Abstract

A tomographiclike method based on the inverse radon transform is used to retrieve the irradiance map of a focused laser beam. The results obtained from multiple knife-edge measurements have been processed through a kriging technique. This technique allows us to map both the beam irradiance and the uncertainty associated with the measurement method. The results are compared with those achieved in the standard fitting of two orthogonal knife-edge profiles to a modeled beam. The application of the tomographiclike technique does not require any beam model and produces a higher signal-to-noise ratio than the conventional method. As a consequence, the quality of the estimation of the spatial response map of an antenna-coupled detector in the visible is improved.

© 2008 Optical Society of America

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References

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  1. M. R. Abdel-Rahman, B. Monacelli, A. R. Weeks, G. Zummo, and G. D. Boreman, “Design, fabrication, and characterization of antenna-coupled metal-oxide-metal diodes for dual-band detection,” Opt. Eng. 44, 066401 (2005).
    [Crossref]
  2. F. J. González, B. Ilic, J. Alda, and G. D. Boreman, “Antenna-coupled infrared detectors for imaging applications,” IEEE J. Sel. Top. Quantum Electron. 11, 117-120 (2005).
    [Crossref]
  3. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
    [Crossref] [PubMed]
  4. K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonators for local field enhancement,” J. Appl. Phys. 94, 4632-4642 (2003).
    [Crossref]
  5. T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28-33 (2007).
    [Crossref] [PubMed]
  6. P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single molecule fluorescence,” Nanotechnology 18, 044017 (2007).
    [Crossref]
  7. C. Fumeaux, J. Alda, and G. Boreman, “Lithographic antennas at visible frequencies,” Opt. Lett. 24, 1629-1631 (1999).
    [Crossref]
  8. J. M. López-Alonso, B. Monacelli, J. Alda, and G. Boreman, “Uncertainty analysis in the measurement of the spatial responsivity of infrared antennas,” Appl. Opt. 21, 4557-4568 (2005).
    [Crossref]
  9. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “The focus of light--theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109-113 (2001).
  10. N. Cressie, Statistics for Spatial Data (Wiley, 1991).
  11. J. Alda, C. Fumeaux, I. Codreanu, J. Schaefer, and G. Boreman, “A deconvolution method for two-dimensional spatial-response mapping of lithographic infrared antennas,” Appl. Opt. 38, 3993-4000 (1999).
    [Crossref]
  12. F. J. González and G. Boreman, “Comparison of dipole, bowtie, spiral and log-periodic IR antennas,” Infrared Phys. Technol. 46, 418-428 (2005).
    [Crossref]
  13. P. Toft, “The radon transform--theory and implementation,” Ph.D. dissertation (Technical University of Denmark, 1996), http://petertoft.dk/PhD.
  14. R. Dorn, S. Quabis, and G. Leuchs, “The focus of light--linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917-1926 (2003).
  15. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
    [Crossref] [PubMed]
  16. O. Mendoza-Yero and J. Alda, “Irradiance map of an apertured Gaussian beam affected by coma,” Opt. Commun. 271, 517-523 (2007).
    [Crossref]
  17. M. Born and E. Wolf, Principles of Optics (Pergamon, 1989).
  18. E. Bernabeu, I. Serroukh, and L. M. Sanchez-Brea, “A geometrical model for wire optical diffraction selected by experimental statistical analysis,” Opt. Eng. 38, 1319-1325 (1999).
    [Crossref]
  19. W. Y. V. Leung, P. J. Bones, and R. G. Lane, “Statistical interpolation of sampled image,” Opt. Eng. 40, 547-553 (2001).
    [Crossref]
  20. L. M. Sanchez-Brea and E. Bernabeu, “Determination of the optimum sampling frequency of noisy images by spatial statistic,” Appl. Opt. 44, 3276-3283 (2005).
    [Crossref] [PubMed]
  21. L. M. Sanchez-Brea and E. Bernabeu, “Uncertainty estimation by convolution using spatial statistics,” IEEE Trans. Image Process. 15, 3131-3137 (2006).
    [Crossref] [PubMed]

2007 (3)

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28-33 (2007).
[Crossref] [PubMed]

P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single molecule fluorescence,” Nanotechnology 18, 044017 (2007).
[Crossref]

O. Mendoza-Yero and J. Alda, “Irradiance map of an apertured Gaussian beam affected by coma,” Opt. Commun. 271, 517-523 (2007).
[Crossref]

