Abstract

We developed a method to convert aberrometry data obtained in one wavelength to the corresponding data in another wavelength using an eye model. A single map of aberrometry data is used to construct a free-form one-surface eye model. A general algorithm for the surface construction is described and implemented for real aberrometry data. Our method can handle varying conjugate distances of the measurement plane of the aberrometer and can also manage the chief ray prism that may be present. The algorithm is validated with the aid of an artificial plastic eye. The wavefronts in different wavelengths are compared through the Zernike analysis not only for lower-order aberrations, but also for higher-order aberrations. The results show that the changes of the Zernike aberration coefficients due to wavelengths are non-uniform. The defocus term has the highest effect from wavelength changes, which is consistent with the previous literature. Our method is compared with two approximate semi-analytical algorithms. The wavelength adjustments from a multi-surface eye model are contrasted with our method. We prove analytically that the conventional method of wavelength adjustment is based on paraxial analysis. In addition, we provide a method of finding the chief ray using back-projection in some cases and discuss different meanings of prism.

© 2010 Optical Society of America

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References

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  1. D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinnemann, 2000).
  2. R. A. Applegate, L. N. Thibos, M. D. Twa, and E. J. Sarver, “Importance of fixation, pupil center, and reference axis in ocular wavefront sensing, videokeratography, and retinal image quality,” J. Cataract Refractive Surg. 35, 139–152 (2009).
    [CrossRef]
  3. ANSI, “American National Standards for Ophthalmics-Methods for reporting optical aberrations of eyes,” American National Standards Institute ANSI Z80.28 (2004).
  4. L. Lundstrom, P. Unsbo, and J. Gustafsson, “Off-axis wave front measurements for optical correction in eccentric viewing,” J. Biomed. Opt. 10, 034002 (2005).
    [CrossRef]
  5. J. Nam and J. Rubinstein, “Weighted Zernike expansion with applications to the optical aberration of the human eye,” J. Opt. Soc. Am. A 22, 1709–1716 (2005).
    [CrossRef]
  6. J. Rubinstein and G. Wolansky, “Reconstruction of optical surfaces from ray data,” Opt. Rev. 8, 281–283 (2001).
    [CrossRef]
  7. V. I. Arnold, Ordinary Differential Equations, 3rd ed. (Springer-Verlag, 1992).
  8. M. Rynders, B. Lidkea, W. Chisholm, and L. N. Thibos, “Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle psi in a population of young adult eyes,” J. Opt. Soc. Am. A 12, 2348–2357 (1995).
    [CrossRef]
  9. L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, and P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
    [CrossRef]
  10. X. Cheng, N. L. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a clinical Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 587–595 (2003).
    [CrossRef]
  11. L. N. Thibos and A. Bradley, “Modeling the refractive and neurosensor systems of the eye,” in Visual Instrumentation, P.Moroulis, ed. (McGraw Hill, 1999).
  12. L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–660 (2002).
  13. J. B. Keller and H. B. Keller, “Determination of reflected and transmitted fields by geometrical optics,” J. Am. Optom. Assoc. 40, 48–52 (1950).
    [CrossRef]
  14. J. A. Kneisly, “Local curvature of wavefront in an optical system,” J. Am. Optom. Assoc. 54, 229–235 (1964).
    [CrossRef]
  15. J. Rubinstein and G. Wolansky, “Eikonal functions: Old and new,” in Applied Mathematics Celebration, D.Givoli, ed. (Kluwer, 2004).
  16. T. O. Salmon, R. W. West, W. Gasser, and T. Kenmore, “Measurement of refractive errors in young myopes using the COAS Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 6–14 (2003).
    [CrossRef]
  17. J. Copeland and D. Neal, “Combined objective and subjective optometer,” presented at the 7th International Congress on Wavefront Sensing and Optimized Refractive Correction, January 26–29, 2006. http://voi.opt.uh.edu/VOI/WavefrontCongress/2006/index.html.
  18. L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
    [CrossRef]
  19. S. Ravikumar, L. N. Thibos, and A. Bradley, “Calculation of retinal image quality for polychromatic light,” J. Opt. Soc. Am. A 25, 2395–2407 (2008).
    [CrossRef]
  20. R. Navarro, J. Santamaria, and J. Bescos, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A 2, 1273–1281 (1985).
    [CrossRef]
  21. L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
    [CrossRef]

