Abstract

We present evidence for the wavelength dependence of the directionality of light reflected from cone receptor cells (optical Stiles–Crawford effect): Blue light is more directional than red. According to the waveguide-scattering model of Marcos et al. [J. Opt. Soc. Am. A 15, 2012 (1998)], directionality is the sum of a waveguide component and a scattering component. The latter is proportional to 1 over wavelength squared, and it is related to the row-to-row spacing of the cone lattice. Our results allow a firm confirmation of Marcos et al.’s theory. For a 1.9-deg foveal area, group mean (n=18) cone spacing was 3.42 µm, in good agreement with anatomical data. Group mean waveguide directionality was 0.077 mm-2.

© 2003 Optical Society of America

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References

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  1. W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
    [CrossRef]
  2. J. Krauskopf, “Some experiments with a photoelectric ophthalmoscope,” in Performance of the Eye at Low Luminances, M. A. Bouman, J. J. Vos, eds. (Excerpta Medica, Amsterdam, 1966), pp. 171–181.
  3. G. J. van Blokland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
    [CrossRef] [PubMed]
  4. G. J. van Blokland, “Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 495–500 (1986).
    [CrossRef] [PubMed]
  5. J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
    [CrossRef] [PubMed]
  6. S. A. Burns, S. Wu, F. C. Delori, A. E. Elsner, “Direct measurement of human-cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1995).
    [CrossRef]
  7. P. J. Delint, T. T. J. M. Berendschot, D. van Norren, “Local photoreceptor alignment measured with a scanning laser ophthalmoscope,” Vision Res. 37, 243–248 (1997).
    [CrossRef] [PubMed]
  8. J. C. He, S. Marcos, S. A. Burns, “Comparison of cone directionality determined by psychophysical and reflectometric techniques,” J. Opt. Soc. Am. A 16, 2363–2369 (1999).
    [CrossRef]
  9. S. Marcos, S. A. Burns, J. C. He, “Model for cone directionality reflectometric measurements based on scattering,” J. Opt. Soc. Am. A 15, 2012–2022 (1998).
    [CrossRef]
  10. S. Marcos, S. A. Burns, “Cone spacing and waveguide properties from cone directionality measurements,” J. Opt. Soc. Am. A 16, 995–1004 (1999).
    [CrossRef]
  11. J. van de Kraats, T. T. J. M. Berendschot, D. van Norren, “The pathways of light measured in fundus reflectometry,” Vision Res. 36, 2229–2247 (1996).
    [CrossRef] [PubMed]
  12. A. M. Laties, P. A. Liebman, C. E. M. Campbell, “Photoreceptor orientation in the primate eye,” Nature 218, 172–173 (1968).
    [CrossRef] [PubMed]
  13. G. Toraldo di Francia, “Retina cones as dielectric antennas,” J. Opt. Soc. Am. 39, 324 (1949).
    [CrossRef]
  14. J. M. Enoch, “Nature of the transmission of energy in the retinal receptors,” J. Opt. Soc. Am. 51, 1122–1127 (1961).
    [CrossRef] [PubMed]
  15. A. W. Snyder, C. Pask, “The Stiles–Crawford effect—explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
    [CrossRef] [PubMed]
  16. P. L. Walraven, M. A. Bouman, “Relation between directional sensitivity and spectral response curves in human cone vision,” J. Opt. Soc. Am. 50, 780–784 (1960).
    [CrossRef] [PubMed]
  17. J. M. Gorrand, F. C. Delori, “A model for assessment of cone directionality,” J. Mod. Opt. 44, 473–491 (1997).
    [CrossRef]
  18. T. T. J. M. Berendschot, J. van de Kraats, D. van Norren, “Wavelength dependence of the Stiles–Crawford effect explained by perception of backscattered light from the choroid,” J. Opt. Soc. Am. A 18, 1445–1451 (2001).
    [CrossRef]
  19. N. P. A. Zagers, J. van de Kraats, T. T. J. M. Berendschot, D. van Norren, “Simultaneous measurement of foveal spectral reflectance and cone-photoreceptor directionality,” Appl. Opt. 41, 4686–4696 (2002).
    [CrossRef] [PubMed]
  20. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982).
  21. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, UK, 1989).
  22. C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. Power 292, 497–523 (1990).
    [CrossRef]
  23. J. J. Vos, F. L. van Os, “The effect of lens density on the Stiles–Crawford effect,” Vision Res. 15, 749–751 (1975).
    [CrossRef] [PubMed]
  24. R. A. Weale, “On the problem of retinal directional sensitivity,” Proc. R. Soc. London Ser. B 212, 113–130 (1981).
    [CrossRef]
  25. D. van Norren, J. J. Vos, “Spectral transmission of the human ocular media,” Vision Res. 14, 1237–1244 (1974).
    [CrossRef]
  26. R. A. Applegate, V. Lakshminarayanan, “Parametric representations of the Stiles–Crawford functions: normal variation of peak location and directionality,” J. Opt. Soc. Am. A 10, 1611–1623 (1993).
    [CrossRef] [PubMed]
  27. D. R. Williams, “Topography of the foveal cone mosaic in the living human eye,” Vision Res. 28, 433–454 (1988).
    [CrossRef] [PubMed]
  28. P. Artal, R. Navarro, “High-resolution imaging of the living human fovea: measurement of the intercenter cone distance by speckle interferometry,” Opt. Lett. 14, 1098–1100 (1989).
    [CrossRef] [PubMed]
  29. S. Marcos, R. Navarro, P. Artal, “Coherent imaging of the cone mosaic in the living human eye,” J. Opt. Soc. Am. A 13, 897–905 (1996).
    [CrossRef]
  30. D. T. Miller, D. R. Williams, G. M. Morris, J. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
    [CrossRef] [PubMed]
  31. J. Liang, D. R. Williams, D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
    [CrossRef]

