Abstract

We introduce the concept of Doppler-assisted tomography (DAT) and show that it can be applied successfully to non-invasive imaging of the internal microstructure of a photonic crystal fiber. The fiber is spun at ~10 Hz around its axis and laterally illuminated with a laser beam. Monitoring the time-dependent Doppler shift of the light scattered by the hollow channels permits the azimuthal angle and radial position of individual channels to be measured. An inverse Radon transform is used to construct an image of the microstructure from the frequency-modulated scattered signal. We also show that DAT can image sub-wavelength features and monitor the structure along a tapered fiber, which is not possible using other techniques without cutting up the taper into several short pieces or filling it with index-matching oil. The non-destructive nature of DAT means that it could potentially be applied to image the fiber microstructure as it emerges from the drawing tower, or indeed to carry out tomography on any transparent microstructured cylindrical object.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  3. J. M. Dudley and J. R. Taylor, Optical Fiber Supercontinuum Generation (Cambridge University Press, 2010), Chap. 7.
  4. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
    [Crossref]
  5. A. D. Yablon, “Multi-Wavelength Optical Fiber Refractive Index Profiling by Spatially Resolved Fourier Transform Spectroscopy,” J. Lightwave Technol. 28(4), 360–364 (2010).
    [Crossref]
  6. A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
    [Crossref] [PubMed]
  7. J. B. Aniano, “System for determining birefringent axes in polarization-maintaining optical fiber,” U.S. patent005317575A (May 31, 1994).
  8. L. S. Watkins, “Scattering from side-illuminated clad glass fibers for determination of fiber parameters,” J. Opt. Soc. Am. 64(6), 767–772 (1974).
    [Crossref]
  9. P.-E. Hansen and S. Burger, “Investigation of microstructured fiber geometries by scatterometry,” Proc. SPIE 8789, 87890R (2013).
    [Crossref]
  10. L. Y. Zang, T. G. Euser, M. S. Kang, M. Scharrer, and P. St. J. Russell, “Structural analysis of photonic crystal fibers by side scattering of laser light,” Opt. Lett. 36(9), 1668–1670 (2011).
    [Crossref] [PubMed]
  11. S. D. Lim, S.-G. Lee, K. Lee, and S. B. Lee, “Determination of Crystallographic Axes of Photonic Crystal Fiber by Transversal Scanning Method,” Jpn. J. Appl. Phys. 49(10), 102503 (2010).
    [Crossref]
  12. A. D. Yablon, “Multifocus tomographic algorithm for measuring optically thick specimens,” Opt. Lett. 38(21), 4393–4396 (2013).
    [Crossref] [PubMed]
  13. M. Jenkins and T. Gaylord, “3D Characterization of the Refractive-Index and Residual-Stress Distributions in Optical Fibers,” in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (Optical Society of America, 2011), paper FMG4.
  14. W. Gorski and W. Osten, “Tomographic imaging of photonic crystal fibers,” Opt. Lett. 32(14), 1977–1979 (2007).
    [Crossref] [PubMed]
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    [Crossref]
  16. H. H. Barrett, “The Radon Transform and its Applications,” in Progress in Optics XXI, E. Wolf ed. (North Holland, 1984).
  17. A. G. Lindgren and P. A. Rattey, “The Inverse Discrete Radon Transform with Applications to Tomographic Imaging Using Projection Data,” in Advances in Electronics and Electron Physics 56, C. Marton ed. (Academic Press, 1981).
  18. C. M. Vest, “Formation of images from projections: Radon and Abel transforms,” J. Opt. Soc. Am. 64(9), 1215–1218 (1974).
    [Crossref]
  19. T. W. Haensch, Nobel Lecture (2005); http://www.nobelprize.org/nobel_prizes/physics/laureates/2005/hansch-lecture.pdf .
  20. A. Lange and M. P. Hentschel, “Direct Iterative Reconstruction of Computed Tomography Trajectories (DIRECTT),” in Proceedings of DIR 2007 - International Symposium on Digital industrial Radiology and Computed Tomography, Technical Digest (CD) (INSA-Lyon, 2007).
  21. L. Zang, M. S. Kang, M. Kolesik, M. Scharrer, and P. St. J. Russell, “Dispersion of photonic Bloch modes in periodically twisted birefringent media,” J. Opt. Soc. Am. B 27(9), 1742–1750 (2010).
    [Crossref]
  22. G. K. L. Wong, L. Zang, M. S. Kang, and P. St. J. Russell, “Measurement of group-velocity dispersion of Bloch modes in photonic-crystal-fiber rocking filters,” Opt. Lett. 35(23), 3982–3984 (2010).
    [Crossref] [PubMed]
  23. G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of Orbital Angular Momentum Resonances in Helically Twisted Photonic Crystal Fiber,” Science 337(6093), 446–449 (2012).
    [Crossref] [PubMed]
  24. M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Vortices and superfluidity in a strongly interacting Fermi gas,” Nature 435(7045), 1047–1051 (2005).
    [Crossref] [PubMed]

