Abstract

As a proof of concept we apply a technique called SLODAR as implemented in astronomy to the human eye. The technique uses single exposures of angularly separated “stars” on a Hartmann-Shack sensor to determine a profile of aberration strength localised in altitude in astronomy, or path length into the eye in our application. We report on the success of this process with both model and real human eyes. There are similarities and significant differences between the astronomy and vision applications.

© 2008 Optical Society of America

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References

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  1. J. C. He, J. Gwiazda, F. Thorn, and R. Held, "Wave-front aberration in the anterior corneal surface and the whole eye," J. Opt. Soc. Am. A 20, 1155-1163 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=josaa-20-7-1155.
    [CrossRef]
  2. P. Artal and A. Guirao, "Contributions of the cornea and the lens to the aberrations of the human eye," Opt. Lett. 23, 1713-1715 (1998), http://www.opticsinfobase.org/abstract.cfm?URI=ol-23-21-1713.
    [CrossRef]
  3. W. Wang, Z.-Q. Wang, Y. Wang, and T. Zuo, "Optical aberration of the cornea and the crystalline lens," Optik 117, 399-404 (2006).
    [CrossRef]
  4. P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberration by the internal optics in the human eye," J. Vis. 1, 1-8 (2001), http://www.journalofvision.org/1/1/1/Artal-2001-jov-1-1-1.pdf.
    [CrossRef]
  5. A. Dubinin, T. Cherezova, A. Belyakov, and A. Kudyashov, "Human retina imaging: widening of high resolution area," J. Mod. Opt. 55, 671-681 (2008), http://dx.doi.org/10.1080/09500340701467710.
    [CrossRef]
  6. G. Smith, D. Atchison, and B. Pierscionek, "Modeling the power of the aging human eye," J. Opt. Soc. Am. A 9, 2111-2117 (1992), http://www.opticsinfobase.org/abstract.cfm?URI=josaa-9-12-2111.
    [CrossRef] [PubMed]
  7. A. V. Goncharov and C. Dainty, "Wide-field schematic eye models with gradient-index lens," J. Opt. Soc. Am. A 24, 2157-2174 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=josaa-24-8-2157.
    [CrossRef]
  8. R. Navarro, F. Palos, and L. Gonzalez, "Adaptive model of the gradient index of the human lens. I. Formulation and model of aging ex vivo lenses," J. Opt. Soc. Am. A 24, 2175-2185 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=josaa-24-8-2175.
    [CrossRef]
  9. D. A. Atchison, "Anterior corneal and internal contributions to peripheral aberrations of human eyes," J. Opt. Soc. Am. A 21, 355-359 (2004),http://www.opticsinfobase.org/abstract.cfm?URI=josaa-21-3-355.
    [CrossRef]
  10. J. A. Sakamoto, H. H. Barrett, and A. V. Goncharov, "Inverse optical design of the human eye using likelihood methods and wavefront sensing," Opt. Express 16, 304-314 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-1-304.
    [CrossRef] [PubMed]
  11. R. Ragazzoni, E. Marchetti, and F. Rigaut, "Modal tomography for adaptive optics," Astron.Astrophys. 342, L53-L56 (1999).
  12. A. S. Goncharov, A. V. Larichev, N. G. Iroshnikov, I. Y. Yu, and S. A. Gorbunov, "Modal tomography of aberration of the human eye," Laser Phys. 16, 1689-1695 (2006).
    [CrossRef]
  13. R. A. Johnston, J. L. Mohr, P. L. Cottrell, and R. G. Lane, "A bread-board SCIDAR system at Mount John," presented at the Image and Vision Computing '04, Akaroa, New Zealand, 21-23 Nov. 2004.
  14. V. A. Kluckers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, and J. C. Dainty, "Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique," Astron. Astrophys. supplement series 130, 141-155 (1998).
    [CrossRef]
  15. R. W. Wilson, "SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor," Mon. Not. R. Astron. Soc. 337, 103-108 (2002), http://www.blackwell-synergy.com/doi/abs/10.1046/j.1365-8711.2002.05847.x.
    [CrossRef]
  16. M. Goodwin, C. Jenkins, and A. Lambert, "Improved detection of atmospheric turbulence with SLODAR," Opt. Express 15, 14844-14860 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14844.
    [CrossRef] [PubMed]
  17. A. Lambert, C. Jenkins, and M. Goodwin, "Turbulence profiling using extended objects for Slope Detection and Ranging (SLODAR)," Proc. SPIE 6316 (2006), http://spie.org/x648.xml?product_id=682428.
    [CrossRef]
  18. A. Mathur, D. A. Atchison, and D. H. Scott, "Ocular aberrations in the peripheral visual field," Opt. Lett. 33, 863-865 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=ol-33-8-863.
    [CrossRef] [PubMed]
  19. L. Diaz-Santana, C. Torti, I. Munro, P. Gasson, and C. Dainty, "Benefit of higher closed-loop bandwidths in ocular adaptive optics," Opt. Express 11, 2597-2605 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-20-2597.
  20. G. R. Ayers and J. C. Dainty, "Iterative blind deconvolution method and its applications," Opt. Lett. 13, 547-549 (1988), http://www.opticsinfobase.org/abstract.cfm?URI=ol-13-7-547.
    [CrossRef] [PubMed]
  21. D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford, 2000).
  22. T. Butterly, R. W. Wilson, and M. Sarazin, "Determination of the profile of atmospheric optical turbulence strength from SLODAR data," Mon. Not. R. Astron. Soc. 369, 835-845 (2006), http://www.blackwell-synergy.com/doi/abs/10.1111/j.1365-2966.2006.10337.x.
    [CrossRef]
  23. A. V. Goncharov, M. Nowakowski, M. T. Sheehan, and C. Dainty, "Reconstruction of the optical system of the human eye with reverse ray-tracing," Opt. Express 16, 1692-1703 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-3-1692.
    [CrossRef] [PubMed]
  24. J. Rouarch, J. Espinosa, J. J. Miret, D. Mas, J. Perez, and C. Illueca, "Propagation and phase reconstruction of ocular wavefronts with SAR techniques," J. Mod. Opt. 55, 717-725 (2008), http://dx.doi.org/10.1080/09500340701470011.
    [CrossRef]

