3D refraction correction and extraction of clinical parameters from spectral domain optical coherence tomography of the cornea

Mingtao Zhao; Anthony N Kuo; Joseph A Izatt

doi:10.1364/OE.18.008923

3D refraction correction and extraction of clinical parameters from spectral domain optical coherence tomography of the cornea

Mingtao Zhao, Anthony N Kuo, and Joseph A Izatt

Optics Express
Vol. 18,
Issue 9,
pp. 8923-8936
(2010)
•doi: 10.1364/OE.18.008923

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Mingtao Zhao, Anthony N Kuo, and Joseph A Izatt, "3D refraction correction and extraction of clinical parameters from spectral domain optical coherence tomography of the cornea," Opt. Express 18, 8923-8936 (2010)

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Abstract

Capable of three-dimensional imaging of the cornea with micrometer-scale resolution, spectral domain-optical coherence tomography (SDOCT) offers potential advantages over Placido ring and Scheimpflug photography based systems for accurate extraction of quantitative keratometric parameters. In this work, an SDOCT scanning protocol and motion correction algorithm were implemented to minimize the effects of patient motion during data acquisition. Procedures are described for correction of image data artifacts resulting from 3D refraction of SDOCT light in the cornea and from non-idealities of the scanning system geometry performed as a pre-requisite for accurate parameter extraction. Zernike polynomial 3D reconstruction and a recursive half searching algorithm (RHSA) were implemented to extract clinical keratometric parameters including anterior and posterior radii of curvature, central cornea optical power, central corneal thickness, and thickness maps of the cornea. Accuracy and repeatability of the extracted parameters obtained using a commercial 859nm SDOCT retinal imaging system with a corneal adapter were assessed using a rigid gas permeable (RGP) contact lens as a phantom target. Extraction of these parameters was performed in vivo in 3 patients and compared to commercial Placido topography and Scheimpflug photography systems. The repeatability of SDOCT central corneal power measured in vivo was 0.18 Diopters, and the difference observed between the systems averaged 0.1 Diopters between SDOCT and Scheimpflug photography, and 0.6 Diopters between SDOCT and Placido topography.

