Abstract

A novel tomographic algorithm for reconstructing the two-dimensional refractive index fluctuations of an optically thick phase object from one-dimensional projections acquired at a multiplicity of focal positions and a multiplicity of angular orientations is described. The new method is validated by measurements of multicore and microstructured optical fibers using interference microscopy. The method will benefit other transverse fiber measurement technologies and is broadly applicable to any tomographic reconstruction problem in which the transverse dimension of the specimen is substantially larger than the depth-of-field of the imaging system.

© 2013 Optical Society of America

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References

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  1. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).
  2. A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, Opt. Commun. 175, 329 (2000).
    [CrossRef]
  3. B. L. Bachim and T. K. Gaylord, Appl. Opt. 44, 316 (2005).
    [CrossRef]
  4. B. L. Bachim, T. K. Gaylord, and S. C. Mettler, Opt. Lett. 30, 1126 (2005).
    [CrossRef]
  5. W. Gorski and W. Osten, Opt. Lett. 32, 1977 (2007).
    [CrossRef]
  6. N. M. Dragomir, X. M. Goh, and A. Roberts, Microsc. Res. Tech. 71, 5 (2008).
    [CrossRef]
  7. P. Kniazewski, T. Kozacki, and M. Kujawinska, Opt. Lasers Eng. 47, 259 (2009).
    [CrossRef]
  8. A. D. Yablon, Opt. Eng. 50, 111603 (2011).
    [CrossRef]
  9. M. Jenkins and T. K. Gaylord, in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of America, 2012), paper FTh3C.2.
  10. B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, Opt. Express 19, 16665 (2011).
    [CrossRef]
  11. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, Opt. Express 19, 16576 (2011).
    [CrossRef]
  12. A. D. Yablon, IEEE J. Lightwave Technol. 28, 360 (2010).
  13. S. W. Smith, The Scientists and Engineer’s Guide to Digital Signal Processing (California Technical Publishing, 1997).
  14. G. N. Ramachandran and A. V. Lakshminarayanan, Proc. Natl. Acad. Sci. USA 68, 2236 (1971).
    [CrossRef]

2011 (3)

2010 (1)

A. D. Yablon, IEEE J. Lightwave Technol. 28, 360 (2010).

2009 (1)

P. Kniazewski, T. Kozacki, and M. Kujawinska, Opt. Lasers Eng. 47, 259 (2009).
[CrossRef]

2008 (1)

N. M. Dragomir, X. M. Goh, and A. Roberts, Microsc. Res. Tech. 71, 5 (2008).
[CrossRef]

2007 (1)

2005 (2)

2000 (1)

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, Opt. Commun. 175, 329 (2000).
[CrossRef]

1971 (1)

G. N. Ramachandran and A. V. Lakshminarayanan, Proc. Natl. Acad. Sci. USA 68, 2236 (1971).
[CrossRef]

Bachim, B. L.

Barty, A.

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, Opt. Commun. 175, 329 (2000).
[CrossRef]

Chandrasekhar, S.

Dimarcello, F. V.

Dragomir, N. M.

N. M. Dragomir, X. M. Goh, and A. Roberts, Microsc. Res. Tech. 71, 5 (2008).
[CrossRef]

Fini, J. M.

Fishteyn, M.

Gaylord, T. K.

B. L. Bachim, T. K. Gaylord, and S. C. Mettler, Opt. Lett. 30, 1126 (2005).
[CrossRef]

B. L. Bachim and T. K. Gaylord, Appl. Opt. 44, 316 (2005).
[CrossRef]

M. Jenkins and T. K. Gaylord, in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of America, 2012), paper FTh3C.2.

Goh, X. M.

N. M. Dragomir, X. M. Goh, and A. Roberts, Microsc. Res. Tech. 71, 5 (2008).
[CrossRef]

Gorski, W.

Hayashi, T.

Jenkins, M.

M. Jenkins and T. K. Gaylord, in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of America, 2012), paper FTh3C.2.

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).

Kniazewski, P.

P. Kniazewski, T. Kozacki, and M. Kujawinska, Opt. Lasers Eng. 47, 259 (2009).
[CrossRef]

Kozacki, T.

