Abstract

A geometrical-optical technique is used to predict the changes in the slope of the eccentric-photorefraction intensity profiles as a function of refractive state. We investigate how the intensity profiles vary with refractive state for different light source configurations and monochromatic aberrations in the eye. The best possible light source configuration extends from zero eccentricity (to increase sensitivity and reduce the dead zone) to a high eccentricity (to increase the working range). An advantage of using the extended light source is that the intensity profile of the eccentric-photorefraction reflex is more linear for extended sources than for point light sources. It is also shown that the change in slope with refractive state is dependent on pupil size. Furthermore, when asymmetric aberrations are present, the change in intensity profile slope with refractive state is dependent on the circumferential position of the light source, but this dependence can be resolved by averaging slope values obtained by using two sources placed on opposite sides of the pupil. The importance of this study to existing eccentric-photorefractor designs is discussed, and recommendations for improved eccentric photorefractors are suggested.

© 1997 Optical Society of America

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References

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  1. K. Kaakinen, “A simple method for screening of children with strabismus, anisometropiaor ametropia by simultaneous photography of the corneal and fundus reflexes,” Acta Ophthalmol. 57, 161–171 (1979).
    [CrossRef]
  2. B. Rosengren, “A method of skiascopy with the electric ophthalmoscope,” Acta Ophthalmol. 15, 501–511 (1937).
  3. K. Kaakinen, H. O. Kaseva, K. Eeva-Raija, “Mass screening of children for strabismus or ametropia with two flashphotoskiascopy,” Acta Ophthalmol. 64, 105–110 (1986).
    [CrossRef]
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    [CrossRef] [PubMed]
  5. H. C. Howland, “Optics of photoretinoscopy: results from ray tracing,” Am. J. Optom. Physiol. Opt. 62, 621–625 (1985).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. F. Schaeffel, H. C. Howland, “Measurement of pupil size, direction of gaze, and refractive state by on-line analysis of digitized video images,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1991 OSA Technical Digest Series (Optical Society of America, Washington D.C.), pp. 76–79.
  15. F. Schaeffel, G. Hagel, J. Eikermann, T. Collett, “Lower-field myopia and astigmatism in amphibians and chickens,” J. Opt. Soc. Am. A 11, 487–495 (1994).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberrationsof the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  24. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1990).
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  26. F. Gekeler, J. Wattam-Bell, F. Schaeffel, “Measurement of human astigmatism with infrared photoretinoscopy,” Invest. Ophthalmol. Visual Sci. 37, 725 (1996) (abstract).
  27. M. E. Andison, J. G. Sivak, M. G. Callender, “Convergence and accommodation in a teleost fish, the Oscar,” Invest. Ophthalmol. Visual Sci. 37, 162 (1996) (abstract).
  28. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

1996

A. M. Thompson, T. Li, L. B. Peck, H. C. Howland, R. Counts, W. R. Bobier, “Accuracy and precision of the Tomey ViVA Infrared Photorefractor,” Optom. Vis. Sci. 73, 644–652 (1996).
[CrossRef] [PubMed]

F. Gekeler, J. Wattam-Bell, F. Schaeffel, “Measurement of human astigmatism with infrared photoretinoscopy,” Invest. Ophthalmol. Visual Sci. 37, 725 (1996) (abstract).

M. E. Andison, J. G. Sivak, M. G. Callender, “Convergence and accommodation in a teleost fish, the Oscar,” Invest. Ophthalmol. Visual Sci. 37, 162 (1996) (abstract).

1995

1994

1993

H. Uozato, M. Saishin, H. Hirai, “Photorefractor PR-2000 for refractive screening of infants,” Invest. Ophthalmol. Visual Sci. 4, 861 (1993) (abstract).

F. Schaeffel, H. Wilhelm, E. Zrenner, “Inter-individual variability in the dynamics of natural accommodationin humans: relation to age and refractive errors,” J. Physiol. (London) 461, 301–320 (1993).

1991

H. Uozato, M. Saishin, D. L. Guyton“Refractive assessment of infants with infra-red video-refractor PR-1000,” Invest. Ophthalmol. Visual Sci. 4, 1238 (1991) (abstract).

I. J. Hodgkinson, K. M. Chong, A. C. B. Molteno, “Photorefraction of the living eye: a model for linear knife edge photoscreening,” Appl. Opt. 30, 2263–2269 (1991).
[CrossRef] [PubMed]

1990

W. R. Bobier, “Eccentric photorefraction: a method to measure accommodation of highlyhypermetropic infants,” Clin. Vision Sci. 5, 45–66 (1990).

