Abstract

Purpose: Ocular wavefront tomography (OWT) is the process of using wavefront aberration maps obtained along multiple lines-of-sight (LoS) to determine the shape and position of the major refracting elements of an eye. One goal of OWT is to create a customized schematic model eye that is anatomically similar and functionally equivalent to the individual eye over a large field of view. Methods: Wavefront aberration maps along multiple LoS were used as design goals for configuring a generic, multisurface model eye with aberrations that match the measurements. The model was constrained by gross anatomical dimensions and optimized to mimic the measured eye. The method was evaluated with two test cases: (1) a physical model eye with a doublet lens measured with a clinical wavefront aberrometer along six LoS between -31 deg and +29 deg eccentricities, and (2) a mathematical model of the myopic eye for which wavefront aberrations were computed by ray tracing. Results: In case 1, the OWT algorithm successfully predicted the structure of the doublet model eye from the experimental on- and off-axis aberration measurements. In case 2, the algorithm started with a symmetric five surface model eye and optimized it to generate the on- and off-axis aberrations of a GRIN myopia model eye. The adjusted model closely mimicked the physical parameters and optical behavior of the expected myopia model eye over a large field of view. The maximum discrepancy between aberrations of the OWT optimized model and measurements was 0.05 microns RMS for test case 1 and 0.2 microns RMS for test case 2. Conclusion: Our implementation of OWT is a valid, feasible, and robust method for constructing an optical model that is anatomically and functionally similar to the eye over a wide field of view.

© 2008 Optical Society of America

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References

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  1. E. Acosta, D. Vazquez, L. Garner, and G. Smith, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. I. The spherical fish lens," J. Opt. Soc. Am. 22, 424-433 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. W. Zou and J. P. Rolland, "Iterative zonal wave-front estimation algorithm for optical testing with general-shaped pupils," J. Opt. Soc. Am. 22, 938-951 (2005).
    [CrossRef]
  16. D. A. Atchison, D. H. Scott, and W. N. Charman, "Measuring ocular aberrations in the peripheral visual field using Hartmann-Shack aberrometry," J. Opt. Soc. Am. 24, 2963-2973 (2007).
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    [CrossRef]
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    [CrossRef] [PubMed]

2008 (3)

2007 (3)

D. A. Atchison, D. H. Scott, and W. N. Charman, "Measuring ocular aberrations in the peripheral visual field using Hartmann-Shack aberrometry," J. Opt. Soc. Am. 24, 2963-2973 (2007).
[CrossRef]

A. S. Goncharov and A. V. Larichev, "Specialized modal tomography of human eye aberrations," Proc. SPIE 6734, 67341V (2007).

A. V. Goncharov and C. Dainty, "Wide-field schematic eye models with gradient-index lens," J. Opt. Soc. Am. 24, 2157-2174 (2007).
[CrossRef]

2006 (3)

D. A. Atchison, "Optical models for human myopic eyes," Vision Res. 46, 2236-2250 (2006).
[CrossRef] [PubMed]

R. Navarro, L. Gonzalez, and J. L. Hernandez-Matamoros, "On the prediction of optical aberrations by personalized eye models," Optom Vis Sci 83, 371-381 (2006).
[CrossRef] [PubMed]

D. Vazquez, E. Acosta, G. Smith, and L. Garner, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens," J. Opt. Soc. Am. 23, 2551-2565 (2006).
[CrossRef]

2005 (3)

E. Acosta, D. Vazquez, L. Garner, and G. Smith, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. I. The spherical fish lens," J. Opt. Soc. Am. 22, 424-433 (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] [PubMed]

W. Zou and J. P. Rolland, "Iterative zonal wave-front estimation algorithm for optical testing with general-shaped pupils," J. Opt. Soc. Am. 22, 938-951 (2005).
[CrossRef]

2002 (2)

D. A. Atchison and D. H. Scott, "Monochromatic aberrations of human eyes in the horizontal visual field," J. Opt. Soc. Am. 19, 2180-2184 (2002).
[CrossRef]

G. Smith, D. A. Atchison, C. Avudainayagam, and K. Avudainayagam, "Designing lenses to correct peripheral refractive errors of the eye," J. Opt. Soc. Am. 19, 10-18 (2002).
[CrossRef]

1999 (1)

I. Escudero-Sanz and R. Navarro, "Off-axis aberrations of a wide-angle schematic eye model," J. Opt. Soc. Am. 16, 1881-1891 (1999).
[CrossRef]

1997 (2)

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, "Spherical aberration of the reduced schematic eye with elliptical refracting surface," Optom Vision Sci. 74, 548-556 (1997).
[CrossRef]

Y. Z. Wang and L. N. Thibos, "Oblique (off-axis) astigmatism of the reduced schematic eye with elliptical refracting surface," Optom Vis Sci 74, 557-562 (1997).
[CrossRef] [PubMed]

1991 (1)

1969 (1)

H. Sumita, "Orthonormal expansion of the aberration difference function and its application to image evaluation," Jpn. J. Appl. Phys. 8, 1027-1036 (1969).
[CrossRef]

Acosta, E.

