Abstract

A forward ray tracing (FRT) model is presented to determine the exact image projection in a general corneal topography system. Consequently, the skew ray error in Placido-based topography is demonstrated. A quantitative analysis comparing FRT-based algorithms and Placido-based algorithms in reconstructing the front surface of the cornea shows that arc step algorithms are more sensitive to noise (imprecise). Furthermore, they are less accurate in determining corneal aberrations particularly the quadrafoil aberration. On the other hand, FRT-based algorithms are more accurate and more precise showing that point to point corneal topography is superior compared to its Placido-based counterpart.

© 2010 OSA

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  2. C. Bauer, “Direct illuminance caching: a way to enhance the performance of RADIANCE,” Lighting Res. Tech. 34(4), 333–345 (2002).
    [CrossRef]
  3. V. A. Sicam, J. J. Snellenburg, R. G. van der Heijde, and I. H. van Stokkum, “Pseudo forward ray-tracing: a new method for surface validation in cornea topography,” Optom. Vis. Sci. 84(9), 915–923 (2007).
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  14. J. H. Massig, E. Lingelbach, and B. Lingelbach, “Videokeratoscope for accurate and detailed measurement of the cornea surface,” Appl. Opt. 44(12), 2281–2287 (2005).
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    [CrossRef] [PubMed]
  24. S. Marcos, P. Rosales, L. Llorente, and I. Jiménez-Alfaro, “Change in corneal aberrations after cataract surgery with 2 types of aspherical intraocular lenses,” J. Cataract Refract. Surg. 33(2), 217–226 (2007).
    [CrossRef] [PubMed]
  25. O. Muftuoglu, P. Prasher, R. W. Bowman, J. P. McCulley, and V. V. Mootha, “Corneal higher-order aberrations after Descemet’s stripping automated endothelial keratoplasty,” Ophthalmology 117(5), 878–884, e6 (2010).
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    [CrossRef]
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    [CrossRef] [PubMed]
  28. F. Lu, J. X. Wu, J. Qu, and ., “Association between offset of the pupil center from the corneal vertex and wavefront aberration,” J. Opt. 1, 8–13 (2008).
  29. 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), 657–669 (2002).
    [CrossRef]
  30. R. A. Applegate, J. D. Marsack, and L. N. Thibos, “Metrics of retinal image quality predict visual performance in eyes with 20/17 or better visual acuity,” Optom. Vis. Sci. 83(9), 635–640 (2006).
    [CrossRef] [PubMed]
  31. B. Braaf, M. Dubbelman, R. G. van der Heijde, and V. A. Sicam, “Performance in specular reflection and slit-imaging corneal topography,” Optom. Vis. Sci. 86(5), 467–475 (2009).
    [CrossRef] [PubMed]

2010 (1)

O. Muftuoglu, P. Prasher, R. W. Bowman, J. P. McCulley, and V. V. Mootha, “Corneal higher-order aberrations after Descemet’s stripping automated endothelial keratoplasty,” Ophthalmology 117(5), 878–884, e6 (2010).
[CrossRef] [PubMed]

2009 (3)

V. Sokurenko and V. Molebny, “Damped least-squares approach for point-source corneal topography,” Ophthalmic Physiol. Opt. 29(3), 330–337 (2009).
[CrossRef] [PubMed]

B. Braaf, M. Dubbelman, R. G. van der Heijde, and V. A. Sicam, “Performance in specular reflection and slit-imaging corneal topography,” Optom. Vis. Sci. 86(5), 467–475 (2009).
[CrossRef] [PubMed]

Y. Mejía and J. C. Galeano, “Corneal topographer based on the Hartmann test,” Optom. Vis. Sci. 86(4), 370–381 (2009).
[CrossRef] [PubMed]

2008 (2)

J. Turuwhenua, “An improved low order method for corneal reconstruction,” Optom. Vis. Sci. 85(3), 211–217 (2008).
[CrossRef] [PubMed]

F. Lu, J. X. Wu, J. Qu, and ., “Association between offset of the pupil center from the corneal vertex and wavefront aberration,” J. Opt. 1, 8–13 (2008).

2007 (4)

J. Turuwhenua, “Corneal surface reconstruction algorithm using Zernike polynomial representation: improvements,” J. Opt. Soc. Am. A 24(6), 1551–1561 (2007).
[CrossRef]

S. Marcos, P. Rosales, L. Llorente, and I. Jiménez-Alfaro, “Change in corneal aberrations after cataract surgery with 2 types of aspherical intraocular lenses,” J. Cataract Refract. Surg. 33(2), 217–226 (2007).
[CrossRef] [PubMed]

V. A. Sicam, J. J. Snellenburg, R. G. van der Heijde, and I. H. van Stokkum, “Pseudo forward ray-tracing: a new method for surface validation in cornea topography,” Optom. Vis. Sci. 84(9), 915–923 (2007).
[CrossRef] [PubMed]

T. Swartz, L. Marten, and M. Wang, “Measuring the cornea: the latest developments in corneal topography,” Curr. Opin. Ophthalmol. 18(4), 325–333 (2007).
[CrossRef] [PubMed]