M. C. W. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to opticalaberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

1989

1987

1986

K. Kaakinen, H. O. Kaseva, K. Eeva-Raija, “Mass screening of children for strabismus or ametropia with two flashphotoskiascopy,” Acta Ophthalmol. 64, 105–110 (1986).
[CrossRef]

1985

W. R. Bobier, O. J. Braddick, “Eccentric photorefraction: optical analysis and empirical measures,” Am. J. Optom. Physiol. Opt. 62, 614–620 (1985).
[CrossRef] [PubMed]

H. C. Howland, “Optics of photoretinoscopy: results from ray tracing,” Am. J. Optom. Physiol. Opt. 62, 621–625 (1985).
[CrossRef] [PubMed]

1984

1979

K. Kaakinen, “A simple method for screening of children with strabismus, anisometropiaor ametropia by simultaneous photography of the corneal and fundus reflexes,” Acta Ophthalmol. 57, 161–171 (1979).
[CrossRef]

1953

1937

B. Rosengren, “A method of skiascopy with the electric ophthalmoscope,” Acta Ophthalmol. 15, 501–511 (1937).

Alpern, M.

Andison, M. E.

M. E. Andison, J. G. Sivak, M. G. Callender, “Convergence and accommodation in a teleost fish, the Oscar,” Invest. Ophthalmol. Visual Sci. 37, 162 (1996) (abstract).

Bobier, W. R.

A. M. Thompson, T. Li, L. B. Peck, H. C. Howland, R. Counts, W. R. Bobier, “Accuracy and precision of the Tomey ViVA Infrared Photorefractor,” Optom. Vis. Sci. 73, 644–652 (1996).
[CrossRef] [PubMed]

M. C. W. Campbell, W. R. Bobier, A. Roorda, “Effect of monochromatic aberrations on photorefractive patterns,” J. Opt. Soc. Am. A 12, 1637–1646 (1995).
[CrossRef]

A. Roorda, M. C. W. Campbell, W. R. Bobier, “Geometrical theory to predict eccentric photorefraction intensity profilesin the human eye,” J. Opt. Soc. Am. A 12, 1647–1656 (1995).
[CrossRef]

W. R. Bobier, “Eccentric photorefraction: a method to measure accommodation of highlyhypermetropic infants,” Clin. Vision Sci. 5, 45–66 (1990).

W. R. Bobier, O. J. Braddick, “Eccentric photorefraction: optical analysis and empirical measures,” Am. J. Optom. Physiol. Opt. 62, 614–620 (1985).
[CrossRef] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Braddick, O. J.

W. R. Bobier, O. J. Braddick, “Eccentric photorefraction: optical analysis and empirical measures,” Am. J. Optom. Physiol. Opt. 62, 614–620 (1985).
[CrossRef] [PubMed]

Callender, M. G.

M. E. Andison, J. G. Sivak, M. G. Callender, “Convergence and accommodation in a teleost fish, the Oscar,” Invest. Ophthalmol. Visual Sci. 37, 162 (1996) (abstract).

Campbell, M. C. W.

M. C. W. Campbell, W. R. Bobier, A. Roorda, “Effect of monochromatic aberrations on photorefractive patterns,” J. Opt. Soc. Am. A 12, 1637–1646 (1995).
[CrossRef]

A. Roorda, M. C. W. Campbell, W. R. Bobier, “Geometrical theory to predict eccentric photorefraction intensity profilesin the human eye,” J. Opt. Soc. Am. A 12, 1647–1656 (1995).
[CrossRef]

M. C. W. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to opticalaberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

C. Cui, M. C. W. Campbell, W. N. Charman, L. Voisin, “Reducing aberration at the fovea by defocus,” in Ophthalmic and Visual Optics, vol. 3 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), pp. 164–167.

Charman, W. N.

G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberrationsof the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
[CrossRef] [PubMed]

C. Cui, M. C. W. Campbell, W. N. Charman, L. Voisin, “Reducing aberration at the fovea by defocus,” in Ophthalmic and Visual Optics, vol. 3 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), pp. 164–167.

Chong, K. M.

Collett, T.

Counts, R.

A. M. Thompson, T. Li, L. B. Peck, H. C. Howland, R. Counts, W. R. Bobier, “Accuracy and precision of the Tomey ViVA Infrared Photorefractor,” Optom. Vis. Sci. 73, 644–652 (1996).
[CrossRef] [PubMed]

Cui, C.

