Abstract

Photorefractive methods have become popular in the measurement of refractive and accommodative states of infants and children owing to their photographic nature and rapid speed of measurement. As in the case of any method that measures the refractive state of the human eye, monochromatic aberrations will reduce the accuracy of the measurement. Monochromatic aberrations cannot be as easily predicted or controlled as chromatic aberrations during the measurement, and accordingly they will introduce measurement errors. This study defines this error or uncertainty by extending the existing paraxial optical analyses of coaxial and eccentric photorefraction. This new optical analysis predicts that, for the amounts of spherical aberration (SA) reported for the human eye, there will be a significant degree of measurement uncertainty introduced for all photorefractive methods. The dioptric amount of this uncertainty may exceed the maximum amount of SA present in the eye. The calculated effects on photorefractive measurement of a real eye with a mixture of spherical aberration and coma are shown to be significant. The ability, developed here, to predict photorefractive patterns corresponding to different amounts and types of monochromatic aberration may in the future lead to an extension of photorefractive methods to the dual measurement of refractive states and aberrations of individual eyes.

© 1995 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  3. J. Atkinson, O. J. Braddick, L. Ayling, E. Pimm-Smith, H. S. Howland, R. M. Ingram, “Isotropic photorefraction: a new method for refractive testing of infants,” in Pathophysiology of the Visual System, L. Maffei, ed., Vol. 30 of Documents in Ophthalmological Proceedings Series (Junk, The Hague, 1981), pp. 217–223.
  4. W. R. Bobier, “Eccentric photorefraction: a method to measure accommodation of highly hypermetropic infants,” Clin. Vision Sci. 5, 45–60 (1990).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  21. A. C. B. Molteno, I. Hoare-Nairne, I. C. Parr, A. Simpson, I. J. Hodgkinson, N. E. O’Brien, S. D. Watts, “The Otago photoscreener, a method for the mass screening of infants to detect squint and refractive errors,” Trans. Ophthalmol. Soc. N.Z. 35, 43–49 (1983).
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  23. J. Knight, H. C. Howland, “Off-axis comatic aberrations of the eye (irregular astigmatism) measured by conventional infrared photoretinoscopy,” Invest. Ophthalmol. Vis. Sci. 30, 508 (1989).
  24. A. C. B. Molteno, G. F. Sanderson, “Spherical aberration in human infant eyes,” Trans. Ophthalmol. Soc. N. Z. 36, 69–71 (1984).
    [PubMed]
  25. W. Wesemann, A. M. Norcia, D. Allen, “Theory of eccentric photorefraction (photoretinoscopy): astigmatic eyes,” J. Opt. Soc. Am. A 8, 2038–2047 (1991).
    [Crossref] [PubMed]
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  27. M. C. W. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
    [Crossref] [PubMed]
  28. M. Millodot, C. Bobier, “The state of accommodation during the measurement of axial chromatic aberration of the eye,” Am. J. Optom. Physiol. Opt. 53, 168–172 (1976).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  31. J. Atkinson, O. Braddick, K. Durden, P. G. Watson, S. Atkinson, “Screening for refractive errors in 6–9 month old infants using photorefraction,” Br. J. Ophthalmol. 68, 105–112 (1984).
    [Crossref] [PubMed]
  32. W. R. Bobier, “Eccentric photorefraction,” Ph.D. dissertation (Darwin College, Cambridge, UK, 1987).
  33. T. C. A Jenkins, “Aberrations of the eye and their effects on vision. Part I. Spherical aberration,” Br. J. Physiol. Opt. 20, 59–91 (1963).
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1992 (3)

W. R. Bobier, M. C. W. Campbell, C. R. McCreary, A. M. Power, K. C. Yang, “Coaxial photorefractive methods: an optical analysis,” Appl. Opt. 31, 3601–3615 (1992).
[Crossref] [PubMed]

W. R. Bobier, M. C. W. Campbell, C. R McCreary, A. M. Power, K. C. Yang, “Geometrical optical analysis of photorefractive methods,” Ophthal. Physiol. Opt. 12, 147–152 (1992).
[Crossref]

W. R. Bobier, A. Roorda, M. C. W. Campbell, “Photorefractive equations for chromatic and spherical aberrations,” Invest. Ophthalmol. Vis. Sci. 33, 709 (1992).

1991 (2)

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, 2253–2269 (1991).
[Crossref]

W. Wesemann, A. M. Norcia, D. Allen, “Theory of eccentric photorefraction (photoretinoscopy): astigmatic eyes,” J. Opt. Soc. Am. A 8, 2038–2047 (1991).
[Crossref] [PubMed]

1990 (2)

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

W. R. Bobier, “Eccentric photorefraction: a method to measure accommodation of highly hypermetropic infants,” Clin. Vision Sci. 5, 45–60 (1990).

