Abstract

Corneal topography allows the assessment of the cornea’s refractive power which is crucial for diagnostics and surgical planning. The use of optical coherence tomography (OCT) for corneal topography is still limited. One limitation is the susceptibility to disturbances like blinking of the eye. This can result in partially corrupted scans that cannot be evaluated using common methods. We present a new scanning method for reliable corneal topography from partial scans. Based on the golden angle, the method features a balanced scan point distribution which refines over measurement time and remains balanced when part of the scan is removed. The performance of the method is assessed numerically and by measurements of test surfaces. The results confirm that the method enables numerically well-conditioned and reliable corneal topography from partially corrupted scans and reduces the need for repeated measurements in case of abrupt disturbances.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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2015 (1)

R. P. McNabb, S. Farsiu, S. S. Stinnett, J. A. Izatt, and A. N. Kuo, “Optical coherence tomography accurately measures corneal power change from laser refractive surgery,” Ophthalmology 122, 677–686 (2015).
[Crossref]

2013 (2)

2012 (3)

2011 (1)

2010 (2)

M. Tang, A. Chen, Y. Li, and D. Huang, “Corneal power measurement with fourier-domain optical coherence tomography,” J. Cataract Refract. Surg. 36, 2115–2122 (2010).
[Crossref] [PubMed]

M. Zhao, A. N. Kuo, and J. 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).
[Crossref] [PubMed]

2009 (2)

R. Navarro, J. Arines, and R. Rivera, “Direct and inverse discrete zernike transform,” Opt. Express 17, 24269–24281 (2009).
[Crossref]

B. Braaf, T. C. van de Watering, K. Spruijt, R. G. van der Heijde, and V. A. D. Sicam, “Calculating angle lambda (λ) using zernike tilt measurements in specular reflection corneal topography,” J Optom 2, 207–214 (2009).
[Crossref]

2005 (2)

M. K. Smolek and S. D. Klyce, “Goodness-of-prediction of zernike polynomial fitting to corneal surfaces,” J. Cataract Refract. Surg. 31, 2350–2355 (2005).
[Crossref]

M. Sarunic, M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous complex conjugate resolved spectral domain and swept-source oct using 3×3 fiber couplers,” Biomed. Opt. Express 13, 957–967 (2005).
[Crossref]

1989 (1)

L. J. Maguire and W. M. Bourne, “Corneal topography of early keratoconus,” Am. J. Ophthalmol. 108, 107–112 (1989).
[Crossref] [PubMed]

Alejandre, N.

Arines, J.

Baumann, B.

Bock, R.

Bourne, W. M.

L. J. Maguire and W. M. Bourne, “Corneal topography of early keratoconus,” Am. J. Ophthalmol. 108, 107–112 (1989).
[Crossref] [PubMed]

Braaf, B.

B. Braaf, T. C. van de Watering, K. Spruijt, R. G. van der Heijde, and V. A. D. Sicam, “Calculating angle lambda (λ) using zernike tilt measurements in specular reflection corneal topography,” J Optom 2, 207–214 (2009).
[Crossref]

Chen, A.

M. Tang, A. Chen, Y. Li, and D. Huang, “Corneal power measurement with fourier-domain optical coherence tomography,” J. Cataract Refract. Surg. 36, 2115–2122 (2010).
[Crossref] [PubMed]

Chiu, S. J.

Choma, M. A.

M. Sarunic, M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous complex conjugate resolved spectral domain and swept-source oct using 3×3 fiber couplers,” Biomed. Opt. Express 13, 957–967 (2005).
[Crossref]

Farsiu, S.

Ferchera, A. F.

R. J. Zawadzki, C. Leissera, R. Leitgeba, M. Pirchera, and A. F. Ferchera, “Three-dimensional ophthalmic optical coherence tomography with a refraction correction algorithm,” in “European Conference on Biomedical Optics,” (Optical Society of America, 2003), p. 5140_20.

Fujimoto, J. G.

Gambra, E.

Hornegger, J.

Huang, D.

M. Tang, A. Chen, Y. Li, and D. Huang, “Corneal power measurement with fourier-domain optical coherence tomography,” J. Cataract Refract. Surg. 36, 2115–2122 (2010).
[Crossref] [PubMed]

Izatt, J. A.

Jimenez-Alfaro, I.

Jones, J. A.

J. A. Jones and N. G. Waller, “Computing confidence intervals for standardized regression coefficients,” Psychological methods 18, 435 (2013).
[Crossref] [PubMed]

Klyce, S. D.