2006 (2)

R. A. Applegate, J. D. Marsack, and L. N. Thibos, “Metrics of retinal image quality predict visual performance in eyes with 20/17 or better visual acuity,” Optom. Vis. Sci. 83(9), 635–640 (2006).
[CrossRef] [PubMed]

V. A. Sicam and R. G. VAN der Heijde, “Topographer reconstruction of the nonrotation-symmetric anterior corneal surface features,” Optom. Vis. Sci. 83(12), 910–918 (2006).
[CrossRef] [PubMed]

2005 (2)

L. A. Carvalho, “Accuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eye,” Invest. Ophthalmol. Vis. Sci. 46(6), 1915–1926 (2005).
[CrossRef] [PubMed]

J. H. Massig, E. Lingelbach, and B. Lingelbach, “Videokeratoscope for accurate and detailed measurement of the cornea surface,” Appl. Opt. 44(12), 2281–2287 (2005).
[CrossRef] [PubMed]

2004 (1)

2002 (4)

C. Bauer, “Direct illuminance caching: a way to enhance the performance of RADIANCE,” Lighting Res. Tech. 34(4), 333–345 (2002).
[CrossRef]

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), 657–669 (2002).
[CrossRef]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19(12), 2329–2348 (2002).
[CrossRef]

L. A. Carvalho, M. Stefani, A. C. Romão, L. Carvalho, J. C. de Castro, S. Tonissi, P. Schor, and W. Chamon, “Videokeratoscopes for dioptric power measurement during surgery,” J. Cataract Refract. Surg. 28(11), 2006–2016 (2002).
[CrossRef] [PubMed]

1997 (5)

R. H. Rand, H. C. Howland, and R. A. Applegate, “Mathematical model of a Placido disk keratometer and its implications for recovery of corneal topography,” Optom. Vis. Sci. 74(11), 926–930 (1997).
[CrossRef] [PubMed]

R. Mattioli and N. K. Tripoli, “Corneal geometry reconstruction with the Keratron videokeratographer,” Optom. Vis. Sci. 74(11), 881–894 (1997).
[CrossRef] [PubMed]

S. A. Klein, “Axial curvature and the skew ray error in corneal topography,” Optom. Vis. Sci. 74(11), 931–944 (1997).
[CrossRef] [PubMed]

S. A. Klein, “Corneal topography reconstruction algorithm that avoids the skew ray ambiguity and the skew ray error,” Optom. Vis. Sci. 74(11), 945–962 (1997).
[CrossRef] [PubMed]

F. M. Vos, R. G. L. van der Heijde, H. J. W. Spoelder, I. H. M. van Stokkum, and F. C. A. Groen, “A New Instrument to Measure the Shape of the Cornea Based on Pseudorandom Color Coding,” IEEE Trans. Instrum. Meas. 46(4), 794–797 (1997).
[CrossRef]

1996 (1)

N. K. Tripoli, K. L. Cohen, P. Obla, J. M. Coggins, and D. E. Holmgren, “Height measurement of astigmatic test surfaces by a keratoscope that uses plane geometry surface reconstruction,” Am. J. Ophthalmol. 121(6), 668–676 (1996).
[PubMed]

1995 (1)

M. A. Halstead, B. A. Barsky, S. A. Klein, and R. B. Mandell, “A spline surface algorithm for reconstruction of corneal topography from a videokeratographic reflection pattern,” Optom. Vis. Sci. 72(11), 821–827 (1995).
[CrossRef] [PubMed]

1992 (1)

S. A. Klein, “A corneal topography algorithm that produces continuous curvature,” Optom. Vis. Sci. 69(11), 829–834 (1992).
[CrossRef] [PubMed]

1989 (1)

J. Y. Wang, D. A. Rice, and S. D. Klyce, “A new reconstruction algorithm for improvement of corneal topographical analysis,” Refract. Corneal Surg. 5(6), 379–387 (1989).
[PubMed]

1984 (1)

J. Amanatides, “Ray tracing with cones,” Comput. Graph. 18(3), 129–135 (1984).
[CrossRef]

1981 (1)

J. D. Doss, R. L. Hutson, J. J. Rowsey, and D. R. Brown, “Method for calculation of corneal profile and power distribution,” Arch. Ophthalmol. 99(7), 1261–1265 (1981).
[PubMed]

Amanatides, J.

J. Amanatides, “Ray tracing with cones,” Comput. Graph. 18(3), 129–135 (1984).
[CrossRef]

Applegate, R. A.

R. A. Applegate, J. D. Marsack, and L. N. Thibos, “Metrics of retinal image quality predict visual performance in eyes with 20/17 or better visual acuity,” Optom. Vis. Sci. 83(9), 635–640 (2006).
[CrossRef] [PubMed]

R. H. Rand, H. C. Howland, and R. A. Applegate, “Mathematical model of a Placido disk keratometer and its implications for recovery of corneal topography,” Optom. Vis. Sci. 74(11), 926–930 (1997).
[CrossRef] [PubMed]

Barsky, B. A.

