferometry ’94: Interferometric Fiber Sensing, E. Udd, R. P. Tatam, eds., Proc. SPIE2341, 238–248 (1994).
  22. H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near field optical microscope,” Eur. Phys. J. (Appl. Phys.) 5, 289–295 (1999).
    [CrossRef]
  23. F. Zenhausern, M. O’Boyle, H. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 20, 1924–1926 (1994).
  24. R. Bachelot, P. Gleyzes, A. Boccara, “Near-field optical microscope based on local perturbation of a diffraction spot,” Opt. Lett. 20, 1924–1926 (1995).
    [CrossRef] [PubMed]
  25. G. Wurtz, R. Bachelot, P. Royer, “Reflection-mode apertureless scanning near-field optical microscope developed from a commercial scanning probe microscope,” Rev. Sci. Instrum. 69, 1735–1743 (1998).
    [CrossRef]

2000 (1)

T. Gharbi, D. Barchiesi, “Local signal processing to evaluate resolution in SNOM images, using 1D wavelets,” Opt. Commun. 177, 85–93 (2000).
[CrossRef]

1999 (5)

D. Barchiesi, T. Gharbi, “Wavelet analysis of near-field data and the resolution problem,” Eur. Phys. J. (Appl. Phys.) 5, 297–301 (1999).
[CrossRef]

D. Barchiesi, “Characterization of R-SNOM and STOM/PSTM working in preliminary approach constant height mode,” J. Microsc. (Oxford) 194, 299–306 (1999).
[CrossRef]

S. Davy, D. Barchiesi, M. Spajer, D. Courjon, “Spectroscopic study of resonant dielectric structures in near-field,” Eur. Phys. J. (Appl. Phys.) 5, 277–281 (1999).
[CrossRef]

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near field optical microscope,” Eur. Phys. J. (Appl. Phys.) 5, 289–295 (1999).
[CrossRef]

D. Barchiesi, T. Gharbi, “Local spectral information in the near field with wavelet analysis and entropy,” Appl. Opt. 38, 6587–6596 (1999).
[CrossRef]

1998 (3)

G. Wurtz, R. Bachelot, P. Royer, “Reflection-mode apertureless scanning near-field optical microscope developed from a commercial scanning probe microscope,” Rev. Sci. Instrum. 69, 1735–1743 (1998).
[CrossRef]

D. Barchiesi, “Pseudo modulation transfer function in reflection scanning near-field optical microscopy,” Opt. Commun. 154, 167–172 (1998).
[CrossRef]

D. Barchiesi, O. Bergossi, C. Pieralli, M. Spajer, “Reflection scanning near-field optical microscopy (R-SNOM) in constant height mode with a dielectric probe: image interpretation and resolution for high topographic variations,” Ultramicroscopy 71, 361–370 (1998).
[CrossRef]

1997 (5)

B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
[CrossRef]

C. Girard, D. Courjon, “The role of scanning mode in near-field optical microscopy,” Surf. Sci. 382, 9–18 (1997).
[CrossRef]

D. Barchiesi, “Application of Fourier algorithm to near field optical images: local resolution estimation,” Microsc. Microanal. Microstruct. 8, 1–10 (1997).
[CrossRef]

S. I. Bozhevolnyi, “Topographical artifacts and optical resolution in near-field optical microscopy,” J. Opt. Soc. Am. B 14, 2254–2259 (1997).
[CrossRef]

D. Barchiesi, O. Bergossi, M. Spajer, C. Pieralli, “Image resolution in reflection scanning near-field optical microscopy using shear-force feedback: characterization with a spline and Fourier spectrum,” Appl. Opt. 36, 2171–2177 (1997).
[CrossRef] [PubMed]

1996 (1)

D. Barchiesi, “A 3-D multilayer model of scattering by nanostructures. Application to the optimisation of thin coated nano-sources,” Opt. Commun. 126, 7–13 (1996).
[CrossRef]

1995 (4)

F. Auger, P. Flandrin, “Improving the readability of time frequency and time-scale representations by the reassignment method,” IEEE Trans. Signal Process. 43, 1068–1089 (1995).
[CrossRef]

