Abstract

A Bayesian model of Snellen visual acuity (VA) has been developed that, as far as we know, is the first one that includes the three main stages of VA: (1) optical degradations, (2) neural image representation and contrast thresholding, and (3) character recognition. The retinal image of a Snellen test chart is obtained from experimental wave-aberration data. Then a subband image decomposition with a set of visual channels tuned to different spatial frequencies and orientations is applied to the retinal image, as in standard computational models of early cortical image representation. A neural threshold is applied to the contrast responses to include the effect of the neural contrast sensitivity. The resulting image representation is the base of a Bayesian pattern-recognition method robust to the presence of optical aberrations. The model is applied to images containing sets of letter optotypes at different scales, and the number of correct answers is obtained at each scale; the final output is the decimal Snellen VA. The model has no free parameters to adjust. The main input data are the eye’s optical aberrations, and standard values are used for all other parameters, including the Stiles–Crawford effect, visual channels, and neural contrast threshold, when no subject specific values are available. When aberrations are large, Snellen VA involving pattern recognition differs from grating acuity, which is based on a simpler detection (or orientation-discrimination) task and hence is basically unaffected by phase distortions introduced by the optical transfer function. A preliminary test of the model in one subject produced close agreement between actual measurements and predicted VA values. Two examples are also included: (1) application of the method to the prediction of the VA in refractive-surgery patients and (2) simulation of the VA attainable by correcting ocular aberrations.

© 2003 Optical Society of America

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2002 (1)

2001 (1)

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

2000 (4)

M. Mrochen, M. Kaemmerer, T. Seiler, “Wavefront-guided laser in situ keratomileusis: early results in three eyes,” J. Refract. Surg. 16, 116–121 (2000).
[PubMed]

E. Moreno-Barriuso, R. Navarro, “Laser ray tracing versus Hartmann–Shack sensor for measuring optical aberrations in the human eye,” J. Opt. Soc. Am. A 17, 974–985 (2000).
[CrossRef]

T. Seiler, M. Kaemmerer, P. Mierdel, H. E. Krinke, “Ocular optical aberrations after photorefractive keratectomy for myopia and myopic astigmatism,” Arch. Ophthalmol. 118, 17–21 (2000).
[CrossRef] [PubMed]

A. Vargas, J. Campos, R. Navarro, “Invariant pattern recognition against defocus based on subband decomposition of the filter,” Opt. Commun. 185, 33–40 (2000).
[CrossRef]

1999 (2)

S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

J. T. Holladay, D. R. Dudeja, J. Chang, “Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing and corneal topography,” J. Cataract Refract. Surg. 25, 663–669 (1999).
[CrossRef] [PubMed]

1998 (3)

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations and visual performance after radial keratotomy,” J. Refract. Surg. 14, 397–407 (1998).
[PubMed]

J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
[CrossRef]

O. Nestares, R. Navarro, J. Portilla, A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166–173 (1998).
[CrossRef]

1997 (3)

J. Liang, D. R. Williams, “Aberrations and retinal image quality of the normal human eye,” J. Opt. Soc. Am. A 14, 2873–2883 (1997).
[CrossRef]

R. Navarro, M. A. Losada, “Aberrations and relative efficiency of light pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997).
[CrossRef]

P. Mierdel, H. E. Krinke, W. Wiegand, M. Kaemmerer, T. Seiler, “Measuring device for determining monochromatic aberration of the human eye,” Ophthalmologe 94, 441–445 (1997).
[CrossRef] [PubMed]

1996 (1)

W. Verdon, M. Bullimore, R. K. Maloney, “Visual performance after photorefractive keratectomy,” Arch. Ophthalmol. 114, 1465–1472 (1996).
[CrossRef] [PubMed]

1995 (1)

J. E. Greivenkamp, J. Schwiegerling, J. M. Miller, M. D. Mellinger, “Visual acuity modeling using optical raytracing of schematic eyes,” Am. J. Ophthalmol. 120, 227–240 (1995).
[PubMed]