M. A. Halstead, B. A. Barsky, S. A. Klein, and R. B. Mandell, “A spline surface algorithm for reconstruction of corneal topography from a videokeratographic reflection pattern,” Optom. Vis. Sci. 72(11), 821–827 (1995).
[CrossRef] [PubMed]

Bauer, C.

C. Bauer, “Direct illuminance caching: a way to enhance the performance of RADIANCE,” Lighting Res. Tech. 34(4), 333–345 (2002).
[CrossRef]

Bowman, R. W.

O. Muftuoglu, P. Prasher, R. W. Bowman, J. P. McCulley, and V. V. Mootha, “Corneal higher-order aberrations after Descemet’s stripping automated endothelial keratoplasty,” Ophthalmology 117(5), 878–884, e6 (2010).
[CrossRef] [PubMed]

Braaf, B.

B. Braaf, M. Dubbelman, R. G. van der Heijde, and V. A. Sicam, “Performance in specular reflection and slit-imaging corneal topography,” Optom. Vis. Sci. 86(5), 467–475 (2009).
[CrossRef] [PubMed]

Bradley, A.

Brown, D. R.

J. D. Doss, R. L. Hutson, J. J. Rowsey, and D. R. Brown, “Method for calculation of corneal profile and power distribution,” Arch. Ophthalmol. 99(7), 1261–1265 (1981).
[PubMed]

Carvalho, L.

L. A. Carvalho, M. Stefani, A. C. Romão, L. Carvalho, J. C. de Castro, S. Tonissi, P. Schor, and W. Chamon, “Videokeratoscopes for dioptric power measurement during surgery,” J. Cataract Refract. Surg. 28(11), 2006–2016 (2002).
[CrossRef] [PubMed]

Carvalho, L. A.

L. A. Carvalho, “Accuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eye,” Invest. Ophthalmol. Vis. Sci. 46(6), 1915–1926 (2005).
[CrossRef] [PubMed]

L. A. Carvalho, M. Stefani, A. C. Romão, L. Carvalho, J. C. de Castro, S. Tonissi, P. Schor, and W. Chamon, “Videokeratoscopes for dioptric power measurement during surgery,” J. Cataract Refract. Surg. 28(11), 2006–2016 (2002).
[CrossRef] [PubMed]

Chamon, W.

L. A. Carvalho, M. Stefani, A. C. Romão, L. Carvalho, J. C. de Castro, S. Tonissi, P. Schor, and W. Chamon, “Videokeratoscopes for dioptric power measurement during surgery,” J. Cataract Refract. Surg. 28(11), 2006–2016 (2002).
[CrossRef] [PubMed]

Cheng, X.

Coggins, J. M.

N. K. Tripoli, K. L. Cohen, P. Obla, J. M. Coggins, and D. E. Holmgren, “Height measurement of astigmatic test surfaces by a keratoscope that uses plane geometry surface reconstruction,” Am. J. Ophthalmol. 121(6), 668–676 (1996).
[PubMed]

Cohen, K. L.

N. K. Tripoli, K. L. Cohen, P. Obla, J. M. Coggins, and D. E. Holmgren, “Height measurement of astigmatic test surfaces by a keratoscope that uses plane geometry surface reconstruction,” Am. J. Ophthalmol. 121(6), 668–676 (1996).
[PubMed]

Coppens, J.

de Castro, J. C.

L. A. Carvalho, M. Stefani, A. C. Romão, L. Carvalho, J. C. de Castro, S. Tonissi, P. Schor, and W. Chamon, “Videokeratoscopes for dioptric power measurement during surgery,” J. Cataract Refract. Surg. 28(11), 2006–2016 (2002).
[CrossRef] [PubMed]

Doss, J. D.

J. D. Doss, R. L. Hutson, J. J. Rowsey, and D. R. Brown, “Method for calculation of corneal profile and power distribution,” Arch. Ophthalmol. 99(7), 1261–1265 (1981).
[PubMed]

Dubbelman, M.

B. Braaf, M. Dubbelman, R. G. van der Heijde, and V. A. Sicam, “Performance in specular reflection and slit-imaging corneal topography,” Optom. Vis. Sci. 86(5), 467–475 (2009).
[CrossRef] [PubMed]

Galeano, J. C.

Y. Mejía and J. C. Galeano, “Corneal topographer based on the Hartmann test,” Optom. Vis. Sci. 86(4), 370–381 (2009).
[CrossRef] [PubMed]

Groen, F. C. A.

F. M. Vos, R. G. L. van der Heijde, H. J. W. Spoelder, I. H. M. van Stokkum, and F. C. A. Groen, “A New Instrument to Measure the Shape of the Cornea Based on Pseudorandom Color Coding,” IEEE Trans. Instrum. Meas. 46(4), 794–797 (1997).
[CrossRef]

Halstead, M. A.