C. Cui, M. C. W. Campbell, W. N. Charman, L. Voisin, “Reducing aberration at the fovea by defocus,” in Ophthalmic and Visual Optics, vol. 3 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), pp. 164–167.

Delori, F. C.

Eeva-Raija, K.

K. Kaakinen, H. O. Kaseva, K. Eeva-Raija, “Mass screening of children for strabismus or ametropia with two flashphotoskiascopy,” Acta Ophthalmol. 64, 105–110 (1986).
[CrossRef]

Eikermann, J.

Farkas, L.

Fry, G. A.

Fukuma, Y.

H. Uozato, M. Saishin, Y. Fukuma, “The photorefractor PR-1000 for refractive screening of infants,” in Current Aspects in Ophthalmology, Vol. 1, K. Shimizu, ed. (Exerpta Medica, London, 1992), pp. 704–708.

Gekeler, F.

F. Gekeler, J. Wattam-Bell, F. Schaeffel, “Measurement of human astigmatism with infrared photoretinoscopy,” Invest. Ophthalmol. Visual Sci. 37, 725 (1996) (abstract).

Greer, P. B.

Guyton, D. L.

H. Uozato, M. Saishin, D. L. Guyton“Refractive assessment of infants with infra-red video-refractor PR-1000,” Invest. Ophthalmol. Visual Sci. 4, 1238 (1991) (abstract).

Hagel, G.

Harrison, E. M.

M. C. W. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to opticalaberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

Hirai, H.

H. Uozato, M. Saishin, H. Hirai, “Photorefractor PR-2000 for refractive screening of infants,” Invest. Ophthalmol. Visual Sci. 4, 861 (1993) (abstract).

Hodgkinson, I. J.

Howland, H. C.

A. M. Thompson, T. Li, L. B. Peck, H. C. Howland, R. Counts, W. R. Bobier, “Accuracy and precision of the Tomey ViVA Infrared Photorefractor,” Optom. Vis. Sci. 73, 644–652 (1996).
[CrossRef] [PubMed]

F. Schaeffel, L. Farkas, H. C. Howland, “Infrared photoretinoscope,” Appl. Opt. 26, 1505–1509 (1987).
[CrossRef] [PubMed]

H. C. Howland, “Optics of photoretinoscopy: results from ray tracing,” Am. J. Optom. Physiol. Opt. 62, 621–625 (1985).
[CrossRef] [PubMed]

G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberrationsof the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
[CrossRef] [PubMed]

F. Schaeffel, H. C. Howland, “Measurement of pupil size, direction of gaze, and refractive state by on-line analysis of digitized video images,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1991 OSA Technical Digest Series (Optical Society of America, Washington D.C.), pp. 76–79.

Kaakinen, K.

K. Kaakinen, H. O. Kaseva, K. Eeva-Raija, “Mass screening of children for strabismus or ametropia with two flashphotoskiascopy,” Acta Ophthalmol. 64, 105–110 (1986).
[CrossRef]

K. Kaakinen, “A simple method for screening of children with strabismus, anisometropiaor ametropia by simultaneous photography of the corneal and fundus reflexes,” Acta Ophthalmol. 57, 161–171 (1979).
[CrossRef]

Kaseva, H. O.

K. Kaakinen, H. O. Kaseva, K. Eeva-Raija, “Mass screening of children for strabismus or ametropia with two flashphotoskiascopy,” Acta Ophthalmol. 64, 105–110 (1986).
[CrossRef]

Li, T.

A. M. Thompson, T. Li, L. B. Peck, H. C. Howland, R. Counts, W. R. Bobier, “Accuracy and precision of the Tomey ViVA Infrared Photorefractor,” Optom. Vis. Sci. 73, 644–652 (1996).
[CrossRef] [PubMed]

Molteno, A. C. B.

Peck, L. B.

A. M. Thompson, T. Li, L. B. Peck, H. C. Howland, R. Counts, W. R. Bobier, “Accuracy and precision of the Tomey ViVA Infrared Photorefractor,” Optom. Vis. Sci. 73, 644–652 (1996).
[CrossRef] [PubMed]

Pflibsen, K. P.

Roorda, A.

Rosengren, B.

B. Rosengren, “A method of skiascopy with the electric ophthalmoscope,” Acta Ophthalmol. 15, 501–511 (1937).

Saishin, M.

