Abstract

The visual impact of light obliquely incident on the retina is diminished due to the Stiles–Crawford effect of the first kind. It is normally analyzed by scanning a small Maxwellian source across the eye pupil while making subjective visibility comparisons to a static reference field that enters the eye near the pupil center. Here, we propose an alternative characterization method with two coherent Maxwellian point sources located at opposing sides of the pupil. This produces interference fringes at the retina with an underlying phase gradient. Altering the power ratio of the two point sources makes tuning of the wavefront inclination at the retina feasible. Thus, the Stiles–Crawford effect of the first kind can be examined without scanning the incident light across the pupil. In this paper, a spatial light modulator with holographic phase maps has been used to generate two Maxwellian point sources at the pupil that project a given phase variation onto the retina. We found that the effective obliqueness of light at the retina is determined by the weighted center-of-mass of the field amplitude at the pupil. Alternative techniques to generate the two secondary point sources may improve the accuracy of the method.

© 2013 Optical Society of America

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References

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  1. W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. B 112, 428–450 (1933).
    [CrossRef]
  2. A. W. Snyder and C. Pask, “The Stiles–Crawford effect—explanation and consequences,” Vis. Res. 13, 1115–1237 (1973).
    [CrossRef]
  3. W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new color effect,” Proc. R. Soc. B 123, 90–118 (1937).
    [CrossRef]
  4. B. Lochocki, D. Rativa, and B. Vohnsen, “Spatial and spectral characterisation of the first and second Stiles–Crawford effects using tuneable liquid-crystal filters,” J. Mod. Opt. 58, 1817–1825 (2011).
    [CrossRef]
  5. R. A. Applegate and V. Lakshminarayanan, “Parametric representation of Stiles–Crawford functions: normal variation of peak location and directionality,” J. Opt. Soc. Am. A 10, 1611–1623 (1993).
    [CrossRef]
  6. B. Vohnsen, I. Iglesias, and P. Artal, “Guided light and diffraction model of human-eye photoreceptors,” J. Opt. Soc. Am. A 22, 2318–2328 (2005).
    [CrossRef]
  7. F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 576–593 (1965).
  8. D. G. Green, “Visual resolution when light enters the eye through different parts of the pupil,” J. Physiol. 190, 583–593 (1967).
  9. D. I. A. MacLeod, D. R. Williams, and W. Makous, “A visual nonlinearity fed by single cones,” Vis. Res. 32, 347–363(1992).
    [CrossRef]
  10. C. Pask and A. Stacey, “Optical properties of retinal photoreceptors and the Campbell effect,” Vis. Res. 38, 953–961 (1998).
    [CrossRef]
  11. M. J. McMahon and D. I. A. MacLeod, “Retinal contrast losses and visual resolution with obliquely incident light,” J. Opt. Soc. Am. A 18, 2692–2703 (2001).
    [CrossRef]
  12. B. Vohnsen and D. Rativa, “Absence of an integrated Stiles–Crawford function for coherent light,” J. Vis. 1, 1–10 (2011).
    [CrossRef]
  13. J. Enoch, “Optical properties of retinal receptors,” J. Opt. Soc. Am. 53, 71–85 (1963).
    [CrossRef]
  14. B. Vohnsen, “Photoreceptor waveguides and effective retinal image quality,” J. Opt. Soc. Am. A 24, 597–607 (2007).
    [CrossRef]
  15. H. H. Emsley, Visual Optics, 5th ed. (Hatton, 1955), Vol. 1.

2011 (2)

B. Lochocki, D. Rativa, and B. Vohnsen, “Spatial and spectral characterisation of the first and second Stiles–Crawford effects using tuneable liquid-crystal filters,” J. Mod. Opt. 58, 1817–1825 (2011).
[CrossRef]

B. Vohnsen and D. Rativa, “Absence of an integrated Stiles–Crawford function for coherent light,” J. Vis. 1, 1–10 (2011).
[CrossRef]

2007 (1)

2005 (1)

2001 (1)

1998 (1)

C. Pask and A. Stacey, “Optical properties of retinal photoreceptors and the Campbell effect,” Vis. Res. 38, 953–961 (1998).
[CrossRef]

1993 (1)

1992 (1)

D. I. A. MacLeod, D. R. Williams, and W. Makous, “A visual nonlinearity fed by single cones,” Vis. Res. 32, 347–363(1992).
[CrossRef]

1973 (1)

A. W. Snyder and C. Pask, “The Stiles–Crawford effect—explanation and consequences,” Vis. Res. 13, 1115–1237 (1973).
[CrossRef]

1967 (1)

D. G. Green, “Visual resolution when light enters the eye through different parts of the pupil,” J. Physiol. 190, 583–593 (1967).