2002 (1)

2001 (1)

1999 (2)

1998 (1)

1997 (3)

J. Liang, D. R. Williams, D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
[CrossRef]

P. J. Delint, T. T. J. M. Berendschot, D. van Norren, “Local photoreceptor alignment measured with a scanning laser ophthalmoscope,” Vision Res. 37, 243–248 (1997).
[CrossRef] [PubMed]

J. M. Gorrand, F. C. Delori, “A model for assessment of cone directionality,” J. Mod. Opt. 44, 473–491 (1997).
[CrossRef]

1996 (3)

S. Marcos, R. Navarro, P. Artal, “Coherent imaging of the cone mosaic in the living human eye,” J. Opt. Soc. Am. A 13, 897–905 (1996).
[CrossRef]

D. T. Miller, D. R. Williams, G. M. Morris, J. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

J. van de Kraats, T. T. J. M. Berendschot, D. van Norren, “The pathways of light measured in fundus reflectometry,” Vision Res. 36, 2229–2247 (1996).
[CrossRef] [PubMed]

1995 (2)

J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[CrossRef] [PubMed]

S. A. Burns, S. Wu, F. C. Delori, A. E. Elsner, “Direct measurement of human-cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1995).
[CrossRef]

1993 (1)

1990 (1)

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. Power 292, 497–523 (1990).
[CrossRef]

1989 (1)

1988 (1)

D. R. Williams, “Topography of the foveal cone mosaic in the living human eye,” Vision Res. 28, 433–454 (1988).
[CrossRef] [PubMed]

1986 (2)

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

G. J. van Blokland, “Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 495–500 (1986).
[CrossRef] [PubMed]

1981 (1)

R. A. Weale, “On the problem of retinal directional sensitivity,” Proc. R. Soc. London Ser. B 212, 113–130 (1981).
[CrossRef]

1975 (1)

J. J. Vos, F. L. van Os, “The effect of lens density on the Stiles–Crawford effect,” Vision Res. 15, 749–751 (1975).
[CrossRef] [PubMed]

1974 (1)

D. van Norren, J. J. Vos, “Spectral transmission of the human ocular media,” Vision Res. 14, 1237–1244 (1974).
[CrossRef]

1973 (1)

A. W. Snyder, C. Pask, “The Stiles–Crawford effect—explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
[CrossRef] [PubMed]

1968 (1)

A. M. Laties, P. A. Liebman, C. E. M. Campbell, “Photoreceptor orientation in the primate eye,” Nature 218, 172–173 (1968).
[CrossRef] [PubMed]

1961 (1)

1960 (1)

1949 (1)

1933 (1)

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Applegate, R. A.

Artal, P.

Berendschot, T. T. J. M.

Bouman, M. A.

Burns, S. A.

Campbell, C. E. M.

A. M. Laties, P. A. Liebman, C. E. M. Campbell, “Photoreceptor orientation in the primate eye,” Nature 218, 172–173 (1968).
[CrossRef] [PubMed]

Crawford, B. H.

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Curcio, C. A.