1989 (1)

J. Knight, H. C. Howland, “Off-axis comatic aberrations of the eye (irregular astigmatism) measured by conventional infrared photoretinoscopy,” Invest. Ophthalmol. Vis. Sci. 30, 508 (1989).

1988 (1)

1985 (3)

G. Walsh, W. N. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthal. Physiol. Opt. 5, 23–31 (1985).
[Crossref]

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 (2)

A. C. B. Molteno, G. F. Sanderson, “Spherical aberration in human infant eyes,” Trans. Ophthalmol. Soc. N. Z. 36, 69–71 (1984).
[PubMed]

J. Atkinson, O. Braddick, K. Durden, P. G. Watson, S. Atkinson, “Screening for refractive errors in 6–9 month old infants using photorefraction,” Br. J. Ophthalmol. 68, 105–112 (1984).
[Crossref] [PubMed]

1983 (2)

A. C. B. Molteno, I. Hoare-Nairne, I. C. Parr, A. Simpson, I. J. Hodgkinson, N. E. O’Brien, S. D. Watts, “The Otago photoscreener, a method for the mass screening of infants to detect squint and refractive errors,” Trans. Ophthalmol. Soc. N.Z. 35, 43–49 (1983).

H. C. Howland, O. J. Braddick, J. S. Atkinson, B. J. Howland, “Optics of photorefraction: orthogonal and isotropic methods,” J. Opt. Soc. Am. 73, 1701–1708 (1983).
[Crossref] [PubMed]

1977 (1)

1976 (1)

M. Millodot, C. Bobier, “The state of accommodation during the measurement of axial chromatic aberration of the eye,” Am. J. Optom. Physiol. Opt. 53, 168–172 (1976).
[Crossref] [PubMed]

1974 (1)

1966 (1)

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. (London) 86, 558–578 (1966).

1963 (1)

T. C. A Jenkins, “Aberrations of the eye and their effects on vision. Part I. Spherical aberration,” Br. J. Physiol. Opt. 20, 59–91 (1963).

1957 (1)

1951 (1)

1949 (1)

M. Koomen, R. Tousey, R. Scolnik, “The spherical aberration of the eye,” J. Am. Optom. Assoc. 39, 370–376 (1949).

1947 (2)

Allen, D.

Artal, P.

Atkinson, J.

J. Atkinson, O. Braddick, K. Durden, P. G. Watson, S. Atkinson, “Screening for refractive errors in 6–9 month old infants using photorefraction,” Br. J. Ophthalmol. 68, 105–112 (1984).
[Crossref] [PubMed]

J. Atkinson, O. J. Braddick, L. Ayling, E. Pimm-Smith, H. S. Howland, R. M. Ingram, “Isotropic photorefraction: a new method for refractive testing of infants,” in Pathophysiology of the Visual System, L. Maffei, ed., Vol. 30 of Documents in Ophthalmological Proceedings Series (Junk, The Hague, 1981), pp. 217–223.

Atkinson, J. S.

Atkinson, S.

J. Atkinson, O. Braddick, K. Durden, P. G. Watson, S. Atkinson, “Screening for refractive errors in 6–9 month old infants using photorefraction,” Br. J. Ophthalmol. 68, 105–112 (1984).
[Crossref] [PubMed]

Ayling, L.

J. Atkinson, O. J. Braddick, L. Ayling, E. Pimm-Smith, H. S. Howland, R. M. Ingram, “Isotropic photorefraction: a new method for refractive testing of infants,” in Pathophysiology of the Visual System, L. Maffei, ed., Vol. 30 of Documents in Ophthalmological Proceedings Series (Junk, The Hague, 1981), pp. 217–223.

Bedford, R. E.

Bennett, A. G.

A. G. Bennett, R. B. Rabbetts, Clinical Visual Optics, 2nd ed. (Butterworth, London, 1989).

Berny, F.

F. Berny, S. Slansky, “Wavefront determination resulting from Foucalt test as applied to the human eye and visual instruments,” in Optical Instruments and Techniques, J. Home Dickon, ed. (Oriel, London, 1969), pp. 375–385.

Bescos, J.

Bobier, C.

M. Millodot, C. Bobier, “The state of accommodation during the measurement of axial chromatic aberration of the eye,” Am. J. Optom. Physiol. Opt. 53, 168–172 (1976).
[Crossref] [PubMed]

Bobier, W. R.

W. R. Bobier, M. C. W. Campbell, C. R. McCreary, A. M. Power, K. C. Yang, “Coaxial photorefractive methods: an optical analysis,” Appl. Opt. 31, 3601–3615 (1992).
[Crossref] [PubMed]

W. R. Bobier, M. C. W. Campbell, C. R McCreary, A. M. Power, K. C. Yang, “Geometrical optical analysis of photorefractive methods,” Ophthal. Physiol. Opt. 12, 147–152 (1992).
[Crossref]

W. R. Bobier, A. Roorda, M. C. W. Campbell, “Photorefractive equations for chromatic and spherical aberrations,” Invest. Ophthalmol. Vis. Sci. 33, 709 (1992).