2013 (2)

P.-E. Hansen and S. Burger, “Investigation of microstructured fiber geometries by scatterometry,” Proc. SPIE 8789, 87890R (2013).
[Crossref]

A. D. Yablon, “Multifocus tomographic algorithm for measuring optically thick specimens,” Opt. Lett. 38(21), 4393–4396 (2013).
[Crossref] [PubMed]

2012 (2)

S. P. Stark, J. C. Travers, and P. St. J. Russell, “Extreme supercontinuum generation to the deep UV,” Opt. Lett. 37(5), 770–772 (2012).
[Crossref] [PubMed]

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of Orbital Angular Momentum Resonances in Helically Twisted Photonic Crystal Fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (4)

2007 (1)

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

2005 (1)

M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Vortices and superfluidity in a strongly interacting Fermi gas,” Nature 435(7045), 1047–1051 (2005).
[Crossref] [PubMed]

2003 (1)

P. St. J. Russell, “Photonic Crystal Fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

1998 (1)

1974 (2)

Abo-Shaeer, J. R.

M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Vortices and superfluidity in a strongly interacting Fermi gas,” Nature 435(7045), 1047–1051 (2005).
[Crossref] [PubMed]

Barty, A.

Biancalana, F.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of Orbital Angular Momentum Resonances in Helically Twisted Photonic Crystal Fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Burger, S.

P.-E. Hansen and S. Burger, “Investigation of microstructured fiber geometries by scatterometry,” Proc. SPIE 8789, 87890R (2013).
[Crossref]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Conti, C.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of Orbital Angular Momentum Resonances in Helically Twisted Photonic Crystal Fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Euser, T. G.

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Gorski, W.

Hansen, P.-E.

P.-E. Hansen and S. Burger, “Investigation of microstructured fiber geometries by scatterometry,” Proc. SPIE 8789, 87890R (2013).
[Crossref]

Kang, M. S.

Ketterle, W.

M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Vortices and superfluidity in a strongly interacting Fermi gas,” Nature 435(7045), 1047–1051 (2005).
[Crossref] [PubMed]

Kolesik, M.

Lee, H. W.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of Orbital Angular Momentum Resonances in Helically Twisted Photonic Crystal Fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Lee, K.

S. D. Lim, S.-G. Lee, K. Lee, and S. B. Lee, “Determination of Crystallographic Axes of Photonic Crystal Fiber by Transversal Scanning Method,” Jpn. J. Appl. Phys. 49(10), 102503 (2010).
[Crossref]

Lee, S. B.

S. D. Lim, S.-G. Lee, K. Lee, and S. B. Lee, “Determination of Crystallographic Axes of Photonic Crystal Fiber by Transversal Scanning Method,” Jpn. J. Appl. Phys. 49(10), 102503 (2010).
[Crossref]

Lee, S.-G.

S. D. Lim, S.-G. Lee, K. Lee, and S. B. Lee, “Determination of Crystallographic Axes of Photonic Crystal Fiber by Transversal Scanning Method,” Jpn. J. Appl. Phys. 49(10), 102503 (2010).
[Crossref]

Lim, S. D.

S. D. Lim, S.-G. Lee, K. Lee, and S. B. Lee, “Determination of Crystallographic Axes of Photonic Crystal Fiber by Transversal Scanning Method,” Jpn. J. Appl. Phys. 49(10), 102503 (2010).
[Crossref]

Nugent, K. A.

Osten, W.

Paganin, D.

Roberts, A.

Russell, P. St. J.

Scharrer, M.

Schirotzek, A.

M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Vortices and superfluidity in a strongly interacting Fermi gas,” Nature 435(7045), 1047–1051 (2005).
[Crossref] [PubMed]

Schunck, C. H.

M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Vortices and superfluidity in a strongly interacting Fermi gas,” Nature 435(7045), 1047–1051 (2005).
[Crossref] [PubMed]

Stark, S. P.

Travers, J. C.

Vest, C. M.

Watkins, L. S.

Weiss, T.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of Orbital Angular Momentum Resonances in Helically Twisted Photonic Crystal Fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Wong, G. K. L.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of Orbital Angular Momentum Resonances in Helically Twisted Photonic Crystal Fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

G. K. L. Wong, L. Zang, M. S. Kang, and P. St. J. Russell, “Measurement of group-velocity dispersion of Bloch modes in photonic-crystal-fiber rocking filters,” Opt. Lett. 35(23), 3982–3984 (2010).
[Crossref] [PubMed]

Yablon, A. D.

Zang, L.

Zang, L. Y.

Zwierlein, M. W.