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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. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 4 (1991).
[Crossref]
M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004).
[Crossref] [PubMed]
A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 17, 6 (1995).
M. Pircher, E. Götzinger, R. Leitgeb, H. Sattmann, O. Findl, and C. Hitzenberger, “Imaging of polarization properties of human retina in vivo with phase resolved transversal PS-OCT,” Opt. Express 12(24), 5940 - 5951 (2004).
[Crossref] [PubMed]
B. Cense, T. C. Chen, B. H. Park, M. C. Pierce, and J. F. de Boer, “In vivo depth-resolved birefringence measurements of the human retinal nerve fiber layer by polarization-sensitive optical coherence tomography,” Opt. Lett. 27(18), 1610 (2002).
[Crossref]
B. Hofer, B. Považay, B. Hermann, A. Unterhuber, G. Matz, and W. Drexler, “Dispersion encoded full range frequency domain optical coherence tomography,” Opt. Express 17(1), 7 – 24 (2009).
[Crossref] [PubMed]
M. Yamanari, Y. Lim, S. Makita, and Y. Yasuno, “Visualization of phase retardation of deep posterior eye by polarization-sensitive swept-source optical coherence tomography with 1-μm probe,” Opt. Express 17(15), 12385 (2009).
[Crossref] [PubMed]
R. Zawadzki, S. Jones, S. Olivier, M. Zhao, B. Bower, J. Izatt, S. Choi, S. Laut, and J. Werner, “Adaptive-optics optical coherence tomography for high-resolution and high-speed 3D retinal in vivo imaging,” Opt. Express 13(21), 8532 – 8546 (2005).
[Crossref] [PubMed]
M. Zhao and J. A. Izatt, “Single-camera sequential-scan-based polarization-sensitive SDOCT for retinal imaging,” Opt. Lett. 34(2), 205 (2009).
[Crossref] [PubMed]
L. An and R. K. Wang, “In vivo volumetric imaging of vascular perfusion within human retina and choroids with optical micro-angiography,” Opt. Express 16(15), 11438 – 11452 (2008).
[Crossref] [PubMed]
R. J. Zawadzki, C. Leisser, R. Leitgeb, M. Pircher, and A. F. Fercher, “Three-dimensional ophthalmic optical coherence tomography with a refraction correction algorithm,” Proc. SPIE 5140, 8 (2003).
V. Westphal, A. Rollins, S. Radhakrishnan, and J. Izatt, “Correction of geometric and refractive image distortions in optical coherence tomography applying Fermat’s principle,” Opt. Express 10, 8 (2002).
M. V. Sarunic, B. E. Applegate, and J. A. Izatt, “Real-time quadrature projection complex conjugate resolved Fourier domain optical coherence tomography,” Opt. Lett. 31(16), 2426 (2006).
[Crossref] [PubMed]
M. V. Sarunic, S. Asrani, and J. A. Izatt, “Imaging the Ocular Anterior Segment With Real-Time, Full-Range Fourier-Domain Optical Coherence Tomography,” Arch. Ophthalmol. 126(4), 6 (2008).
[Crossref]
M. Tang, Y. Li, M. Avila, and D. Huang, “Measuring total corneal power before and after laser in situ keratomileusis with high-speed optical coherence tomography,” J. Cataract Refract. Surg. 32(11), 18438 (2006).
[Crossref]
S. Radhakrishnan, A. M. Rollins, J. E. Roth, S. Yazdanfar, V. Westphal, D. S. Bardenstein, and J. A. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. 119, 7 (2001).
Y. Wang, J. S. Nelson, Z. Chen, B. J. Reiser, R. S. Chuck, and R. S. Windeler, “Optimal wavelength for ultrahigh-resolution optical coherence tomography,” Opt. Express 11(12), 1411 (2003).
[Crossref] [PubMed]
Y. Yasuno, M. Yamanari, K. Kawana, T. Oshika, and M. Miura, “Investigation of post-glaucoma-surgery structures by three-dimensional and polarization sensitive anterior eye segment optical coherence tomography,” Opt. Express 17(5), 3980 (2009).
[Crossref] [PubMed]
M. Yamanari, S. Makita, and Y. Yasuno, “Polarization-sensitive swept-source optical coherence tomography with continuous source polarization modulation,” Opt. Express 16(8), 5892 (2008).
[Crossref] [PubMed]
M. Pircher, E. Götzinger, R. Leitgeb, A. F. Fercher, C. Hitzenberger, and C. K. Hitzenberger, “Measurement and imaging of water concentration in human cornea with differential absorption optical coherence tomography,” Opt. Express 11(18), 2190 (2003).
[Crossref] [PubMed]
C. Kerbage, H. Lim, W. Sun, M. Mujat, and J. F. de Boer, “Large depth-high resolution full 3D imaging of the anterior segments of the eye using high speed optical frequency domain imaging,” Opt. Express 15(12), 7117 (2007).
[Crossref] [PubMed]
M. Akiba, N. Maeda, K. Yumikake, T. Soma, K. Nishida, Y. Tano, and K. P. Chan, “Ultrahigh-resolution imaging of human donor cornea using full-field optical coherence tomography,” J. Biomed. Opt. 12(4), 4 (2007).
[Crossref]
K. Grieve, A. Dubois, M. Simonutti, M. Paques, J. Sahel, J.-F. Le Gargasson, and C. Boccara, “In vivo anterior segment imaging in the rat eye with high speed white light full-field optical coherence tomography,” Opt. Express 13(16), 6286 (2005).
[Crossref] [PubMed]
A. N.Kuo, M. Zhao, and J. A. Izatt, “Corneal aberration measurement with three-dimensional refraction correction for high-speed spectral domain optical coherence tomography,” ARVO E-Abstract, 2 (2009).
M. Tang, Y. Li, and D. Huang, “Corneal topography and power measurement with optical coherence tomography,” ARVO E-Abstract 5791(A93), 2 (2009).
M. Gora, K. Karnowski, M. Szkulmowski, B. J. Kaluzny, R. Huber, A. Kowalczyk, and M. Wojtkowski, “Ultra high-speed swept source OCT imaging of the anterior segment of human eye at 200 kHz with adjustable imaging range,” Opt. Express 17(17), 14880 (2009).
[Crossref] [PubMed]
A. N. S. Institute, “Corneal topography systems - standard terminology, requirements,” ANSI 80, 23–2008 (2008).
V. A. D. P. Sicam, M. Dubbelman, and R. G. L. van der Heijde, “Spherical aberration of the anterior and posterior surfaces of the human cornea,” J. Opt. Soc. Am. A 23(3), 544 (2006).
[Crossref]
R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66(3), 207 (1976).
[Crossref]
V. A. D. P. Sicam, J. Coppens, T. J. T. P. van den Berg, and R. G. L. van der Heijde, “Corneal surface reconstruction algorithm that uses Zernike polynomial representation,” J. Opt. Soc. Am. A 21, 7 (2004).
C. K. Hitzenberger, “Optical measurement of the axial eye length by laser doppler interferometry,” Invest. Ophthalmol. Vis. Sci. 32, 9 (1991).
W. Drexler, C. K. Hitzenberger, A. Baumgartner, O. Findl, H. Sattmann, and A. F. Fercher, “Investigation of disperison effects in ocular media by multiple wavelength partial coherence interferometry,” Exp. Eye Res. 66(1), 25 (1998).
[Crossref] [PubMed]
R. C. Lin, M. A. Shure, A. M. Rollins, J. A. Izatt, and D. Huang, “Group index of the human cornea at 1.3-mm wavelength obtained in vitro by optical coherence domain reflectometry,” Opt. Lett. 29(1), 83 (2004).
[Crossref] [PubMed]
I. Grulkowski, M. Gora, M. Szkulmowski, I. Gorczynska, D. Szlag, S. Marcos, A. Kowalczyk, and M. Wojtkowski, “Anterior segment imaging with Spectral OCT system using a high-speed CMOS camera,” Opt. Express 17(6), 4842 (2009).
[Crossref] [PubMed]
T. O. Salmon and L. N. Thibos, “Videokeratoscope-line-of-sight misalignment and its effect on measurements of corneal and internal ocular aberrations,” J. Opt. Soc. Am. A 19(4), 657 (2002).
[Crossref]