R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of transfer function,” Opt. Commun. 116, 316–321 (1995); erratum, 120, 371 (1995).
[CrossRef]

J. L. Kann, T. D. Milster, F. F. Froehlich, R. W. Ziolkowski, J. B. Judkins, “Linear behavior of near-field optical system,” J. Opt. Soc. Am. A 12, 1677–1682 (1995).
[CrossRef]

R. Bachelot, P. Gleyzes, A. Boccara, “Near-field optical microscope based on local perturbation of a diffraction spot,” Opt. Lett. 20, 1924–1926 (1995).
[CrossRef] [PubMed]

1994 (1)

F. Zenhausern, M. O’Boyle, H. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 20, 1924–1926 (1994).

1992 (1)

1989 (1)

L. Cohen, “Time–frequency distribution—a review,” Proc. IEEE 77, 941–981 (1989).
[CrossRef]

1980 (1)

T. A. C. M. Claasen, W. F. G. Mecklenbräuker, “The Wigner distribution—a tool for time–frequency signal analysis,” Philips J. Res. 35, 217–250 (1980).

Auger, F.

F. Auger, P. Flandrin, “Improving the readability of time frequency and time-scale representations by the reassignment method,” IEEE Trans. Signal Process. 43, 1068–1089 (1995).
[CrossRef]

Bachelot, R.

G. Wurtz, R. Bachelot, P. Royer, “Reflection-mode apertureless scanning near-field optical microscope developed from a commercial scanning probe microscope,” Rev. Sci. Instrum. 69, 1735–1743 (1998).
[CrossRef]

R. Bachelot, P. Gleyzes, A. Boccara, “Near-field optical microscope based on local perturbation of a diffraction spot,” Opt. Lett. 20, 1924–1926 (1995).
[CrossRef] [PubMed]

Baida, F.

D. Courjon, F. Baida, C. Bainier, D. Van Labeke, D. Barchiesi, “Near field instrumentation,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO ASI Series E: Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 59–78.

Bainier, C.

D. Courjon, F. Baida, C. Bainier, D. Van Labeke, D. Barchiesi, “Near field instrumentation,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO ASI Series E: Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 59–78.

Barchiesi, D.

T. Gharbi, D. Barchiesi, “Local signal processing to evaluate resolution in SNOM images, using 1D wavelets,” Opt. Commun. 177, 85–93 (2000).
[CrossRef]

D. Barchiesi, T. Gharbi, “Local spectral information in the near field with wavelet analysis and entropy,” Appl. Opt. 38, 6587–6596 (1999).
[CrossRef]

S. Davy, D. Barchiesi, M. Spajer, D. Courjon, “Spectroscopic study of resonant dielectric structures in near-field,” Eur. Phys. J. (Appl. Phys.) 5, 277–281 (1999).
[CrossRef]

D. Barchiesi, T. Gharbi, “Wavelet analysis of near-field data and the resolution problem,” Eur. Phys. J. (Appl. Phys.) 5, 297–301 (1999).
[CrossRef]

D. Barchiesi, “Characterization of R-SNOM and STOM/PSTM working in preliminary approach constant height mode,” J. Microsc. (Oxford) 194, 299–306 (1999).
[CrossRef]

D. Barchiesi, O. Bergossi, C. Pieralli, M. Spajer, “Reflection scanning near-field optical microscopy (R-SNOM) in constant height mode with a dielectric probe: image interpretation and resolution for high topographic variations,” Ultramicroscopy 71, 361–370 (1998).
[CrossRef]

D. Barchiesi, “Pseudo modulation transfer function in reflection scanning near-field optical microscopy,” Opt. Commun. 154, 167–172 (1998).
[CrossRef]

D. Barchiesi, “Application of Fourier algorithm to near field optical images: local resolution estimation,” Microsc. Microanal. Microstruct. 8, 1–10 (1997).
[CrossRef]