2009 (1)

R. A. Applegate, L. N. Thibos, M. D. Twa, and E. J. Sarver, “Importance of fixation, pupil center, and reference axis in ocular wavefront sensing, videokeratography, and retinal image quality,” J. Cataract Refractive Surg. 35, 139–152 (2009).
[CrossRef]

2008 (1)

2005 (2)

J. Nam and J. Rubinstein, “Weighted Zernike expansion with applications to the optical aberration of the human eye,” J. Opt. Soc. Am. A 22, 1709–1716 (2005).
[CrossRef]

L. Lundstrom, P. Unsbo, and J. Gustafsson, “Off-axis wave front measurements for optical correction in eccentric viewing,” J. Biomed. Opt. 10, 034002 (2005).
[CrossRef]

2004 (2)

ANSI, “American National Standards for Ophthalmics-Methods for reporting optical aberrations of eyes,” American National Standards Institute ANSI Z80.28 (2004).

J. Rubinstein and G. Wolansky, “Eikonal functions: Old and new,” in Applied Mathematics Celebration, D.Givoli, ed. (Kluwer, 2004).

2003 (3)

T. O. Salmon, R. W. West, W. Gasser, and T. Kenmore, “Measurement of refractive errors in young myopes using the COAS Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 6–14 (2003).
[CrossRef]

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
[CrossRef]

X. Cheng, N. L. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a clinical Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 587–595 (2003).
[CrossRef]

2002 (1)

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–660 (2002).

2001 (1)

J. Rubinstein and G. Wolansky, “Reconstruction of optical surfaces from ray data,” Opt. Rev. 8, 281–283 (2001).
[CrossRef]

2000 (1)

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinnemann, 2000).

1999 (1)

L. N. Thibos and A. Bradley, “Modeling the refractive and neurosensor systems of the eye,” in Visual Instrumentation, P.Moroulis, ed. (McGraw Hill, 1999).

1995 (1)

1992 (2)

1990 (1)

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, and P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef]

1985 (1)

1964 (1)

J. A. Kneisly, “Local curvature of wavefront in an optical system,” J. Am. Optom. Assoc. 54, 229–235 (1964).
[CrossRef]

1950 (1)

J. B. Keller and H. B. Keller, “Determination of reflected and transmitted fields by geometrical optics,” J. Am. Optom. Assoc. 40, 48–52 (1950).
[CrossRef]

Applegate, R. A.

R. A. Applegate, L. N. Thibos, M. D. Twa, and E. J. Sarver, “Importance of fixation, pupil center, and reference axis in ocular wavefront sensing, videokeratography, and retinal image quality,” J. Cataract Refractive Surg. 35, 139–152 (2009).
[CrossRef]

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–660 (2002).

Arnold, V. I.

V. I. Arnold, Ordinary Differential Equations, 3rd ed. (Springer-Verlag, 1992).

Atchison, D. A.

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinnemann, 2000).

Bescos, J.

Bradley, A.

S. Ravikumar, L. N. Thibos, and A. Bradley, “Calculation of retinal image quality for polychromatic light,” J. Opt. Soc. Am. A 25, 2395–2407 (2008).
[CrossRef]

X. Cheng, N. L. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a clinical Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 587–595 (2003).
[CrossRef]

L. N. Thibos and A. Bradley, “Modeling the refractive and neurosensor systems of the eye,” in Visual Instrumentation, P.Moroulis, ed. (McGraw Hill, 1999).

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
[CrossRef]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, and P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef]

Cheng, X.

X. Cheng, N. L. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a clinical Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 587–595 (2003).
[CrossRef]

Chisholm, W.

Copeland, J.

J. Copeland and D. Neal, “Combined objective and subjective optometer,” presented at the 7th International Congress on Wavefront Sensing and Optimized Refractive Correction, January 26–29, 2006. http://voi.opt.uh.edu/VOI/WavefrontCongress/2006/index.html.

Diaz-Santana, L.

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
[CrossRef]

Gasser, W.

T. O. Salmon, R. W. West, W. Gasser, and T. Kenmore, “Measurement of refractive errors in young myopes using the COAS Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 6–14 (2003).
[CrossRef]

Gustafsson, J.

