Abstract

In this Letter, we implement a maximum-likelihood estimator to interpret optical coherence tomography (OCT) data for the first time, based on Fourier-domain OCT and a two-interface tear film model. We use the root mean square error as a figure of merit to quantify the system performance of estimating the tear film thickness. With the methodology of task-based assessment, we study the trade-off between system imaging speed (temporal resolution of the dynamics) and the precision of the estimation. Finally, the estimator is validated with a digital tear-film dynamics phantom.

© 2013 Optical Society of America

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References

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  1. R. Montés-Micó, J. Cataract Refract. Surg. 33, 1631 (2007).
    [CrossRef]
  2. D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
    [CrossRef]
  3. J. Rolland, J. O’Daniel, C. Ackay, T. De Lemos, K. S. Lee, K.-L. Cheong, E. Clarkson, R. Chakrabarti, and R. Ferris, J. Opt. Soc. Am. A 22, 1132 (2005).
    [CrossRef]
  4. H. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).
  5. J. Huang, K. Lee, E. Clarkson, M. Kupinski, K. Maki, D. Ross, and J. P. Rolland, “Quantitative measurement of tear film dynamics with optical coherence tomography and statistical decision theory,” Tech. Rep. (University of Rochester, 2013).
  6. Y. Ashtamker, V. Freilikher, and J. C. Dainty, Opt. Express 19, 21658 (2011).
    [CrossRef]
  7. H. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, Invest. Ophthalmol. Visual Sci. 38, 381 (1997).
  8. K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, J. Fluid Mech. 647, 361 (2010).
    [CrossRef]

2012 (1)

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

2011 (1)

2010 (1)

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, J. Fluid Mech. 647, 361 (2010).
[CrossRef]

2007 (1)

R. Montés-Micó, J. Cataract Refract. Surg. 33, 1631 (2007).
[CrossRef]

2005 (1)

1997 (1)

H. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, Invest. Ophthalmol. Visual Sci. 38, 381 (1997).

Ackay, C.

Ashtamker, Y.

Barabino, S.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

Barrett, H. H.

H. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).

Begley, C. G.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

Braun, R. J.

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, J. Fluid Mech. 647, 361 (2010).
[CrossRef]

Chakrabarti, R.

Chen, H.

H. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, Invest. Ophthalmol. Visual Sci. 38, 381 (1997).

Cheong, K.-L.

Clarkson, E.

J. Rolland, J. O’Daniel, C. Ackay, T. De Lemos, K. S. Lee, K.-L. Cheong, E. Clarkson, R. Chakrabarti, and R. Ferris, J. Opt. Soc. Am. A 22, 1132 (2005).
[CrossRef]

J. Huang, K. Lee, E. Clarkson, M. Kupinski, K. Maki, D. Ross, and J. P. Rolland, “Quantitative measurement of tear film dynamics with optical coherence tomography and statistical decision theory,” Tech. Rep. (University of Rochester, 2013).

Dainty, J. C.

Dalton, M.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

De Lemos, T.

Ferris, R.

Freilikher, V.

Garrigue, J.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

Gjorstrup, P.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

Hammitt, K. M.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

Henshaw, W. D.

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, J. Fluid Mech. 647, 361 (2010).
[CrossRef]

Huang, J.

J. Huang, K. Lee, E. Clarkson, M. Kupinski, K. Maki, D. Ross, and J. P. Rolland, “Quantitative measurement of tear film dynamics with optical coherence tomography and statistical decision theory,” Tech. Rep. (University of Rochester, 2013).

King-Smith, P. E.

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, J. Fluid Mech. 647, 361 (2010).
[CrossRef]

Kupinski, M.

J. Huang, K. Lee, E. Clarkson, M. Kupinski, K. Maki, D. Ross, and J. P. Rolland, “Quantitative measurement of tear film dynamics with optical coherence tomography and statistical decision theory,” Tech. Rep. (University of Rochester, 2013).

Lee, K.

J. Huang, K. Lee, E. Clarkson, M. Kupinski, K. Maki, D. Ross, and J. P. Rolland, “Quantitative measurement of tear film dynamics with optical coherence tomography and statistical decision theory,” Tech. Rep. (University of Rochester, 2013).