D. Barchiesi, O. Bergossi, M. Spajer, C. Pieralli, “Image resolution in reflection scanning near-field optical microscopy using shear-force feedback: characterization with a spline and Fourier spectrum,” Appl. Opt. 36, 2171–2177 (1997).
[CrossRef] [PubMed]

D. Barchiesi, “A 3-D multilayer model of scattering by nanostructures. Application to the optimisation of thin coated nano-sources,” Opt. Commun. 126, 7–13 (1996).
[CrossRef]

D. Van Labeke, D. Barchiesi, “Scanning tunneling optical microscopy: a theoretical macroscopic approach,” J. Opt. Soc. Am. A 9, 732–739 (1992).
[CrossRef]

D. Courjon, F. Baida, C. Bainier, D. Van Labeke, D. Barchiesi, “Near field instrumentation,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO ASI Series E: Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 59–78.

Bergossi, O.

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near field optical microscope,” Eur. Phys. J. (Appl. Phys.) 5, 289–295 (1999).
[CrossRef]

D. Barchiesi, O. Bergossi, C. Pieralli, M. Spajer, “Reflection scanning near-field optical microscopy (R-SNOM) in constant height mode with a dielectric probe: image interpretation and resolution for high topographic variations,” Ultramicroscopy 71, 361–370 (1998).
[CrossRef]

D. Barchiesi, O. Bergossi, M. Spajer, C. Pieralli, “Image resolution in reflection scanning near-field optical microscopy using shear-force feedback: characterization with a spline and Fourier spectrum,” Appl. Opt. 36, 2171–2177 (1997).
[CrossRef] [PubMed]

O. Bergossi, M. Spajer, “Scanning local probe interferometer and reflectometer: application to very low relief objects,” in Interferometry ’94: Interferometric Fiber Sensing, E. Udd, R. P. Tatam, eds., Proc. SPIE2341, 238–248 (1994).

Bielefeldt, H.

B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
[CrossRef]

Boccara, A.

Bozhevolnyi, S. I.

Carminati, R.

R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of transfer function,” Opt. Commun. 116, 316–321 (1995); erratum, 120, 371 (1995).
[CrossRef]

Claasen, T. A. C. M.

T. A. C. M. Claasen, W. F. G. Mecklenbräuker, “The Wigner distribution—a tool for time–frequency signal analysis,” Philips J. Res. 35, 217–250 (1980).

Cohen, L.

L. Cohen, “Time–frequency distribution—a review,” Proc. IEEE 77, 941–981 (1989).
[CrossRef]

Courjon, D.

S. Davy, D. Barchiesi, M. Spajer, D. Courjon, “Spectroscopic study of resonant dielectric structures in near-field,” Eur. Phys. J. (Appl. Phys.) 5, 277–281 (1999).
[CrossRef]

C. Girard, D. Courjon, “The role of scanning mode in near-field optical microscopy,” Surf. Sci. 382, 9–18 (1997).
[CrossRef]

D. Courjon, F. Baida, C. Bainier, D. Van Labeke, D. Barchiesi, “Near field instrumentation,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO ASI Series E: Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 59–78.

Davy, S.

S. Davy, D. Barchiesi, M. Spajer, D. Courjon, “Spectroscopic study of resonant dielectric structures in near-field,” Eur. Phys. J. (Appl. Phys.) 5, 277–281 (1999).
[CrossRef]

Flandrin, P.

F. Auger, P. Flandrin, “Improving the readability of time frequency and time-scale representations by the reassignment method,” IEEE Trans. Signal Process. 43, 1068–1089 (1995).
[CrossRef]

Froehlich, F. F.

Gharbi, T.

T. Gharbi, D. Barchiesi, “Local signal processing to evaluate resolution in SNOM images, using 1D wavelets,” Opt. Commun. 177, 85–93 (2000).
[CrossRef]

D. Barchiesi, T. Gharbi, “Local spectral information in the near field with wavelet analysis and entropy,” Appl. Opt. 38, 6587–6596 (1999).
[CrossRef]

D. Barchiesi, T. Gharbi, “Wavelet analysis of near-field data and the resolution problem,” Eur. Phys. J. (Appl. Phys.) 5, 297–301 (1999).
[CrossRef]

Girard, C.