M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Vortices and superfluidity in a strongly interacting Fermi gas,” Nature 435(7045), 1047–1051 (2005).
[Crossref] [PubMed]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (2)

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

Jpn. J. Appl. Phys. (1)

S. D. Lim, S.-G. Lee, K. Lee, and S. B. Lee, “Determination of Crystallographic Axes of Photonic Crystal Fiber by Transversal Scanning Method,” Jpn. J. Appl. Phys. 49(10), 102503 (2010).
[Crossref]

Nature (1)

M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Vortices and superfluidity in a strongly interacting Fermi gas,” Nature 435(7045), 1047–1051 (2005).
[Crossref] [PubMed]

Opt. Lett. (6)

Proc. SPIE (1)

P.-E. Hansen and S. Burger, “Investigation of microstructured fiber geometries by scatterometry,” Proc. SPIE 8789, 87890R (2013).
[Crossref]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Science (2)

P. St. J. Russell, “Photonic Crystal Fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of Orbital Angular Momentum Resonances in Helically Twisted Photonic Crystal Fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Other (8)

J. M. Dudley and J. R. Taylor, Optical Fiber Supercontinuum Generation (Cambridge University Press, 2010), Chap. 7.

J. B. Aniano, “System for determining birefringent axes in polarization-maintaining optical fiber,” U.S. patent005317575A (May 31, 1994).

A. Stefani, M. H. Frosz, T. G. Euser, G. K. L. Wong, and P. St. J. Russell, “Doppler-Assisted Tomography of Photonic Crystal Fiber Structure by Side-Scattering,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America,2014).
[Crossref]

H. H. Barrett, “The Radon Transform and its Applications,” in Progress in Optics XXI, E. Wolf ed. (North Holland, 1984).

A. G. Lindgren and P. A. Rattey, “The Inverse Discrete Radon Transform with Applications to Tomographic Imaging Using Projection Data,” in Advances in Electronics and Electron Physics 56, C. Marton ed. (Academic Press, 1981).

M. Jenkins and T. Gaylord, “3D Characterization of the Refractive-Index and Residual-Stress Distributions in Optical Fibers,” in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (Optical Society of America, 2011), paper FMG4.

T. W. Haensch, Nobel Lecture (2005); http://www.nobelprize.org/nobel_prizes/physics/laureates/2005/hansch-lecture.pdf .

A. Lange and M. P. Hentschel, “Direct Iterative Reconstruction of Computed Tomography Trajectories (DIRECTT),” in Proceedings of DIR 2007 - International Symposium on Digital industrial Radiology and Computed Tomography, Technical Digest (CD) (INSA-Lyon, 2007).

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Figures (8)

Fig. 1
Fig. 1 Schematic of the DAT set-up at t = 0 (not to scale). One part of the laser beam is incident on the rotating fibre, the other being frequency shifted at a pair of Bragg cells. The Doppler-shifted scattered light (fD ~1 kHz is a typical value at frot ~300 rpm) is combined with the frequency-shifted light and the beat-note detected at a square-law detector.
Fig. 2
Fig. 2 Illustration of the working principle of DAT. (a) Sample structure with three holes. (b) Frequency shift fD versus rotation angle assuming single scattering (follows Eq. (1)). The vertical black line indicates the rotation angle θ analyzed further in Fig. 2(c). (c) Possible locations of each hole lie on straight lines, sloping at angle θ, spaced from the origin a distance proportional to fD. (d) Combination of several snap-shots at different angles yields the positions of the scatterers.
Fig. 3
Fig. 3 (a,e) Scanning electron micrographs (SEMs) of simple structures. (b,f) Apertured fast Fourier transforms (FFTs). The y-axis shows the frequency shifts normalized to the rotation frequency. (c,g) Examples of the spectra of the time-apertured FFTs at one rotation angle. (d,h) DAT reconstructions of (a) and (e) using the inverse Radon transform.
Fig. 4
Fig. 4 Schematic of the principle behind reduction of multiple scattering. The illuminating beam is scanned across the structure. (a) to (f) Reconstructions made as more and more of the structure is illuminated by the beam. The scan distance between each measurement was ~4 µm and the laser beam width was ~20 µm FWHM. (g) Image obtained by summing reconstructions (a) to (e).
Fig. 5
Fig. 5 (a) SEM of a PCF with two rings of air-holes. (b) DAT reconstruction obtained by scanning across the structure and by summing the different contributions; 23 different reconstructions were summed.
Fig. 6
Fig. 6 (a) SEM of a PCF with three rings. (b) DAT reconstruction obtained by scanning across the structure and by summing 17 different reconstructions. The reconstruction is plotted with the contours of the actual fiber structure overlaid.
Fig. 7
Fig. 7 Measurements of a fiber taper. (a) Optical side-images of the PCF. (b) Diameter of the internal structure reconstructed by DAT, plotted against position along the taper. Inset: SEM of the fibre structure at the beginning of the taper.
Fig. 8
Fig. 8 (a-c) SEMs of the PCF fabricated for studying the identification of tiny holes. The hole diameter ranges are: (a) 1.15 µm to 530 nm, (b) 340 nm to 40 nm (c) 160 nm. (d-f) DAT reconstructions of the fibers showed in (a-c).

Equations (1)

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f D ( t ) = Ω ρ i n λ cos ( Ω t + ϕ i α 2 ) sin α 2

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