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. Power 292, 497–523 (1990).
[CrossRef]

Delint, P. J.

P. J. Delint, T. T. J. M. Berendschot, D. van Norren, “Local photoreceptor alignment measured with a scanning laser ophthalmoscope,” Vision Res. 37, 243–248 (1997).
[CrossRef] [PubMed]

Delori, F. C.

J. M. Gorrand, F. C. Delori, “A model for assessment of cone directionality,” J. Mod. Opt. 44, 473–491 (1997).
[CrossRef]

J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[CrossRef] [PubMed]

S. A. Burns, S. Wu, F. C. Delori, A. E. Elsner, “Direct measurement of human-cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1995).
[CrossRef]

Elsner, A. E.

Enoch, J. M.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, UK, 1989).

Gorrand, J. M.

J. M. Gorrand, F. C. Delori, “A model for assessment of cone directionality,” J. Mod. Opt. 44, 473–491 (1997).
[CrossRef]

J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[CrossRef] [PubMed]

He, J. C.

Hendrickson, A. E.

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. Power 292, 497–523 (1990).
[CrossRef]

Kalina, R. E.

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. Power 292, 497–523 (1990).
[CrossRef]

Krauskopf, J.

J. Krauskopf, “Some experiments with a photoelectric ophthalmoscope,” in Performance of the Eye at Low Luminances, M. A. Bouman, J. J. Vos, eds. (Excerpta Medica, Amsterdam, 1966), pp. 171–181.

Lakshminarayanan, V.

Laties, A. M.

A. M. Laties, P. A. Liebman, C. E. M. Campbell, “Photoreceptor orientation in the primate eye,” Nature 218, 172–173 (1968).
[CrossRef] [PubMed]

Liang, J.

J. Liang, D. R. Williams, D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
[CrossRef]

D. T. Miller, D. R. Williams, G. M. Morris, J. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

Liebman, P. A.

A. M. Laties, P. A. Liebman, C. E. M. Campbell, “Photoreceptor orientation in the primate eye,” Nature 218, 172–173 (1968).
[CrossRef] [PubMed]

Marcos, S.

Miller, D. T.

J. Liang, D. R. Williams, D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
[CrossRef]

D. T. Miller, D. R. Williams, G. M. Morris, J. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

Morris, G. M.

D. T. Miller, D. R. Williams, G. M. Morris, J. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

Navarro, R.

Pask, C.

A. W. Snyder, C. Pask, “The Stiles–Crawford effect—explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, UK, 1989).

Sloan, K. R.

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. Power 292, 497–523 (1990).
[CrossRef]

Snyder, A. W.

A. W. Snyder, C. Pask, “The Stiles–Crawford effect—explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
[CrossRef] [PubMed]

Stiles, W. S.

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, UK, 1989).

Toraldo di Francia, G.

van Blokland, G. J.

G. J. van Blokland, “Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 495–500 (1986).
[CrossRef] [PubMed]

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

van de Kraats, J.

van Norren, D.

N. P. A. Zagers, J. van de Kraats, T. T. J. M. Berendschot, D. van Norren, “Simultaneous measurement of foveal spectral reflectance and cone-photoreceptor directionality,” Appl. Opt. 41, 4686–4696 (2002).
[CrossRef] [PubMed]

T. T. J. M. Berendschot, J. van de Kraats, D. van Norren, “Wavelength dependence of the Stiles–Crawford effect explained by perception of backscattered light from the choroid,” J. Opt. Soc. Am. A 18, 1445–1451 (2001).
[CrossRef]

P. J. Delint, T. T. J. M. Berendschot, D. van Norren, “Local photoreceptor alignment measured with a scanning laser ophthalmoscope,” Vision Res. 37, 243–248 (1997).
[CrossRef] [PubMed]

J. van de Kraats, T. T. J. M. Berendschot, D. van Norren, “The pathways of light measured in fundus reflectometry,” Vision Res. 36, 2229–2247 (1996).
[CrossRef] [PubMed]

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

D. van Norren, J. J. Vos, “Spectral transmission of the human ocular media,” Vision Res. 14, 1237–1244 (1974).
[CrossRef]

van Os, F. L.

J. J. Vos, F. L. van Os, “The effect of lens density on the Stiles–Crawford effect,” Vision Res. 15, 749–751 (1975).
[CrossRef] [PubMed]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, UK, 1989).

Vos, J. J.