1994 (2)

1993 (2)

R. A. Applegate, 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] [PubMed]

M. A. Losada, R. Navarro, J. Santamaria, “Relative contributions of optical and neural limitations to human contrast sensitivity at different luminance levels,” Vision Res. 33, 2321–2336 (1993).
[CrossRef] [PubMed]

1991 (1)

A. Bradley, T. Thomas, M. Kalaher, M. Hoerres, “Effects of spherical and astigmatic defocus on acuity and contrast sensitivity: a comparison of three clinical charts,” Optom. Vision Sci. 68, 418–426 (1991).
[CrossRef]

1990 (3)

E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032–2040 (1990).
[CrossRef] [PubMed]

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

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

1987 (1)

1985 (2)

1982 (1)

G. Smith, “Ocular defocus, spurious resolution and contrast reversal,” Ophthalmic Physiol. Opt. 2, 398–404 (1982).

1977 (1)

1974 (1)

A. Van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

1970 (1)

H. H. Hopkins, M. J. Yzuel, “The computation of diffraction patterns in the presence of aberrations,” Opt. Acta 17, 157–182 (1970).
[CrossRef]

1965 (1)

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

1961 (1)

H. B. Peters, “The relationship between refractive error and visual acuity at three age levels,” Am. J. Ophthalmol. 38, 194–199 (1961).

Applegate, R. A.

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations and visual performance after radial keratotomy,” J. Refract. Surg. 14, 397–407 (1998).
[PubMed]

R. A. Applegate, 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] [PubMed]

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 232–244.

Artal, P.

Barbero, S.

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

Bescós, J.

Bille, J.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1993).

Bradley, A.

A. Bradley, T. Thomas, M. Kalaher, M. Hoerres, “Effects of spherical and astigmatic defocus on acuity and contrast sensitivity: a comparison of three clinical charts,” Optom. Vision Sci. 68, 418–426 (1991).
[CrossRef]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Bullimore, M.

W. Verdon, M. Bullimore, R. K. Maloney, “Visual performance after photorefractive keratectomy,” Arch. Ophthalmol. 114, 1465–1472 (1996).
[CrossRef] [PubMed]

Burns, S. A.

S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
[CrossRef]

Campbell, F. W. G.

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

Campos, J.

A. Vargas, J. Campos, R. Navarro, “Invariant pattern recognition against defocus based on subband decomposition of the filter,” Opt. Commun. 185, 33–40 (2000).
[CrossRef]

Chang, J.

J. T. Holladay, D. R. Dudeja, J. Chang, “Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing and corneal topography,” J. Cataract Refract. Surg. 25, 663–669 (1999).
[CrossRef] [PubMed]

Cottingham, A. J.

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations and visual performance after radial keratotomy,” J. Refract. Surg. 14, 397–407 (1998).
[PubMed]

Cox, I. G.

Curcio, C. A.

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

Dudeja, D. R.

J. T. Holladay, D. R. Dudeja, J. Chang, “Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing and corneal topography,” J. Cataract Refract. Surg. 25, 663–669 (1999).
[CrossRef] [PubMed]

Geisler, W. S.

W. S. Geisler, “Ideal-observer analysis of visual discrimination,” in Frontiers of Visual Science (National Academy Press, Washington, D.C., 1987).

Giles, M.

Goelz, S.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Green, D. G.

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

Greivenkamp, J. E.

J. E. Greivenkamp, J. Schwiegerling, J. M. Miller, M. D. Mellinger, “Visual acuity modeling using optical raytracing of schematic eyes,” Am. J. Ophthalmol. 120, 227–240 (1995).
[PubMed]

Grimm, B.

Guirao, A.

He, J. C.

Hendrickson, A. E.

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

Hoerres, M.

