Abstract

In near-field optical microscopy the resolution is strongly related to the experimental illumination conditions and to the separation between tip and sample. Therefore the spectral information in near-field data (related to the resolution in images) can be described only locally as a function of the tip–sample position. To make a local study of the spectral information in near-field data, we use wavelet decomposition that is associated with the calculation of entropy. We deduce the resolution from the characteristics of the wavelet, which leads to an automatic and numerical evaluation of the resolution in near-field data.

© 1999 Optical Society of America

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References

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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., NATO ASI Ser. E300, 59–78 (1995).
  2. D. van Labeke, D. Barchiesi, “Scanning–tunneling optical microscopy: a theoretical macroscopic approach,” J. Opt. Soc. Am. A 9, 732–739 (1992).
    [CrossRef]
  3. 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]
  4. R. U. Maheswari, H. Tatsumi, Y. Katayama, M. Ohtsu, “Observation of subcellular nanostructure of single neurons with an illumination mode photon scanning tunneling microscope,” Opt. Commun. 120, 325–334 (1995).
    [CrossRef]
  5. O. Bergossi, M. Spajer, P. Schiavone, “Visualization of latent images by reflection near-field optical microscopy,” Ultramicroscopy 61, 241–246 (1995).
    [CrossRef]
  6. R. U. Maheswari, H. Kadono, M. Ohtsu, “Power spectral analysis for evaluating optical near-field images of 20 nm gold particles,” Opt. Commun. 131, 133–142 (1996).
    [CrossRef]
  7. D. Barchiesi, “Pseudo modulation transfer function in reflection scanning near-field optical microscopy,” Opt. Commun. 154, 167–172 (1998).
    [CrossRef]
  8. D. Barchiesi, “Application of the Fourier algorithm to near field optical images: local resolution estimation,” Microsc. Microanal. Microstruct. 8, 1–10 (1997).
    [CrossRef]
  9. L. Cohen, “Time–frequency distribution—a review,” Proc. IEEE 77, 941–981 (1989).
    [CrossRef]
  10. D. Gabor, “Theory of communication,” J. IEE 93, 429–457 (1946).
  11. S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
    [CrossRef]
  12. See the entire issue of Opt. Eng. 33, 2104–2486 (1994).
  13. P. Sandoz, “Wavelet transform as a processing tool in white-light interferometry,” Opt. Lett. 22, 1065–1067 (1997).
    [CrossRef] [PubMed]
  14. A. V. Bronnikov, G. Duifhuis, “Wavelet-based image enhancement in x-ray imaging and tomography,” Appl. Opt. 37, 4437–4448 (1998).
    [CrossRef]
  15. 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]
  16. C. Girard, D. Courjon, “The role of scanning mode in near-field optical microscopy,” Surf. Sci. 382, 9–18 (1997).
    [CrossRef]
  17. N. Bonnet, “On the use of correlation functions for improving the image signal-to-noise ratio,” Optik (Stuttgart) 80, 103–106 (1988).
  18. G. Strang, T. Nguyen, Wavelets and Filter Banks (Wellesley-Cambridge Press, Wellesley, Mass., 1996).
  19. D. Charraut, D. Courjon, C. Bainier, L. Moulinier, “Analysis of optical near-field images by Karhunen–Loève transformation,” Appl. Opt. 35, 3853–3861 (1996).
    [CrossRef] [PubMed]
  20. P. W. Hawkes, E. Kasper, Wave Optics (Academic, London, 1994).
  21. D. Barchiesi, “A 3-D multilayer model of scattering by nanostructures. Application to the optimization of thin coated nanosources,” Opt. Commun. 126, 7–13 (1996).
    [CrossRef]
  22. D. Barchiesi, C. Girard, O. J. F. Martin, D. van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
    [CrossRef]
  23. A. Vial, D. Barchiesi, G. Parent, “Spectroscopic study of the image formation in near-field microscopy, near an evanescent-homogeneous switching,” J. Microsc. 194, 265–270 (1999).
    [CrossRef]
  24. S. Davy, D. Barchiesi, M. Spajer, D. Courjon, “Spectroscopic study of resonant dielectric structures in the near field,” Eur. Phys. J. (Appl. Phy.) 5, 277–281 (1999).
    [CrossRef]
  25. K. Jang, W. Jhe, “Nonglobal model for a near-field scanning optical microscope using diffraction of the optical near field,” Opt. Lett. 21, 236–238 (1996).
    [CrossRef] [PubMed]
  26. T. Saiki, M. Ohtsu, K. Jang, W. Jhe, “Direct observation of size-dependant features of the optical near field on a subwavelength spherical surface,” Opt. Lett. 21, 674–676 (1996).
    [CrossRef] [PubMed]
  27. J. L. Kann, T. D. Milster, F. F. Froehlich, R. W. Ziolkowski, J. B. Judkins, “Linear behavior of a near-field optical system,” J. Opt. Soc. Am. A 12, 1677–1682 (1995).
    [CrossRef]