1965 (1)

F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 576–593 (1965).

1963 (1)

1937 (1)

W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new color effect,” Proc. R. Soc. B 123, 90–118 (1937).
[CrossRef]

1933 (1)

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

Applegate, R. A.

Artal, P.

Campbell, F. W.

F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 576–593 (1965).

Crawford, B. H.

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

Emsley, H. H.

H. H. Emsley, Visual Optics, 5th ed. (Hatton, 1955), Vol. 1.

Enoch, J.

Green, D. G.

D. G. Green, “Visual resolution when light enters the eye through different parts of the pupil,” J. Physiol. 190, 583–593 (1967).

F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 576–593 (1965).

Iglesias, I.

Lakshminarayanan, V.

Lochocki, B.

B. Lochocki, D. Rativa, and B. Vohnsen, “Spatial and spectral characterisation of the first and second Stiles–Crawford effects using tuneable liquid-crystal filters,” J. Mod. Opt. 58, 1817–1825 (2011).
[CrossRef]

MacLeod, D. I. A.

M. J. McMahon and D. I. A. MacLeod, “Retinal contrast losses and visual resolution with obliquely incident light,” J. Opt. Soc. Am. A 18, 2692–2703 (2001).
[CrossRef]

D. I. A. MacLeod, D. R. Williams, and W. Makous, “A visual nonlinearity fed by single cones,” Vis. Res. 32, 347–363(1992).
[CrossRef]

Makous, W.

D. I. A. MacLeod, D. R. Williams, and W. Makous, “A visual nonlinearity fed by single cones,” Vis. Res. 32, 347–363(1992).
[CrossRef]

McMahon, M. J.

Pask, C.

C. Pask and A. Stacey, “Optical properties of retinal photoreceptors and the Campbell effect,” Vis. Res. 38, 953–961 (1998).
[CrossRef]

A. W. Snyder and C. Pask, “The Stiles–Crawford effect—explanation and consequences,” Vis. Res. 13, 1115–1237 (1973).
[CrossRef]

Rativa, D.

B. Lochocki, D. Rativa, and B. Vohnsen, “Spatial and spectral characterisation of the first and second Stiles–Crawford effects using tuneable liquid-crystal filters,” J. Mod. Opt. 58, 1817–1825 (2011).
[CrossRef]

B. Vohnsen and D. Rativa, “Absence of an integrated Stiles–Crawford function for coherent light,” J. Vis. 1, 1–10 (2011).
[CrossRef]

Snyder, A. W.

A. W. Snyder and C. Pask, “The Stiles–Crawford effect—explanation and consequences,” Vis. Res. 13, 1115–1237 (1973).
[CrossRef]

Stacey, A.

C. Pask and A. Stacey, “Optical properties of retinal photoreceptors and the Campbell effect,” Vis. Res. 38, 953–961 (1998).
[CrossRef]

Stiles, W. S.

W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new color effect,” Proc. R. Soc. B 123, 90–118 (1937).
[CrossRef]

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

Vohnsen, B.

B. Lochocki, D. Rativa, and B. Vohnsen, “Spatial and spectral characterisation of the first and second Stiles–Crawford effects using tuneable liquid-crystal filters,” J. Mod. Opt. 58, 1817–1825 (2011).
[CrossRef]

B. Vohnsen and D. Rativa, “Absence of an integrated Stiles–Crawford function for coherent light,” J. Vis. 1, 1–10 (2011).
[CrossRef]

B. Vohnsen, “Photoreceptor waveguides and effective retinal image quality,” J. Opt. Soc. Am. A 24, 597–607 (2007).
[CrossRef]

B. Vohnsen, I. Iglesias, and P. Artal, “Guided light and diffraction model of human-eye photoreceptors,” J. Opt. Soc. Am. A 22, 2318–2328 (2005).
[CrossRef]

Williams, D. R.

D. I. A. MacLeod, D. R. Williams, and W. Makous, “A visual nonlinearity fed by single cones,” Vis. Res. 32, 347–363(1992).
[CrossRef]

J. Mod. Opt. (1)

B. Lochocki, D. Rativa, and B. Vohnsen, “Spatial and spectral characterisation of the first and second Stiles–Crawford effects using tuneable liquid-crystal filters,” J. Mod. Opt. 58, 1817–1825 (2011).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Physiol. (2)

F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 576–593 (1965).

D. G. Green, “Visual resolution when light enters the eye through different parts of the pupil,” J. Physiol. 190, 583–593 (1967).