M. A. Halstead, B. A. Barsky, S. A. Klein, and R. B. Mandell, “A spline surface algorithm for reconstruction of corneal topography from a videokeratographic reflection pattern,” Optom. Vis. Sci. 72(11), 821–827 (1995).
[CrossRef] [PubMed]

Holmgren, D. E.

N. K. Tripoli, K. L. Cohen, P. Obla, J. M. Coggins, and D. E. Holmgren, “Height measurement of astigmatic test surfaces by a keratoscope that uses plane geometry surface reconstruction,” Am. J. Ophthalmol. 121(6), 668–676 (1996).
[PubMed]

Hong, X.

Howland, H. C.

R. H. Rand, H. C. Howland, and R. A. Applegate, “Mathematical model of a Placido disk keratometer and its implications for recovery of corneal topography,” Optom. Vis. Sci. 74(11), 926–930 (1997).
[CrossRef] [PubMed]

Hutson, R. L.

J. D. Doss, R. L. Hutson, J. J. Rowsey, and D. R. Brown, “Method for calculation of corneal profile and power distribution,” Arch. Ophthalmol. 99(7), 1261–1265 (1981).
[PubMed]

Jiménez-Alfaro, I.

S. Marcos, P. Rosales, L. Llorente, and I. Jiménez-Alfaro, “Change in corneal aberrations after cataract surgery with 2 types of aspherical intraocular lenses,” J. Cataract Refract. Surg. 33(2), 217–226 (2007).
[CrossRef] [PubMed]

Klein, S. A.

S. A. Klein, “Axial curvature and the skew ray error in corneal topography,” Optom. Vis. Sci. 74(11), 931–944 (1997).
[CrossRef] [PubMed]

S. A. Klein, “Corneal topography reconstruction algorithm that avoids the skew ray ambiguity and the skew ray error,” Optom. Vis. Sci. 74(11), 945–962 (1997).
[CrossRef] [PubMed]

M. A. Halstead, B. A. Barsky, S. A. Klein, and R. B. Mandell, “A spline surface algorithm for reconstruction of corneal topography from a videokeratographic reflection pattern,” Optom. Vis. Sci. 72(11), 821–827 (1995).
[CrossRef] [PubMed]

S. A. Klein, “A corneal topography algorithm that produces continuous curvature,” Optom. Vis. Sci. 69(11), 829–834 (1992).
[CrossRef] [PubMed]

Klyce, S. D.

J. Y. Wang, D. A. Rice, and S. D. Klyce, “A new reconstruction algorithm for improvement of corneal topographical analysis,” Refract. Corneal Surg. 5(6), 379–387 (1989).
[PubMed]

Lingelbach, B.

Lingelbach, E.

Llorente, L.

S. Marcos, P. Rosales, L. Llorente, and I. Jiménez-Alfaro, “Change in corneal aberrations after cataract surgery with 2 types of aspherical intraocular lenses,” J. Cataract Refract. Surg. 33(2), 217–226 (2007).
[CrossRef] [PubMed]

Lu, F.

F. Lu, J. X. Wu, J. Qu, and ., “Association between offset of the pupil center from the corneal vertex and wavefront aberration,” J. Opt. 1, 8–13 (2008).

Mandell, R. B.

M. A. Halstead, B. A. Barsky, S. A. Klein, and R. B. Mandell, “A spline surface algorithm for reconstruction of corneal topography from a videokeratographic reflection pattern,” Optom. Vis. Sci. 72(11), 821–827 (1995).
[CrossRef] [PubMed]

Marcos, S.

S. Marcos, P. Rosales, L. Llorente, and I. Jiménez-Alfaro, “Change in corneal aberrations after cataract surgery with 2 types of aspherical intraocular lenses,” J. Cataract Refract. Surg. 33(2), 217–226 (2007).
[CrossRef] [PubMed]

Marsack, J. D.

R. A. Applegate, J. D. Marsack, and L. N. Thibos, “Metrics of retinal image quality predict visual performance in eyes with 20/17 or better visual acuity,” Optom. Vis. Sci. 83(9), 635–640 (2006).
[CrossRef] [PubMed]

Marten, L.

T. Swartz, L. Marten, and M. Wang, “Measuring the cornea: the latest developments in corneal topography,” Curr. Opin. Ophthalmol. 18(4), 325–333 (2007).
[CrossRef] [PubMed]

Massig, J. H.

Mattioli, R.

R. Mattioli and N. K. Tripoli, “Corneal geometry reconstruction with the Keratron videokeratographer,” Optom. Vis. Sci. 74(11), 881–894 (1997).
[CrossRef] [PubMed]

McCulley, J. P.

O. Muftuoglu, P. Prasher, R. W. Bowman, J. P. McCulley, and V. V. Mootha, “Corneal higher-order aberrations after Descemet’s stripping automated endothelial keratoplasty,” Ophthalmology 117(5), 878–884, e6 (2010).
[CrossRef] [PubMed]

Mejía, Y.

Y. Mejía and J. C. Galeano, “Corneal topographer based on the Hartmann test,” Optom. Vis. Sci. 86(4), 370–381 (2009).
[CrossRef] [PubMed]

Molebny, V.