A. Bradley, T. Thomas, M. Kalaher, M. Hoerres, “Effects of spherical and astigmatic defocus on acuity and contrast sensitivity: a comparison of three clinical charts,” Optom. Vision Sci. 68, 418–426 (1991).
[CrossRef]

Holladay, J. T.

J. T. Holladay, D. R. Dudeja, J. Chang, “Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing and corneal topography,” J. Cataract Refract. Surg. 25, 663–669 (1999).
[CrossRef] [PubMed]

Hopkins, H. H.

H. H. Hopkins, M. J. Yzuel, “The computation of diffraction patterns in the presence of aberrations,” Opt. Acta 17, 157–182 (1970).
[CrossRef]

Howarth, P. A.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Howland, H. C.

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations and visual performance after radial keratotomy,” J. Refract. Surg. 14, 397–407 (1998).
[PubMed]

Kaemmerer, M.

M. Mrochen, M. Kaemmerer, T. Seiler, “Wavefront-guided laser in situ keratomileusis: early results in three eyes,” J. Refract. Surg. 16, 116–121 (2000).
[PubMed]

T. Seiler, M. Kaemmerer, P. Mierdel, H. E. Krinke, “Ocular optical aberrations after photorefractive keratectomy for myopia and myopic astigmatism,” Arch. Ophthalmol. 118, 17–21 (2000).
[CrossRef] [PubMed]

P. Mierdel, H. E. Krinke, W. Wiegand, M. Kaemmerer, T. Seiler, “Measuring device for determining monochromatic aberration of the human eye,” Ophthalmologe 94, 441–445 (1997).
[CrossRef] [PubMed]

Kalaher, M.

A. Bradley, T. Thomas, M. Kalaher, M. Hoerres, “Effects of spherical and astigmatic defocus on acuity and contrast sensitivity: a comparison of three clinical charts,” Optom. Vision Sci. 68, 418–426 (1991).
[CrossRef]

Kalina, R. E.

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

Krinke, H. E.

T. Seiler, M. Kaemmerer, P. Mierdel, H. E. Krinke, “Ocular optical aberrations after photorefractive keratectomy for myopia and myopic astigmatism,” Arch. Ophthalmol. 118, 17–21 (2000).
[CrossRef] [PubMed]

P. Mierdel, H. E. Krinke, W. Wiegand, M. Kaemmerer, T. Seiler, “Measuring device for determining monochromatic aberration of the human eye,” Ophthalmologe 94, 441–445 (1997).
[CrossRef] [PubMed]

Lakshminarayanan, V.

Landy, M. S.

M. S. Landy, J. A. Movshon, Computational Models of Visual Processing (MIT Press, Cambridge, Mass., 1991).

Liang, J.

Llorente, L.

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

Losada, M. A.

R. Navarro, M. A. Losada, “Aberrations and relative efficiency of light pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997).
[CrossRef]

M. A. Losada, R. Navarro, J. Santamaria, “Relative contributions of optical and neural limitations to human contrast sensitivity at different luminance levels,” Vision Res. 33, 2321–2336 (1993).
[CrossRef] [PubMed]

Maloney, R. K.

W. Verdon, M. Bullimore, R. K. Maloney, “Visual performance after photorefractive keratectomy,” Arch. Ophthalmol. 114, 1465–1472 (1996).
[CrossRef] [PubMed]

Marcos, S.

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
[CrossRef]

Mellinger, M. D.

J. E. Greivenkamp, J. Schwiegerling, J. M. Miller, M. D. Mellinger, “Visual acuity modeling using optical raytracing of schematic eyes,” Am. J. Ophthalmol. 120, 227–240 (1995).
[PubMed]

Merayo-Lloves, J.

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

Mierdel, P.

T. Seiler, M. Kaemmerer, P. Mierdel, H. E. Krinke, “Ocular optical aberrations after photorefractive keratectomy for myopia and myopic astigmatism,” Arch. Ophthalmol. 118, 17–21 (2000).
[CrossRef] [PubMed]

P. Mierdel, H. E. Krinke, W. Wiegand, M. Kaemmerer, T. Seiler, “Measuring device for determining monochromatic aberration of the human eye,” Ophthalmologe 94, 441–445 (1997).
[CrossRef] [PubMed]

Miller, J. M.