2006 (1)

L. M. Sanchez-Brea and E. Bernabeu, “Uncertainty estimation by convolution using spatial statistics,” IEEE Trans. Image Process. 15, 3131-3137 (2006).
[Crossref] [PubMed]

2005 (6)

L. M. Sanchez-Brea and E. Bernabeu, “Determination of the optimum sampling frequency of noisy images by spatial statistic,” Appl. Opt. 44, 3276-3283 (2005).
[Crossref] [PubMed]

F. J. González and G. Boreman, “Comparison of dipole, bowtie, spiral and log-periodic IR antennas,” Infrared Phys. Technol. 46, 418-428 (2005).
[Crossref]

J. M. López-Alonso, B. Monacelli, J. Alda, and G. Boreman, “Uncertainty analysis in the measurement of the spatial responsivity of infrared antennas,” Appl. Opt. 21, 4557-4568 (2005).
[Crossref]

M. R. Abdel-Rahman, B. Monacelli, A. R. Weeks, G. Zummo, and G. D. Boreman, “Design, fabrication, and characterization of antenna-coupled metal-oxide-metal diodes for dual-band detection,” Opt. Eng. 44, 066401 (2005).
[Crossref]

F. J. González, B. Ilic, J. Alda, and G. D. Boreman, “Antenna-coupled infrared detectors for imaging applications,” IEEE J. Sel. Top. Quantum Electron. 11, 117-120 (2005).
[Crossref]

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[Crossref] [PubMed]

2003 (3)

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonators for local field enhancement,” J. Appl. Phys. 94, 4632-4642 (2003).
[Crossref]

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light--linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917-1926 (2003).

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

2001 (2)

W. Y. V. Leung, P. J. Bones, and R. G. Lane, “Statistical interpolation of sampled image,” Opt. Eng. 40, 547-553 (2001).
[Crossref]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “The focus of light--theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109-113 (2001).

1999 (3)

Abdel-Rahman, M. R.

M. R. Abdel-Rahman, B. Monacelli, A. R. Weeks, G. Zummo, and G. D. Boreman, “Design, fabrication, and characterization of antenna-coupled metal-oxide-metal diodes for dual-band detection,” Opt. Eng. 44, 066401 (2005).
[Crossref]

Alda, J.

O. Mendoza-Yero and J. Alda, “Irradiance map of an apertured Gaussian beam affected by coma,” Opt. Commun. 271, 517-523 (2007).
[Crossref]

J. M. López-Alonso, B. Monacelli, J. Alda, and G. Boreman, “Uncertainty analysis in the measurement of the spatial responsivity of infrared antennas,” Appl. Opt. 21, 4557-4568 (2005).
[Crossref]

F. J. González, B. Ilic, J. Alda, and G. D. Boreman, “Antenna-coupled infrared detectors for imaging applications,” IEEE J. Sel. Top. Quantum Electron. 11, 117-120 (2005).
[Crossref]

C. Fumeaux, J. Alda, and G. Boreman, “Lithographic antennas at visible frequencies,” Opt. Lett. 24, 1629-1631 (1999).
[Crossref]

J. Alda, C. Fumeaux, I. Codreanu, J. Schaefer, and G. Boreman, “A deconvolution method for two-dimensional spatial-response mapping of lithographic infrared antennas,” Appl. Opt. 38, 3993-4000 (1999).
[Crossref]

Anger, P.

P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single molecule fluorescence,” Nanotechnology 18, 044017 (2007).
[Crossref]

Bernabeu, E.

L. M. Sanchez-Brea and E. Bernabeu, “Uncertainty estimation by convolution using spatial statistics,” IEEE Trans. Image Process. 15, 3131-3137 (2006).
[Crossref] [PubMed]

L. M. Sanchez-Brea and E. Bernabeu, “Determination of the optimum sampling frequency of noisy images by spatial statistic,” Appl. Opt. 44, 3276-3283 (2005).
[Crossref] [PubMed]

E. Bernabeu, I. Serroukh, and L. M. Sanchez-Brea, “A geometrical model for wire optical diffraction selected by experimental statistical analysis,” Opt. Eng. 38, 1319-1325 (1999).
[Crossref]

Bharadwaj, P.

P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single molecule fluorescence,” Nanotechnology 18, 044017 (2007).
[Crossref]

Bones, P. J.

