Abstract

We present an analytical method that yields the real and imaginary parts of the refractive index (RI) from low- coherence interferometry measurements, leading to the separation of the scattering and absorption coefficients of turbid samples. The imaginary RI is measured using time-frequency analysis, with the real part obtained by analyzing the nonlinear phase induced by a sample. A derivation relating the real part of the RI to the nonlinear phase term of the signal is presented, along with measurements from scattering and nonscattering samples that exhibit absorption due to hemoglobin.

© 2010 Optical Society of America

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References

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  1. M. Friebel, A. Roggan, G. Müller, and M. Meinke, J. Biomed. Opt. 11, 034021 (2006).
    [CrossRef]
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    [CrossRef]
  3. D. Faber, E. Mik, M. Aalders, and T. van Leeuwen, Opt. Lett. 30, 1015 (2005).
    [CrossRef] [PubMed]
  4. F. Robles, R. N. Graf, and A. Wax, Opt. Express 17, 6799(2009).
    [CrossRef] [PubMed]
  5. D. J. Faber and T. van Leeuwen, Opt. Lett. 34, 1435 (2009).
    [CrossRef] [PubMed]
  6. Y. Park, T. Yamauchi, W. Choi, R. Dasari, and M. S. Feld, Opt. Lett. 34, 3668 (2009).
    [CrossRef] [PubMed]
  7. J. A. Izatt and M. A. Choma, in Optical Coherence Tomography: Technology and Applications, W.Drexler and J.G.Fujimoto, eds. (Springer, 2008), pp. 47–72.
    [CrossRef]
  8. F. Robles and A. Wax, Opt. Lett. 35, 360 (2010).
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  9. Y. Zhu, N. Terry, and A. Wax, Opt. Lett. 34, 3196 (2009).
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  10. S. Prahl, “Optical Absorption of Hemoglobin,” http://omlc.ogi.edu/spectra/hemoglobin/.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2010 (1)

2009 (5)

2006 (1)

M. Friebel, A. Roggan, G. Müller, and M. Meinke, J. Biomed. Opt. 11, 034021 (2006).
[CrossRef]

2005 (1)

2004 (1)

D. Faber, M. Aalders, E. Mik, B. Hooper, M. van Gemert, and T. van Leeuwen, Phys. Rev. Lett. 93, 028102 (2004).
[CrossRef] [PubMed]

1991 (1)

Aalders, M.

D. Faber, E. Mik, M. Aalders, and T. van Leeuwen, Opt. Lett. 30, 1015 (2005).
[CrossRef] [PubMed]

D. Faber, M. Aalders, E. Mik, B. Hooper, M. van Gemert, and T. van Leeuwen, Phys. Rev. Lett. 93, 028102 (2004).
[CrossRef] [PubMed]

Choi, W.

Choma, M. A.

J. A. Izatt and M. A. Choma, in Optical Coherence Tomography: Technology and Applications, W.Drexler and J.G.Fujimoto, eds. (Springer, 2008), pp. 47–72.
[CrossRef]

Dasari, R.

Drexler, W.

Faber, D.

D. Faber, E. Mik, M. Aalders, and T. van Leeuwen, Opt. Lett. 30, 1015 (2005).
[CrossRef] [PubMed]

D. Faber, M. Aalders, E. Mik, B. Hooper, M. van Gemert, and T. van Leeuwen, Phys. Rev. Lett. 93, 028102 (2004).
[CrossRef] [PubMed]

Faber, D. J.

Feld, M. S.

Friebel, M.

M. Friebel, A. Roggan, G. Müller, and M. Meinke, J. Biomed. Opt. 11, 034021 (2006).
[CrossRef]

Graf, R. N.

Hermann, B.

Hofer, B.

Hooper, B.

D. Faber, M. Aalders, E. Mik, B. Hooper, M. van Gemert, and T. van Leeuwen, Phys. Rev. Lett. 93, 028102 (2004).
[CrossRef] [PubMed]

Izatt, J. A.