J. E. Greivenkamp, J. Schwiegerling, J. M. Miller, M. D. Mellinger, “Visual acuity modeling using optical raytracing of schematic eyes,” Am. J. Ophthalmol. 120, 227–240 (1995).
[PubMed]

Moreno-Barriuso, E.

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

E. Moreno-Barriuso, R. Navarro, “Laser ray tracing versus Hartmann–Shack sensor for measuring optical aberrations in the human eye,” J. Opt. Soc. Am. A 17, 974–985 (2000).
[CrossRef]

S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

Movshon, J. A.

M. S. Landy, J. A. Movshon, Computational Models of Visual Processing (MIT Press, Cambridge, Mass., 1991).

Mrochen, M.

M. Mrochen, M. Kaemmerer, T. Seiler, “Wavefront-guided laser in situ keratomileusis: early results in three eyes,” J. Refract. Surg. 16, 116–121 (2000).
[PubMed]

Navarro, R.

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

E. Moreno-Barriuso, R. Navarro, “Laser ray tracing versus Hartmann–Shack sensor for measuring optical aberrations in the human eye,” J. Opt. Soc. Am. A 17, 974–985 (2000).
[CrossRef]

A. Vargas, J. Campos, R. Navarro, “Invariant pattern recognition against defocus based on subband decomposition of the filter,” Opt. Commun. 185, 33–40 (2000).
[CrossRef]

S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

O. Nestares, R. Navarro, J. Portilla, A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166–173 (1998).
[CrossRef]

R. Navarro, M. A. Losada, “Aberrations and relative efficiency of light pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997).
[CrossRef]

P. Artal, R. Navarro, “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytical expression,” J. Opt. Soc. Am. A 11, 246–249 (1994).
[CrossRef]

M. A. Losada, R. Navarro, J. Santamaria, “Relative contributions of optical and neural limitations to human contrast sensitivity at different luminance levels,” Vision Res. 33, 2321–2336 (1993).
[CrossRef] [PubMed]

R. Navarro, J. Santamarı́a, J. Bescós, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A 2, 1273–1281 (1985).
[CrossRef] [PubMed]

Nestares, O.

O. Nestares, R. Navarro, J. Portilla, A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166–173 (1998).
[CrossRef]

Peli, E.

Peters, H. B.

H. B. Peters, “The relationship between refractive error and visual acuity at three age levels,” Am. J. Ophthalmol. 38, 194–199 (1961).

Porter, J.

Portilla, J.

O. Nestares, R. Navarro, J. Portilla, A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166–173 (1998).
[CrossRef]

Santamari´a, J.

Santamaria, J.

M. A. Losada, R. Navarro, J. Santamaria, “Relative contributions of optical and neural limitations to human contrast sensitivity at different luminance levels,” Vision Res. 33, 2321–2336 (1993).
[CrossRef] [PubMed]

Schwiegerling, J.

J. E. Greivenkamp, J. Schwiegerling, J. M. Miller, M. D. Mellinger, “Visual acuity modeling using optical raytracing of schematic eyes,” Am. J. Ophthalmol. 120, 227–240 (1995).
[PubMed]

Schwiegerling, J. T.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 232–244.

Seiler, T.

M. Mrochen, M. Kaemmerer, T. Seiler, “Wavefront-guided laser in situ keratomileusis: early results in three eyes,” J. Refract. Surg. 16, 116–121 (2000).
[PubMed]

T. Seiler, M. Kaemmerer, P. Mierdel, H. E. Krinke, “Ocular optical aberrations after photorefractive keratectomy for myopia and myopic astigmatism,” Arch. Ophthalmol. 118, 17–21 (2000).
[CrossRef] [PubMed]

P. Mierdel, H. E. Krinke, W. Wiegand, M. Kaemmerer, T. Seiler, “Measuring device for determining monochromatic aberration of the human eye,” Ophthalmologe 94, 441–445 (1997).
[CrossRef] [PubMed]

Sharp, R. P.