W. Y. V. Leung, P. J. Bones, and R. G. Lane, “Statistical interpolation of sampled image,” Opt. Eng. 40, 547-553 (2001).
[Crossref]

Boreman, G.

J. M. López-Alonso, B. Monacelli, J. Alda, and G. Boreman, “Uncertainty analysis in the measurement of the spatial responsivity of infrared antennas,” Appl. Opt. 21, 4557-4568 (2005).
[Crossref]

F. J. González and G. Boreman, “Comparison of dipole, bowtie, spiral and log-periodic IR antennas,” Infrared Phys. Technol. 46, 418-428 (2005).
[Crossref]

J. Alda, C. Fumeaux, I. Codreanu, J. Schaefer, and G. Boreman, “A deconvolution method for two-dimensional spatial-response mapping of lithographic infrared antennas,” Appl. Opt. 38, 3993-4000 (1999).
[Crossref]

C. Fumeaux, J. Alda, and G. Boreman, “Lithographic antennas at visible frequencies,” Opt. Lett. 24, 1629-1631 (1999).
[Crossref]

Boreman, G. D.

F. J. González, B. Ilic, J. Alda, and G. D. Boreman, “Antenna-coupled infrared detectors for imaging applications,” IEEE J. Sel. Top. Quantum Electron. 11, 117-120 (2005).
[Crossref]

M. R. Abdel-Rahman, B. Monacelli, A. R. Weeks, G. Zummo, and G. D. Boreman, “Design, fabrication, and characterization of antenna-coupled metal-oxide-metal diodes for dual-band detection,” Opt. Eng. 44, 066401 (2005).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1989).

Codreanu, I.

Cressie, N.

N. Cressie, Statistics for Spatial Data (Wiley, 1991).

Crozier, K. B.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonators for local field enhancement,” J. Appl. Phys. 94, 4632-4642 (2003).
[Crossref]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light--linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917-1926 (2003).

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “The focus of light--theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109-113 (2001).

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “The focus of light--theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109-113 (2001).

Eisler, H.-J.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[Crossref] [PubMed]

Fumeaux, C.

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “The focus of light--theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109-113 (2001).

González, F. J.

F. J. González, B. Ilic, J. Alda, and G. D. Boreman, “Antenna-coupled infrared detectors for imaging applications,” IEEE J. Sel. Top. Quantum Electron. 11, 117-120 (2005).
[Crossref]

F. J. González and G. Boreman, “Comparison of dipole, bowtie, spiral and log-periodic IR antennas,” Infrared Phys. Technol. 46, 418-428 (2005).
[Crossref]

Hecht, B.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[Crossref] [PubMed]

Ilic, B.

F. J. González, B. Ilic, J. Alda, and G. D. Boreman, “Antenna-coupled infrared detectors for imaging applications,” IEEE J. Sel. Top. Quantum Electron. 11, 117-120 (2005).
[Crossref]

Kino, G. S.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonators for local field enhancement,” J. Appl. Phys. 94, 4632-4642 (2003).
[Crossref]

Kuipers, L.

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28-33 (2007).
[Crossref] [PubMed]

Lane, R. G.

W. Y. V. Leung, P. J. Bones, and R. G. Lane, “Statistical interpolation of sampled image,” Opt. Eng. 40, 547-553 (2001).
[Crossref]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light--linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917-1926 (2003).

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “The focus of light--theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109-113 (2001).

Leung, W. Y. V.

W. Y. V. Leung, P. J. Bones, and R. G. Lane, “Statistical interpolation of sampled image,” Opt. Eng. 40, 547-553 (2001).
[Crossref]

López-Alonso, J. M.

J. M. López-Alonso, B. Monacelli, J. Alda, and G. Boreman, “Uncertainty analysis in the measurement of the spatial responsivity of infrared antennas,” Appl. Opt. 21, 4557-4568 (2005).
[Crossref]

Martin, O. J. F.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[Crossref] [PubMed]

Mendoza-Yero, O.

O. Mendoza-Yero and J. Alda, “Irradiance map of an apertured Gaussian beam affected by coma,” Opt. Commun. 271, 517-523 (2007).
[Crossref]

Moerland, R. J.

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28-33 (2007).
[Crossref] [PubMed]

Monacelli, B.