2008

2007

2006

W. Wang, Z.-Q. Wang, Y. Wang, and T. Zuo, "Optical aberration of the cornea and the crystalline lens," Optik 117, 399-404 (2006).
[CrossRef]

A. S. Goncharov, A. V. Larichev, N. G. Iroshnikov, I. Y. Yu, and S. A. Gorbunov, "Modal tomography of aberration of the human eye," Laser Phys. 16, 1689-1695 (2006).
[CrossRef]

T. Butterly, R. W. Wilson, and M. Sarazin, "Determination of the profile of atmospheric optical turbulence strength from SLODAR data," Mon. Not. R. Astron. Soc. 369, 835-845 (2006), http://www.blackwell-synergy.com/doi/abs/10.1111/j.1365-2966.2006.10337.x.
[CrossRef]

2004

2003

2002

R. W. Wilson, "SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor," Mon. Not. R. Astron. Soc. 337, 103-108 (2002), http://www.blackwell-synergy.com/doi/abs/10.1046/j.1365-8711.2002.05847.x.
[CrossRef]

2001

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberration by the internal optics in the human eye," J. Vis. 1, 1-8 (2001), http://www.journalofvision.org/1/1/1/Artal-2001-jov-1-1-1.pdf.
[CrossRef]

1999

R. Ragazzoni, E. Marchetti, and F. Rigaut, "Modal tomography for adaptive optics," Astron.Astrophys. 342, L53-L56 (1999).

1998

V. A. Kluckers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, and J. C. Dainty, "Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique," Astron. Astrophys. supplement series 130, 141-155 (1998).
[CrossRef]

P. Artal and A. Guirao, "Contributions of the cornea and the lens to the aberrations of the human eye," Opt. Lett. 23, 1713-1715 (1998), http://www.opticsinfobase.org/abstract.cfm?URI=ol-23-21-1713.
[CrossRef]

1992

1988

Adcock, M. J.