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations and visual performance after radial keratotomy,” J. Refract. Surg. 14, 397–407 (1998).
[PubMed]

Sloan, K. R.

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

Smith, G.

G. Smith, “Ocular defocus, spurious resolution and contrast reversal,” Ophthalmic Physiol. Opt. 2, 398–404 (1982).

Stiles, W. S.

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

Still, D. L.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Tabernero, A.

O. Nestares, R. Navarro, J. Portilla, A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166–173 (1998).
[CrossRef]

Thibos, L. N.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 232–244.

Thomas, T.

A. Bradley, T. Thomas, M. Kalaher, M. Hoerres, “Effects of spherical and astigmatic defocus on acuity and contrast sensitivity: a comparison of three clinical charts,” Optom. Vision Sci. 68, 418–426 (1991).
[CrossRef]

Van Meeteren, A.

A. Van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

Vargas, A.

A. Vargas, J. Campos, R. Navarro, “Invariant pattern recognition against defocus based on subband decomposition of the filter,” Opt. Commun. 185, 33–40 (2000).
[CrossRef]

Verdon, W.

W. Verdon, M. Bullimore, R. K. Maloney, “Visual performance after photorefractive keratectomy,” Arch. Ophthalmol. 114, 1465–1472 (1996).
[CrossRef] [PubMed]

Watson, A. B.

Webb, R.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 232–244.

Webb, R. H.

Wiegand, W.

P. Mierdel, H. E. Krinke, W. Wiegand, M. Kaemmerer, T. Seiler, “Measuring device for determining monochromatic aberration of the human eye,” Ophthalmologe 94, 441–445 (1997).
[CrossRef] [PubMed]

Williams, D. R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1993).

Wyszecki, G.

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

Yee, R. W.

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations and visual performance after radial keratotomy,” J. Refract. Surg. 14, 397–407 (1998).
[PubMed]

Yzuel, M. J.

H. H. Hopkins, M. J. Yzuel, “The computation of diffraction patterns in the presence of aberrations,” Opt. Acta 17, 157–182 (1970).
[CrossRef]

Zhang, X.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Am. J. Ophthalmol. (2)

H. B. Peters, “The relationship between refractive error and visual acuity at three age levels,” Am. J. Ophthalmol. 38, 194–199 (1961).

J. E. Greivenkamp, J. Schwiegerling, J. M. Miller, M. D. Mellinger, “Visual acuity modeling using optical raytracing of schematic eyes,” Am. J. Ophthalmol. 120, 227–240 (1995).
[PubMed]

Arch. Ophthalmol. (2)

W. Verdon, M. Bullimore, R. K. Maloney, “Visual performance after photorefractive keratectomy,” Arch. Ophthalmol. 114, 1465–1472 (1996).
[CrossRef] [PubMed]

T. Seiler, M. Kaemmerer, P. Mierdel, H. E. Krinke, “Ocular optical aberrations after photorefractive keratectomy for myopia and myopic astigmatism,” Arch. Ophthalmol. 118, 17–21 (2000).
[CrossRef] [PubMed]

Invest. Ophthalmol. Visual Sci. (1)

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

J. Cataract Refract. Surg. (1)

J. T. Holladay, D. R. Dudeja, J. Chang, “Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing and corneal topography,” J. Cataract Refract. Surg. 25, 663–669 (1999).
[CrossRef] [PubMed]

J. Comp. Neurol. (1)

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

J. Electron. Imaging (1)

O. Nestares, R. Navarro, J. Portilla, A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166–173 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (11)

