Abstract

The tomographic reconstruction of the refractive index distribution in a large-mode-area photonic fiber is presented. The results of the diffraction tomographic algorithm and classical filtered backprojection method are compared. Additionally, the application of the synthetic aperture technique to tomographic interferometry, as a tool for resolution enhancement, is presented and discussed.

© 2007 Optical Society of America

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References

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  1. H. Phillip, T. Neger, and H. Jager, Measurement 10, 170 (1992).
    [CrossRef]
  2. W. Gorski, Opt. Eng. 45, 125002 (2006).
    [CrossRef]
  3. B. L. Bachim, and T. K. Gaylord, Appl. Opt. 44, 316 (2005).
    [CrossRef] [PubMed]
  4. W. Gorski, Opt. Lasers Eng. 41, 565 (2002).
    [CrossRef]
  5. P. Kniazewski, W. Gorski, and M. Kujawinska, Proc. SPIE 5145, 107 (2003).
    [CrossRef]
  6. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).
  7. J. C. Russ, The Image Processing Handbook, 3rd ed. (CRC Press, 1999).
  8. Thorlabs Online Catalog (Nanopositioning section), http://www.thorlabs.com/Navigation.cfm?GuidelowbarID=144&VisuallowbarID=2248.
  9. D.W.Robinson and G.T.Reid, eds., Interferogram analysis: Digital Fringe Pattern Measurement Techniques (Institue of Physics, 1993).
  10. F. Natterer, The Mathematics of Computerized Tomography (Wiley, 1986).
  11. C. J. Schwarz, Y. Kuznetsova, and S. R. J. Brueck, Opt. Lett. 28, 1424 (2003).
    [CrossRef] [PubMed]

2006 (1)

W. Gorski, Opt. Eng. 45, 125002 (2006).
[CrossRef]

2005 (1)

2003 (2)

P. Kniazewski, W. Gorski, and M. Kujawinska, Proc. SPIE 5145, 107 (2003).
[CrossRef]

C. J. Schwarz, Y. Kuznetsova, and S. R. J. Brueck, Opt. Lett. 28, 1424 (2003).
[CrossRef] [PubMed]

2002 (1)

W. Gorski, Opt. Lasers Eng. 41, 565 (2002).
[CrossRef]

1992 (1)

H. Phillip, T. Neger, and H. Jager, Measurement 10, 170 (1992).
[CrossRef]

Bachim, B. L.

Brueck, S. R. J.

Gaylord, T. K.

Gorski, W.

W. Gorski, Opt. Eng. 45, 125002 (2006).
[CrossRef]

P. Kniazewski, W. Gorski, and M. Kujawinska, Proc. SPIE 5145, 107 (2003).
[CrossRef]

W. Gorski, Opt. Lasers Eng. 41, 565 (2002).
[CrossRef]

Jager, H.

H. Phillip, T. Neger, and H. Jager, Measurement 10, 170 (1992).
[CrossRef]

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

Kniazewski, P.

P. Kniazewski, W. Gorski, and M. Kujawinska, Proc. SPIE 5145, 107 (2003).
[CrossRef]

Kujawinska, M.

P. Kniazewski, W. Gorski, and M. Kujawinska, Proc. SPIE 5145, 107 (2003).
[CrossRef]

Kuznetsova, Y.

Natterer, F.

F. Natterer, The Mathematics of Computerized Tomography (Wiley, 1986).

Neger, T.

H. Phillip, T. Neger, and H. Jager, Measurement 10, 170 (1992).
[CrossRef]

Phillip, H.

H. Phillip, T. Neger, and H. Jager, Measurement 10, 170 (1992).
[CrossRef]

Russ, J. C.

J. C. Russ, The Image Processing Handbook, 3rd ed. (CRC Press, 1999).

Schwarz, C. J.

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

Appl. Opt. (1)

Measurement (1)

H. Phillip, T. Neger, and H. Jager, Measurement 10, 170 (1992).
[CrossRef]

Opt. Eng. (1)

W. Gorski, Opt. Eng. 45, 125002 (2006).
[CrossRef]

Opt. Lasers Eng. (1)

W. Gorski, Opt. Lasers Eng. 41, 565 (2002).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

P. Kniazewski, W. Gorski, and M. Kujawinska, Proc. SPIE 5145, 107 (2003).
[CrossRef]

Other (5)

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

J. C. Russ, The Image Processing Handbook, 3rd ed. (CRC Press, 1999).

Thorlabs Online Catalog (Nanopositioning section), http://www.thorlabs.com/Navigation.cfm?GuidelowbarID=144&VisuallowbarID=2248.

D.W.Robinson and G.T.Reid, eds., Interferogram analysis: Digital Fringe Pattern Measurement Techniques (Institue of Physics, 1993).

F. Natterer, The Mathematics of Computerized Tomography (Wiley, 1986).

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Figures (5)

Fig. 1
Fig. 1

Interferometric tomography principle using Fourier diffraction theorem.

Fig. 2
Fig. 2

Experimental setup of a tomographic microinterferometer that allows the tilting of the imaging system. The microscope objectives are either 20 × ( NA = 0.4 ) or 4 × ( NA = 0.1 ) .

Fig. 3
Fig. 3

Single tomogram [ n ( x , y , z 0 ) layer] of a photonic crystal fiber ESM 12-01, (a) reference SEM image of the cross-section of the fiber (from www.blazephotonics.com); (b) reconstruction using diffraction tomography; (c) reconstruction using filtered backprojection.

Fig. 4
Fig. 4

Tomographic reconstruction using diffraction tomography, with scaling to the refractive index values, (a) full cross-section of the fiber; (b) refractive index profile along line A - A from Fig. 4a. Resolution, fiber diameter ( 125 μ m ) = 365   pixels , imaging system NA = 0.4 .

Fig. 5
Fig. 5

Single tomogram (a layer) of a photonic crystal fiber ESM 12-01, measured with the synthetic aperture method and diffraction tomography (zoomed central area only); (a) on-axis only ( NA = 0.1 ) , (b) synthetic aperture resulting in NA = 0.15 .

Equations (1)

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res = λ 2 NA .

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