C. Girard, D. Courjon, “The role of scanning mode in near-field optical microscopy,” Surf. Sci. 382, 9–18 (1997).
[CrossRef]

Gleyzes, P.

Greffet, J.-J.

R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of transfer function,” Opt. Commun. 116, 316–321 (1995); erratum, 120, 371 (1995).
[CrossRef]

Hecht, B.

B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
[CrossRef]

Hudlet, S.

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near field optical microscope,” Eur. Phys. J. (Appl. Phys.) 5, 289–295 (1999).
[CrossRef]

Inouye, Y.

B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
[CrossRef]

Judkins, J. B.

Kann, J. L.

Mackay, K.

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near field optical microscope,” Eur. Phys. J. (Appl. Phys.) 5, 289–295 (1999).
[CrossRef]

Mecklenbräuker, W. F. G.

T. A. C. M. Claasen, W. F. G. Mecklenbräuker, “The Wigner distribution—a tool for time–frequency signal analysis,” Philips J. Res. 35, 217–250 (1980).

Milster, T. D.

Novotny, L.

B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
[CrossRef]

O’Boyle, M.

F. Zenhausern, M. O’Boyle, H. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 20, 1924–1926 (1994).

Pieralli, C.

D. Barchiesi, O. Bergossi, C. Pieralli, M. Spajer, “Reflection scanning near-field optical microscopy (R-SNOM) in constant height mode with a dielectric probe: image interpretation and resolution for high topographic variations,” Ultramicroscopy 71, 361–370 (1998).
[CrossRef]

D. Barchiesi, O. Bergossi, M. Spajer, C. Pieralli, “Image resolution in reflection scanning near-field optical microscopy using shear-force feedback: characterization with a spline and Fourier spectrum,” Appl. Opt. 36, 2171–2177 (1997).
[CrossRef] [PubMed]

Pohl, D. W.

B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
[CrossRef]

Royer, P.

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near field optical microscope,” Eur. Phys. J. (Appl. Phys.) 5, 289–295 (1999).
[CrossRef]

G. Wurtz, R. Bachelot, P. Royer, “Reflection-mode apertureless scanning near-field optical microscope developed from a commercial scanning probe microscope,” Rev. Sci. Instrum. 69, 1735–1743 (1998).
[CrossRef]

Spajer, M.

S. Davy, D. Barchiesi, M. Spajer, D. Courjon, “Spectroscopic study of resonant dielectric structures in near-field,” Eur. Phys. J. (Appl. Phys.) 5, 277–281 (1999).
[CrossRef]

D. Barchiesi, O. Bergossi, C. Pieralli, M. Spajer, “Reflection scanning near-field optical microscopy (R-SNOM) in constant height mode with a dielectric probe: image interpretation and resolution for high topographic variations,” Ultramicroscopy 71, 361–370 (1998).
[CrossRef]

D. Barchiesi, O. Bergossi, M. Spajer, C. Pieralli, “Image resolution in reflection scanning near-field optical microscopy using shear-force feedback: characterization with a spline and Fourier spectrum,” Appl. Opt. 36, 2171–2177 (1997).
[CrossRef] [PubMed]

O. Bergossi, M. Spajer, “Scanning local probe interferometer and reflectometer: application to very low relief objects,” in Interferometry ’94: Interferometric Fiber Sensing, E. Udd, R. P. Tatam, eds., Proc. SPIE2341, 238–248 (1994).

Van Labeke, D.

D. Van Labeke, D. Barchiesi, “Scanning tunneling optical microscopy: a theoretical macroscopic approach,” J. Opt. Soc. Am. A 9, 732–739 (1992).
[CrossRef]

D. Courjon, F. Baida, C. Bainier, D. Van Labeke, D. Barchiesi, “Near field instrumentation,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO ASI Series E: Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 59–78.

Wickramasinghe, H.

F. Zenhausern, M. O’Boyle, H. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 20, 1924–1926 (1994).

Wioland, H.

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near field optical microscope,” Eur. Phys. J. (Appl. Phys.) 5, 289–295 (1999).
[CrossRef]

Wurtz, G.