J. A. Izatt and M. A. Choma, in Optical Coherence Tomography: Technology and Applications, W.Drexler and J.G.Fujimoto, eds. (Springer, 2008), pp. 47–72.
[CrossRef]

Meier, C.

Meinke, M.

M. Friebel, A. Roggan, G. Müller, and M. Meinke, J. Biomed. Opt. 11, 034021 (2006).
[CrossRef]

Mik, E.

D. Faber, E. Mik, M. Aalders, and T. van Leeuwen, Opt. Lett. 30, 1015 (2005).
[CrossRef] [PubMed]

D. Faber, M. Aalders, E. Mik, B. Hooper, M. van Gemert, and T. van Leeuwen, Phys. Rev. Lett. 93, 028102 (2004).
[CrossRef] [PubMed]

Moes, J. M.

Müller, G.

M. Friebel, A. Roggan, G. Müller, and M. Meinke, J. Biomed. Opt. 11, 034021 (2006).
[CrossRef]

Park, Y.

Prahl, S.

S. Prahl, “Optical Absorption of Hemoglobin,” http://omlc.ogi.edu/spectra/hemoglobin/.

Prahl, S. A.

Robles, F.

Roggan, A.

M. Friebel, A. Roggan, G. Müller, and M. Meinke, J. Biomed. Opt. 11, 034021 (2006).
[CrossRef]

Terry, N.

van Gemert, M.

D. Faber, M. Aalders, E. Mik, B. Hooper, M. van Gemert, and T. van Leeuwen, Phys. Rev. Lett. 93, 028102 (2004).
[CrossRef] [PubMed]

van Leeuwen, T.

van Marle, J.

van Staveren, H. J.

Wax, A.

Yamauchi, T.

Zhu, Y.

Appl. Opt. (1)

J. Biomed. Opt. (1)

M. Friebel, A. Roggan, G. Müller, and M. Meinke, J. Biomed. Opt. 11, 034021 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. Lett. (1)

D. Faber, M. Aalders, E. Mik, B. Hooper, M. van Gemert, and T. van Leeuwen, Phys. Rev. Lett. 93, 028102 (2004).
[CrossRef] [PubMed]

Other (2)

J. A. Izatt and M. A. Choma, in Optical Coherence Tomography: Technology and Applications, W.Drexler and J.G.Fujimoto, eds. (Springer, 2008), pp. 47–72.
[CrossRef]

S. Prahl, “Optical Absorption of Hemoglobin,” http://omlc.ogi.edu/spectra/hemoglobin/.

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Figures (3)

Fig. 1
Fig. 1

(a) Measured cumulative absorption and (b) total attenuation coefficient of the Hb phantoms without scattering (case A) and with scattering (case B). The theoretical absorption with (a) d = 400 μm and C = 40 g/L and (b) corresponding absorption coefficient are also plotted.

Fig. 2
Fig. 2

Measured change in the real part of the RI of the Hb phantoms (a) without scattering (case A) and (b) with scattering (case B). The theoretical change in the real part of the RI of Hb, with a concentration of 40 g/L, is also plotted. The inset illustrates the source’s spectrum, S, with the dotted lines denoting the bandwidth used for estimating concentration using the real part of the RI.

Fig. 3
Fig. 3

Measured and theoretical scattering coefficient of 10% IL with a 10.75% concentration.

Equations (3)

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E s ( ω ) = m I s ( m ) ( ω ) · e i ( ω / c 0 ) 2 z d e i ( ω / c 0 ) n ( ω ) 2 ( z s ( m ) z d ) ,
I ˜ ( ω ) = 2 I s ( ω ) I r ( ω ) · e i ( ω / c 0 ) 2 ( z d n ( ω ) ) = 2 I r ( ω ) e μ tot ( ω ) d · e i ( ω / c 0 ) 2 ( z d n ( ω ) ) ,
I ˜ ( ω ) = 2 I r ( ω ) e μ tot ( ω ) d · e i ( ω / c 0 ) · 2 ( z d n ( ω 0 ) ) · e i ( ω / c 0 ) · 2 d Δ n ( ω ) .

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