Abstract

The validity of double-pass wave-front measurements in the eye is reviewed analytically and computationally. A mathematical description of the scalar optical field in the exit pupil plane after an ocular double-pass process is presented. With the help of this description, the relationship between the phase information losses and the statistical properties of retinal scattering is demonstrated.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. L. Fante, “Imaging of an object behind a random phase screen using light of arbitrary coherence,” J. Opt. Soc. Am. A 2, 2318–2328 (1985).
    [CrossRef]
  2. C. J. Solomon, J. C. Dainty, “Imaging a coherently illuminated object through a random screen using a dilute aperture,” J. Opt. Soc. Am. A 9, 1385–1390 (1992).
    [CrossRef]
  3. P. Artal, S. Marcos, R. Navarro, D. R. Williams, “Odd aberrations and double pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195–201 (1995).
    [CrossRef]
  4. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  5. R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, San Diego, Calif., 1991).
  6. S. Marcos, S. A. Burns, J. Chang He, “Model for cone directionality reflectometric measurements based on scattering,” J. Opt. Soc. Am. A 15, 2012–2022 (1998).
    [CrossRef]
  7. P. Beckman, A. Spizzichinio, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
  8. F. G. Bass, I. M. Fuks, “Wave scattering from statistically rough surfaces,” in International Series in Natural Philosophy (Pergamon, New York, 1979), Vol. 93.
  9. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, Bristol, UK, 1991).
  10. L. Diaz Santana Haro, J. C. Dainty, “Single vs symmetric and asymmetric double-pass measurements of the wavefront aberration of the human eye,” in Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, Singapore, 2000), pp. 45–50.
  11. W. M. Hart, ed., Adler’s Physiology of the Eye. Clinical Application, Mosby Year Book, 9th ed. (Mosby, St. Louis, Mo., 1993).
  12. S. Marcos, S. A. Burns, “Cone spacing waveguide properties from cone directionality measurements,” J. Opt. Soc. Am. A 16, 995–1004 (1999).
    [CrossRef]
  13. L. Diaz Santana Haro, J. C. Dainty, “Single-pass measurements of the wave-front aberrations of the human eye by use of retinal lipofuscin autofluorescence,” Opt. Lett. 24, 61–63 (1999).
    [CrossRef]
  14. F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Visual Sci. 36, 718–729 (1995).
  15. G. J. van Blockland, “Ellipsometry of the human retina in vivo: preservation of polarization,” J. Opt. Soc. Am. A 2, 72–75 (1985).
    [CrossRef]
  16. B. F. Hochheimer, H. A. Kues, “Retinal polarization effects,” Appl. Opt. 21, 3811–3818 (1982).
    [CrossRef] [PubMed]
  17. G. J. van Blockland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
    [CrossRef]
  18. R. Navarro, M. A. Losada, “Phase transfer and point spread function of the human eye determined by a new asymmetric double-pass method,” J. Opt. Soc. Am. A 12, 2386–2392 (1995).
    [CrossRef]
  19. P. Artal, I. Iglesias, N. López-Gil, D. G. Green, “Double-pass measurements of the retinal-image quality with unequal entrance and exit pupil sizes and the reversibility of the eye’s optical system,” J. Opt. Soc. Am. A 12, 2358–2366 (1995).
    [CrossRef]

1999 (2)

1998 (1)

1995 (4)

F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Visual Sci. 36, 718–729 (1995).

R. Navarro, M. A. Losada, “Phase transfer and point spread function of the human eye determined by a new asymmetric double-pass method,” J. Opt. Soc. Am. A 12, 2386–2392 (1995).
[CrossRef]

P. Artal, S. Marcos, R. Navarro, D. R. Williams, “Odd aberrations and double pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195–201 (1995).
[CrossRef]

P. Artal, I. Iglesias, N. López-Gil, D. G. Green, “Double-pass measurements of the retinal-image quality with unequal entrance and exit pupil sizes and the reversibility of the eye’s optical system,” J. Opt. Soc. Am. A 12, 2358–2366 (1995).
[CrossRef]

1992 (1)

1986 (1)

G. J. van Blockland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef]

1985 (2)

1982 (1)

Arend, O.

F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Visual Sci. 36, 718–729 (1995).

Artal, P.

Bass, F. G.

F. G. Bass, I. M. Fuks, “Wave scattering from statistically rough surfaces,” in International Series in Natural Philosophy (Pergamon, New York, 1979), Vol. 93.

Beckman, P.

P. Beckman, A. Spizzichinio, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Burns, S. A.

Chang He, J.

Dainty, J. C.

L. Diaz Santana Haro, J. C. Dainty, “Single-pass measurements of the wave-front aberrations of the human eye by use of retinal lipofuscin autofluorescence,” Opt. Lett. 24, 61–63 (1999).
[CrossRef]

C. J. Solomon, J. C. Dainty, “Imaging a coherently illuminated object through a random screen using a dilute aperture,” J. Opt. Soc. Am. A 9, 1385–1390 (1992).
[CrossRef]

L. Diaz Santana Haro, J. C. Dainty, “Single vs symmetric and asymmetric double-pass measurements of the wavefront aberration of the human eye,” in Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, Singapore, 2000), pp. 45–50.

Delori, F. C.

F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Visual Sci. 36, 718–729 (1995).

Diaz Santana Haro, L.

L. Diaz Santana Haro, J. C. Dainty, “Single-pass measurements of the wave-front aberrations of the human eye by use of retinal lipofuscin autofluorescence,” Opt. Lett. 24, 61–63 (1999).
[CrossRef]

L. Diaz Santana Haro, J. C. Dainty, “Single vs symmetric and asymmetric double-pass measurements of the wavefront aberration of the human eye,” in Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, Singapore, 2000), pp. 45–50.