1999 (2)

A. Vial, D. Barchiesi, G. Parent, “Spectroscopic study of the image formation in near-field microscopy, near an evanescent-homogeneous switching,” J. Microsc. 194, 265–270 (1999).
[CrossRef]

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

1998 (3)

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]

A. V. Bronnikov, G. Duifhuis, “Wavelet-based image enhancement in x-ray imaging and tomography,” Appl. Opt. 37, 4437–4448 (1998).
[CrossRef]

1997 (4)

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

P. Sandoz, “Wavelet transform as a processing tool in white-light interferometry,” Opt. Lett. 22, 1065–1067 (1997).
[CrossRef] [PubMed]

1996 (6)

K. Jang, W. Jhe, “Nonglobal model for a near-field scanning optical microscope using diffraction of the optical near field,” Opt. Lett. 21, 236–238 (1996).
[CrossRef] [PubMed]

T. Saiki, M. Ohtsu, K. Jang, W. Jhe, “Direct observation of size-dependant features of the optical near field on a subwavelength spherical surface,” Opt. Lett. 21, 674–676 (1996).
[CrossRef] [PubMed]

R. U. Maheswari, H. Kadono, M. Ohtsu, “Power spectral analysis for evaluating optical near-field images of 20 nm gold particles,” Opt. Commun. 131, 133–142 (1996).
[CrossRef]

D. Charraut, D. Courjon, C. Bainier, L. Moulinier, “Analysis of optical near-field images by Karhunen–Loève transformation,” Appl. Opt. 35, 3853–3861 (1996).
[CrossRef] [PubMed]

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

D. Barchiesi, C. Girard, O. J. F. Martin, D. van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[CrossRef]

1995 (3)

R. U. Maheswari, H. Tatsumi, Y. Katayama, M. Ohtsu, “Observation of subcellular nanostructure of single neurons with an illumination mode photon scanning tunneling microscope,” Opt. Commun. 120, 325–334 (1995).
[CrossRef]

O. Bergossi, M. Spajer, P. Schiavone, “Visualization of latent images by reflection near-field optical microscopy,” Ultramicroscopy 61, 241–246 (1995).
[CrossRef]

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

1994 (1)

See the entire issue of Opt. Eng. 33, 2104–2486 (1994).

1992 (1)

1989 (2)

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

S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

1988 (1)

N. Bonnet, “On the use of correlation functions for improving the image signal-to-noise ratio,” Optik (Stuttgart) 80, 103–106 (1988).

1946 (1)

D. Gabor, “Theory of communication,” J. IEE 93, 429–457 (1946).

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., NATO ASI Ser. E300, 59–78 (1995).

Bainier, C.

D. Charraut, D. Courjon, C. Bainier, L. Moulinier, “Analysis of optical near-field images by Karhunen–Loève transformation,” Appl. Opt. 35, 3853–3861 (1996).
[CrossRef] [PubMed]

D. Courjon, F. Baida, C. Bainier, D. van Labeke, D. Barchiesi, “Near field instrumentation,” in Photons and Local Probes, O. Marti, R. Möller, eds., NATO ASI Ser. E300, 59–78 (1995).