V. Sokurenko and V. Molebny, “Damped least-squares approach for point-source corneal topography,” Ophthalmic Physiol. Opt. 29(3), 330–337 (2009).
[CrossRef] [PubMed]

Mootha, V. V.

O. Muftuoglu, P. Prasher, R. W. Bowman, J. P. McCulley, and V. V. Mootha, “Corneal higher-order aberrations after Descemet’s stripping automated endothelial keratoplasty,” Ophthalmology 117(5), 878–884, e6 (2010).
[CrossRef] [PubMed]

Muftuoglu, O.

O. Muftuoglu, P. Prasher, R. W. Bowman, J. P. McCulley, and V. V. Mootha, “Corneal higher-order aberrations after Descemet’s stripping automated endothelial keratoplasty,” Ophthalmology 117(5), 878–884, e6 (2010).
[CrossRef] [PubMed]

Obla, P.

N. K. Tripoli, K. L. Cohen, P. Obla, J. M. Coggins, and D. E. Holmgren, “Height measurement of astigmatic test surfaces by a keratoscope that uses plane geometry surface reconstruction,” Am. J. Ophthalmol. 121(6), 668–676 (1996).
[PubMed]

Prasher, P.

O. Muftuoglu, P. Prasher, R. W. Bowman, J. P. McCulley, and V. V. Mootha, “Corneal higher-order aberrations after Descemet’s stripping automated endothelial keratoplasty,” Ophthalmology 117(5), 878–884, e6 (2010).
[CrossRef] [PubMed]

Qu, J.

F. Lu, J. X. Wu, J. Qu, and ., “Association between offset of the pupil center from the corneal vertex and wavefront aberration,” J. Opt. 1, 8–13 (2008).

Rand, R. H.

R. H. Rand, H. C. Howland, and R. A. Applegate, “Mathematical model of a Placido disk keratometer and its implications for recovery of corneal topography,” Optom. Vis. Sci. 74(11), 926–930 (1997).
[CrossRef] [PubMed]

Rice, D. A.

J. Y. Wang, D. A. Rice, and S. D. Klyce, “A new reconstruction algorithm for improvement of corneal topographical analysis,” Refract. Corneal Surg. 5(6), 379–387 (1989).
[PubMed]

Romão, A. C.

L. A. Carvalho, M. Stefani, A. C. Romão, L. Carvalho, J. C. de Castro, S. Tonissi, P. Schor, and W. Chamon, “Videokeratoscopes for dioptric power measurement during surgery,” J. Cataract Refract. Surg. 28(11), 2006–2016 (2002).
[CrossRef] [PubMed]

Rosales, P.

S. Marcos, P. Rosales, L. Llorente, and I. Jiménez-Alfaro, “Change in corneal aberrations after cataract surgery with 2 types of aspherical intraocular lenses,” J. Cataract Refract. Surg. 33(2), 217–226 (2007).
[CrossRef] [PubMed]

Rowsey, J. J.

J. D. Doss, R. L. Hutson, J. J. Rowsey, and D. R. Brown, “Method for calculation of corneal profile and power distribution,” Arch. Ophthalmol. 99(7), 1261–1265 (1981).
[PubMed]

Salmon, T. O.

Schor, P.

L. A. Carvalho, M. Stefani, A. C. Romão, L. Carvalho, J. C. de Castro, S. Tonissi, P. Schor, and W. Chamon, “Videokeratoscopes for dioptric power measurement during surgery,” J. Cataract Refract. Surg. 28(11), 2006–2016 (2002).
[CrossRef] [PubMed]

Sicam, V. A.

B. Braaf, M. Dubbelman, R. G. van der Heijde, and V. A. Sicam, “Performance in specular reflection and slit-imaging corneal topography,” Optom. Vis. Sci. 86(5), 467–475 (2009).
[CrossRef] [PubMed]

V. A. Sicam, J. J. Snellenburg, R. G. van der Heijde, and I. H. van Stokkum, “Pseudo forward ray-tracing: a new method for surface validation in cornea topography,” Optom. Vis. Sci. 84(9), 915–923 (2007).
[CrossRef] [PubMed]

V. A. Sicam and R. G. VAN der Heijde, “Topographer reconstruction of the nonrotation-symmetric anterior corneal surface features,” Optom. Vis. Sci. 83(12), 910–918 (2006).
[CrossRef] [PubMed]

V. A. Sicam, J. Coppens, T. J. van den Berg, and R. G. van der Heijde, “Corneal surface reconstruction algorithm that uses Zernike polynomial representation,” J. Opt. Soc. Am. A 21(7), 1300–1306 (2004).
[CrossRef]

Snellenburg, J. J.

V. A. Sicam, J. J. Snellenburg, R. G. van der Heijde, and I. H. van Stokkum, “Pseudo forward ray-tracing: a new method for surface validation in cornea topography,” Optom. Vis. Sci. 84(9), 915–923 (2007).
[CrossRef] [PubMed]

Sokurenko, V.