V. A. Kluckers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, and J. C. Dainty, "Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique," Astron. Astrophys. supplement series 130, 141-155 (1998).
[CrossRef]

Artal, P.

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberration by the internal optics in the human eye," J. Vis. 1, 1-8 (2001), http://www.journalofvision.org/1/1/1/Artal-2001-jov-1-1-1.pdf.
[CrossRef]

P. Artal and A. Guirao, "Contributions of the cornea and the lens to the aberrations of the human eye," Opt. Lett. 23, 1713-1715 (1998), http://www.opticsinfobase.org/abstract.cfm?URI=ol-23-21-1713.
[CrossRef]

Atchison, D.

Atchison, D. A.

Ayers, G. R.

Barrett, H. H.

Belyakov, A.

A. Dubinin, T. Cherezova, A. Belyakov, and A. Kudyashov, "Human retina imaging: widening of high resolution area," J. Mod. Opt. 55, 671-681 (2008), http://dx.doi.org/10.1080/09500340701467710.
[CrossRef]

Berrio, E.

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberration by the internal optics in the human eye," J. Vis. 1, 1-8 (2001), http://www.journalofvision.org/1/1/1/Artal-2001-jov-1-1-1.pdf.
[CrossRef]

Butterly, T.

T. Butterly, R. W. Wilson, and M. Sarazin, "Determination of the profile of atmospheric optical turbulence strength from SLODAR data," Mon. Not. R. Astron. Soc. 369, 835-845 (2006), http://www.blackwell-synergy.com/doi/abs/10.1111/j.1365-2966.2006.10337.x.
[CrossRef]

Cherezova, T.

A. Dubinin, T. Cherezova, A. Belyakov, and A. Kudyashov, "Human retina imaging: widening of high resolution area," J. Mod. Opt. 55, 671-681 (2008), http://dx.doi.org/10.1080/09500340701467710.
[CrossRef]

Dainty, C.

Dainty, J. C.

V. A. Kluckers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, and J. C. Dainty, "Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique," Astron. Astrophys. supplement series 130, 141-155 (1998).
[CrossRef]

G. R. Ayers and J. C. Dainty, "Iterative blind deconvolution method and its applications," Opt. Lett. 13, 547-549 (1988), http://www.opticsinfobase.org/abstract.cfm?URI=ol-13-7-547.
[CrossRef] [PubMed]

Diaz-Santana, L.

Dubinin, A.

A. Dubinin, T. Cherezova, A. Belyakov, and A. Kudyashov, "Human retina imaging: widening of high resolution area," J. Mod. Opt. 55, 671-681 (2008), http://dx.doi.org/10.1080/09500340701467710.
[CrossRef]

Espinosa, J.

J. Rouarch, J. Espinosa, J. J. Miret, D. Mas, J. Perez, and C. Illueca, "Propagation and phase reconstruction of ocular wavefronts with SAR techniques," J. Mod. Opt. 55, 717-725 (2008), http://dx.doi.org/10.1080/09500340701470011.
[CrossRef]

Gasson, P.

Goncharov, A. S.

A. S. Goncharov, A. V. Larichev, N. G. Iroshnikov, I. Y. Yu, and S. A. Gorbunov, "Modal tomography of aberration of the human eye," Laser Phys. 16, 1689-1695 (2006).
[CrossRef]

Goncharov, A. V.

Gonzalez, L.

Goodwin, M.

Gorbunov, S. A.

A. S. Goncharov, A. V. Larichev, N. G. Iroshnikov, I. Y. Yu, and S. A. Gorbunov, "Modal tomography of aberration of the human eye," Laser Phys. 16, 1689-1695 (2006).
[CrossRef]

Guirao, A.