J. M. López-Alonso, B. Monacelli, J. Alda, and G. Boreman, “Uncertainty analysis in the measurement of the spatial responsivity of infrared antennas,” Appl. Opt. 21, 4557-4568 (2005).
[Crossref]

M. R. Abdel-Rahman, B. Monacelli, A. R. Weeks, G. Zummo, and G. D. Boreman, “Design, fabrication, and characterization of antenna-coupled metal-oxide-metal diodes for dual-band detection,” Opt. Eng. 44, 066401 (2005).
[Crossref]

Mühlschlegel, P.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[Crossref] [PubMed]

Novotny, L.

P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single molecule fluorescence,” Nanotechnology 18, 044017 (2007).
[Crossref]

Pohl, D. W.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[Crossref] [PubMed]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light--linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917-1926 (2003).

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “The focus of light--theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109-113 (2001).

Quate, C. F.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonators for local field enhancement,” J. Appl. Phys. 94, 4632-4642 (2003).
[Crossref]

Sanchez-Brea, L. M.

L. M. Sanchez-Brea and E. Bernabeu, “Uncertainty estimation by convolution using spatial statistics,” IEEE Trans. Image Process. 15, 3131-3137 (2006).
[Crossref] [PubMed]

L. M. Sanchez-Brea and E. Bernabeu, “Determination of the optimum sampling frequency of noisy images by spatial statistic,” Appl. Opt. 44, 3276-3283 (2005).
[Crossref] [PubMed]

E. Bernabeu, I. Serroukh, and L. M. Sanchez-Brea, “A geometrical model for wire optical diffraction selected by experimental statistical analysis,” Opt. Eng. 38, 1319-1325 (1999).
[Crossref]

Schaefer, J.

Segerink, F. B.

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28-33 (2007).
[Crossref] [PubMed]

Serroukh, I.

E. Bernabeu, I. Serroukh, and L. M. Sanchez-Brea, “A geometrical model for wire optical diffraction selected by experimental statistical analysis,” Opt. Eng. 38, 1319-1325 (1999).
[Crossref]

Sundaramurthy, A.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonators for local field enhancement,” J. Appl. Phys. 94, 4632-4642 (2003).
[Crossref]

Taminiau, T. H.

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28-33 (2007).
[Crossref] [PubMed]

Toft, P.

P. Toft, “The radon transform--theory and implementation,” Ph.D. dissertation (Technical University of Denmark, 1996), http://petertoft.dk/PhD.

van Hulst, N. F.

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28-33 (2007).
[Crossref] [PubMed]

Weeks, A. R.

M. R. Abdel-Rahman, B. Monacelli, A. R. Weeks, G. Zummo, and G. D. Boreman, “Design, fabrication, and characterization of antenna-coupled metal-oxide-metal diodes for dual-band detection,” Opt. Eng. 44, 066401 (2005).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1989).

Zummo, G.

M. R. Abdel-Rahman, B. Monacelli, A. R. Weeks, G. Zummo, and G. D. Boreman, “Design, fabrication, and characterization of antenna-coupled metal-oxide-metal diodes for dual-band detection,” Opt. Eng. 44, 066401 (2005).
[Crossref]

Appl. Opt. (3)

Appl. Phys. B (1)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “The focus of light--theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109-113 (2001).

IEEE J. Sel. Top. Quantum Electron. (1)

F. J. González, B. Ilic, J. Alda, and G. D. Boreman, “Antenna-coupled infrared detectors for imaging applications,” IEEE J. Sel. Top. Quantum Electron. 11, 117-120 (2005).
[Crossref]

IEEE Trans. Image Process. (1)

L. M. Sanchez-Brea and E. Bernabeu, “Uncertainty estimation by convolution using spatial statistics,” IEEE Trans. Image Process. 15, 3131-3137 (2006).
[Crossref] [PubMed]

Infrared Phys. Technol. (1)

F. J. González and G. Boreman, “Comparison of dipole, bowtie, spiral and log-periodic IR antennas,” Infrared Phys. Technol. 46, 418-428 (2005).
[Crossref]

J. Appl. Phys. (1)

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonators for local field enhancement,” J. Appl. Phys. 94, 4632-4642 (2003).
[Crossref]

J. Mod. Opt. (1)

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light--linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917-1926 (2003).