2009 (7)

M. Zhao and J. A. Izatt, “Single-camera sequential-scan-based polarization-sensitive SDOCT for retinal imaging,” Opt. Lett. 34(2), 205 (2009).
[Crossref] [PubMed]

B. Hofer, B. Považay, B. Hermann, A. Unterhuber, G. Matz, and W. Drexler, “Dispersion encoded full range frequency domain optical coherence tomography,” Opt. Express 17(1), 7 – 24 (2009).
[Crossref] [PubMed]

M. Yamanari, Y. Lim, S. Makita, and Y. Yasuno, “Visualization of phase retardation of deep posterior eye by polarization-sensitive swept-source optical coherence tomography with 1-μm probe,” Opt. Express 17(15), 12385 (2009).
[Crossref] [PubMed]

Y. Yasuno, M. Yamanari, K. Kawana, T. Oshika, and M. Miura, “Investigation of post-glaucoma-surgery structures by three-dimensional and polarization sensitive anterior eye segment optical coherence tomography,” Opt. Express 17(5), 3980 (2009).
[Crossref] [PubMed]

M. Tang, Y. Li, and D. Huang, “Corneal topography and power measurement with optical coherence tomography,” ARVO E-Abstract 5791(A93), 2 (2009).

M. Gora, K. Karnowski, M. Szkulmowski, B. J. Kaluzny, R. Huber, A. Kowalczyk, and M. Wojtkowski, “Ultra high-speed swept source OCT imaging of the anterior segment of human eye at 200 kHz with adjustable imaging range,” Opt. Express 17(17), 14880 (2009).
[Crossref] [PubMed]

I. Grulkowski, M. Gora, M. Szkulmowski, I. Gorczynska, D. Szlag, S. Marcos, A. Kowalczyk, and M. Wojtkowski, “Anterior segment imaging with Spectral OCT system using a high-speed CMOS camera,” Opt. Express 17(6), 4842 (2009).
[Crossref] [PubMed]

2008 (4)

A. N. S. Institute, “Corneal topography systems - standard terminology, requirements,” ANSI 80, 23–2008 (2008).

M. Yamanari, S. Makita, and Y. Yasuno, “Polarization-sensitive swept-source optical coherence tomography with continuous source polarization modulation,” Opt. Express 16(8), 5892 (2008).
[Crossref] [PubMed]

M. V. Sarunic, S. Asrani, and J. A. Izatt, “Imaging the Ocular Anterior Segment With Real-Time, Full-Range Fourier-Domain Optical Coherence Tomography,” Arch. Ophthalmol. 126(4), 6 (2008).
[Crossref]

L. An and R. K. Wang, “In vivo volumetric imaging of vascular perfusion within human retina and choroids with optical micro-angiography,” Opt. Express 16(15), 11438 – 11452 (2008).
[Crossref] [PubMed]

2007 (2)

C. Kerbage, H. Lim, W. Sun, M. Mujat, and J. F. de Boer, “Large depth-high resolution full 3D imaging of the anterior segments of the eye using high speed optical frequency domain imaging,” Opt. Express 15(12), 7117 (2007).
[Crossref] [PubMed]

