Abstract

Understanding tear film dynamics is a prerequisite for advancing the management of Dry Eye Disease (DED). In this paper, we discuss the use of optical coherence tomography (OCT) and statistical decision theory to analyze the tear film dynamics of a digital phantom. We implement a maximum-likelihood (ML) estimator to interpret OCT data based on mathematical models of Fourier-Domain OCT and the tear film. With the methodology of task-based assessment, we quantify the tradeoffs among key imaging system parameters. We find, on the assumption that the broadband light source is characterized by circular Gaussian statistics, ML estimates of 40 nm +/− 4 nm for an axial resolution of 1 μm and an integration time of 5 μs. Finally, the estimator is validated with a digital phantom of tear film dynamics, which reveals estimates of nanometer precision.

© 2013 OSA

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    [CrossRef] [PubMed]
  2. B. Miljanović, R. Dana, D. A. Sullivan, and D. A. Schaumberg, “Impact of dry eye syndrome on vision-related quality of life,” Am. J. Ophthalmol.143(3), 409–415, 415.e2 (2007).
    [CrossRef] [PubMed]
  3. R. Montés-Micó, “Role of the tear film in the optical quality of the human eye,” J. Cataract Refract. Surg.33(9), 1631–1635 (2007).
    [CrossRef] [PubMed]
  4. D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
    [CrossRef] [PubMed]
  5. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
    [CrossRef] [PubMed]
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  17. K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, “Tear film dynamics on an eye-shaped domain II: flux boundary conditions,” J. Fluid Mech.647, 361–389 (2010).
    [CrossRef]

2013

2012

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

2011

2010

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, “Tear film dynamics on an eye-shaped domain II: flux boundary conditions,” J. Fluid Mech.647, 361–389 (2010).
[CrossRef]

2007

M. A. Lemp, C. Baudouin, J. Baum, and ., “The definition and classification of dry eye disease: report of the definition and classification subcommittee of the International Dry Eye WorkShop (2007),” Ocul. Surf.5(2), 75–92 (2007).
[CrossRef] [PubMed]

B. Miljanović, R. Dana, D. A. Sullivan, and D. A. Schaumberg, “Impact of dry eye syndrome on vision-related quality of life,” Am. J. Ophthalmol.143(3), 409–415, 415.e2 (2007).
[CrossRef] [PubMed]

R. Montés-Micó, “Role of the tear film in the optical quality of the human eye,” J. Cataract Refract. Surg.33(9), 1631–1635 (2007).
[CrossRef] [PubMed]

2005

2004

P. E. King-Smith, B. A. Fink, R. M. Hill, K. W. Koelling, and J. M. Tiffany, “The thickness of the tear film,” Curr. Eye Res.29(4-5), 357–368 (2004).
[CrossRef] [PubMed]

2002

2000

1997

H. B. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, “Structure and composition of rat precorneal tear film. A study by an in vivo cryofixation,” Invest. Ophthalmol. Vis. Sci.38(2), 381–387 (1997).
[PubMed]

1991

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Akcay, A. C.

Akcay, C.

Aquavella, J. V.

Ashtamker, Y.

Barabino, S.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

Baudouin, C.

M. A. Lemp, C. Baudouin, J. Baum, and ., “The definition and classification of dry eye disease: report of the definition and classification subcommittee of the International Dry Eye WorkShop (2007),” Ocul. Surf.5(2), 75–92 (2007).
[CrossRef] [PubMed]

Baum, J.

M. A. Lemp, C. Baudouin, J. Baum, and ., “The definition and classification of dry eye disease: report of the definition and classification subcommittee of the International Dry Eye WorkShop (2007),” Ocul. Surf.5(2), 75–92 (2007).
[CrossRef] [PubMed]

Begley, C. G.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

Braun, R. J.

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, “Tear film dynamics on an eye-shaped domain II: flux boundary conditions,” J. Fluid Mech.647, 361–389 (2010).
[CrossRef]

Chakrabarti, R.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Chen, H. B.

H. B. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, “Structure and composition of rat precorneal tear film. A study by an in vivo cryofixation,” Invest. Ophthalmol. Vis. Sci.38(2), 381–387 (1997).
[PubMed]

Cheong, K. I.

Clarkson, E.

Dainty, J. C.

Dalton, M.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

Dana, R.

B. Miljanović, R. Dana, D. A. Sullivan, and D. A. Schaumberg, “Impact of dry eye syndrome on vision-related quality of life,” Am. J. Ophthalmol.143(3), 409–415, 415.e2 (2007).
[CrossRef] [PubMed]

DeLemos, T.

Ferris, R.

Fink, B. A.

P. E. King-Smith, B. A. Fink, R. M. Hill, K. W. Koelling, and J. M. Tiffany, “The thickness of the tear film,” Curr. Eye Res.29(4-5), 357–368 (2004).
[CrossRef] [PubMed]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Freilikher, V.