P. Kniazewski, T. Kozacki, and M. Kujawinska, Opt. Lasers Eng. 47, 259 (2009).
[CrossRef]

Kujawinska, M.

P. Kniazewski, T. Kozacki, and M. Kujawinska, Opt. Lasers Eng. 47, 259 (2009).
[CrossRef]

Lakshminarayanan, A. V.

G. N. Ramachandran and A. V. Lakshminarayanan, Proc. Natl. Acad. Sci. USA 68, 2236 (1971).
[CrossRef]

Liu, X.

Mettler, S. C.

Monberg, E. M.

Nugent, K. A.

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, Opt. Commun. 175, 329 (2000).
[CrossRef]

Osten, W.

Paganin, D.

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, Opt. Commun. 175, 329 (2000).
[CrossRef]

Ramachandran, G. N.

G. N. Ramachandran and A. V. Lakshminarayanan, Proc. Natl. Acad. Sci. USA 68, 2236 (1971).
[CrossRef]

Roberts, A.

N. M. Dragomir, X. M. Goh, and A. Roberts, Microsc. Res. Tech. 71, 5 (2008).
[CrossRef]

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, Opt. Commun. 175, 329 (2000).
[CrossRef]

Sasaki, T.

Sasaoka, E.

Shimakawa, O.

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).

Smith, S. W.

S. W. Smith, The Scientists and Engineer’s Guide to Digital Signal Processing (California Technical Publishing, 1997).

Taru, T.

Taunay, T. F.

Yablon, A. D.

A. D. Yablon, Opt. Eng. 50, 111603 (2011).
[CrossRef]

A. D. Yablon, IEEE J. Lightwave Technol. 28, 360 (2010).

Yan, M. F.

Zhu, B.

Appl. Opt. (1)

IEEE J. Lightwave Technol. (1)

A. D. Yablon, IEEE J. Lightwave Technol. 28, 360 (2010).

Microsc. Res. Tech. (1)

N. M. Dragomir, X. M. Goh, and A. Roberts, Microsc. Res. Tech. 71, 5 (2008).
[CrossRef]

Opt. Commun. (1)

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, Opt. Commun. 175, 329 (2000).
[CrossRef]

Opt. Eng. (1)

A. D. Yablon, Opt. Eng. 50, 111603 (2011).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (1)

P. Kniazewski, T. Kozacki, and M. Kujawinska, Opt. Lasers Eng. 47, 259 (2009).
[CrossRef]

Opt. Lett. (2)

Proc. Natl. Acad. Sci. USA (1)

G. N. Ramachandran and A. V. Lakshminarayanan, Proc. Natl. Acad. Sci. USA 68, 2236 (1971).
[CrossRef]

Other (3)

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).

M. Jenkins and T. K. Gaylord, in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of America, 2012), paper FTh3C.2.

S. W. Smith, The Scientists and Engineer’s Guide to Digital Signal Processing (California Technical Publishing, 1997).

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Figures (4)

Fig. 1.
Fig. 1.

Effect of focal position on measured optical path length when the specimen is larger than the imaging depth-of-field.

Fig. 2.
Fig. 2.

Schematic illustration of new multifocus tomographic reconstruction algorithm applied to a single off-center core. The dashed lines schematically illustrate locations of (filtered) one-dimensional projections, each acquired at distinct focal plane locations. The collection of one-dimensional projections at a particular angular orientation comprise a two-dimensional matrix that is represented here as a gray-scale image (for brevity only the 0°, 45°, and 90° angles are shown here). The gray-scale images are accumulated in a final unified coordinate system as illustrated in this figure. Note that the gray-scale images produced by the new algorithm vary as a function of lateral position (parallel to the dashed lines) and also as a function of focal position (perpendicular to the dashed lines). Conventional filtered backprojection does not consider any variation with respect to focal position, so that the data comprising the gray-scale images does not vary as a function of focal position when performing conventional filtered backprojection. Compare to Figs. 25–17 of [13].

Fig. 3.
Fig. 3.

Refractive index measurement of four-core multicore fiber reconstructed using (a) conventional filtered backprojection and (b) using the new algorithm. False color is Δn, the difference between the measured refractive index and the surrounding refractive index matching oil.

Fig. 4.
Fig. 4.

Refractive index measurement of air-silica microstructured optical fiber at 632.8 nm.

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