D. Vazquez, E. Acosta, G. Smith, and L. Garner, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens," J. Opt. Soc. Am. 23, 2551-2565 (2006).
[CrossRef]

E. Acosta, D. Vazquez, L. Garner, and G. Smith, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. I. The spherical fish lens," J. Opt. Soc. Am. 22, 424-433 (2005).
[CrossRef]

Atchison, D. A.

A. Lambert, B. J. Birt, D. A. Atchison, and H. Guo, "Applying SLODAR to measure aberrations in the eye," Opt. Express 16, 7309-7322 (2008).
[CrossRef] [PubMed]

D. A. Atchison, D. H. Scott, and W. N. Charman, "Measuring ocular aberrations in the peripheral visual field using Hartmann-Shack aberrometry," J. Opt. Soc. Am. 24, 2963-2973 (2007).
[CrossRef]

D. A. Atchison, "Optical models for human myopic eyes," Vision Res. 46, 2236-2250 (2006).
[CrossRef] [PubMed]

D. A. Atchison and D. H. Scott, "Monochromatic aberrations of human eyes in the horizontal visual field," J. Opt. Soc. Am. 19, 2180-2184 (2002).
[CrossRef]

G. Smith, D. A. Atchison, C. Avudainayagam, and K. Avudainayagam, "Designing lenses to correct peripheral refractive errors of the eye," J. Opt. Soc. Am. 19, 10-18 (2002).
[CrossRef]

Avudainayagam, C.

G. Smith, D. A. Atchison, C. Avudainayagam, and K. Avudainayagam, "Designing lenses to correct peripheral refractive errors of the eye," J. Opt. Soc. Am. 19, 10-18 (2002).
[CrossRef]

Avudainayagam, K.

G. Smith, D. A. Atchison, C. Avudainayagam, and K. Avudainayagam, "Designing lenses to correct peripheral refractive errors of the eye," J. Opt. Soc. Am. 19, 10-18 (2002).
[CrossRef]

Barrett, H. H.

Birt, B. J.

Bradley, A.

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, "Spherical aberration of the reduced schematic eye with elliptical refracting surface," Optom Vision Sci. 74, 548-556 (1997).
[CrossRef]

Charman, W. N.

D. A. Atchison, D. H. Scott, and W. N. Charman, "Measuring ocular aberrations in the peripheral visual field using Hartmann-Shack aberrometry," J. Opt. Soc. Am. 24, 2963-2973 (2007).
[CrossRef]

Dainty, C.

Escudero-Sanz, I.

I. Escudero-Sanz and R. Navarro, "Off-axis aberrations of a wide-angle schematic eye model," J. Opt. Soc. Am. 16, 1881-1891 (1999).
[CrossRef]

Garner, L.

D. Vazquez, E. Acosta, G. Smith, and L. Garner, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens," J. Opt. Soc. Am. 23, 2551-2565 (2006).
[CrossRef]

E. Acosta, D. Vazquez, L. Garner, and G. Smith, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. I. The spherical fish lens," J. Opt. Soc. Am. 22, 424-433 (2005).
[CrossRef]

Goncharov, A. S.

A. S. Goncharov and A. V. Larichev, "Specialized modal tomography of human eye aberrations," Proc. SPIE 6734, 67341V (2007).

Goncharov, A. V.

Gonzalez, L.

R. Navarro, L. Gonzalez, and J. L. Hernandez-Matamoros, "On the prediction of optical aberrations by personalized eye models," Optom Vis Sci 83, 371-381 (2006).
[CrossRef] [PubMed]

Guo, H.

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] [PubMed]

Hernandez-Matamoros, J. L.

R. Navarro, L. Gonzalez, and J. L. Hernandez-Matamoros, "On the prediction of optical aberrations by personalized eye models," Optom Vis Sci 83, 371-381 (2006).
[CrossRef] [PubMed]

Lambert, A.

Larichev, A. V.

A. S. Goncharov and A. V. Larichev, "Specialized modal tomography of human eye aberrations," Proc. SPIE 6734, 67341V (2007).

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] [PubMed]

Navarro, R.

R. Navarro, L. Gonzalez, and J. L. Hernandez-Matamoros, "On the prediction of optical aberrations by personalized eye models," Optom Vis Sci 83, 371-381 (2006).
[CrossRef] [PubMed]

I. Escudero-Sanz and R. Navarro, "Off-axis aberrations of a wide-angle schematic eye model," J. Opt. Soc. Am. 16, 1881-1891 (1999).
[CrossRef]

Nowakowski, M.