Fujimoto, J.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Garrigue, J. S.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

Gjorstrup, P.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Hammitt, K. M.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Henshaw, W. D.

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, “Tear film dynamics on an eye-shaped domain II: flux boundary conditions,” J. Fluid Mech.647, 361–389 (2010).
[CrossRef]

Hill, R. M.

P. E. King-Smith, B. A. Fink, R. M. Hill, K. W. Koelling, and J. M. Tiffany, “The thickness of the tear film,” Curr. Eye Res.29(4-5), 357–368 (2004).
[CrossRef] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Huang, J.

King-Smith, P. E.

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, “Tear film dynamics on an eye-shaped domain II: flux boundary conditions,” J. Fluid Mech.647, 361–389 (2010).
[CrossRef]

P. E. King-Smith, B. A. Fink, R. M. Hill, K. W. Koelling, and J. M. Tiffany, “The thickness of the tear film,” Curr. Eye Res.29(4-5), 357–368 (2004).
[CrossRef] [PubMed]

Koelling, K. W.

P. E. King-Smith, B. A. Fink, R. M. Hill, K. W. Koelling, and J. M. Tiffany, “The thickness of the tear film,” Curr. Eye Res.29(4-5), 357–368 (2004).
[CrossRef] [PubMed]

Kupinski, M.

Lee, K. S.

Lemp, M. A.

M. A. Lemp, C. Baudouin, J. Baum, and ., “The definition and classification of dry eye disease: report of the definition and classification subcommittee of the International Dry Eye WorkShop (2007),” Ocul. Surf.5(2), 75–92 (2007).
[CrossRef] [PubMed]

Leskova, T. A.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Maki, K. L.

J. Huang, K. S. Lee, E. Clarkson, M. Kupinski, K. L. Maki, D. S. Ross, J. V. Aquavella, and J. P. Rolland, “Phantom study of tear film dynamics with optical coherence tomography and maximum-likelihood estimation,” Opt. Lett.38(10), 1721–1723 (2013).
[CrossRef] [PubMed]

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, “Tear film dynamics on an eye-shaped domain II: flux boundary conditions,” J. Fluid Mech.647, 361–389 (2010).
[CrossRef]

Maradudin, A. A.

Miljanovic, B.

B. Miljanović, R. Dana, D. A. Sullivan, and D. A. Schaumberg, “Impact of dry eye syndrome on vision-related quality of life,” Am. J. Ophthalmol.143(3), 409–415, 415.e2 (2007).
[CrossRef] [PubMed]

Montés-Micó, R.

R. Montés-Micó, “Role of the tear film in the optical quality of the human eye,” J. Cataract Refract. Surg.33(9), 1631–1635 (2007).
[CrossRef] [PubMed]

Nakamura, M.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

Novack, G. D.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

Novikov, I. V.

O’Daniel, J.

Ohno, S.

H. B. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, “Structure and composition of rat precorneal tear film. A study by an in vivo cryofixation,” Invest. Ophthalmol. Vis. Sci.38(2), 381–387 (1997).
[PubMed]

Ou, B.

H. B. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, “Structure and composition of rat precorneal tear film. A study by an in vivo cryofixation,” Invest. Ophthalmol. Vis. Sci.38(2), 381–387 (1997).
[PubMed]

Parrein, P.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Quentric, Y.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

Rolland, J.

Rolland, J. P.

Ross, D. S.

Schaumberg, D. A.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

B. Miljanović, R. Dana, D. A. Sullivan, and D. A. Schaumberg, “Impact of dry eye syndrome on vision-related quality of life,” Am. J. Ophthalmol.143(3), 409–415, 415.e2 (2007).
[CrossRef] [PubMed]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Sullivan, B. D.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

Sullivan, D. A.

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

B. Miljanović, R. Dana, D. A. Sullivan, and D. A. Schaumberg, “Impact of dry eye syndrome on vision-related quality of life,” Am. J. Ophthalmol.143(3), 409–415, 415.e2 (2007).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Tanaka, Y.

H. B. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, “Structure and composition of rat precorneal tear film. A study by an in vivo cryofixation,” Invest. Ophthalmol. Vis. Sci.38(2), 381–387 (1997).
[PubMed]

Tiffany, J. M.

P. E. King-Smith, B. A. Fink, R. M. Hill, K. W. Koelling, and J. M. Tiffany, “The thickness of the tear film,” Curr. Eye Res.29(4-5), 357–368 (2004).
[CrossRef] [PubMed]

Tsukahara, S.

H. B. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, “Structure and composition of rat precorneal tear film. A study by an in vivo cryofixation,” Invest. Ophthalmol. Vis. Sci.38(2), 381–387 (1997).
[PubMed]

Ucciferro, P.