M. K. Smolek and S. D. Klyce, “Goodness-of-prediction of zernike polynomial fitting to corneal surfaces,” J. Cataract Refract. Surg. 31, 2350–2355 (2005).
[Crossref]

Köhler, T.

T. Köhler, “A projection access scheme for iterative reconstruction based on the golden section,” in “Nuclear Science Symposium Conference Record,” Vol. 6 (2004), pp. 3961.

Kraus, M. F.

Kuo, A. N.

LaRocca, F.

Leissera, C.

R. J. Zawadzki, C. Leissera, R. Leitgeba, M. Pirchera, and A. F. Ferchera, “Three-dimensional ophthalmic optical coherence tomography with a refraction correction algorithm,” in “European Conference on Biomedical Optics,” (Optical Society of America, 2003), p. 5140_20.

Leitgeba, R.

R. J. Zawadzki, C. Leissera, R. Leitgeba, M. Pirchera, and A. F. Ferchera, “Three-dimensional ophthalmic optical coherence tomography with a refraction correction algorithm,” in “European Conference on Biomedical Optics,” (Optical Society of America, 2003), p. 5140_20.

Li, Y.

M. Tang, A. Chen, Y. Li, and D. Huang, “Corneal power measurement with fourier-domain optical coherence tomography,” J. Cataract Refract. Surg. 36, 2115–2122 (2010).
[Crossref] [PubMed]

Lindenmayer, A.

P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants (Springer Science & Business Media, 2012).

Liu, J. J.

Maguire, L. J.

L. J. Maguire and W. M. Bourne, “Corneal topography of early keratoconus,” Am. J. Ophthalmol. 108, 107–112 (1989).
[Crossref] [PubMed]

Marcos, S.

Mayer, M. A.

McNabb, R. P.

Navarro, R.

Ortiz, S.

Pérez-Merino, P.

Pirchera, M.

R. J. Zawadzki, C. Leissera, R. Leitgeba, M. Pirchera, and A. F. Ferchera, “Three-dimensional ophthalmic optical coherence tomography with a refraction correction algorithm,” in “European Conference on Biomedical Optics,” (Optical Society of America, 2003), p. 5140_20.

Potsaid, B.

Prusinkiewicz, P.

P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants (Springer Science & Business Media, 2012).

Rivera, R.

Sarunic, M.

M. Sarunic, M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous complex conjugate resolved spectral domain and swept-source oct using 3×3 fiber couplers,” Biomed. Opt. Express 13, 957–967 (2005).
[Crossref]

Sicam, V. A. D.

B. Braaf, T. C. van de Watering, K. Spruijt, R. G. van der Heijde, and V. A. D. Sicam, “Calculating angle lambda (λ) using zernike tilt measurements in specular reflection corneal topography,” J Optom 2, 207–214 (2009).
[Crossref]

Smolek, M. K.

M. K. Smolek and S. D. Klyce, “Goodness-of-prediction of zernike polynomial fitting to corneal surfaces,” J. Cataract Refract. Surg. 31, 2350–2355 (2005).
[Crossref]

Spruijt, K.

B. Braaf, T. C. van de Watering, K. Spruijt, R. G. van der Heijde, and V. A. D. Sicam, “Calculating angle lambda (λ) using zernike tilt measurements in specular reflection corneal topography,” J Optom 2, 207–214 (2009).
[Crossref]

Stinnett, S. S.

R. P. McNabb, S. Farsiu, S. S. Stinnett, J. A. Izatt, and A. N. Kuo, “Optical coherence tomography accurately measures corneal power change from laser refractive surgery,” Ophthalmology 122, 677–686 (2015).
[Crossref]

Tang, M.

M. Tang, A. Chen, Y. Li, and D. Huang, “Corneal power measurement with fourier-domain optical coherence tomography,” J. Cataract Refract. Surg. 36, 2115–2122 (2010).
[Crossref] [PubMed]

van de Watering, T. C.

B. Braaf, T. C. van de Watering, K. Spruijt, R. G. van der Heijde, and V. A. D. Sicam, “Calculating angle lambda (λ) using zernike tilt measurements in specular reflection corneal topography,” J Optom 2, 207–214 (2009).
[Crossref]

van der Heijde, R. G.

B. Braaf, T. C. van de Watering, K. Spruijt, R. G. van der Heijde, and V. A. D. Sicam, “Calculating angle lambda (λ) using zernike tilt measurements in specular reflection corneal topography,” J Optom 2, 207–214 (2009).
[Crossref]

Waller, N. G.