J. J. Vos, F. L. van Os, “The effect of lens density on the Stiles–Crawford effect,” Vision Res. 15, 749–751 (1975).
[CrossRef] [PubMed]

D. van Norren, J. J. Vos, “Spectral transmission of the human ocular media,” Vision Res. 14, 1237–1244 (1974).
[CrossRef]

Walraven, P. L.

Weale, R. A.

R. A. Weale, “On the problem of retinal directional sensitivity,” Proc. R. Soc. London Ser. B 212, 113–130 (1981).
[CrossRef]

Williams, D. R.

J. Liang, D. R. Williams, D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
[CrossRef]

D. T. Miller, D. R. Williams, G. M. Morris, J. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

D. R. Williams, “Topography of the foveal cone mosaic in the living human eye,” Vision Res. 28, 433–454 (1988).
[CrossRef] [PubMed]

Wu, S.

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982).

Zagers, N. P. A.

Appl. Opt. (1)

J. Comp. Neurol. Power (1)

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. Power 292, 497–523 (1990).
[CrossRef]

J. Mod. Opt. (1)

J. M. Gorrand, F. C. Delori, “A model for assessment of cone directionality,” J. Mod. Opt. 44, 473–491 (1997).
[CrossRef]

J. Opt. Soc. Am. (3)

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

Nature (1)

A. M. Laties, P. A. Liebman, C. E. M. Campbell, “Photoreceptor orientation in the primate eye,” Nature 218, 172–173 (1968).
[CrossRef] [PubMed]

Opt. Lett. (1)

Proc. R. Soc. London Ser. B (2)

R. A. Weale, “On the problem of retinal directional sensitivity,” Proc. R. Soc. London Ser. B 212, 113–130 (1981).
[CrossRef]

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Vision Res. (10)

J. J. Vos, F. L. van Os, “The effect of lens density on the Stiles–Crawford effect,” Vision Res. 15, 749–751 (1975).
[CrossRef] [PubMed]

D. van Norren, J. J. Vos, “Spectral transmission of the human ocular media,” Vision Res. 14, 1237–1244 (1974).
[CrossRef]

D. R. Williams, “Topography of the foveal cone mosaic in the living human eye,” Vision Res. 28, 433–454 (1988).
[CrossRef] [PubMed]

D. T. Miller, D. R. Williams, G. M. Morris, J. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

P. J. Delint, T. T. J. M. Berendschot, D. van Norren, “Local photoreceptor alignment measured with a scanning laser ophthalmoscope,” Vision Res. 37, 243–248 (1997).
[CrossRef] [PubMed]

A. W. Snyder, C. Pask, “The Stiles–Crawford effect—explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
[CrossRef] [PubMed]

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

G. J. van Blokland, “Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 495–500 (1986).
[CrossRef] [PubMed]

J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[CrossRef] [PubMed]

J. van de Kraats, T. T. J. M. Berendschot, D. van Norren, “The pathways of light measured in fundus reflectometry,” Vision Res. 36, 2229–2247 (1996).
[CrossRef] [PubMed]

Other (3)

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982).

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, UK, 1989).

J. Krauskopf, “Some experiments with a photoelectric ophthalmoscope,” in Performance of the Eye at Low Luminances, M. A. Bouman, J. J. Vos, eds. (Excerpta Medica, Amsterdam, 1966), pp. 171–181.

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Figures (3)

Fig. 1
Fig. 1

Optical Stiles–Crawford effect directionality ρ versus wavelength for all 21 subjects. Data shown are the mean of five measurements within a series. Error bars (not discernible in some cases) indicate the standard deviation. The solid curves represent model fits to the data. Most subjects show the expected decrease with 1 over wavelength squared. The wavelength range varies between subjects owing to selection criteria defined in Section 2.

Fig. 2
Fig. 2

Mean optical SCE directionality ρ versus wavelength for all subjects except 9, 17, and 21. The solid curve is a model fit to the data. The decrease with 1 over wavelength squared as predicted by theory is clearly present. Error bars represent the between-subjects standard error.

Fig. 3
Fig. 3

Mean waveguide directionality ρwg and row-to-row cone spacing s. Squares depict the mean of five series; triangles, the mean of four series. Error bars represent between-series standard deviation; solid horizontal lines show the group mean. Crosses indicate all data was discarded.

Equations (3)

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ρ(λ)=ρwg(λ)+ρscatt(λ),
R(x)=B+A×10-ρ(x-xC)2,
ρ(λ)=ρwg+αλ-2

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