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, “Tear film dynamics on an eye-shaped domain II: flux boundary conditions,” J. Fluid Mech.647, 361–389 (2010).
[CrossRef]

Yamabayashi, S.

H. B. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, “Structure and composition of rat precorneal tear film. A study by an in vivo cryofixation,” Invest. Ophthalmol. Vis. Sci.38(2), 381–387 (1997).
[PubMed]

Am. J. Ophthalmol.

B. Miljanović, R. Dana, D. A. Sullivan, and D. A. Schaumberg, “Impact of dry eye syndrome on vision-related quality of life,” Am. J. Ophthalmol.143(3), 409–415, 415.e2 (2007).
[CrossRef] [PubMed]

Appl. Opt.

Curr. Eye Res.

P. E. King-Smith, B. A. Fink, R. M. Hill, K. W. Koelling, and J. M. Tiffany, “The thickness of the tear film,” Curr. Eye Res.29(4-5), 357–368 (2004).
[CrossRef] [PubMed]

Invest. Ophthalmol. Vis. Sci.

H. B. Chen, S. Yamabayashi, B. Ou, Y. Tanaka, S. Ohno, and S. Tsukahara, “Structure and composition of rat precorneal tear film. A study by an in vivo cryofixation,” Invest. Ophthalmol. Vis. Sci.38(2), 381–387 (1997).
[PubMed]

J. Cataract Refract. Surg.

R. Montés-Micó, “Role of the tear film in the optical quality of the human eye,” J. Cataract Refract. Surg.33(9), 1631–1635 (2007).
[CrossRef] [PubMed]

J. Fluid Mech.

K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, “Tear film dynamics on an eye-shaped domain II: flux boundary conditions,” J. Fluid Mech.647, 361–389 (2010).
[CrossRef]

J. Opt. Soc. Am. A

Ocul. Surf.

M. A. Lemp, C. Baudouin, J. Baum, and ., “The definition and classification of dry eye disease: report of the definition and classification subcommittee of the International Dry Eye WorkShop (2007),” Ocul. Surf.5(2), 75–92 (2007).
[CrossRef] [PubMed]

D. A. Sullivan, K. M. Hammitt, D. A. Schaumberg, B. D. Sullivan, C. G. Begley, P. Gjorstrup, J. S. Garrigue, M. Nakamura, Y. Quentric, S. Barabino, M. Dalton, and G. D. Novack, “Report of the TFOS/ARVO symposium on global treatments for dry eye disease: an unmet need,” Ocul. Surf.10(2), 108–116 (2012).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Science

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Other

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, Hoboken, 2004), Chap. 14.

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, Hoboken, 2004), Chap. 8.

American National Standards Institute, “American national standard for safe use of lasers,” ANSI Z136.1–2007 (2007).

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Figures (6)

Fig. 1
Fig. 1

FD-OCT setup.

Fig. 2
Fig. 2

Tear film model.

Fig. 3
Fig. 3

Principle of the ML estimator illustrated with different axial resolutions of 1 μm, 2 μm, and 4 μm.

Fig. 4
Fig. 4

Impact of integration time on the RMSE of the estimation.

Fig. 5
Fig. 5

Estimation limit in relative error of the ML estimator as a function of the tear-film thickness.

Fig. 6
Fig. 6

Validation of the tear film dynamics with a digital phantom.

Equations (30)