W. R. Bobier, “Eccentric photorefraction: a method to measure accommodation of highly hypermetropic infants,” Clin. Vision Sci. 5, 45–60 (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]

M. C. W. Campbell, W. R. Bobier, C. R. McCreary, A. M. Power, K. C. Yang, “The effect of the eye’s chromatic aberration on coaxial photorefractive patterns: a geometrical optical analysis,” in Ophthalmic and Visual Optics, Vol. 3 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 8–11.

W. R. Bobier, “Eccentric photorefraction,” Ph.D. dissertation (Darwin College, Cambridge, UK, 1987).

Braddick, O.

J. Atkinson, O. Braddick, K. Durden, P. G. Watson, S. Atkinson, “Screening for refractive errors in 6–9 month old infants using photorefraction,” Br. J. Ophthalmol. 68, 105–112 (1984).
[Crossref] [PubMed]

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]

H. C. Howland, O. J. Braddick, J. S. Atkinson, B. J. Howland, “Optics of photorefraction: orthogonal and isotropic methods,” J. Opt. Soc. Am. 73, 1701–1708 (1983).
[Crossref] [PubMed]

J. Atkinson, O. J. Braddick, L. Ayling, E. Pimm-Smith, H. S. Howland, R. M. Ingram, “Isotropic photorefraction: a new method for refractive testing of infants,” in Pathophysiology of the Visual System, L. Maffei, ed., Vol. 30 of Documents in Ophthalmological Proceedings Series (Junk, The Hague, 1981), pp. 217–223.

Campbell, F. W.

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. (London) 86, 558–578 (1966).

Campbell, M. C. W.

W. R. Bobier, M. C. W. Campbell, C. R McCreary, A. M. Power, K. C. Yang, “Geometrical optical analysis of photorefractive methods,” Ophthal. Physiol. Opt. 12, 147–152 (1992).
[Crossref]

W. R. Bobier, A. Roorda, M. C. W. Campbell, “Photorefractive equations for chromatic and spherical aberrations,” Invest. Ophthalmol. Vis. Sci. 33, 709 (1992).

W. R. Bobier, M. C. W. Campbell, C. R. McCreary, A. M. Power, K. C. Yang, “Coaxial photorefractive methods: an optical analysis,” Appl. Opt. 31, 3601–3615 (1992).
[Crossref] [PubMed]

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

M. C. W. Campbell, W. R. Bobier, C. R. McCreary, A. M. Power, K. C. Yang, “The effect of the eye’s chromatic aberration on coaxial photorefractive patterns: a geometrical optical analysis,” in Ophthalmic and Visual Optics, Vol. 3 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 8–11.

Charman, W. N.

G. Walsh, W. N. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthal. Physiol. Opt. 5, 23–31 (1985).
[Crossref]

W. N. Charman, “Optics of the human eye,” in Vision and Visual Dysfunction, J. Cronly-Dillon, ed. (CRC, Boca Raton, Fla., 1991), Vol. 1, W. N. Charman, ed., pp. 1–26.

Chong, K. M.

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, 2253–2269 (1991).
[Crossref]

Durden, K.

J. Atkinson, O. Braddick, K. Durden, P. G. Watson, S. Atkinson, “Screening for refractive errors in 6–9 month old infants using photorefraction,” Br. J. Ophthalmol. 68, 105–112 (1984).
[Crossref] [PubMed]

Griffin, D. R.

Gubisch, R. W.

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. (London) 86, 558–578 (1966).

Harrison, E. M.

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

Hoare-Nairne, I.

A. C. B. Molteno, I. Hoare-Nairne, I. C. Parr, A. Simpson, I. J. Hodgkinson, N. E. O’Brien, S. D. Watts, “The Otago photoscreener, a method for the mass screening of infants to detect squint and refractive errors,” Trans. Ophthalmol. Soc. N.Z. 35, 43–49 (1983).

Hodgkinson, I. J.

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, 2253–2269 (1991).
[Crossref]

A. C. B. Molteno, I. Hoare-Nairne, I. C. Parr, A. Simpson, I. J. Hodgkinson, N. E. O’Brien, S. D. Watts, “The Otago photoscreener, a method for the mass screening of infants to detect squint and refractive errors,” Trans. Ophthalmol. Soc. N.Z. 35, 43–49 (1983).

Howland, B.

Howland, B. J.

Howland, H. C.

Howland, H. S.