V. Sokurenko and V. Molebny, “Damped least-squares approach for point-source corneal topography,” Ophthalmic Physiol. Opt. 29(3), 330–337 (2009).
[CrossRef] [PubMed]

Spoelder, H. J. W.

F. M. Vos, R. G. L. van der Heijde, H. J. W. Spoelder, I. H. M. van Stokkum, and F. C. A. Groen, “A New Instrument to Measure the Shape of the Cornea Based on Pseudorandom Color Coding,” IEEE Trans. Instrum. Meas. 46(4), 794–797 (1997).
[CrossRef]

Stefani, M.

L. A. Carvalho, M. Stefani, A. C. Romão, L. Carvalho, J. C. de Castro, S. Tonissi, P. Schor, and W. Chamon, “Videokeratoscopes for dioptric power measurement during surgery,” J. Cataract Refract. Surg. 28(11), 2006–2016 (2002).
[CrossRef] [PubMed]

Swartz, T.

T. Swartz, L. Marten, and M. Wang, “Measuring the cornea: the latest developments in corneal topography,” Curr. Opin. Ophthalmol. 18(4), 325–333 (2007).
[CrossRef] [PubMed]

Thibos, L. N.

Tonissi, S.

L. A. Carvalho, M. Stefani, A. C. Romão, L. Carvalho, J. C. de Castro, S. Tonissi, P. Schor, and W. Chamon, “Videokeratoscopes for dioptric power measurement during surgery,” J. Cataract Refract. Surg. 28(11), 2006–2016 (2002).
[CrossRef] [PubMed]

Tripoli, N. K.

R. Mattioli and N. K. Tripoli, “Corneal geometry reconstruction with the Keratron videokeratographer,” Optom. Vis. Sci. 74(11), 881–894 (1997).
[CrossRef] [PubMed]

N. K. Tripoli, K. L. Cohen, P. Obla, J. M. Coggins, and D. E. Holmgren, “Height measurement of astigmatic test surfaces by a keratoscope that uses plane geometry surface reconstruction,” Am. J. Ophthalmol. 121(6), 668–676 (1996).
[PubMed]

Turuwhenua, J.

van den Berg, T. J.

van der Heijde, R. G.

B. Braaf, M. Dubbelman, R. G. van der Heijde, and V. A. Sicam, “Performance in specular reflection and slit-imaging corneal topography,” Optom. Vis. Sci. 86(5), 467–475 (2009).
[CrossRef] [PubMed]

V. A. Sicam, J. J. Snellenburg, R. G. van der Heijde, and I. H. van Stokkum, “Pseudo forward ray-tracing: a new method for surface validation in cornea topography,” Optom. Vis. Sci. 84(9), 915–923 (2007).
[CrossRef] [PubMed]

V. A. Sicam and R. G. VAN der Heijde, “Topographer reconstruction of the nonrotation-symmetric anterior corneal surface features,” Optom. Vis. Sci. 83(12), 910–918 (2006).
[CrossRef] [PubMed]

V. A. Sicam, J. Coppens, T. J. van den Berg, and R. G. van der Heijde, “Corneal surface reconstruction algorithm that uses Zernike polynomial representation,” J. Opt. Soc. Am. A 21(7), 1300–1306 (2004).
[CrossRef]

van der Heijde, R. G. L.

F. M. Vos, R. G. L. van der Heijde, H. J. W. Spoelder, I. H. M. van Stokkum, and F. C. A. Groen, “A New Instrument to Measure the Shape of the Cornea Based on Pseudorandom Color Coding,” IEEE Trans. Instrum. Meas. 46(4), 794–797 (1997).
[CrossRef]

van Stokkum, I. H.

V. A. Sicam, J. J. Snellenburg, R. G. van der Heijde, and I. H. van Stokkum, “Pseudo forward ray-tracing: a new method for surface validation in cornea topography,” Optom. Vis. Sci. 84(9), 915–923 (2007).
[CrossRef] [PubMed]

van Stokkum, I. H. M.

F. M. Vos, R. G. L. van der Heijde, H. J. W. Spoelder, I. H. M. van Stokkum, and F. C. A. Groen, “A New Instrument to Measure the Shape of the Cornea Based on Pseudorandom Color Coding,” IEEE Trans. Instrum. Meas. 46(4), 794–797 (1997).
[CrossRef]

Vos, F. M.

F. M. Vos, R. G. L. van der Heijde, H. J. W. Spoelder, I. H. M. van Stokkum, and F. C. A. Groen, “A New Instrument to Measure the Shape of the Cornea Based on Pseudorandom Color Coding,” IEEE Trans. Instrum. Meas. 46(4), 794–797 (1997).
[CrossRef]

Wang, J. Y.

J. Y. Wang, D. A. Rice, and S. D. Klyce, “A new reconstruction algorithm for improvement of corneal topographical analysis,” Refract. Corneal Surg. 5(6), 379–387 (1989).
[PubMed]

Wang, M.

T. Swartz, L. Marten, and M. Wang, “Measuring the cornea: the latest developments in corneal topography,” Curr. Opin. Ophthalmol. 18(4), 325–333 (2007).
[CrossRef] [PubMed]

Wu, J. X.