Lee, K. S.

Maki, K.

J. Huang, K. Lee, E. Clarkson, M. Kupinski, K. Maki, D. Ross, and J. P. Rolland, “Quantitative measurement of tear film dynamics with optical coherence tomography and statistical decision theory,” Tech. Rep. (University of Rochester, 2013).

Maki, K. L.

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, J. Fluid Mech. 647, 361 (2010).
[CrossRef]

Montés-Micó, R.

R. Montés-Micó, J. Cataract Refract. Surg. 33, 1631 (2007).
[CrossRef]

Myers, K.

H. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).

Nakamura, M.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

Novack, G. D.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

O’Daniel, J.

Ohno, S.

H. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, Invest. Ophthalmol. Visual Sci. 38, 381 (1997).

Ou, B.

H. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, Invest. Ophthalmol. Visual Sci. 38, 381 (1997).

Quentric, Y.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

Rolland, J.

Rolland, J. P.

J. Huang, K. Lee, E. Clarkson, M. Kupinski, K. Maki, D. Ross, and J. P. Rolland, “Quantitative measurement of tear film dynamics with optical coherence tomography and statistical decision theory,” Tech. Rep. (University of Rochester, 2013).

Ross, D.

J. Huang, K. Lee, E. Clarkson, M. Kupinski, K. Maki, D. Ross, and J. P. Rolland, “Quantitative measurement of tear film dynamics with optical coherence tomography and statistical decision theory,” Tech. Rep. (University of Rochester, 2013).

Schaumberg, D. A.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

Sullivan, B. D.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

Sullivan, D. A.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

Tanaka, Y.

H. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, Invest. Ophthalmol. Visual Sci. 38, 381 (1997).

Tsukahara, S.

H. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, Invest. Ophthalmol. Visual Sci. 38, 381 (1997).

Ucciferro, P.

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, J. Fluid Mech. 647, 361 (2010).
[CrossRef]

Yamabayashi, S.

H. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, Invest. Ophthalmol. Visual Sci. 38, 381 (1997).

Invest. Ophthalmol. Visual Sci. (1)

H. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, Invest. Ophthalmol. Visual Sci. 38, 381 (1997).

J. Cataract Refract. Surg. (1)

R. Montés-Micó, J. Cataract Refract. Surg. 33, 1631 (2007).
[CrossRef]

J. Fluid Mech. (1)

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, J. Fluid Mech. 647, 361 (2010).
[CrossRef]

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

Ocul. Surf. (1)

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, Ocul. Surf. 10, 108 (2012).
[CrossRef]

Opt. Express (1)

Other (2)

H. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).

J. Huang, K. Lee, E. Clarkson, M. Kupinski, K. Maki, D. Ross, and J. P. Rolland, “Quantitative measurement of tear film dynamics with optical coherence tomography and statistical decision theory,” Tech. Rep. (University of Rochester, 2013).

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Figures (3)

Fig. 1.
Fig. 1.

ML estimator for different axial resolutions.

Fig. 2.
Fig. 2.

Impact of integration time.

Fig. 3.
Fig. 3.

Validation with a digital phantom of the tear film dynamics.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

N(x,Δt)=Np(x,Δt)+Nd(x,Δt),
N(x,Δt)D|P,GP|GG=NP(x,Δt)P|GG+Nd(x,Δt)D,
KN(x,x;Δt)=KNp(x,x;Δt)+KNd(x,x;Δt),
Np(x,Δt)P|GG=R(x)eΔtωxΔωxωx|m(ω)|2S(ω)dω,
KNp(x,x;Δt)=R(x)eδxxΔtωxΔωxωx|m(ω)|2S(ω)dω+R(x)R(x)e2×δxxΔtωxΔωxωx|m(ω)|4S2(ω)dω,
m(ω)=rrefexp(i2klref)+(n2n3n2+n3exp(2ε2σ2k2)×exp(i2kd)+n1n2n1+n2)exp(i2klsam),
P(Nl|d)=1(2π)M2Det[KN]12exp[12x(Nl(x,Δt)N(x,Δt))2KN(x,x;Δt)],
d^=argmind(log(P(Nl|d))).

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