J. Vis. (1)

B. Vohnsen and D. Rativa, “Absence of an integrated Stiles–Crawford function for coherent light,” J. Vis. 1, 1–10 (2011).
[CrossRef]

Proc. R. Soc. B (2)

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

W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new color effect,” Proc. R. Soc. B 123, 90–118 (1937).
[CrossRef]

Vis. Res. (3)

A. W. Snyder and C. Pask, “The Stiles–Crawford effect—explanation and consequences,” Vis. Res. 13, 1115–1237 (1973).
[CrossRef]

D. I. A. MacLeod, D. R. Williams, and W. Makous, “A visual nonlinearity fed by single cones,” Vis. Res. 32, 347–363(1992).
[CrossRef]

C. Pask and A. Stacey, “Optical properties of retinal photoreceptors and the Campbell effect,” Vis. Res. 38, 953–961 (1998).
[CrossRef]

Other (1)

H. H. Emsley, Visual Optics, 5th ed. (Hatton, 1955), Vol. 1.

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Figures (7)

Fig. 1.
Fig. 1.

Two symmetrically incident Maxwellian sources at pupil point (±r) with adjustable intensities (I1 and I2) interfering at the retina. The two gray filters in the beams indicate the adjustable filters used to alter the wavefront slope at the retina and thus to tune the SCE at the retina.

Fig. 2.
Fig. 2.

Resulting phase ΦT (a) as a function of the α parameter for a fixed retinal location where kxx=π/4; (b) as a function of kxx for α=1.00 (horizontal blue line), α=0.50 (solid red line), α=0.25 (dashed–dotted green line) and α=0 (dashed violet line) respectively; and (c) corresponding intensity distributions |AT|2.

Fig. 3.
Fig. 3.

Predicted effective SCE visibility curves for different α parameters. The curves have been obtained for ρSCE=0.05/mm2.

Fig. 4.
Fig. 4.

Schematic of the experimental setup. An expanded collimated He-Ne laser beam is spatially phase modulated by the SLM to produce two coherent Maxwellian point sources with adjustable relative brightness and separation in the pupil plane. A rapid uploading of phase maps cause the two points to rotate in the pupil plane. The subject compares the perceived visibility of this test field with that of an adjustable reference field from the same laser that enters the eye near the pupil center.

Fig. 5.
Fig. 5.

Numerical generation of two Maxwellian point sources in the pupil plane for the special case of α=0.50, (middle) the resulting SLM phase maps wrapped onto 0 to 2π, and (right) the numerical reconstruction when imaged onto the pupil. The upper case is for a pupil entrance point of r=1.5mm, whereas the lower case shows the case of r=3.0mm. In either case, the dual Maxwellian sources have been generated at a pupil projection angle of 30°. A set of 12 such individual phase maps uploaded onto the SLM in rapid sequence are used when performing the visual tests in the eye for any given α and r values.

Fig. 6.
Fig. 6.

Projected series (12 images) of the two Maxwellian point sources recorded in the pupil plane while rotating in angular increments of 30° for r=3mm. The 0 order has been blocked by the reflective stop. The picture is shown with inverted grayscale.

Fig. 7.
Fig. 7.

Measured effective SCE visibility dependencies for the right eye of subjects: (a) BV, (b) BL, and (c) SC, where the continuous line (blue) corresponds to phase maps generated for α=1.00, dashed line (red) to α=0.50, dashed–dotted line (green) to α=0.25 and long-dashed line (violet) to α=0.00. Standard deviations are for the four repeated measurement series. (d) Visibility variation as a function of the α parameter is shown at a fixed pupil point of r=3.5mm for the three subjects. For comparison also η(α)=10ρeff(α)(3.5mm)2 using Eq. (7) with ρSCE=0.050/mm2 is shown as the solid line (red).

Tables (2)

Tables Icon

Table 1. Theoretical (from the Holographic Phase-map Generation) and Measured α Parameters During the Calibration Found As an Average for All the Projection Angles Using a Series of Phase Mapsa

Tables Icon

Table 2. Experimental Results for the α Parameter Fitted for Each Subject on the Basis of the Data Shown in Fig. 7 Compared to the α Parameter (Theory) Used When Coding the SLM Phase Maps

Equations (9)

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ψT=A1eikxx+A2eikxx=ATeiΦT,
IT=AT2=1+2α1+αcos(2kxx),
ΦT=tan1(1α1+αtan(kxx)).
rCM=1α1+αr.
dΦTdx|x=0=1α1+αkx.
dΦTdx|x=0=1α1+αr2πλneyefeye=rCM2πλneyefeye,
ρeffρSCE=1+α2α1+α+2α,
ψSLM=exp[i(F1{ψPUPIL})],
ρeffρSCE=(arα1α+1)2.

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