Roddier, C.

Roddier, F.

Rolland, J. P.

W. Zou and J. P. Rolland, "Iterative zonal wave-front estimation algorithm for optical testing with general-shaped pupils," J. Opt. Soc. Am. 22, 938-951 (2005).
[CrossRef]

Sakamoto, J. A.

Scott, D. H.

D. A. Atchison, D. H. Scott, and W. N. Charman, "Measuring ocular aberrations in the peripheral visual field using Hartmann-Shack aberrometry," J. Opt. Soc. Am. 24, 2963-2973 (2007).
[CrossRef]

D. A. Atchison and D. H. Scott, "Monochromatic aberrations of human eyes in the horizontal visual field," J. Opt. Soc. Am. 19, 2180-2184 (2002).
[CrossRef]

Sheehan, M. T.

Smith, G.

D. Vazquez, E. Acosta, G. Smith, and L. Garner, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens," J. Opt. Soc. Am. 23, 2551-2565 (2006).
[CrossRef]

E. Acosta, D. Vazquez, L. Garner, and G. Smith, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. I. The spherical fish lens," J. Opt. Soc. Am. 22, 424-433 (2005).
[CrossRef]

G. Smith, D. A. Atchison, C. Avudainayagam, and K. Avudainayagam, "Designing lenses to correct peripheral refractive errors of the eye," J. Opt. Soc. Am. 19, 10-18 (2002).
[CrossRef]

Sumita, H.

H. Sumita, "Orthonormal expansion of the aberration difference function and its application to image evaluation," Jpn. J. Appl. Phys. 8, 1027-1036 (1969).
[CrossRef]

Thibos, L. N.

Y. Z. Wang and L. N. Thibos, "Oblique (off-axis) astigmatism of the reduced schematic eye with elliptical refracting surface," Optom Vis Sci 74, 557-562 (1997).
[CrossRef] [PubMed]

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, "Spherical aberration of the reduced schematic eye with elliptical refracting surface," Optom Vision Sci. 74, 548-556 (1997).
[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] [PubMed]

Vazquez, D.

D. Vazquez, E. Acosta, G. Smith, and L. Garner, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens," J. Opt. Soc. Am. 23, 2551-2565 (2006).
[CrossRef]

E. Acosta, D. Vazquez, L. Garner, and G. Smith, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. I. The spherical fish lens," J. Opt. Soc. Am. 22, 424-433 (2005).
[CrossRef]

Wang, Y. Z.

Y. Z. Wang and L. N. Thibos, "Oblique (off-axis) astigmatism of the reduced schematic eye with elliptical refracting surface," Optom Vis Sci 74, 557-562 (1997).
[CrossRef] [PubMed]

Ye, M.

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, "Spherical aberration of the reduced schematic eye with elliptical refracting surface," Optom Vision Sci. 74, 548-556 (1997).
[CrossRef]

Zhang, X.

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, "Spherical aberration of the reduced schematic eye with elliptical refracting surface," Optom Vision Sci. 74, 548-556 (1997).
[CrossRef]

Zou, W.

W. Zou and J. P. Rolland, "Iterative zonal wave-front estimation algorithm for optical testing with general-shaped pupils," J. Opt. Soc. Am. 22, 938-951 (2005).
[CrossRef]

Appl. Opt. (1)

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] [PubMed]

J. Opt. Soc. Am. (8)

W. Zou and J. P. Rolland, "Iterative zonal wave-front estimation algorithm for optical testing with general-shaped pupils," J. Opt. Soc. Am. 22, 938-951 (2005).
[CrossRef]

D. A. Atchison, D. H. Scott, and W. N. Charman, "Measuring ocular aberrations in the peripheral visual field using Hartmann-Shack aberrometry," J. Opt. Soc. Am. 24, 2963-2973 (2007).
[CrossRef]

E. Acosta, D. Vazquez, L. Garner, and G. Smith, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. I. The spherical fish lens," J. Opt. Soc. Am. 22, 424-433 (2005).
[CrossRef]

D. Vazquez, E. Acosta, G. Smith, and L. Garner, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens," J. Opt. Soc. Am. 23, 2551-2565 (2006).
[CrossRef]

A. V. Goncharov and C. Dainty, "Wide-field schematic eye models with gradient-index lens," J. Opt. Soc. Am. 24, 2157-2174 (2007).
[CrossRef]

D. A. Atchison and D. H. Scott, "Monochromatic aberrations of human eyes in the horizontal visual field," J. Opt. Soc. Am. 19, 2180-2184 (2002).
[CrossRef]

G. Smith, D. A. Atchison, C. Avudainayagam, and K. Avudainayagam, "Designing lenses to correct peripheral refractive errors of the eye," J. Opt. Soc. Am. 19, 10-18 (2002).
[CrossRef]