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberration by the internal optics in the human eye," J. Vis. 1, 1-8 (2001), http://www.journalofvision.org/1/1/1/Artal-2001-jov-1-1-1.pdf.
[CrossRef]

P. Artal and A. Guirao, "Contributions of the cornea and the lens to the aberrations of the human eye," Opt. Lett. 23, 1713-1715 (1998), http://www.opticsinfobase.org/abstract.cfm?URI=ol-23-21-1713.
[CrossRef]

Gwiazda, J.

He, J. C.

Held, R.

Illueca, C.

J. Rouarch, J. Espinosa, J. J. Miret, D. Mas, J. Perez, and C. Illueca, "Propagation and phase reconstruction of ocular wavefronts with SAR techniques," J. Mod. Opt. 55, 717-725 (2008), http://dx.doi.org/10.1080/09500340701470011.
[CrossRef]

Iroshnikov, N. G.

A. S. Goncharov, A. V. Larichev, N. G. Iroshnikov, I. Y. Yu, and S. A. Gorbunov, "Modal tomography of aberration of the human eye," Laser Phys. 16, 1689-1695 (2006).
[CrossRef]

Jenkins, C.

Kluckers, V. A.

V. A. Kluckers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, and J. C. Dainty, "Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique," Astron. Astrophys. supplement series 130, 141-155 (1998).
[CrossRef]

Kudyashov, A.

A. Dubinin, T. Cherezova, A. Belyakov, and A. Kudyashov, "Human retina imaging: widening of high resolution area," J. Mod. Opt. 55, 671-681 (2008), http://dx.doi.org/10.1080/09500340701467710.
[CrossRef]

Lambert, A.

Larichev, A. V.

A. S. Goncharov, A. V. Larichev, N. G. Iroshnikov, I. Y. Yu, and S. A. Gorbunov, "Modal tomography of aberration of the human eye," Laser Phys. 16, 1689-1695 (2006).
[CrossRef]

Marchetti, E.

R. Ragazzoni, E. Marchetti, and F. Rigaut, "Modal tomography for adaptive optics," Astron.Astrophys. 342, L53-L56 (1999).

Mas, D.

J. Rouarch, J. Espinosa, J. J. Miret, D. Mas, J. Perez, and C. Illueca, "Propagation and phase reconstruction of ocular wavefronts with SAR techniques," J. Mod. Opt. 55, 717-725 (2008), http://dx.doi.org/10.1080/09500340701470011.
[CrossRef]

Mathur, A.

Miret, J. J.

J. Rouarch, J. Espinosa, J. J. Miret, D. Mas, J. Perez, and C. Illueca, "Propagation and phase reconstruction of ocular wavefronts with SAR techniques," J. Mod. Opt. 55, 717-725 (2008), http://dx.doi.org/10.1080/09500340701470011.
[CrossRef]

Munro, I.

L. Diaz-Santana, C. Torti, I. Munro, P. Gasson, and C. Dainty, "Benefit of higher closed-loop bandwidths in ocular adaptive optics," Opt. Express 11, 2597-2605 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-20-2597.

V. A. Kluckers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, and J. C. Dainty, "Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique," Astron. Astrophys. supplement series 130, 141-155 (1998).
[CrossRef]

Navarro, R.

Nicholls, T. W.

V. A. Kluckers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, and J. C. Dainty, "Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique," Astron. Astrophys. supplement series 130, 141-155 (1998).
[CrossRef]

Nowakowski, M.

Palos, F.

Perez, J.

J. Rouarch, J. Espinosa, J. J. Miret, D. Mas, J. Perez, and C. Illueca, "Propagation and phase reconstruction of ocular wavefronts with SAR techniques," J. Mod. Opt. 55, 717-725 (2008), http://dx.doi.org/10.1080/09500340701470011.
[CrossRef]

Pierscionek, B.

Ragazzoni, R.

R. Ragazzoni, E. Marchetti, and F. Rigaut, "Modal tomography for adaptive optics," Astron.Astrophys. 342, L53-L56 (1999).

Rigaut, F.

R. Ragazzoni, E. Marchetti, and F. Rigaut, "Modal tomography for adaptive optics," Astron.Astrophys. 342, L53-L56 (1999).