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E s ( t )= E 0 ( ω )exp( iωt ) dω.
E s ( ω,t )= E 0 ( ω )exp( iωt ).
E d ( x,t )= ω x Δ ω x ω x [ α( ω )exp( i ϕ 1 ( ω ) )+β( ω )exp( i ϕ 2 ( ω ) ) ] E 0 ( ω )exp( iωt )dω .
m( ω )=α( ω )exp( i ϕ 1 ( ω ) )+β( ω )exp( i ϕ 2 ( ω ) ).
E d ( x,t )= ω x Δ ω x ω x m( ω ) E 0 ( ω )exp( iωt ) dω;
N g ( x,Δt )= N p ( x,Δt )+ N d ( x,Δt );
N g ( x,Δt ) D|P|G P|G G = N P ( x,Δt ) P|G G + N d ( x,Δt ) D ,
K N g ( x, x ;Δt )= K N p ( x, x ;Δt )+ K N d ( x, x ;Δt ).
N p ( x,Δt )= 0 Δt N( x, t ) d t ,
N p ( x,Δt ) P|G G = 0 Δt N( x, t ) P|G G d t .
N( x,t ) P|G G = N ¯ ( x,t ) G = R( x )A e η 0 E d ( x,t ) E d ( x,t ) G = R( x )A e η 0 ω x Δ ω x ω x ω x Δ ω x ω x m( ω ) m * ( ω ) E 0 ( ω ) E 0 ( ω ) G exp( i( ω ω )t )dωd ω ,
A η 0 E 0 ( ω ) E 0 ( ω ) G =δ( ω ω )S( ω ),
N( x,t ) P|G G = R( x ) e ω x Δ ω x ω x | m( ω ) | 2 S( ω ) dω.
N p ( x,Δt ) P|G G = R( x ) e Δt ω x Δ ω x ω x | m( ω ) | 2 S( ω ) dω.
K N p ( x, x ;Δt )= N p ( x,Δt ) N p ( x ,Δt ) P|G G N p ( x,Δt ) P|G G N p ( x ,Δt ) P|G G .
N p ( x,Δt ) N p ( x ,Δt ) P|G G = 0 Δt 0 Δt N( x, t )N( x , t ) d t d t P|G G = 0 Δt 0 Δt [ N ¯ ( x, t ) G δ x x δ( t t )+ K N ¯ ( x, x ; t , t ) + N ¯ ( x, t ) G N ¯ ( x , t ) G ]d t d t = 0 Δt N ¯ ( x, t ) G δ x x d t + 0 Δt 0 Δt K N ¯ ( x, x ; t , t ) d t d t + N ¯ p ( x,Δt ) G N ¯ p ( x ,Δt ) G .
K N p ( x, x ;Δt )= 0 Δt N ¯ ( x, t ) G δ x x d t + 0 Δt 0 Δt K N ¯ ( x, x ; t , t ) d t d t .
K N ¯ ( x, x ; t , t )= N ¯ ( x, t ) N ¯ ( x , t ) G N ¯ ( x, t ) G N ¯ ( x , t ) G .
N ¯ ( x, t ) N ¯ ( x , t ) G = R( x )A e η 0 R( x )A e η 0 E d ( x, t ) E d * ( x, t ) E d ( x , t ) E d * ( x , t ) G = R( x )R( x ) A 2 e 2 η 0 2 ( E d ( x, t ) E d * ( x, t ) G E d ( x , t ) E d * ( x , t ) G + E d ( x, t ) E d * ( x , t ) G E d ( x , t ) E d * ( x, t ) G ) = N ¯ ( x, t ) G N ¯ ( x , t ) G + R( x )R( x ) A 2 e 2 η 0 2 × E d ( x, t ) E d * ( x , t ) G E d ( x , t ) E d * ( x, t ) G .
K N ¯ ( x, x ; t , t )= R( x )R( x ) A 2 e 2 η 0 2 E d ( x, t ) E d * ( x , t ) G E d ( x , t ) E d * ( x, t ) G .
A η 0 E d ( x, t ) E d * ( x , t ) G = δ x x ω x Δ ω x ω x | m( ω ) | 2 S( ω )exp( i ω ( t t ) )d ω ,
A η 0 E d ( x , t ) E d * ( x, t ) G = δ x x ω x Δ ω x ω x | m( ω ) | 2 S( ω )exp( i ω ( t t ) )d ω .
K N ¯ ( x, x ; t , t )= R( x )R( x ) e 2 δ xx' ω x Δ ω x ω x ω x Δ ω x ω x | m( ω ) | 2 | m( ω ) | 2 S( ω )S( ω ) exp( i( ω ω )( t t ) )d ω d ω .
K N p ( x, x ;Δt )= R( x ) e δ x x Δt ω x Δ ω x ω x | m( ω ) | 2 S( ω ) dω+ δ x x 0 Δt 0 Δt R( x )R( x ) e 2 ω x Δ ω x ω x ω x Δ ω x ω x | m( ω ) | 2 | m( ω ) | 2 S( ω )S( ω )exp( i( ω ω )( t t ) )d ω d ω d t d t = R( x ) e δ x x Δt ω x Δ ω x ω x | m( ω ) | 2 S( ω ) dω+ δ x x Δt R( x )R( x ) e 2 ω x Δ ω x ω x | m( ω ) | 4 S 2 ( ω ) dω.
r 2 = n 2 n 3 n 2 + n 3 exp( 2 ε 2 σ 2 k 2 ),
r 1 = n 1 n 2 n 1 + n 2 .
N lg ( x,Δt )~Normal( N lg ( x,Δt ) D|P|G P|G G , K N lg ( x,x;Δt ) ).
P( N lg |d)= 1 ( 2π ) M 2 Det [ K N dg ] 1 2 exp[ 1 2 x ( N lg ( x,Δt ) N dg ( x,Δt ) D|P|G P|G G ) 2 K N dg ( x,x;Δt ) ],
qln( P( N lg |d) ).
d ^ = argmin d [ x ( N lg ( x,Δt ) N dg ( x,Δt ) ) 2 2 K N dg ( x,x;Δt ) + 1 2 x ln( K N dg ( x,x;Δt ) )+ M 2 ln( 2π ) ].

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