F. Lu, J. X. Wu, J. Qu, and ., “Association between offset of the pupil center from the corneal vertex and wavefront aberration,” J. Opt. 1, 8–13 (2008).

Am. J. Ophthalmol. (1)

N. K. Tripoli, K. L. Cohen, P. Obla, J. M. Coggins, and D. E. Holmgren, “Height measurement of astigmatic test surfaces by a keratoscope that uses plane geometry surface reconstruction,” Am. J. Ophthalmol. 121(6), 668–676 (1996).
[PubMed]

Appl. Opt. (1)

Arch. Ophthalmol. (1)

J. D. Doss, R. L. Hutson, J. J. Rowsey, and D. R. Brown, “Method for calculation of corneal profile and power distribution,” Arch. Ophthalmol. 99(7), 1261–1265 (1981).
[PubMed]

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J. Amanatides, “Ray tracing with cones,” Comput. Graph. 18(3), 129–135 (1984).
[CrossRef]

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T. Swartz, L. Marten, and M. Wang, “Measuring the cornea: the latest developments in corneal topography,” Curr. Opin. Ophthalmol. 18(4), 325–333 (2007).
[CrossRef] [PubMed]

IEEE Trans. Instrum. Meas. (1)

F. M. Vos, R. G. L. van der Heijde, H. J. W. Spoelder, I. H. M. van Stokkum, and F. C. A. Groen, “A New Instrument to Measure the Shape of the Cornea Based on Pseudorandom Color Coding,” IEEE Trans. Instrum. Meas. 46(4), 794–797 (1997).
[CrossRef]

Invest. Ophthalmol. Vis. Sci. (1)

L. A. Carvalho, “Accuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eye,” Invest. Ophthalmol. Vis. Sci. 46(6), 1915–1926 (2005).
[CrossRef] [PubMed]

J. Cataract Refract. Surg. (2)

S. Marcos, P. Rosales, L. Llorente, and I. Jiménez-Alfaro, “Change in corneal aberrations after cataract surgery with 2 types of aspherical intraocular lenses,” J. Cataract Refract. Surg. 33(2), 217–226 (2007).
[CrossRef] [PubMed]

L. A. Carvalho, M. Stefani, A. C. Romão, L. Carvalho, J. C. de Castro, S. Tonissi, P. Schor, and W. Chamon, “Videokeratoscopes for dioptric power measurement during surgery,” J. Cataract Refract. Surg. 28(11), 2006–2016 (2002).
[CrossRef] [PubMed]

J. Opt. (1)

F. Lu, J. X. Wu, J. Qu, and ., “Association between offset of the pupil center from the corneal vertex and wavefront aberration,” J. Opt. 1, 8–13 (2008).

J. Opt. Soc. Am. A (4)

Lighting Res. Tech. (1)

C. Bauer, “Direct illuminance caching: a way to enhance the performance of RADIANCE,” Lighting Res. Tech. 34(4), 333–345 (2002).
[CrossRef]

Ophthalmic Physiol. Opt. (1)

V. Sokurenko and V. Molebny, “Damped least-squares approach for point-source corneal topography,” Ophthalmic Physiol. Opt. 29(3), 330–337 (2009).
[CrossRef] [PubMed]

Ophthalmology (1)

O. Muftuoglu, P. Prasher, R. W. Bowman, J. P. McCulley, and V. V. Mootha, “Corneal higher-order aberrations after Descemet’s stripping automated endothelial keratoplasty,” Ophthalmology 117(5), 878–884, e6 (2010).
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R. H. Rand, H. C. Howland, and R. A. Applegate, “Mathematical model of a Placido disk keratometer and its implications for recovery of corneal topography,” Optom. Vis. Sci. 74(11), 926–930 (1997).
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[CrossRef] [PubMed]

B. Braaf, M. Dubbelman, R. G. van der Heijde, and V. A. Sicam, “Performance in specular reflection and slit-imaging corneal topography,” Optom. Vis. Sci. 86(5), 467–475 (2009).
[CrossRef] [PubMed]

V. A. Sicam, J. J. Snellenburg, R. G. van der Heijde, and I. H. van Stokkum, “Pseudo forward ray-tracing: a new method for surface validation in cornea topography,” Optom. Vis. Sci. 84(9), 915–923 (2007).
[CrossRef] [PubMed]

S. A. Klein, “Axial curvature and the skew ray error in corneal topography,” Optom. Vis. Sci. 74(11), 931–944 (1997).
[CrossRef] [PubMed]

S. A. Klein, “Corneal topography reconstruction algorithm that avoids the skew ray ambiguity and the skew ray error,” Optom. Vis. Sci. 74(11), 945–962 (1997).
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S. A. Klein, “A corneal topography algorithm that produces continuous curvature,” Optom. Vis. Sci. 69(11), 829–834 (1992).
[CrossRef] [PubMed]

R. Mattioli and N. K. Tripoli, “Corneal geometry reconstruction with the Keratron videokeratographer,” Optom. Vis. Sci. 74(11), 881–894 (1997).
[CrossRef] [PubMed]