G. Wurtz, R. Bachelot, P. Royer, “Reflection-mode apertureless scanning near-field optical microscope developed from a commercial scanning probe microscope,” Rev. Sci. Instrum. 69, 1735–1743 (1998).
[CrossRef]

Zenhausern, F.

F. Zenhausern, M. O’Boyle, H. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 20, 1924–1926 (1994).

Ziolkowski, R. W.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

F. Zenhausern, M. O’Boyle, H. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 20, 1924–1926 (1994).

Eur. Phys. J. (Appl. Phys.) (3)

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near field optical microscope,” Eur. Phys. J. (Appl. Phys.) 5, 289–295 (1999).
[CrossRef]

D. Barchiesi, T. Gharbi, “Wavelet analysis of near-field data and the resolution problem,” Eur. Phys. J. (Appl. Phys.) 5, 297–301 (1999).
[CrossRef]

S. Davy, D. Barchiesi, M. Spajer, D. Courjon, “Spectroscopic study of resonant dielectric structures in near-field,” Eur. Phys. J. (Appl. Phys.) 5, 277–281 (1999).
[CrossRef]

IEEE Trans. Signal Process. (1)

F. Auger, P. Flandrin, “Improving the readability of time frequency and time-scale representations by the reassignment method,” IEEE Trans. Signal Process. 43, 1068–1089 (1995).
[CrossRef]

J. Appl. Phys. (1)

B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
[CrossRef]

J. Microsc. (Oxford) (1)

D. Barchiesi, “Characterization of R-SNOM and STOM/PSTM working in preliminary approach constant height mode,” J. Microsc. (Oxford) 194, 299–306 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

Microsc. Microanal. Microstruct. (1)

D. Barchiesi, “Application of Fourier algorithm to near field optical images: local resolution estimation,” Microsc. Microanal. Microstruct. 8, 1–10 (1997).
[CrossRef]

Opt. Commun. (4)

T. Gharbi, D. Barchiesi, “Local signal processing to evaluate resolution in SNOM images, using 1D wavelets,” Opt. Commun. 177, 85–93 (2000).
[CrossRef]

R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of transfer function,” Opt. Commun. 116, 316–321 (1995); erratum, 120, 371 (1995).
[CrossRef]

D. Barchiesi, “Pseudo modulation transfer function in reflection scanning near-field optical microscopy,” Opt. Commun. 154, 167–172 (1998).
[CrossRef]

D. Barchiesi, “A 3-D multilayer model of scattering by nanostructures. Application to the optimisation of thin coated nano-sources,” Opt. Commun. 126, 7–13 (1996).
[CrossRef]

Opt. Lett. (1)

Philips J. Res. (1)

T. A. C. M. Claasen, W. F. G. Mecklenbräuker, “The Wigner distribution—a tool for time–frequency signal analysis,” Philips J. Res. 35, 217–250 (1980).

Proc. IEEE (1)

L. Cohen, “Time–frequency distribution—a review,” Proc. IEEE 77, 941–981 (1989).
[CrossRef]

Rev. Sci. Instrum. (1)

G. Wurtz, R. Bachelot, P. Royer, “Reflection-mode apertureless scanning near-field optical microscope developed from a commercial scanning probe microscope,” Rev. Sci. Instrum. 69, 1735–1743 (1998).
[CrossRef]

Surf. Sci. (1)

C. Girard, D. Courjon, “The role of scanning mode in near-field optical microscopy,” Surf. Sci. 382, 9–18 (1997).
[CrossRef]

Ultramicroscopy (1)

D. Barchiesi, O. Bergossi, C. Pieralli, M. Spajer, “Reflection scanning near-field optical microscopy (R-SNOM) in constant height mode with a dielectric probe: image interpretation and resolution for high topographic variations,” Ultramicroscopy 71, 361–370 (1998).
[CrossRef]

Other (2)

O. Bergossi, M. Spajer, “Scanning local probe interferometer and reflectometer: application to very low relief objects,” in Interferometry ’94: Interferometric Fiber Sensing, E. Udd, R. P. Tatam, eds., Proc. SPIE2341, 238–248 (1994).