Barchiesi, D.

A. Vial, D. Barchiesi, G. Parent, “Spectroscopic study of the image formation in near-field microscopy, near an evanescent-homogeneous switching,” J. Microsc. 194, 265–270 (1999).
[CrossRef]

S. Davy, D. Barchiesi, M. Spajer, D. Courjon, “Spectroscopic study of resonant dielectric structures in the near field,” Eur. Phys. J. (Appl. Phy.) 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, “Pseudo modulation transfer function in reflection scanning near-field optical microscopy,” Opt. Commun. 154, 167–172 (1998).
[CrossRef]

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

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

D. Barchiesi, C. Girard, O. J. F. Martin, D. van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (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., NATO ASI Ser. E300, 59–78 (1995).

Bergossi, O.

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]

O. Bergossi, M. Spajer, P. Schiavone, “Visualization of latent images by reflection near-field optical microscopy,” Ultramicroscopy 61, 241–246 (1995).
[CrossRef]

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]

Bonnet, N.

N. Bonnet, “On the use of correlation functions for improving the image signal-to-noise ratio,” Optik (Stuttgart) 80, 103–106 (1988).

Bronnikov, A. V.

Charraut, D.

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 the near field,” Eur. Phys. J. (Appl. Phy.) 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. Charraut, D. Courjon, C. Bainier, L. Moulinier, “Analysis of optical near-field images by Karhunen–Loève transformation,” Appl. Opt. 35, 3853–3861 (1996).
[CrossRef] [PubMed]

D. Barchiesi, C. Girard, O. J. F. Martin, D. van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[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., NATO ASI Ser. E300, 59–78 (1995).

Davy, S.

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

Duifhuis, G.

Froehlich, F. F.

Gabor, D.

D. Gabor, “Theory of communication,” J. IEE 93, 429–457 (1946).

Girard, C.

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

D. Barchiesi, C. Girard, O. J. F. Martin, D. van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[CrossRef]

Hawkes, P. W.

P. W. Hawkes, E. Kasper, Wave Optics (Academic, London, 1994).

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]

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]

Jang, K.

Jhe, W.

Judkins, J. B.

Kadono, H.

R. U. Maheswari, H. Kadono, M. Ohtsu, “Power spectral analysis for evaluating optical near-field images of 20 nm gold particles,” Opt. Commun. 131, 133–142 (1996).
[CrossRef]

Kann, J. L.

Kasper, E.

P. W. Hawkes, E. Kasper, Wave Optics (Academic, London, 1994).

Katayama, Y.

R. U. Maheswari, H. Tatsumi, Y. Katayama, M. Ohtsu, “Observation of subcellular nanostructure of single neurons with an illumination mode photon scanning tunneling microscope,” Opt. Commun. 120, 325–334 (1995).
[CrossRef]

Maheswari, R. U.

R. U. Maheswari, H. Kadono, M. Ohtsu, “Power spectral analysis for evaluating optical near-field images of 20 nm gold particles,” Opt. Commun. 131, 133–142 (1996).
[CrossRef]

R. U. Maheswari, H. Tatsumi, Y. Katayama, M. Ohtsu, “Observation of subcellular nanostructure of single neurons with an illumination mode photon scanning tunneling microscope,” Opt. Commun. 120, 325–334 (1995).
[CrossRef]

Mallat, S.

S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

Martin, O. J. F.

D. Barchiesi, C. Girard, O. J. F. Martin, D. van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[CrossRef]

Milster, T. D.

Moulinier, L.

Nguyen, T.

G. Strang, T. Nguyen, Wavelets and Filter Banks (Wellesley-Cambridge Press, Wellesley, Mass., 1996).

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]

Ohtsu, M.