L. Lundstrom, P. Unsbo, and J. Gustafsson, “Off-axis wave front measurements for optical correction in eccentric viewing,” J. Biomed. Opt. 10, 034002 (2005).
[CrossRef]

Himebaugh, N. L.

X. Cheng, N. L. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a clinical Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 587–595 (2003).
[CrossRef]

Howarth, P. A.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, and P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef]

Keller, H. B.

J. B. Keller and H. B. Keller, “Determination of reflected and transmitted fields by geometrical optics,” J. Am. Optom. Assoc. 40, 48–52 (1950).
[CrossRef]

Keller, J. B.

J. B. Keller and H. B. Keller, “Determination of reflected and transmitted fields by geometrical optics,” J. Am. Optom. Assoc. 40, 48–52 (1950).
[CrossRef]

Kenmore, T.

T. O. Salmon, R. W. West, W. Gasser, and T. Kenmore, “Measurement of refractive errors in young myopes using the COAS Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 6–14 (2003).
[CrossRef]

Kneisly, J. A.

J. A. Kneisly, “Local curvature of wavefront in an optical system,” J. Am. Optom. Assoc. 54, 229–235 (1964).
[CrossRef]

Kollbaum, P. S.

X. Cheng, N. L. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a clinical Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 587–595 (2003).
[CrossRef]

Lara-Saucedo, D.

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
[CrossRef]

Lidkea, B.

Llorente, L.

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
[CrossRef]

Lundstrom, L.

L. Lundstrom, P. Unsbo, and J. Gustafsson, “Off-axis wave front measurements for optical correction in eccentric viewing,” J. Biomed. Opt. 10, 034002 (2005).
[CrossRef]

Marcos, S.

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
[CrossRef]

Nam, J.

Navarro, R.

Neal, D.

J. Copeland and D. Neal, “Combined objective and subjective optometer,” presented at the 7th International Congress on Wavefront Sensing and Optimized Refractive Correction, January 26–29, 2006. http://voi.opt.uh.edu/VOI/WavefrontCongress/2006/index.html.

Ravikumar, S.

Rubinstein, J.

J. Nam and J. Rubinstein, “Weighted Zernike expansion with applications to the optical aberration of the human eye,” J. Opt. Soc. Am. A 22, 1709–1716 (2005).
[CrossRef]

J. Rubinstein and G. Wolansky, “Eikonal functions: Old and new,” in Applied Mathematics Celebration, D.Givoli, ed. (Kluwer, 2004).

J. Rubinstein and G. Wolansky, “Reconstruction of optical surfaces from ray data,” Opt. Rev. 8, 281–283 (2001).
[CrossRef]

Rynders, M.

Salmon, T. O.

T. O. Salmon, R. W. West, W. Gasser, and T. Kenmore, “Measurement of refractive errors in young myopes using the COAS Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 6–14 (2003).
[CrossRef]

Santamaria, J.

Sarver, E. J.

R. A. Applegate, L. N. Thibos, M. D. Twa, and E. J. Sarver, “Importance of fixation, pupil center, and reference axis in ocular wavefront sensing, videokeratography, and retinal image quality,” J. Cataract Refractive Surg. 35, 139–152 (2009).
[CrossRef]

Schwiegerling, J. T.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–660 (2002).

Smith, G.

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinnemann, 2000).

Still, D. L.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, and P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef]

Thibos, L. N.

R. A. Applegate, L. N. Thibos, M. D. Twa, and E. J. Sarver, “Importance of fixation, pupil center, and reference axis in ocular wavefront sensing, videokeratography, and retinal image quality,” J. Cataract Refractive Surg. 35, 139–152 (2009).
[CrossRef]

S. Ravikumar, L. N. Thibos, and A. Bradley, “Calculation of retinal image quality for polychromatic light,” J. Opt. Soc. Am. A 25, 2395–2407 (2008).
[CrossRef]

X. Cheng, N. L. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a clinical Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 587–595 (2003).
[CrossRef]

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–660 (2002).

L. N. Thibos and A. Bradley, “Modeling the refractive and neurosensor systems of the eye,” in Visual Instrumentation, P.Moroulis, ed. (McGraw Hill, 1999).