H. Uozato, M. Saishin, H. Hirai, “Photorefractor PR-2000 for refractive screening of infants,” Invest. Ophthalmol. Visual Sci. 4, 861 (1993) (abstract).

H. Uozato, M. Saishin, D. L. Guyton“Refractive assessment of infants with infra-red video-refractor PR-1000,” Invest. Ophthalmol. Visual Sci. 4, 1238 (1991) (abstract).

H. Uozato, M. Saishin, Y. Fukuma, “The photorefractor PR-1000 for refractive screening of infants,” in Current Aspects in Ophthalmology, Vol. 1, K. Shimizu, ed. (Exerpta Medica, London, 1992), pp. 704–708.

Schaeffel, F.

F. Gekeler, J. Wattam-Bell, F. Schaeffel, “Measurement of human astigmatism with infrared photoretinoscopy,” Invest. Ophthalmol. Visual Sci. 37, 725 (1996) (abstract).

F. Schaeffel, G. Hagel, J. Eikermann, T. Collett, “Lower-field myopia and astigmatism in amphibians and chickens,” J. Opt. Soc. Am. A 11, 487–495 (1994).
[CrossRef]

F. Schaeffel, H. Wilhelm, E. Zrenner, “Inter-individual variability in the dynamics of natural accommodationin humans: relation to age and refractive errors,” J. Physiol. (London) 461, 301–320 (1993).

F. Schaeffel, L. Farkas, H. C. Howland, “Infrared photoretinoscope,” Appl. Opt. 26, 1505–1509 (1987).
[CrossRef] [PubMed]

F. Schaeffel, H. C. Howland, “Measurement of pupil size, direction of gaze, and refractive state by on-line analysis of digitized video images,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1991 OSA Technical Digest Series (Optical Society of America, Washington D.C.), pp. 76–79.

Simonet, P.

M. C. W. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to opticalaberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

Sivak, J. G.

M. E. Andison, J. G. Sivak, M. G. Callender, “Convergence and accommodation in a teleost fish, the Oscar,” Invest. Ophthalmol. Visual Sci. 37, 162 (1996) (abstract).

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1990).

Thompson, A. M.

A. M. Thompson, T. Li, L. B. Peck, H. C. Howland, R. Counts, W. R. Bobier, “Accuracy and precision of the Tomey ViVA Infrared Photorefractor,” Optom. Vis. Sci. 73, 644–652 (1996).
[CrossRef] [PubMed]

Uozato, H.

H. Uozato, M. Saishin, H. Hirai, “Photorefractor PR-2000 for refractive screening of infants,” Invest. Ophthalmol. Visual Sci. 4, 861 (1993) (abstract).

H. Uozato, M. Saishin, D. L. Guyton“Refractive assessment of infants with infra-red video-refractor PR-1000,” Invest. Ophthalmol. Visual Sci. 4, 1238 (1991) (abstract).

H. Uozato, M. Saishin, Y. Fukuma, “The photorefractor PR-1000 for refractive screening of infants,” in Current Aspects in Ophthalmology, Vol. 1, K. Shimizu, ed. (Exerpta Medica, London, 1992), pp. 704–708.

Voisin, L.

C. Cui, M. C. W. Campbell, W. N. Charman, L. Voisin, “Reducing aberration at the fovea by defocus,” in Ophthalmic and Visual Optics, vol. 3 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), pp. 164–167.

Walsh, G.

Wattam-Bell, J.

F. Gekeler, J. Wattam-Bell, F. Schaeffel, “Measurement of human astigmatism with infrared photoretinoscopy,” Invest. Ophthalmol. Visual Sci. 37, 725 (1996) (abstract).

Wilhelm, H.

F. Schaeffel, H. Wilhelm, E. Zrenner, “Inter-individual variability in the dynamics of natural accommodationin humans: relation to age and refractive errors,” J. Physiol. (London) 461, 301–320 (1993).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Zrenner, E.

F. Schaeffel, H. Wilhelm, E. Zrenner, “Inter-individual variability in the dynamics of natural accommodationin humans: relation to age and refractive errors,” J. Physiol. (London) 461, 301–320 (1993).

Acta Ophthalmol.