R. U. Maheswari, H. Kadono, M. Ohtsu, “Power spectral analysis for evaluating optical near-field images of 20 nm gold particles,” Opt. Commun. 131, 133–142 (1996).
[CrossRef]

T. Saiki, M. Ohtsu, K. Jang, W. Jhe, “Direct observation of size-dependant features of the optical near field on a subwavelength spherical surface,” Opt. Lett. 21, 674–676 (1996).
[CrossRef] [PubMed]

R. U. Maheswari, H. Tatsumi, Y. Katayama, M. Ohtsu, “Observation of subcellular nanostructure of single neurons with an illumination mode photon scanning tunneling microscope,” Opt. Commun. 120, 325–334 (1995).
[CrossRef]

Parent, G.

A. Vial, D. Barchiesi, G. Parent, “Spectroscopic study of the image formation in near-field microscopy, near an evanescent-homogeneous switching,” J. Microsc. 194, 265–270 (1999).
[CrossRef]

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]

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]

Saiki, T.

Sandoz, P.

Schiavone, P.

O. Bergossi, M. Spajer, P. Schiavone, “Visualization of latent images by reflection near-field optical microscopy,” Ultramicroscopy 61, 241–246 (1995).
[CrossRef]

Spajer, M.

S. Davy, D. Barchiesi, M. Spajer, D. Courjon, “Spectroscopic study of resonant dielectric structures in the near field,” Eur. Phys. J. (Appl. Phy.) 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]

O. Bergossi, M. Spajer, P. Schiavone, “Visualization of latent images by reflection near-field optical microscopy,” Ultramicroscopy 61, 241–246 (1995).
[CrossRef]

Strang, G.

G. Strang, T. Nguyen, Wavelets and Filter Banks (Wellesley-Cambridge Press, Wellesley, Mass., 1996).

Tatsumi, H.

R. U. Maheswari, H. Tatsumi, Y. Katayama, M. Ohtsu, “Observation of subcellular nanostructure of single neurons with an illumination mode photon scanning tunneling microscope,” Opt. Commun. 120, 325–334 (1995).
[CrossRef]

van Labeke, D.

D. Barchiesi, C. Girard, O. J. F. Martin, D. van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (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., NATO ASI Ser. E300, 59–78 (1995).

Vial, A.

A. Vial, D. Barchiesi, G. Parent, “Spectroscopic study of the image formation in near-field microscopy, near an evanescent-homogeneous switching,” J. Microsc. 194, 265–270 (1999).
[CrossRef]

Ziolkowski, R. W.

Appl. Opt. (2)

Eur. Phys. J. (Appl. Phy.) (1)

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

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
[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. IEE (1)

D. Gabor, “Theory of communication,” J. IEE 93, 429–457 (1946).

J. Microsc. (1)

A. Vial, D. Barchiesi, G. Parent, “Spectroscopic study of the image formation in near-field microscopy, near an evanescent-homogeneous switching,” J. Microsc. 194, 265–270 (1999).
[CrossRef]

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

Microsc. Microanal. Microstruct. (1)

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

Opt. Commun. (4)

R. U. Maheswari, H. Kadono, M. Ohtsu, “Power spectral analysis for evaluating optical near-field images of 20 nm gold particles,” Opt. Commun. 131, 133–142 (1996).
[CrossRef]

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

R. U. Maheswari, H. Tatsumi, Y. Katayama, M. Ohtsu, “Observation of subcellular nanostructure of single neurons with an illumination mode photon scanning tunneling microscope,” Opt. Commun. 120, 325–334 (1995).
[CrossRef]

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

Opt. Eng. (1)

See the entire issue of Opt. Eng. 33, 2104–2486 (1994).

Opt. Lett. (3)

Optik (Stuttgart) (1)

N. Bonnet, “On the use of correlation functions for improving the image signal-to-noise ratio,” Optik (Stuttgart) 80, 103–106 (1988).