D. Courjon, F. Baida, C. Bainier, D. Van Labeke, D. Barchiesi, “Near field instrumentation,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO ASI Series E: Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 59–78.

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Figures (9)

Fig. 1
Fig. 1

Experimental schematic of SNOM. The nanometric tip is placed a few nanometers away from the sample surface and scans the sample. The electromagnetic interaction between the tip end, of subwavelength size, and the sample enables us to get high resolution. λ is the incoming light wavelength.

Fig. 2
Fig. 2

WV distribution of a signal in time (a.u.) composed of two sinusoids of normalized frequency 0.2 and 0.35, with the amplitude of the latter being modulated by a Gaussian function. The vertical axis represents normalized frequency (between 0 and 0.5), and the horizontal axis is given in pixels. Interferences can be observed between the two signal components located at the normalized frequencies 0.2 and 0.35. The energy spectral density can be seen in the left-hand plot, with log scale.

Fig. 3
Fig. 3

SPWV distribution of the same signal as is shown in Fig. 2. Interferences are attenuated. The time and frequency filters are given in Fig. 4.

Fig. 4
Fig. 4

Smoothing functions h(t) and g(t) used to evaluate the SPWV distribution shown in Fig. 3.

Fig. 5
Fig. 5

RSPWV distribution of the same signal as is shown in Fig. 3. Time and frequency resolutions are enhanced.

Fig. 6
Fig. 6

Simulated near-field optical data (a.u.) and SPWV representation, shown for comparison with the RSPWV representation given in Fig. 7.

Fig. 7
Fig. 7

Simulated near-field optical data (a.u.) and RSPWV representation. The high frequencies are more precisely localized than in Fig. 6.

Fig. 8
Fig. 8

RSPWV distribution of near-field optical data. The sample characteristics and the image acquisition process are described in Ref. 21. (a) SNOM image raw data, (d) extracted line 80, (b) RSPWV representation of the whole image at the normalized frequency 0.46875, (e) RSPWV representation of line 80 performed at the same frequency. The circles surround a star-shape intensity pattern. (c) SNOM and shear-force signals of line 80. (f) The two signals are processed by the spline-fitting method, as described in Ref. 20. The normalized cutoff frequency of the SNOM signal, indicated by the arrow, is nearly 0.18.

Fig. 9
Fig. 9

Simultaneous (a) AFM and (b) magneto-optical near-field optical images and raw data. Image size is 10×10 µm. The sample characteristics and the image acquisition process are described in Ref. 22. The RSPWV representations are calculated at the normalized spatial frequencies (c) 0.08203 and (d) 0.01171. The arrows indicate a topographical line visible in (a), (b), and (c). The circles surround a nanometric dust in (a), (b), and (c). The letters B and S are placed at the bubble domain wall and at a magnetic stripe wall, respectively, which are visible only in (b) and (d).

Equations (8)

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Cs(t, f; Φ)=-+Φ(u-t, θ-f)su+τ2s*u-τ2×exp(-2jπθτ)dτdudθ,
Ws(t, f)=-+st+τ2s*t-τ2exp(-j2πfτ)dτ.
Cs(t, f; Φ)=-+Φ(u-t, θ-f)Ws(u, θ)dudθ.
Φ(t, f)=g(t)H(-f).
SPWs(t, f; Φ)=-+g(u-t)H(f-θ)Ws(u, θ)dudθ.
RCs(t, f; Φ)=-+Cs(t, f; Φ)×δ[t-tˆ(s, t, f)]δ[f-fˆ(s, t, f)]dtd f,
tˆ(s, t, f)=-+ηΦ(η-t, ξ-f)Ws(η, ξ)dηdξ-+Φ(η-t, ξ-f)Ws(η, ξ)dηdξ,
fˆ(s, t, f)=-+ξΦ(η-t, ξ-f)Ws(η, ξ)dηdξ-+Φ(η-t, ξ-f)Ws(η, ξ)dηdξ.

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