Rouarch, J.

J. Rouarch, J. Espinosa, J. J. Miret, D. Mas, J. Perez, and C. Illueca, "Propagation and phase reconstruction of ocular wavefronts with SAR techniques," J. Mod. Opt. 55, 717-725 (2008), http://dx.doi.org/10.1080/09500340701470011.
[CrossRef]

Sakamoto, J. A.

Sarazin, M.

T. Butterly, R. W. Wilson, and M. Sarazin, "Determination of the profile of atmospheric optical turbulence strength from SLODAR data," Mon. Not. R. Astron. Soc. 369, 835-845 (2006), http://www.blackwell-synergy.com/doi/abs/10.1111/j.1365-2966.2006.10337.x.
[CrossRef]

Scott, D. H.

Sheehan, M. T.

Smith, G.

Thorn, F.

Torti, C.

Wang, W.

W. Wang, Z.-Q. Wang, Y. Wang, and T. Zuo, "Optical aberration of the cornea and the crystalline lens," Optik 117, 399-404 (2006).
[CrossRef]

Wang, Z.-Q.

W. Wang, Z.-Q. Wang, Y. Wang, and T. Zuo, "Optical aberration of the cornea and the crystalline lens," Optik 117, 399-404 (2006).
[CrossRef]

Williams, D. R.

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberration by the internal optics in the human eye," J. Vis. 1, 1-8 (2001), http://www.journalofvision.org/1/1/1/Artal-2001-jov-1-1-1.pdf.
[CrossRef]

Wilson, R. W.

T. Butterly, R. W. Wilson, and M. Sarazin, "Determination of the profile of atmospheric optical turbulence strength from SLODAR data," Mon. Not. R. Astron. Soc. 369, 835-845 (2006), http://www.blackwell-synergy.com/doi/abs/10.1111/j.1365-2966.2006.10337.x.
[CrossRef]

R. W. Wilson, "SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor," Mon. Not. R. Astron. Soc. 337, 103-108 (2002), http://www.blackwell-synergy.com/doi/abs/10.1046/j.1365-8711.2002.05847.x.
[CrossRef]

Wooder, N. J.

V. A. Kluckers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, and J. C. Dainty, "Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique," Astron. Astrophys. supplement series 130, 141-155 (1998).
[CrossRef]

Yu, I. Y.

A. S. Goncharov, A. V. Larichev, N. G. Iroshnikov, I. Y. Yu, and S. A. Gorbunov, "Modal tomography of aberration of the human eye," Laser Phys. 16, 1689-1695 (2006).
[CrossRef]

Astron. Astrophys. supplement series

V. A. Kluckers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, and J. C. Dainty, "Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique," Astron. Astrophys. supplement series 130, 141-155 (1998).
[CrossRef]

Astron.Astrophys.

R. Ragazzoni, E. Marchetti, and F. Rigaut, "Modal tomography for adaptive optics," Astron.Astrophys. 342, L53-L56 (1999).

J. Mod. Opt.

A. Dubinin, T. Cherezova, A. Belyakov, and A. Kudyashov, "Human retina imaging: widening of high resolution area," J. Mod. Opt. 55, 671-681 (2008), http://dx.doi.org/10.1080/09500340701467710.
[CrossRef]

J. Rouarch, J. Espinosa, J. J. Miret, D. Mas, J. Perez, and C. Illueca, "Propagation and phase reconstruction of ocular wavefronts with SAR techniques," J. Mod. Opt. 55, 717-725 (2008), http://dx.doi.org/10.1080/09500340701470011.
[CrossRef]

J. Opt. Soc. Am. A

J. Vis.

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberration by the internal optics in the human eye," J. Vis. 1, 1-8 (2001), http://www.journalofvision.org/1/1/1/Artal-2001-jov-1-1-1.pdf.
[CrossRef]

Laser Phys.

A. S. Goncharov, A. V. Larichev, N. G. Iroshnikov, I. Y. Yu, and S. A. Gorbunov, "Modal tomography of aberration of the human eye," Laser Phys. 16, 1689-1695 (2006).
[CrossRef]

Mon. Not. R. Astron. Soc.