M. Rynders, B. Lidkea, W. Chisholm, and L. N. Thibos, “Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle psi in a population of young adult eyes,” J. Opt. Soc. Am. A 12, 2348–2357 (1995).
[CrossRef]

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
[CrossRef]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, and P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef]

Twa, M. D.

R. A. Applegate, L. N. Thibos, M. D. Twa, and E. J. Sarver, “Importance of fixation, pupil center, and reference axis in ocular wavefront sensing, videokeratography, and retinal image quality,” J. Cataract Refractive Surg. 35, 139–152 (2009).
[CrossRef]

Unsbo, P.

L. Lundstrom, P. Unsbo, and J. Gustafsson, “Off-axis wave front measurements for optical correction in eccentric viewing,” J. Biomed. Opt. 10, 034002 (2005).
[CrossRef]

Webb, R.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–660 (2002).

West, R. W.

T. O. Salmon, R. W. West, W. Gasser, and T. Kenmore, “Measurement of refractive errors in young myopes using the COAS Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 6–14 (2003).
[CrossRef]

Wolansky, G.

J. Rubinstein and G. Wolansky, “Eikonal functions: Old and new,” in Applied Mathematics Celebration, D.Givoli, ed. (Kluwer, 2004).

J. Rubinstein and G. Wolansky, “Reconstruction of optical surfaces from ray data,” Opt. Rev. 8, 281–283 (2001).
[CrossRef]

Ye, M.

Zhang, X.

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
[CrossRef]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, and P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef]

Appl. Opt. (1)

J. Am. Optom. Assoc. (2)

J. B. Keller and H. B. Keller, “Determination of reflected and transmitted fields by geometrical optics,” J. Am. Optom. Assoc. 40, 48–52 (1950).
[CrossRef]

J. A. Kneisly, “Local curvature of wavefront in an optical system,” J. Am. Optom. Assoc. 54, 229–235 (1964).
[CrossRef]

J. Biomed. Opt. (1)

L. Lundstrom, P. Unsbo, and J. Gustafsson, “Off-axis wave front measurements for optical correction in eccentric viewing,” J. Biomed. Opt. 10, 034002 (2005).
[CrossRef]

J. Cataract Refractive Surg. (1)

R. A. Applegate, L. N. Thibos, M. D. Twa, and E. J. Sarver, “Importance of fixation, pupil center, and reference axis in ocular wavefront sensing, videokeratography, and retinal image quality,” J. Cataract Refractive Surg. 35, 139–152 (2009).
[CrossRef]

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

J. Refract. Surg. (1)

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–660 (2002).

Opt. Rev. (1)

J. Rubinstein and G. Wolansky, “Reconstruction of optical surfaces from ray data,” Opt. Rev. 8, 281–283 (2001).
[CrossRef]

Optom. Vision Sci. (3)

X. Cheng, N. L. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a clinical Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 587–595 (2003).
[CrossRef]

T. O. Salmon, R. W. West, W. Gasser, and T. Kenmore, “Measurement of refractive errors in young myopes using the COAS Shack–Hartmann aberrometer,” Optom. Vision Sci. 80, 6–14 (2003).
[CrossRef]

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
[CrossRef]

Vision Res. (1)

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, and P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef]

Other (6)

L. N. Thibos and A. Bradley, “Modeling the refractive and neurosensor systems of the eye,” in Visual Instrumentation, P.Moroulis, ed. (McGraw Hill, 1999).

J. Copeland and D. Neal, “Combined objective and subjective optometer,” presented at the 7th International Congress on Wavefront Sensing and Optimized Refractive Correction, January 26–29, 2006. http://voi.opt.uh.edu/VOI/WavefrontCongress/2006/index.html.

J. Rubinstein and G. Wolansky, “Eikonal functions: Old and new,” in Applied Mathematics Celebration, D.Givoli, ed. (Kluwer, 2004).

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinnemann, 2000).

ANSI, “American National Standards for Ophthalmics-Methods for reporting optical aberrations of eyes,” American National Standards Institute ANSI Z80.28 (2004).

V. I. Arnold, Ordinary Differential Equations, 3rd ed. (Springer-Verlag, 1992).

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