J. Atkinson, O. J. Braddick, L. Ayling, E. Pimm-Smith, H. S. Howland, R. M. Ingram, “Isotropic photorefraction: a new method for refractive testing of infants,” in Pathophysiology of the Visual System, L. Maffei, ed., Vol. 30 of Documents in Ophthalmological Proceedings Series (Junk, The Hague, 1981), pp. 217–223.

Ingram, R. M.

J. Atkinson, O. J. Braddick, L. Ayling, E. Pimm-Smith, H. S. Howland, R. M. Ingram, “Isotropic photorefraction: a new method for refractive testing of infants,” in Pathophysiology of the Visual System, L. Maffei, ed., Vol. 30 of Documents in Ophthalmological Proceedings Series (Junk, The Hague, 1981), pp. 217–223.

Ivanoff, A.

Jenkins, T. C. A

T. C. A Jenkins, “Aberrations of the eye and their effects on vision. Part I. Spherical aberration,” Br. J. Physiol. Opt. 20, 59–91 (1963).

Knight, J.

J. Knight, H. C. Howland, “Off-axis comatic aberrations of the eye (irregular astigmatism) measured by conventional infrared photoretinoscopy,” Invest. Ophthalmol. Vis. Sci. 30, 508 (1989).

Koomen, M.

M. Koomen, R. Scolnik, R. Tousey, “A study of night myopia,” J. Opt. Soc. Am. 41, 80–90 (1951).
[Crossref]

M. Koomen, R. Tousey, R. Scolnik, “The spherical aberration of the eye,” J. Am. Optom. Assoc. 39, 370–376 (1949).

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics, 2nd ed. (Longman, London, 1967).

McCreary, C. R

W. R. Bobier, M. C. W. Campbell, C. R McCreary, A. M. Power, K. C. Yang, “Geometrical optical analysis of photorefractive methods,” Ophthal. Physiol. Opt. 12, 147–152 (1992).
[Crossref]

McCreary, C. R.

W. R. Bobier, M. C. W. Campbell, C. R. McCreary, A. M. Power, K. C. Yang, “Coaxial photorefractive methods: an optical analysis,” Appl. Opt. 31, 3601–3615 (1992).
[Crossref] [PubMed]

M. C. W. Campbell, W. R. Bobier, C. R. McCreary, A. M. Power, K. C. Yang, “The effect of the eye’s chromatic aberration on coaxial photorefractive patterns: a geometrical optical analysis,” in Ophthalmic and Visual Optics, Vol. 3 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 8–11.

Millodot, M.

M. Millodot, C. Bobier, “The state of accommodation during the measurement of axial chromatic aberration of the eye,” Am. J. Optom. Physiol. Opt. 53, 168–172 (1976).
[Crossref] [PubMed]

M. Millodot, “Accommodation and refraction of the eye,” in The Senses, H. B. Barlow, J. D. Mollon, eds. (Cambridge U. Press, Cambridge, 1982), pp. 62–81.

Molteno, A. C. B.

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, 2253–2269 (1991).
[Crossref]

A. C. B. Molteno, G. F. Sanderson, “Spherical aberration in human infant eyes,” Trans. Ophthalmol. Soc. N. Z. 36, 69–71 (1984).
[PubMed]

A. C. B. Molteno, I. Hoare-Nairne, I. C. Parr, A. Simpson, I. J. Hodgkinson, N. E. O’Brien, S. D. Watts, “The Otago photoscreener, a method for the mass screening of infants to detect squint and refractive errors,” Trans. Ophthalmol. Soc. N.Z. 35, 43–49 (1983).

Norcia, A. M.

O’Brien, N. E.

A. C. B. Molteno, I. Hoare-Nairne, I. C. Parr, A. Simpson, I. J. Hodgkinson, N. E. O’Brien, S. D. Watts, “The Otago photoscreener, a method for the mass screening of infants to detect squint and refractive errors,” Trans. Ophthalmol. Soc. N.Z. 35, 43–49 (1983).

Parr, I. C.

A. C. B. Molteno, I. Hoare-Nairne, I. C. Parr, A. Simpson, I. J. Hodgkinson, N. E. O’Brien, S. D. Watts, “The Otago photoscreener, a method for the mass screening of infants to detect squint and refractive errors,” Trans. Ophthalmol. Soc. N.Z. 35, 43–49 (1983).

Pimm-Smith, E.

J. Atkinson, O. J. Braddick, L. Ayling, E. Pimm-Smith, H. S. Howland, R. M. Ingram, “Isotropic photorefraction: a new method for refractive testing of infants,” in Pathophysiology of the Visual System, L. Maffei, ed., Vol. 30 of Documents in Ophthalmological Proceedings Series (Junk, The Hague, 1981), pp. 217–223.

Power, A. M.