R. W. Wilson, "SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor," Mon. Not. R. Astron. Soc. 337, 103-108 (2002), http://www.blackwell-synergy.com/doi/abs/10.1046/j.1365-8711.2002.05847.x.
[CrossRef]

T. Butterly, R. W. Wilson, and M. Sarazin, "Determination of the profile of atmospheric optical turbulence strength from SLODAR data," Mon. Not. R. Astron. Soc. 369, 835-845 (2006), http://www.blackwell-synergy.com/doi/abs/10.1111/j.1365-2966.2006.10337.x.
[CrossRef]

Opt. Express

Opt. Lett.

Optik

W. Wang, Z.-Q. Wang, Y. Wang, and T. Zuo, "Optical aberration of the cornea and the crystalline lens," Optik 117, 399-404 (2006).
[CrossRef]

Other

R. A. Johnston, J. L. Mohr, P. L. Cottrell, and R. G. Lane, "A bread-board SCIDAR system at Mount John," presented at the Image and Vision Computing '04, Akaroa, New Zealand, 21-23 Nov. 2004.

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

A. Lambert, C. Jenkins, and M. Goodwin, "Turbulence profiling using extended objects for Slope Detection and Ranging (SLODAR)," Proc. SPIE 6316 (2006), http://spie.org/x648.xml?product_id=682428.
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Illustration of SLODAR in the eye showing light traveling from the two scattering sources created on the retina with a “star” separation (Ω)) of 7°. Rays are traced in Zemax to the centres of the lenslets on the Shack-Hartmann sensor using an eye model. The lenslet array is conjugate with the pupil. The lens and cornea are shown in the diagram as well as the relay system and Hartmann-Shack sensor. Also shown in red are the surfaces of triangulation at different depths in the eye, some of which fall within the refractive elements and provide information about the aberration closest to that depth.

Fig. 2.
Fig. 2.

A schematic of the illumination and recording systems for examination of the eye. The relocation of the centre of the diffractive function on the SLM facilitates the angular change required for the illumination system. Polarisation and phase effects are manipulated using the quarter wave plates (QWP) and linear polarisers (LP). The Lens System yields angular magnification of the illumination of the eye. The Hartmann-Shack sensor (HSWS), which provides data for the SLODAR algorithm, may be translated to conjugate to different depths into the eye.

Fig. 3.
Fig. 3.

SLODAR profile for the model eye using stars of separation 5.8 degrees and 14×14 lenslet Shack-Hartmann sensors. The aberration strength is plotted at each depth layer resolved by SLODAR. The horizontal depth axis is scaled by the layer spacing, and is a function of the star separation and intervening refractive index changes in the elements of the eye, and the vertical strength axis is normalised but would be scaled to C n 2 using an estimate of ro , in astronomy. Such scaling does not make sense in our application – the relative structure is the desired observation. This would not normally resolve many layers, but there is evidence for the refractive effect of the curved front face of the plano-convex lens around layer -5 of the red curve. The contributions between layers -5 and -6 moves to layers -4 to -5 when the sensor is reconjugated by 5mm (blue curve). Notice there is a dominant but erroneous peak in the SLODAR profile depth of zero. Evident is that a contribution that was masked by the erroneous peak at zero depth, appears unmasked now at layer +1 of the blue curve. This illustrates the versatility of generalised SLODAR where fine depth information can still be achieved for small angular separations between the stars. The error bars indicate the standard deviation in the deconvolution result over ten observations.

Fig. 4.
Fig. 4.