M. Akiba, N. Maeda, K. Yumikake, T. Soma, K. Nishida, Y. Tano, and K. P. Chan, “Ultrahigh-resolution imaging of human donor cornea using full-field optical coherence tomography,” J. Biomed. Opt. 12(4), 4 (2007).
[Crossref]

2006 (3)

V. A. D. P. Sicam, M. Dubbelman, and R. G. L. van der Heijde, “Spherical aberration of the anterior and posterior surfaces of the human cornea,” J. Opt. Soc. Am. A 23(3), 544 (2006).
[Crossref]

M. Tang, Y. Li, M. Avila, and D. Huang, “Measuring total corneal power before and after laser in situ keratomileusis with high-speed optical coherence tomography,” J. Cataract Refract. Surg. 32(11), 18438 (2006).
[Crossref]

M. V. Sarunic, B. E. Applegate, and J. A. Izatt, “Real-time quadrature projection complex conjugate resolved Fourier domain optical coherence tomography,” Opt. Lett. 31(16), 2426 (2006).
[Crossref] [PubMed]

2005 (2)

R. Zawadzki, S. Jones, S. Olivier, M. Zhao, B. Bower, J. Izatt, S. Choi, S. Laut, and J. Werner, “Adaptive-optics optical coherence tomography for high-resolution and high-speed 3D retinal in vivo imaging,” Opt. Express 13(21), 8532 – 8546 (2005).
[Crossref] [PubMed]

K. Grieve, A. Dubois, M. Simonutti, M. Paques, J. Sahel, J.-F. Le Gargasson, and C. Boccara, “In vivo anterior segment imaging in the rat eye with high speed white light full-field optical coherence tomography,” Opt. Express 13(16), 6286 (2005).
[Crossref] [PubMed]

2004 (4)

V. A. D. P. Sicam, J. Coppens, T. J. T. P. van den Berg, and R. G. L. van der Heijde, “Corneal surface reconstruction algorithm that uses Zernike polynomial representation,” J. Opt. Soc. Am. A 21, 7 (2004).

R. C. Lin, M. A. Shure, A. M. Rollins, J. A. Izatt, and D. Huang, “Group index of the human cornea at 1.3-mm wavelength obtained in vitro by optical coherence domain reflectometry,” Opt. Lett. 29(1), 83 (2004).
[Crossref] [PubMed]

M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004).
[Crossref] [PubMed]

M. Pircher, E. Götzinger, R. Leitgeb, H. Sattmann, O. Findl, and C. Hitzenberger, “Imaging of polarization properties of human retina in vivo with phase resolved transversal PS-OCT,” Opt. Express 12(24), 5940 - 5951 (2004).
[Crossref] [PubMed]

2003 (3)

R. J. Zawadzki, C. Leisser, R. Leitgeb, M. Pircher, and A. F. Fercher, “Three-dimensional ophthalmic optical coherence tomography with a refraction correction algorithm,” Proc. SPIE 5140, 8 (2003).

M. Pircher, E. Götzinger, R. Leitgeb, A. F. Fercher, C. Hitzenberger, and C. K. Hitzenberger, “Measurement and imaging of water concentration in human cornea with differential absorption optical coherence tomography,” Opt. Express 11(18), 2190 (2003).
[Crossref] [PubMed]

Y. Wang, J. S. Nelson, Z. Chen, B. J. Reiser, R. S. Chuck, and R. S. Windeler, “Optimal wavelength for ultrahigh-resolution optical coherence tomography,” Opt. Express 11(12), 1411 (2003).
[Crossref] [PubMed]

2002 (3)

T. O. Salmon and L. N. Thibos, “Videokeratoscope-line-of-sight misalignment and its effect on measurements of corneal and internal ocular aberrations,” J. Opt. Soc. Am. A 19(4), 657 (2002).
[Crossref]

V. Westphal, A. Rollins, S. Radhakrishnan, and J. Izatt, “Correction of geometric and refractive image distortions in optical coherence tomography applying Fermat’s principle,” Opt. Express 10, 8 (2002).

B. Cense, T. C. Chen, B. H. Park, M. C. Pierce, and J. F. de Boer, “In vivo depth-resolved birefringence measurements of the human retinal nerve fiber layer by polarization-sensitive optical coherence tomography,” Opt. Lett. 27(18), 1610 (2002).
[Crossref]

2001 (1)

S. Radhakrishnan, A. M. Rollins, J. E. Roth, S. Yazdanfar, V. Westphal, D. S. Bardenstein, and J. A. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. 119, 7 (2001).