W. R. Bobier, M. C. W. Campbell, C. R McCreary, A. M. Power, K. C. Yang, “Geometrical optical analysis of photorefractive methods,” Ophthal. Physiol. Opt. 12, 147–152 (1992).
[Crossref]

W. R. Bobier, M. C. W. Campbell, C. R. McCreary, A. M. Power, K. C. Yang, “Coaxial photorefractive methods: an optical analysis,” Appl. Opt. 31, 3601–3615 (1992).
[Crossref] [PubMed]

M. C. W. Campbell, W. R. Bobier, C. R. McCreary, A. M. Power, K. C. Yang, “The effect of the eye’s chromatic aberration on coaxial photorefractive patterns: a geometrical optical analysis,” in Ophthalmic and Visual Optics, Vol. 3 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 8–11.

Rabbetts, R. B.

A. G. Bennett, R. B. Rabbetts, Clinical Visual Optics, 2nd ed. (Butterworth, London, 1989).

Roorda, A.

W. R. Bobier, A. Roorda, M. C. W. Campbell, “Photorefractive equations for chromatic and spherical aberrations,” Invest. Ophthalmol. Vis. Sci. 33, 709 (1992).

Sanderson, G. F.

A. C. B. Molteno, G. F. Sanderson, “Spherical aberration in human infant eyes,” Trans. Ophthalmol. Soc. N. Z. 36, 69–71 (1984).
[PubMed]

Santamaría, J.

Scolnik, R.

M. Koomen, R. Scolnik, R. Tousey, “A study of night myopia,” J. Opt. Soc. Am. 41, 80–90 (1951).
[Crossref]

M. Koomen, R. Tousey, R. Scolnik, “The spherical aberration of the eye,” J. Am. Optom. Assoc. 39, 370–376 (1949).

Simonet, P.

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

Simpson, A.

A. C. B. Molteno, I. Hoare-Nairne, I. C. Parr, A. Simpson, I. J. Hodgkinson, N. E. O’Brien, S. D. Watts, “The Otago photoscreener, a method for the mass screening of infants to detect squint and refractive errors,” Trans. Ophthalmol. Soc. N.Z. 35, 43–49 (1983).

Slansky, S.

F. Berny, S. Slansky, “Wavefront determination resulting from Foucalt test as applied to the human eye and visual instruments,” in Optical Instruments and Techniques, J. Home Dickon, ed. (Oriel, London, 1969), pp. 375–385.

Tousey, R.

M. Koomen, R. Scolnik, R. Tousey, “A study of night myopia,” J. Opt. Soc. Am. 41, 80–90 (1951).
[Crossref]

M. Koomen, R. Tousey, R. Scolnik, “The spherical aberration of the eye,” J. Am. Optom. Assoc. 39, 370–376 (1949).

Wald, G.

Walsh, G.

G. Walsh, W. N. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthal. Physiol. Opt. 5, 23–31 (1985).
[Crossref]

Watson, P. G.

J. Atkinson, O. Braddick, K. Durden, P. G. Watson, S. Atkinson, “Screening for refractive errors in 6–9 month old infants using photorefraction,” Br. J. Ophthalmol. 68, 105–112 (1984).
[Crossref] [PubMed]

Watts, S. D.

A. C. B. Molteno, I. Hoare-Nairne, I. C. Parr, A. Simpson, I. J. Hodgkinson, N. E. O’Brien, S. D. Watts, “The Otago photoscreener, a method for the mass screening of infants to detect squint and refractive errors,” Trans. Ophthalmol. Soc. N.Z. 35, 43–49 (1983).

Wesemann, W.

Wyszecki, G.

Yang, K. C.

W. R. Bobier, M. C. W. Campbell, C. R. McCreary, A. M. Power, K. C. Yang, “Coaxial photorefractive methods: an optical analysis,” Appl. Opt. 31, 3601–3615 (1992).
[Crossref] [PubMed]

W. R. Bobier, M. C. W. Campbell, C. R McCreary, A. M. Power, K. C. Yang, “Geometrical optical analysis of photorefractive methods,” Ophthal. Physiol. Opt. 12, 147–152 (1992).
[Crossref]

M. C. W. Campbell, W. R. Bobier, C. R. McCreary, A. M. Power, K. C. Yang, “The effect of the eye’s chromatic aberration on coaxial photorefractive patterns: a geometrical optical analysis,” in Ophthalmic and Visual Optics, Vol. 3 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 8–11.

Am. J. Optom. Physiol. Opt. (3)

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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W. R. Bobier, M. C. W. Campbell, C. R. McCreary, A. M. Power, K. C. Yang, “Coaxial photorefractive methods: an optical analysis,” Appl. Opt. 31, 3601–3615 (1992).
[Crossref] [PubMed]

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, 2253–2269 (1991).
[Crossref]

Br. J. Ophthalmol. (1)

J. Atkinson, O. Braddick, K. Durden, P. G. Watson, S. Atkinson, “Screening for refractive errors in 6–9 month old infants using photorefraction,” Br. J. Ophthalmol. 68, 105–112 (1984).
[Crossref] [PubMed]

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Clin. Vision Sci. (1)

W. R. Bobier, “Eccentric photorefraction: a method to measure accommodation of highly hypermetropic infants,” Clin. Vision Sci. 5, 45–60 (1990).