J. Turuwhenua, “An improved low order method for corneal reconstruction,” Optom. Vis. Sci. 85(3), 211–217 (2008).
[CrossRef] [PubMed]

V. A. Sicam and R. G. VAN der Heijde, “Topographer reconstruction of the nonrotation-symmetric anterior corneal surface features,” Optom. Vis. Sci. 83(12), 910–918 (2006).
[CrossRef] [PubMed]

Y. Mejía and J. C. Galeano, “Corneal topographer based on the Hartmann test,” Optom. Vis. Sci. 86(4), 370–381 (2009).
[CrossRef] [PubMed]

M. A. Halstead, B. A. Barsky, S. A. Klein, and R. B. Mandell, “A spline surface algorithm for reconstruction of corneal topography from a videokeratographic reflection pattern,” Optom. Vis. Sci. 72(11), 821–827 (1995).
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Refract. Corneal Surg. (1)

J. Y. Wang, D. A. Rice, and S. D. Klyce, “A new reconstruction algorithm for improvement of corneal topographical analysis,” Refract. Corneal Surg. 5(6), 379–387 (1989).
[PubMed]

Other (1)

Matlab, The Mathworks, Massachusetts, USA.

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Figures (11)

Fig. 1
Fig. 1

Diagram of forward ray tracing model

Fig. 2
Fig. 2

Illustration of skew ray error in Placido-based corneal topography. Depicted are the forward ray traced simulated Placido reflection patterns of a 6 Diopter toric surface (a,b) and the Rand surface (c,d) with 8 mm base radius. The surfaces are evaluated in an 8mm corneal region for 20 rings with either 256 meridians (a,c) or 8 meridians (b,d). The two red circle outlines corresponds to the reflection of the 10th and 20th ring on a sphere with 8 mm radius. Red dots are image points on the meridian and blue squares are the actual forward ray traced image points.

Fig. 4
Fig. 4

Astigmatism error in RMS (up to Zernike order 8) of artificial surface. The results for the MRT algorithm are plotted with respect to the secondary y-axis.

Fig. 3
Fig. 3

Residual curvature map in Diopter for a simulated cornea with no abnormalities. Here (a) represents the reconstruction by the FRT algorithm, (b) is the reconstruction by MRT algorithm, (c) is the reconstruction by the Basic AS algorithm and (d) is the SREC AS algorithm.

Fig. 5
Fig. 5

Trefoil error in RMS (up to Zernike order 8) of artificial surface. The results for the MRT algorithm are plotted with respect to the secondary y-axis.

Fig. 6
Fig. 6

Quadrafoil error in RMS (up to Zernike order 8) of artificial surface. The results for the MRT algorithm are plotted with respect to the secondary y-axis.

Fig. 7
Fig. 7

Octafoil error in RMS (up to Zernike order 8) of artificial surface. The results for the MRT algorithm and the SREC AS algorithm are plotted with respect to the secondary y-axis.

Fig. 9
Fig. 9

Trefoil error in RMS (up to Zernike order 8) of normal eye.

Fig. 8
Fig. 8

Astigmatism error in RMS (up to Zernike order 8) of normal eye.

Fig. 10
Fig. 10

Quadrafoil RMS error (up to Zernike order 8) of normal eye.

Fig. 11
Fig. 11

Curvature maps (a,b,c,d) and residual curvature maps (e,f,g) (in Diopter) of the reconstruction of a cornea with no abnormalities by different algorithms at a noise level of 10 micrometer. The simulated reference surface is represented by (a). The algorithms used for reconstruction are FRT (b,e), MRT (c,f) and Basic AS (d,g). The SKEC AS algorithm was excluded here because of numerical instability at this noise level. The curvature isolines of the curvature maps a,b,c and d are 6/5th diopter apart, and the curvature isolines of the residual curvature maps e, f and g are 1/8th diopter apart.

Tables (4)

Tables Icon

Table 1 Definitions and equations for the forward ray tracing model

Tables Icon

Table 2 Corneal aberration of a simulated surface of a real cornea

Tables Icon

Table 3 Performance of the four algorithms on four artificial surfaces. The error in μm of the aberration corresponding to the most dominant feature of the surface is evaluated.

Tables Icon

Table 4 Performance of the four algorithms on a simulated corneal surface. The error in μm of the non-rotationally symmetric aberration is evaluated.

Equations (8)

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

x i , y i , z i = R R x , R y , R z
z c r p = M ( x c r p , y c r p ) C
I x R x = ( I z R z ) M x C
I y R y = ( I z R z ) M y C
A ( x c , y c , z c ) = B ( x c , y c , z c ) C
C = [ B T B ] 1 [ B T A ]
z = r r 2 ρ 2 + g ( ρ , θ )
g ( ρ , θ ) = { ε sin ( n θ ) 2 ( ρ 1.5 ) ε sin ( n θ ) 0 } f o r     ρ 2 m m 1.5 < ρ < 2 m m f o r     ρ 2 m m

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