1998 (1)

W. Drexler, C. K. Hitzenberger, A. Baumgartner, O. Findl, H. Sattmann, and A. F. Fercher, “Investigation of disperison effects in ocular media by multiple wavelength partial coherence interferometry,” Exp. Eye Res. 66(1), 25 (1998).
[Crossref] [PubMed]

1995 (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 17, 6 (1995).

1991 (2)

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. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 4 (1991).
[Crossref]

C. K. Hitzenberger, “Optical measurement of the axial eye length by laser doppler interferometry,” Invest. Ophthalmol. Vis. Sci. 32, 9 (1991).

1976 (1)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66(3), 207 (1976).
[Crossref]

Akiba, M.

An, L.

Applegate, B. E.

Asrani, S.

Avila, M.

Bardenstein, D. S.

Baumgartner, A.

Boccara, C.

Bower, B.

Cense, B.

Chan, K. P.

Chang, W.

Chen, T. C.

Chen, Z.

Choi, S.

Chuck, R. S.

Coppens, J.

de Boer, J. F.

Drexler, W.

Dubbelman, M.

V. A. D. P. Sicam, M. Dubbelman, and R. G. L. van der Heijde, “Spherical aberration of the anterior and posterior surfaces of the human cornea,” J. Opt. Soc. Am. A 23(3), 544 (2006).
[Crossref]

Dubois, A.

Duker, J.

El-Zaiat, S. Y.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 17, 6 (1995).

Fercher, A. F.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 17, 6 (1995).

Findl, O.

Flotte, T.

Fujimoto, J.

Fujimoto, J. G.

Gora, M.

Gorczynska, I.

Götzinger, E.

Gregory, K.

Grieve, K.

Grulkowski, I.

Hee, M. R.

Hermann, B.

Hitzenberger, C.

Hitzenberger, C. K.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 17, 6 (1995).

C. K. Hitzenberger, “Optical measurement of the axial eye length by laser doppler interferometry,” Invest. Ophthalmol. Vis. Sci. 32, 9 (1991).

Hofer, B.

Huang, D.

M. Tang, Y. Li, and D. Huang, “Corneal topography and power measurement with optical coherence tomography,” ARVO E-Abstract 5791(A93), 2 (2009).

Huber, R.

Institute, A. N. S.

A. N. S. Institute, “Corneal topography systems - standard terminology, requirements,” ANSI 80, 23–2008 (2008).

Izatt, J.

Izatt, J. A.

M. Zhao and J. A. Izatt, “Single-camera sequential-scan-based polarization-sensitive SDOCT for retinal imaging,” Opt. Lett. 34(2), 205 (2009).
[Crossref] [PubMed]

Jones, S.

Kaluzny, B. J.

Kamp, G.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 17, 6 (1995).

Karnowski, K.

Kawana, K.

Kerbage, C.

Ko, T.

Kowalczyk, A.

Laut, S.

Le Gargasson, J.-F.

Leisser, C.

Leitgeb, R.

Li, Y.

M. Tang, Y. Li, and D. Huang, “Corneal topography and power measurement with optical coherence tomography,” ARVO E-Abstract 5791(A93), 2 (2009).

Lim, H.

Lim, Y.

Lin, C. P.

Lin, R. C.

Maeda, N.

Makita, S.

Marcos, S.

Matz, G.

Miura, M.

Mujat, M.

Nelson, J. S.

Nishida, K.

Noll, R. J.

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66(3), 207 (1976).
[Crossref]

Olivier, S.

Oshika, T.

Paques, M.

Park, B. H.

Pierce, M. C.

Pircher, M.

Považay, B.

Puliafito, C. A.

Radhakrishnan, S.

Reiser, B. J.

Rollins, A.

Rollins, A. M.

Roth, J. E.

Sahel, J.

Salmon, T. O.

Sarunic, M. V.

Sattmann, H.

Schuman, J. S.

Shure, M. A.

Sicam, V. A. D. P.

V. A. D. P. Sicam, M. Dubbelman, and R. G. L. van der Heijde, “Spherical aberration of the anterior and posterior surfaces of the human cornea,” J. Opt. Soc. Am. A 23(3), 544 (2006).
[Crossref]

Simonutti, M.

Soma, T.

Srinivasan, V.

Stinson, W. G.

Sun, W.

Swanson, E. A.

Szkulmowski, M.

Szlag, D.

Tang, M.