K. Kaakinen, “A simple method for screening of children with strabismus, anisometropiaor ametropia by simultaneous photography of the corneal and fundus reflexes,” Acta Ophthalmol. 57, 161–171 (1979).
[CrossRef]

B. Rosengren, “A method of skiascopy with the electric ophthalmoscope,” Acta Ophthalmol. 15, 501–511 (1937).

K. Kaakinen, H. O. Kaseva, K. Eeva-Raija, “Mass screening of children for strabismus or ametropia with two flashphotoskiascopy,” Acta Ophthalmol. 64, 105–110 (1986).
[CrossRef]

Am. J. Optom. Physiol. Opt.

W. R. Bobier, O. J. Braddick, “Eccentric photorefraction: optical analysis and empirical measures,” Am. J. Optom. Physiol. Opt. 62, 614–620 (1985).
[CrossRef] [PubMed]

H. C. Howland, “Optics of photoretinoscopy: results from ray tracing,” Am. J. Optom. Physiol. Opt. 62, 621–625 (1985).
[CrossRef] [PubMed]

Appl. Opt.

Clin. Vision Sci.

W. R. Bobier, “Eccentric photorefraction: a method to measure accommodation of highlyhypermetropic infants,” Clin. Vision Sci. 5, 45–66 (1990).

Invest. Ophthalmol. Visual Sci.

H. Uozato, M. Saishin, D. L. Guyton“Refractive assessment of infants with infra-red video-refractor PR-1000,” Invest. Ophthalmol. Visual Sci. 4, 1238 (1991) (abstract).

H. Uozato, M. Saishin, H. Hirai, “Photorefractor PR-2000 for refractive screening of infants,” Invest. Ophthalmol. Visual Sci. 4, 861 (1993) (abstract).

F. Gekeler, J. Wattam-Bell, F. Schaeffel, “Measurement of human astigmatism with infrared photoretinoscopy,” Invest. Ophthalmol. Visual Sci. 37, 725 (1996) (abstract).

M. E. Andison, J. G. Sivak, M. G. Callender, “Convergence and accommodation in a teleost fish, the Oscar,” Invest. Ophthalmol. Visual Sci. 37, 162 (1996) (abstract).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Physiol. (London)

F. Schaeffel, H. Wilhelm, E. Zrenner, “Inter-individual variability in the dynamics of natural accommodationin humans: relation to age and refractive errors,” J. Physiol. (London) 461, 301–320 (1993).

Optom. Vis. Sci.

A. M. Thompson, T. Li, L. B. Peck, H. C. Howland, R. Counts, W. R. Bobier, “Accuracy and precision of the Tomey ViVA Infrared Photorefractor,” Optom. Vis. Sci. 73, 644–652 (1996).
[CrossRef] [PubMed]

Vision Res.

M. C. W. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to opticalaberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

Other

A. Roorda, Double Pass Reflections in the Human Eye (Ph.D. dissertation, University of Waterloo, Waterloo, Canada, 1996).

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1990).

C. Cui, M. C. W. Campbell, W. N. Charman, L. Voisin, “Reducing aberration at the fovea by defocus,” in Ophthalmic and Visual Optics, vol. 3 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), pp. 164–167.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

H. Uozato, M. Saishin, Y. Fukuma, “The photorefractor PR-1000 for refractive screening of infants,” in Current Aspects in Ophthalmology, Vol. 1, K. Shimizu, ed. (Exerpta Medica, London, 1992), pp. 704–708.

F. Schaeffel, H. C. Howland, “Measurement of pupil size, direction of gaze, and refractive state by on-line analysis of digitized video images,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1991 OSA Technical Digest Series (Optical Society of America, Washington D.C.), pp. 76–79.

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Figures (8)

Fig. 1
Fig. 1

Typical reflexes observed in eccentric photorefraction. The left-hand figure shows an example of a photorefractor configuration that would be used for the intensity profile measurements, based on a design by Schaeffel et al.13 The right-hand figures show the intensity distribution or reflex that appears in the pupil. The reflex fills the pupil, and the slope of the intensity profile is used to deduce the refractive state. The line to the left of each pupil shows the intensity profile across the vertical meridian of the pupil. If the eye is focused in front of the photorefractor, the reflex appears on the same side of the eye as the light source. The opposite occurs for eyes that are hyperopic with respect to the photorefractor. If the eye is focused on the photorefractor, the pupil is dim and the slope is 0.