Invest. Ophthalmol. Vis. Sci. (2)

W. R. Bobier, A. Roorda, M. C. W. Campbell, “Photorefractive equations for chromatic and spherical aberrations,” Invest. Ophthalmol. Vis. Sci. 33, 709 (1992).

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M. Koomen, R. Tousey, R. Scolnik, “The spherical aberration of the eye,” J. Am. Optom. Assoc. 39, 370–376 (1949).

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W. R. Bobier, M. C. W. Campbell, C. R McCreary, A. M. Power, K. C. Yang, “Geometrical optical analysis of photorefractive methods,” Ophthal. Physiol. Opt. 12, 147–152 (1992).
[Crossref]

G. Walsh, W. N. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthal. Physiol. Opt. 5, 23–31 (1985).
[Crossref]

Trans. Ophthalmol. Soc. N. Z. (1)

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[PubMed]

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A. C. B. Molteno, I. Hoare-Nairne, I. C. Parr, A. Simpson, I. J. Hodgkinson, N. E. O’Brien, S. D. Watts, “The Otago photoscreener, a method for the mass screening of infants to detect squint and refractive errors,” Trans. Ophthalmol. Soc. N.Z. 35, 43–49 (1983).

Vision Res. (1)

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

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W. R. Bobier, “Eccentric photorefraction,” Ph.D. dissertation (Darwin College, Cambridge, UK, 1987).

F. Berny, S. Slansky, “Wavefront determination resulting from Foucalt test as applied to the human eye and visual instruments,” in Optical Instruments and Techniques, J. Home Dickon, ed. (Oriel, London, 1969), pp. 375–385.

M. C. W. Campbell, W. R. Bobier, C. R. McCreary, A. M. Power, K. C. Yang, “The effect of the eye’s chromatic aberration on coaxial photorefractive patterns: a geometrical optical analysis,” in Ophthalmic and Visual Optics, Vol. 3 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 8–11.

W. N. Charman, “Optics of the human eye,” in Vision and Visual Dysfunction, J. Cronly-Dillon, ed. (CRC, Boca Raton, Fla., 1991), Vol. 1, W. N. Charman, ed., pp. 1–26.

A. G. Bennett, R. B. Rabbetts, Clinical Visual Optics, 2nd ed. (Butterworth, London, 1989).

J. Atkinson, O. J. Braddick, L. Ayling, E. Pimm-Smith, H. S. Howland, R. M. Ingram, “Isotropic photorefraction: a new method for refractive testing of infants,” in Pathophysiology of the Visual System, L. Maffei, ed., Vol. 30 of Documents in Ophthalmological Proceedings Series (Junk, The Hague, 1981), pp. 217–223.

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Figures (11)

Fig. 1
Fig. 1

Photorefractive images for orthogonal, isotropic, and eccentric photorefraction. For the coaxial methods (orthogonal and isotropic) the photorefractive pattern is achieved by defocusing of the light returning to the camera by a cylinder lens assembly in the former case and by defocusing the camera lens itself in the latter case. Over the working range of the instrument the length of the pattern varies in proportion to the eye’s refractive error and pupil size. Eccentric photorefraction takes an in-focus picture of the pupil of the eye. Over this instrument’s working range a photorefractive crescent is found in the margin of the pupil whose length varies in proportion to the eye’s refractive error and pupil size. The location of the crescent is dependent on the sign of the refractive error and the circumferential position of the eccentric source. (From Bobier et al.8)

Fig. 2
Fig. 2

(a) Coaxial photorefraction for myopia in the absence of aberrations. CF denotes the photorefraction pattern size at the camera plane of focus a distance l from the eye. A refractive error within the working range of the instrument is shown for a myopic eye with the distance to the far point of the eye, k, between the eye and the camera’s plane of focus (k > l). The flash source, S, is centered in the aperture of the camera a distance p from the pupil. Light from source S forms a retinal image, UV. An aerial image, denoted VU′, conjugate to UV, is formed at the far point of the eye. The extreme rays leaving the pupil (GH) continue from VU′ to the camera plane of focus and define the extreme edges of the photorefractive pattern. p.r.’s denote the principal rays passing through the pupil center. Geometrical relationships can be used to define the extent of this pattern. CD, DE, and EF can be defined by use of the similar triangles CDV′ ~ GHV′, EFU′ ~ GHU′, and DES ~ GHS. The blur diameter, CF, is given by CF = [(2K + P)/L − 1]GH, where K, P, and L are dioptric equivalents of k, p, and l. Similar relations have been derived for both myopic and hyperopic errors through the working ranges, dead zones, and vignetting regions.7 (Figure adapted from Bobier et al.7) (b) Eccentric photorefraction for myopia in the absence of aberrations. CF denotes the extent of the photorefractive crescent size at the camera’s plane of focus on the pupil (GH). Light source S is offset vertically a distance e from the edge of the limiting aperture A of the camera. As in the coaxial case, light from source S forms a retinal image UV. An aerial image VU′ conjugate with UV is formed at the far point of the eye. The extreme ray leaving the pupil at F continues from U′ to the aperture of the camera, where it represents the most extreme ray entering the camera and hence dictating the extreme edge of the photorefractive pattern. All rays emerging from between points C and F contribute to the crescent. Geometrical relationships can be used to define the extent of the pattern. Comparing the similar triangles FHU′ ~ SAU′, one can derive the following relationship for the crescent width: CF = GH − [eP/(−KP)]. Again a similar equation has been derived for hyperopic errors.8 (Figure adapted from Bobier et al.8)