The COAS-HD data used to assess the suitability of a SLODAR algorithm, corresponds to the above ray-traced figure with the vertical axis describing linear separation of the point source scatterers or “stars” for the two angles at the sensor of 0 and -20.55 degrees. The rays originate at the star on the retina and arrive at each of the lenslets in the Hartmann-Shack sensor. Shown are the estimated posterior and anterior surfaces of the refractive elements. Observe that there are two intersection surfaces (shown by red dotted patterns) at the cornea and almost six within the structure of the crystalline lens. In actuality, there will be three times as many surfaces as shown for the 44×44 lenslet measurements as we have limited the number of rays to 15 for clarity. Expected is a region of non-aberration in the aqueous humor of two layers. Notice that the “layers” are in fact curved surfaces fitting the intersection of rays because of the variable optical path length along each ray’s path to a lenslet. Also observe that the silhouette of the pupil defines a cone either side of the pupil over which SLODAR may collect information, and this arrives with only limited overlap at the cornea, the implications of which are discussed in the second to last paragraph of section 4. Overlaid is a schematic of the positioning of the stars relative to line of sight for the COAS-HD data.

Fig. 5.
Fig. 5.

The profile of aberration strength with depth into the eye determined by SLODAR from the COAS-HD data. Whether the star is (a) 20.55 degrees to the left of the common on-axis one, or (b) 20.55 degrees to the right defines the direction of depth in the profile. In (a) the corneal contribution is shown around the layers -15 to -9 with the lens occupying layers -3 to 18, and in (b) the corneal contribution is shown around layers 12 to 18 with the lens contribution spread over 3 to -17. There is reasonable symmetry between the profiles, but one would expect significant differences also at these examine different volumes into the eye. We have also annotated the locations of the cornea and lens using the ray-tracing to predict the location and number of layers to which these would be approximately confined.

Fig. 6.
Fig. 6.

The profile of aberration strength with depth into the eye determined by SLODAR from the COAS-HD data. As the angular separation of the stars doubles so does the spread of the refractive strength into more layers. (a) 3.84 degree separation shows cornea at -2, and posterior lens from layers 0 to 3, (b) 7.12 degree separation with cornea around -5 and lens from layer -1 to 3, and (c) ~14 degree separation with cornea around -10, and lens spread to the right across layers -3 to 12. With more separation the information is spread across more depth range and hence is harder to extract.

Fig. 7.
Fig. 7.

The profile of aberration strength with depth into the eye determined by SLODAR from the COAS-HD data. The COAS-HD results for stars that are widely separated illustrate a corneal contribution to the right and a distributed lens contribution left and centre. (a) ~27 degree separation with cornea within layers 17 to 26 and lens occupying layers -13 to 11; and (b) by ~41 degrees with cornea to the right of layer 27 and larger spread of information about the lens. The corneal contribution is reduced because it is collected from very few lenslet combinations. Note that the layer spacing is a very small depth at these star separations, and while we supposedly are conjugated to the pupil of the eye, and we would therefore expect the contribution of the crystalline lens to be to the left of the zero layer, there is significant detectable misalignment in the instrument setup, and consequently a spread to the right also.

Fig. 8.
Fig. 8.

The SLODAR profiles in earlier figures are extracted from the deconvolution results, which in turn are from cross-correlation of the centroids in the lenslets from each star. (a) From the deconvolution of the widely separated stars shown in Fig. 6 it is evident there is information not confined to the inter-stellar axis. This results from rough rotational symmetry of the refractive elements. The outer ring is the extent of the correlation exacerbated by the limited number of baselines and hence poorer signal to noise at the largest lenslet separation. The SLODAR profile is a cut through the centre of this image at the angle set by the interstellar axis, which would not incorporate this extra information. (b) The result in (a) is generated from the cross-correlation information, which exhibits features such as the “plateau” made prominent by the larger refractive power of the cornea. The diameter of this feature is a function of the number of baselines examining the cornea. The same phenomenon is seen in the cross-correlations of the 14×14 lenslets in the generalised SLODAR experiment; (c) the correlation shows the ring caused by the corneal contribution when conjugate to the pupil of the model eye, has relocated as a result of a shift behind the pupil by 5mm (d). Finer depth resolution is possible from the generalised SLODAR approach, but this demonstrates the artifact as a real feature. Interestingly enough such dominant features do not arise in astronomy as statistical variation effectively washes them out even if they are clearly defined.

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