Nano Lett. (1)

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28-33 (2007).
[Crossref] [PubMed]

Nanotechnology (1)

P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single molecule fluorescence,” Nanotechnology 18, 044017 (2007).
[Crossref]

Opt. Commun. (1)

O. Mendoza-Yero and J. Alda, “Irradiance map of an apertured Gaussian beam affected by coma,” Opt. Commun. 271, 517-523 (2007).
[Crossref]

Opt. Eng. (3)

E. Bernabeu, I. Serroukh, and L. M. Sanchez-Brea, “A geometrical model for wire optical diffraction selected by experimental statistical analysis,” Opt. Eng. 38, 1319-1325 (1999).
[Crossref]

W. Y. V. Leung, P. J. Bones, and R. G. Lane, “Statistical interpolation of sampled image,” Opt. Eng. 40, 547-553 (2001).
[Crossref]

M. R. Abdel-Rahman, B. Monacelli, A. R. Weeks, G. Zummo, and G. D. Boreman, “Design, fabrication, and characterization of antenna-coupled metal-oxide-metal diodes for dual-band detection,” Opt. Eng. 44, 066401 (2005).
[Crossref]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

Science (1)

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[Crossref] [PubMed]

Other (3)

N. Cressie, Statistics for Spatial Data (Wiley, 1991).

P. Toft, “The radon transform--theory and implementation,” Ph.D. dissertation (Technical University of Denmark, 1996), http://petertoft.dk/PhD.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1989).

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Figures (8)

Fig. 1
Fig. 1

(Color online) Experimental setup.

Fig. 2
Fig. 2

Profiles Q ( u , θ ) . The spatial step is Δ x = 35.3   nm . Eighteen profiles have been measured from 0° to 170° each Δ θ = 10 ° ± 2 ° . The inset contains a diagram of the measurement of Q ( u , θ ) .

Fig. 3
Fig. 3

Sinogram P ^ ( u , θ ) and sinogram error Δ P ^ ( u , θ ) . The sinogram error is practically independent from θ, meaning that all the information about the error in the measurement of P ^ ( u , θ ) is contained in any of the slices of Δ P ^ ( u , θ ) . However, a complete reconstruction of the beam needs all the slices.

Fig. 4
Fig. 4

Beam irradiance map in arbitrary units employing the radon transform and its SNR.

Fig. 5
Fig. 5

Beam irradiance map in arbitrary units employing the fitting method and its SNR.

Fig. 6
Fig. 6

Kriging versus Golay filtering approaches. The figure on the top shows the derivative of Q ( u , θ = 70 ° ) , the Golay filter, and the kriging filter estimations of it. On the bottom, we zoom the previous data, adding the kriging error curves. The light gray curve is the derivative of Q ( u θ ) . The smooth thick solid curve is the kriging estimation. The dashed curves above and below the previous one represent the error in the kriging estimation. Finally, the thin solid curve is the result after applying the Golay filter to the derivative of Q ( u θ ) .

Fig. 7
Fig. 7

Beam irradiance map in abitrary units after applying the Golay filter. Please note that the negative values of the irradiance map are unphysical. They are artifacts inherently linked to the noise induced by the derivative of Q ( u , θ ) in the beam tails, where the irradiance is close to zero.

Fig. 8
Fig. 8

Top: A, the spatial response computed with the radon transform method. Bottom: B, the spatial response obtained from the fitting to a beam model.

Equations (10)

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P ( u , θ ) = I ( x , y ) δ ( u x   cos   θ y   sin   θ ) d x d y ,
Q ( u , θ ) = u P ( u , θ ) d u ,
P ( u , θ ) = Q ( u , θ ) u .
I ( x , y ) = 1 ( P ( u , θ ) ) = 0 π d ρ d θ | ρ | [ P ( u , θ ) e i ρ u d u ] × e i ρ ( x   cos   θ + y   sin   θ )
E ( x , y ) = e [ ( x 2 + y 2 ) / ω 0 2 ] { 2 J 1 ( ν ) ν ( cos   ϕ 2 J 4 ( ν ) ν ) α 1 2 ν ( J 1 ( ν ) 4 J 3 ( ν ) 20 + J 5 ( ν ) 4 9 J 7 ( ν ) 20 cos   2 ϕ ( 2 J 3 ( ν ) 5 + 3 J 7 ( ν ) 5 ) ) α 2 } .
P error ± = P ^ ± Δ P ^ .
I error ± = 1 ( P error ± ) .
Δ I = 1 ( Δ P ^ ) = I error + I error 2 .
SNR = I ( x , y ) Δ I ( x , y ) .
S ( x , y ) = I ( x , y ) R ( x x , y y ) d x d y ,

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