Phys. Rev. E (1)

D. Barchiesi, C. Girard, O. J. F. Martin, D. van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[CrossRef]

Proc. IEEE (1)

L. Cohen, “Time–frequency distribution—a review,” Proc. IEEE 77, 941–981 (1989).
[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 (2)

O. Bergossi, M. Spajer, P. Schiavone, “Visualization of latent images by reflection near-field optical microscopy,” Ultramicroscopy 61, 241–246 (1995).
[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]

Other (3)

G. Strang, T. Nguyen, Wavelets and Filter Banks (Wellesley-Cambridge Press, Wellesley, Mass., 1996).

D. Courjon, F. Baida, C. Bainier, D. van Labeke, D. Barchiesi, “Near field instrumentation,” in Photons and Local Probes, O. Marti, R. Möller, eds., NATO ASI Ser. E300, 59–78 (1995).

P. W. Hawkes, E. Kasper, Wave Optics (Academic, London, 1994).

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Figures (11)

Fig. 1
Fig. 1

(a) Experimental setup and (b) 7 µm × 7 µm (128 × 128 pixel) intensity map of the image.

Fig. 2
Fig. 2

Plots of the Hamming windows and the associated modulus of the discrete Fourier transform spectrum as functions of the normalized Fourier frequency. The abscissas represent the normalized Fourier frequency with a maximum of 1/2, which corresponds to the Shannon–Wittaker limit, i.e., more than two pixels are necessary to define the signal. The normalized Fourier frequency is independent of the size of the original function.

Fig. 3
Fig. 3

Daubechies wavelets (dbN has a length of 2N) and the associated modulus of the discrete Fourier transform spectrum plotted as functions of the normalized Fourier frequency. The abscissas represent the normalized Fourier frequency. The Fourier spectrum is slightly dependent on the size of the wavelet.

Fig. 4
Fig. 4

Chart of the general principles of multilevel analysis.

Fig. 5
Fig. 5

Illustration of the effects of filtering induced by multilevel wavelet analysis (db16). Shown are the Fourier spectra of the filters involved in cDi and cAi analysis with a Daubechies wavelet of the order 16. The abscissas represent the Fourier frequency number.

Fig. 6
Fig. 6

Effects of filtering induced by multilevel wavelet analysis with db16. Shown are the spectra for wavelet filters of recomposition W L r and W H r and decomposition W L d and W H d that are associated with the order-16 Daubechies wavelet.

Fig. 7
Fig. 7

Effects of filtering induced by multilevel wavelet analysis with db16.

Fig. 8
Fig. 8

Simulated R-SNOM signal. The resolution depends strongly on the distance between the tip and the sample.

Fig. 9
Fig. 9

Simulated signals for cD1, cD2, cD2 - cD1, and entropy. The abscissas are in units of pixels. The analysis was carried out with db16 and db5.

Fig. 10
Fig. 10

Experimental R-SNOM data: Level-1 and level-2 decompositions of the detail channels of an experimental image with a Daubechies order-4 wavelet (db4). (a) The original experimental data that correspond to the image shown in Fig. 1(b). (b) Detail channels cD1 (left-hand side) and cD2 (right-hand side). (c) Symmetric entropy corresponding to cD1 (left-hand side) and cD2 (right-hand side) from (b). The data were acquired in constant-height mode.

Fig. 11
Fig. 11

Experimental R-SNOM data: Location of the resolution in an experimental image obtained by use of various orders of wavelets. (a) The original experimental data, which correspond to the image shown in Fig. 1(b). (b) Locations of the resolution for wavelet orders db1 (left-hand side) and db2 (right-hand side). (c) Locations of the resolution for wavelet orders db3 (left-hand side) and db4 (right-hand side). The data were acquired in constant-height mode.

Equations (11)

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sˆf=-+ stT*t, fdt=s, T.
Tt, f=expj2πft.
Tt, f, h, t0=ht-t0expj2πft.
Tt, a, Ψ=|a|-1/2Ψt-t0a,
HWn, p=0.54-0.46 cos2πn-1 p, p0, n-1.
cD1=s, WHd, WHr,
cA1=s, WLd, WLr,
cD2=cA1, WHd, WHr,
cA2=cA1, WLd, WLr.
s=cD1++cDi+cAi.
Est=-st1.5 log st1.5.

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