Fig. 3
Fig. 3

Coaxial photorefraction for a myope with undercorrected spherical aberration. The paraxial far point (k0) and the far points corresponding to increasingly more marginal rays (k1k4) are shifted monotonically from the camera plane of focus toward the eye. In this special case the photorefractive pattern extent is determined by the rays entering and leaving the extreme edges of the pupil. The geometry is the same as for the paraxial case [Fig. 2(a)], except that the far point is varying with the position of the ray entering the pupil. The returning rays, determining the pattern extent, pass through the far point corresponding to rays at the margin of the pupil. As a result, the photorefractive pattern increases in size. The size of the blur in this case can be calculated by insertion of the marginal far-point value into the equation in the caption to Fig. 1.

Fig. 4
Fig. 4

For some combinations of refractive error and spherical aberration the maximum blur spot diameter on the retina is not necessarily defined by the beam entering the margin of the pupil, as illustrated here for a myope with overcorrected spherical aberration. (a) Enlarged view of what takes place in the eye with respect to the focus as a function of the radius. The focal points for the different entering radii are denoted ki′. In this example the maximum spot size is determined by the ray entering pupil position 2. (b) The most divergent principal ray emerges from the maximum extent of the blur on the retina, U2. Therefore, when the most divergent ray is found, the maximum extent of the blur on the retina has also been found. p.r. i are the principal rays originating at points Ui on the retina.

Fig. 5
Fig. 5

This ray diagram demonstrates that in most cases, for spherical aberration, when the far points do not increase monotonically from the camera plane of focus, more in-depth analysis is required for coaxial photorefraction. It can be seen that the marginal ray does not define the maximum blur spot on the retina or the maximum pattern extent at the camera plane of focus. It can also be seen that the maximum pattern extent is dependent on the plane of focus of the camera. In this case the maximum pattern extent is determined by the rays leaving the pupil at the points labeled 3. If the plane of focus were positioned slightly closer to the eye, the maximum would be defined by a different exiting ray. The method of determining the maximum pattern extent is detailed in Figs. 6 and 7. All outgoing rays drawn originate from points Umax and Vmax at the edge of the retinal blur.

Fig. 6
Fig. 6

This figure defines the principal ray corresponding to the edges of the image: (a) and (b) are ray traces used to find the intersection of the principal ray from the edges of the image with the camera plane for coaxial and eccentric methods, respectively. The distance of the intersection of the principal ray, xi, is measured from the source S, so the treatment for both methods is the same. As the radius of entry r of ray SR varies, the intersection point of the principal ray OX also varies. Ray OX goes through U′(r) conjugate with the position of the blur on the retina, U(r), where U(r) varies with the radius r of the entering ray. The distance x between intersection point X and source S can be defined by the use of the similar triangles, SXU′(r) ~ ORU′(r) and XDU ′(r) ~ OEU′(r). Finding the most divergent principal ray requires maximizing the resulting equation [Eq. (2) in the text] with respect to the entering radius r. (DE is a construction.)

Fig. 7
Fig. 7

Maximum photorefractive pattern extent for coaxial photorefraction. This diagram is a ray trace of the rays leaving the pupil. Point Umax on the retina represents the most extreme edge of the spot on the retina found by maximizing the distance SX in Fig. 6. The ray emerging from Umax, which passes through the center of the pupil (dotted curve), is the most divergent principal ray found previously. Rays reflected from point Umax will intersect the principal ray at far points determined by the type of monochromatic aberration and the exit radius r of these rays in the pupil. The figure shows only one such ray, leaving the pupil at R, striking the source plane at X, and intersecting the principal ray at U′(r) a distance k(r) from the eye. The objective is to define the extent, AC, of the photorefracted pattern from the eye at the camera plane of focus as a function of the radius r where the ray leaves the pupil. xmax represents the distance at which the most divergent principal ray intersects the source plane. This ray intersects the camera plane of focus at B, a distance (x*l)/p from the optical axis. The distance BC within which returning rays intersect the camera plane of focus can be determined by the use of the similar triangles, BCU′(r) ~ ORU′(r), where U′(r) is the far point corresponding to a ray originating at the edge of the image and leaving the pupil at position r. The resulting equation [Eq. (5) in the text] must be maximized with respect to the exiting radius to yield the maximum blur diameter.