M. Tang, Y. Li, and D. Huang, “Corneal topography and power measurement with optical coherence tomography,” ARVO E-Abstract 5791(A93), 2 (2009).

Tano, Y.

Thibos, L. N.

Unterhuber, A.

van den Berg, T. J. T. P.

van der Heijde, R. G. L.

V. A. D. P. Sicam, M. Dubbelman, and R. G. L. van der Heijde, “Spherical aberration of the anterior and posterior surfaces of the human cornea,” J. Opt. Soc. Am. A 23(3), 544 (2006).
[Crossref]

Wang, R. K.

Wang, Y.

Werner, J.

Westphal, V.

Windeler, R. S.

Wojtkowski, M.

Yamanari, M.

Yasuno, Y.

Yazdanfar, S.

Yumikake, K.

Zawadzki, R.

Zawadzki, R. J.

Zhao, M.

M. Zhao and J. A. Izatt, “Single-camera sequential-scan-based polarization-sensitive SDOCT for retinal imaging,” Opt. Lett. 34(2), 205 (2009).
[Crossref] [PubMed]

ANSI (1)

A. N. S. Institute, “Corneal topography systems - standard terminology, requirements,” ANSI 80, 23–2008 (2008).

Arch. Ophthalmol. (2)

ARVO E-Abstract (1)

M. Tang, Y. Li, and D. Huang, “Corneal topography and power measurement with optical coherence tomography,” ARVO E-Abstract 5791(A93), 2 (2009).

Exp. Eye Res. (1)

Invest. Ophthalmol. Vis. Sci. (1)

C. K. Hitzenberger, “Optical measurement of the axial eye length by laser doppler interferometry,” Invest. Ophthalmol. Vis. Sci. 32, 9 (1991).

J. Biomed. Opt. (1)

J. Cataract Refract. Surg. (1)

J. Opt. Soc. Am. (1)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66(3), 207 (1976).
[Crossref]

J. Opt. Soc. Am. A (3)

V. A. D. P. Sicam, M. Dubbelman, and R. G. L. van der Heijde, “Spherical aberration of the anterior and posterior surfaces of the human cornea,” J. Opt. Soc. Am. A 23(3), 544 (2006).
[Crossref]

Opt. Commun. (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 17, 6 (1995).

Opt. Express (15)

Opt. Lett. (4)

M. Zhao and J. A. Izatt, “Single-camera sequential-scan-based polarization-sensitive SDOCT for retinal imaging,” Opt. Lett. 34(2), 205 (2009).
[Crossref] [PubMed]

Proc. SPIE (1)

Science (1)

Other (1)

A. N.Kuo, M. Zhao, and J. A. Izatt, “Corneal aberration measurement with three-dimensional refraction correction for high-speed spectral domain optical coherence tomography,” ARVO E-Abstract, 2 (2009).

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Fig. 1

Patient bulk motion and sag error analysis. Here the z axis represents the axial direction of motion, and r is the radial (lateral) distance from the z axis. At a lateral position of r= 1.5mm corresponding to a 3mm diameter fitting area, axial motion (dz) of more than 46 µm and lateral motion (dr) of more than 234 µm will change the calculated power of an average cornea with an anterior radius of curvature R_a = 7.79mm by more than 0.25D.

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Fig. 2

Illustration of nontelecentric illumination. ISP: imaging scanning pivot; x: lateral axis; D: pivot scanning distance; z: axial coordinate; φ_Max: extreme lateral scanning angle.

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Fig. 3

Schematic of the principle of 3D refraction correction. θ₁: Angle between surface normal of epithelium and z-axis; θ_in: incidence angle; θ_Ref: refraction angle; OPL: optical path length. Δz: Projection of OPL on z-axis. V_IN = (a,b,c) is the incidence unit vector;(x₀,y₀,z₀) is the coordinate of the epithelium; (x,y,z) is the coordinate of the refraction corrected endothelium.

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Fig. 4

Demonstration of the re-sampling issue in the radial scanning pattern. (a) Radial scanning pattern centered on the apex. (b) Radial scanning pattern non-even sampling issue. The sampling points are much sparser in the outer circles than that in the inner circles. (c) Zernike polynomial even-grid interpolation for both the epithelium and endothelium surfaces based on the noneven-grid radial sampling points.

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Fig. 5

Illustration of Zernike 3D interpolation. (a) The refraction corrected voxels (e.g., voxels on the endothelial surface) are no longer on an even sampling grid after 3D Snell’s law correction; (b) Regenerated evenly sampled voxels after Zernike 3D interpolation. Elevation value of arbitrary points is obtained using Zernike interpolation coefficients.