Fig. 2
Fig. 2

(a) A ray (single arrow) emerging from a retinal point passing through the exit pupil at a radius r crosses the principal ray (double arrow) from the same retinal point at a distance k(r) (the far point distance). The transverse aberration t(r) is a measure of the distance from the emerging ray's intercept position to the principal ray's intercept position in a plane perpendicular to the optical axis at a specified distance l from the exit pupil. (b) The reverse situation is shown where the ray emerges from a distance l and crosses the principal ray before the retina at a distance k(r) with a transverse aberration t(r). The aberrations from object to image space are identical between conjugate planes (except for a magnification difference).28 We consider only rays in a single (x) meridian.

Fig. 3
Fig. 3

Plot of eccentric-photorefraction intensity profiles as a function of refractive state. The cross sections at each refractive state of the surface plot represent the intensity across the meridian of the pupil. The intensity profiles are generated by a geometrical-optical technique. 16 For myopic refractive states (negative refractive states), the intensity profiles ramp to the same side of the pupil as the eccentric light source and to the opposite side for hyperopic refractive states (positive refractive states). When the eye is focused on or near the camera (at -1 D), no intensity distribution is observed; this region is called the dead zone. This simulation is for a point light source at 2 mm eccentricity, a 1-m working distance, and a 7-mm pupil. The slopes for the intensity profiles as a function of refractive state are shown for this surface plot in Fig. 4(a).

Fig. 4
Fig. 4

Plots of eccentric-photorefraction intensity profile slopes as a function of refractive state. The solid curves represent the slope of the intensity profile as a function of refractive state (see Fig. 3). The heavy dashed curves represent the r2 value for the best-fit line to the calculated intensity profile. (a) and (b), point light source at 2 mm eccentricity; (c) and (d), point light source at 8 mm eccentricity. In (a), the light dashed curve represents the gain (the derivative of slope with respect to refractive state). The gain versus the refractive-state curve is used to define the limits of the working range (shaded area; see Section 3). Plots (a), (c), and (d) have a region near the camera position (-1 D) for which no changes in slope with refractive state are observed. This dead zone is four times larger for the 8-mm-eccentric source than for the 2-mm-eccentric source. At the limits of the working range, the gain decreases and the slope changes very slowly with refractive state. This quick reduction in gain is referred to as saturation. In general, the fits are least linear for refractive states near the camera position.

Fig. 5
Fig. 5

Plots of slope versus refractive state for an eccentric photorefractor with an extended source made up of point sources at 2, 5, 8, 11, and 14 mm. The solid curves represent the slope of the intensity profile. The dashed curves represent the r2 value for the slopes best fitted to the calculated intensity profile. With the extended source, the working range is increased over the point light source simulations of Fig. 4. The slopes for each of the plots have been normalized by the same value. The quality of the fits of the best-fit line to the intensity profiles are best for the no-aberration case.

Fig. 6
Fig. 6

Effects of asymmetric aberrations can be canceled by averaging the slope for diametrically opposite sources. The curves of slope versus refractive state from Figs. 5(c) and 5(d) are plotted and averaged. The curve for the temporal source is 11% flatter and for the nasal source is 11% steeper than in the no-aberration case. If the two are averaged, the gain is less than 1% different from the no-aberration case. In this example the curves for the combination of symmetric and asymmetric aberration are shifted toward the best focal plane for the aberrated eye.

Fig. 7
Fig. 7

Plots of slope versus refractive state for an eccentric photorefractor with an extended source made up of point light sources at 0, 3…, 30 mm. The solid curves represent the slope of the intensity profile. The dashed curves represent the r2 value for the slopes best fitted to the calculated intensity profile. The use of a light source at 0 mm eccentricity eliminates the dead zone, even for the no-aberration case. Extension of the source to a 30 mm maximum eccentricity increases the working range. The working range is nearly twice that of the range for the maximum eccentricity of 14 mm used in Fig. 5. The quality of the fit is excellent over most of the working range when the larger extended source is used.

Fig. 8
Fig. 8

Effect of pupil size on gain. Both plots show slope as a function of refractive state for three pupil sizes. All slope values have been scaled by the same value. The gain with the 7-mm pupil is the greatest, and it decreases with decreasing pupil diameter. The gain is highest for the 7-mm pupil since more light can enter and exit the eye. When spherical aberration is present in the eye, similar changes in gain occur, and the curve is also shifted horizontally toward the optimal focal state for the amount of aberration present. Differences of more than 1 D in refractive state occur at the ends of the working range.

Tables (1)

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Table 1 Summary of Results for All Light Source Configurations

Equations (3)

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Itotal(x)=eIe(x),
t(x)=-0.6737-0.1918x3+0.04394x4,
k(x)=l1-t(x)x.

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