Dorey, C. K.

F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Visual Sci. 36, 718–729 (1995).

Fante, R. L.

Fuks, I. M.

F. G. Bass, I. M. Fuks, “Wave scattering from statistically rough surfaces,” in International Series in Natural Philosophy (Pergamon, New York, 1979), Vol. 93.

Goger, D. G.

F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Visual Sci. 36, 718–729 (1995).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Green, D. G.

Hochheimer, B. F.

Iglesias, I.

Kues, H. A.

López-Gil, N.

Losada, M. A.

R. Navarro, M. A. Losada, “Phase transfer and point spread function of the human eye determined by a new asymmetric double-pass method,” J. Opt. Soc. Am. A 12, 2386–2392 (1995).
[CrossRef]

Marcos, S.

Navarro, R.

P. Artal, S. Marcos, R. Navarro, D. R. Williams, “Odd aberrations and double pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195–201 (1995).
[CrossRef]

R. Navarro, M. A. Losada, “Phase transfer and point spread function of the human eye determined by a new asymmetric double-pass method,” J. Opt. Soc. Am. A 12, 2386–2392 (1995).
[CrossRef]

Ogilvy, J. A.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, Bristol, UK, 1991).

Solomon, C. J.

Spizzichinio, A.

P. Beckman, A. Spizzichinio, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Staurenghi, G.

F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Visual Sci. 36, 718–729 (1995).

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, San Diego, Calif., 1991).

van Blockland, G. J.

G. J. van Blockland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef]

G. J. van Blockland, “Ellipsometry of the human retina in vivo: preservation of polarization,” J. Opt. Soc. Am. A 2, 72–75 (1985).
[CrossRef]

van Norren, D.

G. J. van Blockland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef]

Weiter, J. J.

F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Visual Sci. 36, 718–729 (1995).

Williams, D. R.

Appl. Opt. (1)

Invest. Ophthalmol. Visual Sci. (1)

F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Visual Sci. 36, 718–729 (1995).

J. Opt. Soc. Am. A (8)

Opt. Lett. (1)

Vision Res. (1)

G. J. van Blockland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef]

Other (7)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, San Diego, Calif., 1991).

P. Beckman, A. Spizzichinio, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

F. G. Bass, I. M. Fuks, “Wave scattering from statistically rough surfaces,” in International Series in Natural Philosophy (Pergamon, New York, 1979), Vol. 93.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, Bristol, UK, 1991).

L. Diaz Santana Haro, J. C. Dainty, “Single vs symmetric and asymmetric double-pass measurements of the wavefront aberration of the human eye,” in Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, Singapore, 2000), pp. 45–50.

W. M. Hart, ed., Adler’s Physiology of the Eye. Clinical Application, Mosby Year Book, 9th ed. (Mosby, St. Louis, Mo., 1993).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Propagation geometry.

Fig. 2
Fig. 2

Instantaneous double-pass wave front after scattering. The dashed curve is the single-pass wave front, and the solid curve is the double-pass wave front.

Fig. 3
Fig. 3

Amplitude used to simulate a single cone in one dimension.

Fig. 4
Fig. 4

Simulated versus predicted values of ρ.

Fig. 5
Fig. 5

Average double-pass wave front after scattering. In each plot, the dashed curve is the single-pass wave front, the solid curve is the double-pass wave front, and the dotted curve is the phase of the scattered field. (a) Defocus. Cone spacing: 1 μm. (b) Coma. Cone spacing: 1 μm. (c) Defocus. Cone spacing: 2 μm. (d) Coma. Cone spacing: 2 μm. (e) Defocus. Cone spacing: 5 μm. (f) Coma. Cone spacing: 5 μm.

Fig. 6
Fig. 6

Interaction of the optical field with the retinal mosaic. Larger cones keep phase information of larger sections of the optical field.

Fig. 7
Fig. 7

Schematic representation of the imaging process of the PSF of a symmetric double-pass process for a system with a comatic aberration.

Equations (11)

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

Aj(xj, yj)=expik2sj (xj2+yj2)iλsjdξjdηjLj(ξj, ηj)×exp-i 2πλsj (xjξj+yjηj).
A1(x1, y1; t)=A1(x1, y1)R(x1, y1; t).
Ldp(ξ2, η2; t)=CFT[R(x1, y1; t)A1(x1, y1)]L2(ξ2, η2)=C{FT[R(x1, y1; t)]FT[A1(x1, y1)]}×L2(ξ2, η2)=C{R(ξ2, η2; t)L1(-ξ2, -η2)}×L2(ξ2, η2),
FT[FT[f(ξ1, η1)]]=f(-ξ2, -η2).
Ldp(ξ2, η2; t)=|Ldp(ξ2, η2; t)|×exp-i 2πλ Wdp(ξ2, η2; t),
[1000P1000P1000P].
ρ=π2(0.4p)2f 2λ2ln 10,
L1(ξ1)=exp-i 2πλ We/o(ξ1),
I¯dp(x2, y2; t)=D|FT[{R(-ξ2, -η2)L1(-ξ2, -η2)}×L2(ξ2, η2)]|2=D|[R(-x2, -y2) A1(-x2, -y2)]A2(x2, y2)|2,
R(-x2, -y2; t)R*(-x2, -y2; t)=δ(x2-x2, y2-y2),
I¯dp(x2, y2; t)=D|A1(-x2, -y2)|2|A2(x2, y2)|2=DI1(-x2, -y2)I2(x2, y2)=DI1(x2, y2)I2(x2, y2),

Metrics