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Fig. 6

Principle of searching intersection points between the surface normal equation of epithelial and refraction-corrected endothelial surface. The top surface is epithelium and the second is endothelium. Z^̍: Obtained using Eq. (9) after half distance recursion; Z^̎: retrieved using Zernike coefficients in Eq. (10).

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Fig. 7

nontelecentric calibration (a) Surface volume projection of 50-frames raster scanning B-scan image with FOV of 6mm ×6mm. (b) Deformed field curvature in blue color of the top surface of the calibration target caused by nontelecentric illumination. Least square curve fitting in red color is used to find imaging scanning pivot distance D. The original segmented deformed FOV is 6mm ×6mm in this figure. All the units are in millimeters.

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Fig. 8

Demonstration of power measurement accuracy in a rigid gas-permeable contact lens phantom. (a) Phantom contact lens. (b) Pachymetry map (thickness map) of the contact lens using RHSA algorithm. (c) 3D surface rendering after 3D refraction correction. Axes are in millimeters.

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Fig. 9

In vivo anterior segment imaging results (a) In vivo corneal B-scan image which is saturated at the apex. (b) Patient bulk motion before aligning centered on the apex, which indicates maximum patient motion of 156µm in the axial direction during the duration of volume acquisition. 50 anterior surfaces are plotted in this figure. The units are in millimeters. (c) Pachymetry map (thickness map) in micrometers of an in vivo corneal volume using our recursive half searching algorithm. The central thickness is 578.5μm. The image range is 6mm × 6mm. The color scale reflects those used clinically.

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Tables (3)

Table 1 Phantom contact lens measurement results

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Table 2 Comparison between SDOCT, Topography and Scheimpflug Camera

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Table 3 Repeatability of SDOCT, Topography and Scheimpflug Camera

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Equations (17)

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P_{k} = (n_{k} - n_{0}) / R_{a}

ρ^{'} (x^{'}, y^{'}) = A r c \tan (ρ (x, y) / [D - Z]) * D = ϕ * D; ρ = \sqrt{x^{2} + y^{2}}, ρ^{'} = \sqrt{x^{' 2} + y^{' 2}}

\begin{array}{l} \overset{⇀}{n} = \nabla (z - z_{E P I}) / | \nabla (z - z_{E P I}) | \\ = (- \partial z_{E P I} / \partial x, - \partial z_{E P I} / \partial y, 1) / [(\partial z_{E P I} / \partial x)^{2} + (\partial z_{E P I} / \partial y)^{2} + 1]^{1 / 2} \end{array}

\vec{C C^{'}} = (x - x_{0}, y - y_{0}, z - z_{0}) / {[{(x - x_{0})}^{2} + {(y - y_{0})}^{2} + {(z - z_{0})}^{2}]}^{1 / 2}

\vec{n} \times ({\vec{E}}_{i n} - {\vec{E}}_{r e f}) = \vec{M} = 0

\vec{M C} \times (- \vec{n}) • n_{a i r} = \vec{C C^{'}} \times (- \vec{n}) • n_{c} .

{\begin{array}{l} L = O P L / n_{c} \\ z = z_{0} + L * \cos (θ_{1} - θ Re f) \\ x = x_{0} + \frac{a \cdot L}{n_{c}} - \frac{\partial z_{E P I}}{\partial x} [\frac{c \cdot L}{n_{c}} + (z - z_{0})] \\ y = y_{0} + \frac{b \cdot L}{n_{c}} - \frac{\partial z_{E P I}}{\partial y} [\frac{c \cdot L}{n_{c}} + (z - z_{0})] \end{array}

\begin{array}{l} Z_{i} (r, θ) = R_{n}^{| m |} (r) Θ^{m} (θ); R_{n}^{| m |} (r) = \sum_{s = 0}^{(n - | m |) / 2} \frac{{(- 1)}^{s} \sqrt{n + 1} (n - s)! r^{n - 2 s}}{s! [(n + m) / 2 - s]! [(n - m) / 2 - s]!} \\ Θ^{m} (θ) = {\begin{cases} \sqrt{2} \cos | m | θ \begin{matrix} (m > 0) \end{matrix} \\ 1 \begin{matrix} \begin{matrix} \begin{matrix}  \end{matrix} \end{matrix} & (m = 0) \end{matrix} \\ \sqrt{2} \sin | m | θ \begin{matrix} (m < 0) \end{matrix} \end{cases} \end{array}

A (R r, θ) = \sum_{i = 0}^{\infty} c_{i} Z_{i} (r, θ); c_{i} = \frac{1}{π} \int_{0}^{2 π} \int_{0}^{1} A (R r, θ) Z_{i} (r, θ) r d r d θ

(x - x_{0}) / [\partial F (x, y, z) / \partial x] = (y - y_{0}) / [\partial F (x, y, z) / \partial y] = (z - z_{0}) / - 1.