J. A. Jones and N. G. Waller, “Computing confidence intervals for standardized regression coefficients,” Psychological methods 18, 435 (2013).
[Crossref] [PubMed]

Yang, C.

M. Sarunic, M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous complex conjugate resolved spectral domain and swept-source oct using 3×3 fiber couplers,” Biomed. Opt. Express 13, 957–967 (2005).
[Crossref]

Zawadzki, R. J.

R. J. Zawadzki, C. Leissera, R. Leitgeba, M. Pirchera, and A. F. Ferchera, “Three-dimensional ophthalmic optical coherence tomography with a refraction correction algorithm,” in “European Conference on Biomedical Optics,” (Optical Society of America, 2003), p. 5140_20.

Zhao, M.

Am. J. Ophthalmol. (1)

L. J. Maguire and W. M. Bourne, “Corneal topography of early keratoconus,” Am. J. Ophthalmol. 108, 107–112 (1989).
[Crossref] [PubMed]

Biomed. Opt. Express (5)

J Optom (1)

B. Braaf, T. C. van de Watering, K. Spruijt, R. G. van der Heijde, and V. A. D. Sicam, “Calculating angle lambda (λ) using zernike tilt measurements in specular reflection corneal topography,” J Optom 2, 207–214 (2009).
[Crossref]

J. Cataract Refract. Surg. (2)

M. Tang, A. Chen, Y. Li, and D. Huang, “Corneal power measurement with fourier-domain optical coherence tomography,” J. Cataract Refract. Surg. 36, 2115–2122 (2010).
[Crossref] [PubMed]

M. K. Smolek and S. D. Klyce, “Goodness-of-prediction of zernike polynomial fitting to corneal surfaces,” J. Cataract Refract. Surg. 31, 2350–2355 (2005).
[Crossref]

Ophthalmology (1)

R. P. McNabb, S. Farsiu, S. S. Stinnett, J. A. Izatt, and A. N. Kuo, “Optical coherence tomography accurately measures corneal power change from laser refractive surgery,” Ophthalmology 122, 677–686 (2015).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Psychological methods (1)

J. A. Jones and N. G. Waller, “Computing confidence intervals for standardized regression coefficients,” Psychological methods 18, 435 (2013).
[Crossref] [PubMed]

Other (4)

ANSI Z80.23-2008, “Corneal Topography Systems - Standard Terminology, Requirements,” American National Standards Institute (2008).

R. J. Zawadzki, C. Leissera, R. Leitgeba, M. Pirchera, and A. F. Ferchera, “Three-dimensional ophthalmic optical coherence tomography with a refraction correction algorithm,” in “European Conference on Biomedical Optics,” (Optical Society of America, 2003), p. 5140_20.

P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants (Springer Science & Business Media, 2012).

T. Köhler, “A projection access scheme for iterative reconstruction based on the golden section,” in “Nuclear Science Symposium Conference Record,” Vol. 6 (2004), pp. 3961.

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Figures (5)

Fig. 1
Fig. 1 The refining scan pattern with a sampling rate of 2 kHz. (a) Scan points of the first cycle and the initial orientations of the first four cycles. Each successive cycle is rotated with respect to the previous one by an approximation of golden angle. (b) Scan points of the complete pattern consisting of eight cycles.
Fig. 2
Fig. 2 (a) Condition number of the Zernike reconstruction depending on the number of adjacent cycles included for the proposed refining pattern (blue) and repeated first cycle (green). (b) Coefficients standard error (blue) and the convergence of the Zernike coefficients (green) for the four test surface reconstructions depending on the number of adjacent cycles included.
Fig. 3
Fig. 3 The eight individual cycles of a scan with a blinking artifact in the lower row. The segmentation of the anterior cornea is shown in white.
Fig. 4
Fig. 4 Generated corneal topography maps in diopters and the scan points used for Zernike reconstruction. (a) Topography map from a scan with blinking artifact. (b) Topography map from a disturbance free rescan.
Fig. 5
Fig. 5 The first four cycles from the proposed refining scan pattern (a) with golden angle rotation and an alternative refining scan pattern (b) with an angle shift of 1 8 × 2 π radians.

Equations (5)

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θ g = 1 1 + Φ 2 π 0.381966 × 2 π ,
( X T X ) β ^ = X T z ,
κ ( X ) = σ max ( X ) σ min ( X ) .
s = diag ( Σ )
Σ = ( X T X ) 1 s 2 ,

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