Fig. 8
Fig. 8

Maximum photorefractive pattern extent for eccentric photorefraction. This example is a ray trace for a myopic eye with positive spherical aberration. In this case the marginal entering ray defines the most extreme edge of the blur on the retina. Each returning ray (from Umax), through position i in the pupil, intersects the principal ray at the corresponding far point, ki. The returning ray that defines the crescent width is the ray that intersects the limiting aperture of the camera lens. In the example this ray emerges from point F on the pupil. Rays from C to F define the crescent that will appear in the pupil. A detailed analysis is given in the following figures.

Fig. 9
Fig. 9

Maximum crescent width for eccentric photorefraction. This diagram is a ray trace of the rays leaving the pupil. Point Umax on the retina represents the most extreme edge of the blur on the retina, and the ray emerging from it that passes through the center of the pupil (dotted line) is the most divergent principal ray, which was found in Fig. 6(b). Rays reflected from point Umax will intersect the principal ray at far points U′(r) determined by the type of monochromatic aberration and their position r of exit in the entrance pupil. The objective is to define the point where the returning rays intersect the source plane. The ray that intersects the source plane at the limiting aperture defines the crescent width. The point where the principal ray intersects the source plane is at a distance xmax from the source. The returning rays intersect at a distance z(r) from this point. This distance can be determined by use of the similar triangles XYU′(r) ~ ORU′(r). The position of the intersection of the ray from the source is given by y = x + z. The crescent width is then defined by the radius r for which y = e, the eccentricity.

Fig. 10
Fig. 10

Results for a numerical calculation performed with two opposite signs of spherical aberration (SA) of 1.5 D for (a) coaxial and (b) eccentric photorefraction. (a) For coaxial photorefraction a camera distance of 1 m, a camera defocus of 0.2 m in front of the subject, and a pupil size of 8 mm were assumed. We find that there is a linear shift in the pattern extent in the direction of the SA. This is because the rays that are defining the maximum pattern extent generally exit at the margin of the pupil. The SA also affects the dead-zone region. The refractive error estimate will generally be off by the amount of aberration at the margin of the pupil. (b) For eccentric photorefraction the source eccentricity was 18 mm, the pupil size was 8 mm, and the camera distance was 1 m. The shift in pattern extent with SA is not linear but varies with the crescent width. In eccentric photorefraction, 1.5 D SA can affect the uncertainty in the refractive error estimate by amounts well above this.

Fig. 11
Fig. 11

(a) Coaxial and (b) eccentric photorefractive pattern extents expected for a perfect eye compared with that expected for a real eye. The aberrations across the horizontal meridian of the eye of one of the authors (subject MC) have been measured and consist of both spherical aberration and comatic-type aberrations. The coaxial and eccentric equations were solved given the measured variation of the far point with pupil position k(r). Because of the asymmetry of the aberrations, the pattern extent was calculated for rays entering the pupil on either side of the center of the pupil. The total expected pattern extent in the horizontal as a function of artificially induced refractive error is shown. A pupil size of 7 mm and a camera distance of 1 mm were simulated. For (a) the camera defocus was 0.2 m in front of the eye. For (b) the eccentricity used was 18 mm.

Equations (14)

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C F = { 2 K y + P L - 1 } G H ,
x ( r ) = r · [ p + k ( r ) ] - k ( r ) ,
x max = r [ p + k ] - k ,
A B = - x max l p .
C A ( r ) = - x max l p + r · [ - l + k ( r ) ] - k ( r ) .
y ( r ) = x max + r · [ p + k ( r ) ] - k ( r ) .
k ( r ) = k 0 + c r 2 ,
Blur ( r ) = b 1 ( r - r 0 ) 2 + c 1 ( r - r 0 ) 3 + b 2 ( r - r 0 ) 4 ,
K ( r ) = blur ( r ) ( r l ) ,
K ( r ) = B 1 ( r - r 0 ) + C 1 ( r - r 0 ) 2 + B 2 ( r - r 0 ) 3 ,
x ( r ) = r · [ p + k ( r ) ] - k ( r ) ;
C A ( r ) = - x max l p + r · [ - l + k ( r ) ] - k ( r ) ;
x ( r ) = r · [ p + k ( r ) ] - k ( r )             ( same as for coaxial ) .
y ( r ) = x max + r · [ p + k ( r ) ] - k ( r ) ;

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