I. Escudero-Sanz and R. Navarro, "Off-axis aberrations of a wide-angle schematic eye model," J. Opt. Soc. Am. 16, 1881-1891 (1999).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Sumita, "Orthonormal expansion of the aberration difference function and its application to image evaluation," Jpn. J. Appl. Phys. 8, 1027-1036 (1969).
[CrossRef]

Opt. Express (3)

Optom Vis Sci (2)

Y. Z. Wang and L. N. Thibos, "Oblique (off-axis) astigmatism of the reduced schematic eye with elliptical refracting surface," Optom Vis Sci 74, 557-562 (1997).
[CrossRef] [PubMed]

R. Navarro, L. Gonzalez, and J. L. Hernandez-Matamoros, "On the prediction of optical aberrations by personalized eye models," Optom Vis Sci 83, 371-381 (2006).
[CrossRef] [PubMed]

Optom Vision Sci. (1)

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, "Spherical aberration of the reduced schematic eye with elliptical refracting surface," Optom Vision Sci. 74, 548-556 (1997).
[CrossRef]

Proc. SPIE (1)

A. S. Goncharov and A. V. Larichev, "Specialized modal tomography of human eye aberrations," Proc. SPIE 6734, 67341V (2007).

Vision Res. (1)

D. A. Atchison, "Optical models for human myopic eyes," Vision Res. 46, 2236-2250 (2006).
[CrossRef] [PubMed]

Other (3)

Zemax User Guide (Zemax Development Corporation, 2006).

R. Shannon, The Art and Science of Optical Design (Cambridge Univ Press, 1997).

M. Kidger, Intermediate Optical Design (SPIE, 2004).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Geometry of the eye’s entrance pupil for off-axis viewing along a secondary line-ofsight. (a) A cross-section of the cornea and pupil in the plane formed by the primary and secondary lines-of-sight. Wavefront aberrations measured with respect to the x’,y’ plane of the secondary entrance pupil are transferred mathematically to the x,y plane of the primary entrance pupil. (b) Measurement axis of the aberrometer is aligned with a secondary line-ofsight (bold arrow) by rotating the instrument by the angle ε in a plane inclined by angle θ with the horizontal. (c) When projected into the x,y plane of the primary entrance pupil, the x’,y’ plane of the secondary entrance pupil is tilted by angle θ. The secondary entrance pupil is elliptical with minor and major axes aligned with the x’ and y’ axes, respectively. The aspect ratio of the elliptical pupil (i.e. minor axis/major axis) equals cos ε.

Fig. 2.
Fig. 2.

Schematic diagram of the tested doublet. The goal of ocular wavefront tomography is to recover the 7 parameters that characterize the lens (3 radii of curvature, 2 thicknesses, 2 indices of refraction) based on wavefront maps measured along 6 lines of sight.

Fig. 3.
Fig. 3.

Outcome of OWT for the doublet test case. (a) Error in Zernike coefficients for the starting model (open symbols) and the final model produced by OWT (filled symbols). (b) Wavefront difference between starting model and theoretical model (upper row) and difference maps between the final model and the theoretical model (bottom row).

Fig. 4.
Fig. 4.

Structural changes in the WAS model to meet MYO model’s optical performance from - 30 degree to +30 degree horizontally.

Fig. 5.
Fig. 5.

Outcome of OWT for the schematic eyes test case. (a) RMS difference between the original WAS model and MYO model (open symbols) is compared with RMS difference between the modified WAS model and MYO model (filled symbols). (b) Wavefront difference between the original WAS model and MYO model (upper row) and difference maps between the modified WAS model and MYO model (bottom row).

Fig. 6.
Fig. 6.

Specification of the 2-surface model eye. R1 and R2: radius of the 1st and 2nd surface; K1 and K2: conic constant of the 1st and 2nd surface; T1 and T2: the distances of the 1st and 2nd surfaces relative to the iris aperture. N: refractive index.

Fig. 7.
Fig. 7.

Comparison of Off-axis wavefront aberrations between the two models (6mm entrance pupil). The wavelength used to calculate the off-axis wavefront aberrations for WAS model is 589 nm.

Tables (3)

Tables Icon

Table 1. Results of using OWT to retrieve the structural parameters of a doublet lens from simulated measurements of wavefront aberrations calculated by ray tracing along different LoS.

Tables Icon

Table 2. Comparison table of physical parameters

Tables Icon

Table 3. Comparison table of physical parameters among WAS model, OWT model, and MYO model.

Equations (2)

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( x ' y ' ) = ( cos θ sin θ sin θ cos θ ) ( cos ε 0 0 1 ) ( cos θ sin θ sin θ cos θ ) ( x y )
tan η = m l , tan ε = m 2 + l 2 n

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