S t e p 1 : {\begin{matrix} z^{'} = z \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix}  \end{matrix} \end{matrix} \end{matrix} \end{matrix} \end{matrix} \\ x^{'} = x_{0} - \partial F (x, y, z) / \partial x_{(x 0, y 0, z 0)} (z^{'} - z_{0}) \\ y^{'} = y_{0} - \partial F (x, y, z) / \partial y_{(x 0, y 0, z 0)} (z^{'} - z_{0}) \end{matrix}

S t e p 2 : {\begin{matrix} z^{"} = \sum_{i = 0}^{\infty} c_{i} Z_{i} (r (x^{'}, y^{'}, z^{'}), θ (x^{'}, y^{'}, z^{'})) \\ i f | z^{'} - z^{"} | \leq ε, t h e n s t o p a n d (x^{'}, y^{'}, z^{'}) w i l l b e t h e t \arg e t p o int \end{matrix}

Step 3: {\begin{matrix} if | z^{'} - z^{"} | > ε then \\ z^{'} = z^{'} + | z^{'} - z^{"} | / 2 if z^{'} < z^{"} search point is below endothelium \\ \begin{array}{l} z^{'} = z^{'} - | z^{'} - z^{"} | / 2 if z^{'} > z^{"} search point is above endothelium \\ Repeat Step 1 and Step 2 \end{array} \end{matrix}

z - z_{0} = \frac{c {(r - r_{0})}^{2}}{1 + \sqrt{1 + k c^{2} {(r - r_{0})}^{2}}}

P_{t} = (n_{c o r n e a} - 1) / R_{a} + (n_{a q u e o u s} - n_{c o r n e a}) / R_{p}

P_{k} = (1.3375 - 1) / R_{a}

{\begin{matrix} L = OPL / n_{c} \\ z = z_{0} + L * \cos (θ_{1} - θ_{Re f}) \\ x = x_{0} + \frac{a • L}{n_{c}} - \frac{\partial z_{E P I}}{\partial x} [\frac{c • L}{n_{c}} + (z - z_{0})] \\ y = y_{0} + \frac{b • L}{n_{c}} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix}  \end{matrix} \end{matrix} \end{matrix} \end{matrix} \end{matrix}

	Posterior radius	Anterior radius	Power	Central thickness
Manufacturer values	7.6mm	7.99mm(calculated)	-3.00D	130±20µm
OCT values	7.63±0.02mm	8.04±0.03mm	-3.18±0.04D	136.2±1.6µm
Zygo^TM values		8.10mm

	SDOCT			Topography		Scheimpflug Camera
	R_a(mm)	R_p(mm)	P_t(D)	R_a(mm)	P_k(D)	R_a(mm)	R_p(mm)	P_t(D)
Eye1	8.01	6.66	40.6	8.26	40.9	8.31	6.87	40.6
Eye2	7.69	6.18	42.1	7.87	42.9	7.98	6.52	42.2
Eye3	7.59	6.27	42.9	7.74	43.6	7.79	6.41	43.1

SDOCT			Topography		Scheimpflug Camera
R_a(mm)	R_p(mm)	P_t(D)	R_a(mm)	P_k(D)	R_a(mm)	R_p (mm)	P_t(D)
±0.021	±0.025	±0.18	±0.034	±0.17	±0.015	±0.046	±0.15

	Posterior radius	Anterior radius	Power	Central thickness
Manufacturer values	7.6mm	7.99mm(calculated)	-3.00D	130±20µm
OCT values	7.63±0.02mm	8.04±0.03mm	-3.18±0.04D	136.2±1.6µm
Zygo^TM values		8.10mm

	SDOCT			Topography		Scheimpflug Camera
	R_a(mm)	R_p(mm)	P_t(D)	R_a(mm)	P_k(D)	R_a(mm)	R_p(mm)	P_t(D)
Eye1	8.01	6.66	40.6	8.26	40.9	8.31	6.87	40.6
Eye2	7.69	6.18	42.1	7.87	42.9	7.98	6.52	42.2
Eye3	7.59	6.27	42.9	7.74	43.6	7.79	6.41	43.1