A. Guirao, J. Porter, D. R. Williams, I. G. Cox, “Calculated impact of higher-order monochromatic aberrations on retinal image quality in a population of human eyes,” J. Opt. Soc. Am. A 19, 1–9 (2002).
[CrossRef]

J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
[CrossRef]

E. Moreno-Barriuso, R. Navarro, “Laser ray tracing versus Hartmann–Shack sensor for measuring optical aberrations in the human eye,” J. Opt. Soc. Am. A 17, 974–985 (2000).
[CrossRef]

J. Liang, B. Grimm, S. Goelz, J. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann–Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994).
[CrossRef]

D. R. Williams, “Visibility of interference fringes near the resolution limit,” J. Opt. Soc. Am. A 2, 1087–1093 (1985).
[CrossRef] [PubMed]

P. Artal, R. Navarro, “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytical expression,” J. Opt. Soc. Am. A 11, 246–249 (1994).
[CrossRef]

R. A. Applegate, 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] [PubMed]

R. Navarro, J. Santamarı́a, J. Bescós, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A 2, 1273–1281 (1985).
[CrossRef] [PubMed]

A. B. Watson, “Efficiency of a model human image code,” J. Opt. Soc. Am. A 4, 2401–2417 (1987).
[CrossRef] [PubMed]

J. Liang, D. R. Williams, “Aberrations and retinal image quality of the normal human eye,” J. Opt. Soc. Am. A 14, 2873–2883 (1997).
[CrossRef]

E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032–2040 (1990).
[CrossRef] [PubMed]

J. Physiol. (London) (1)

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

J. Refract. Surg. (2)

M. Mrochen, M. Kaemmerer, T. Seiler, “Wavefront-guided laser in situ keratomileusis: early results in three eyes,” J. Refract. Surg. 16, 116–121 (2000).
[PubMed]

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations and visual performance after radial keratotomy,” J. Refract. Surg. 14, 397–407 (1998).
[PubMed]

Ophthalmic Physiol. Opt. (1)

G. Smith, “Ocular defocus, spurious resolution and contrast reversal,” Ophthalmic Physiol. Opt. 2, 398–404 (1982).

Ophthalmologe (1)

P. Mierdel, H. E. Krinke, W. Wiegand, M. Kaemmerer, T. Seiler, “Measuring device for determining monochromatic aberration of the human eye,” Ophthalmologe 94, 441–445 (1997).
[CrossRef] [PubMed]

Opt. Acta (2)

A. Van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

H. H. Hopkins, M. J. Yzuel, “The computation of diffraction patterns in the presence of aberrations,” Opt. Acta 17, 157–182 (1970).
[CrossRef]

Opt. Commun. (1)

A. Vargas, J. Campos, R. Navarro, “Invariant pattern recognition against defocus based on subband decomposition of the filter,” Opt. Commun. 185, 33–40 (2000).
[CrossRef]

Optom. Vision Sci. (2)

R. Navarro, M. A. Losada, “Aberrations and relative efficiency of light pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997).
[CrossRef]

A. Bradley, T. Thomas, M. Kalaher, M. Hoerres, “Effects of spherical and astigmatic defocus on acuity and contrast sensitivity: a comparison of three clinical charts,” Optom. Vision Sci. 68, 418–426 (1991).
[CrossRef]

Vision Res. (3)

M. A. Losada, R. Navarro, J. Santamaria, “Relative contributions of optical and neural limitations to human contrast sensitivity at different luminance levels,” Vision Res. 33, 2321–2336 (1993).
[CrossRef] [PubMed]

S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Other (6)

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

M. S. Landy, J. A. Movshon, Computational Models of Visual Processing (MIT Press, Cambridge, Mass., 1991).

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 232–244.

W. S. Geisler, “Ideal-observer analysis of visual discrimination,” in Frontiers of Visual Science (National Academy Press, Washington, D.C., 1987).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1993).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the model. The input data of the optical model are ocular aberrations and Stiles-Crawford-effect parameters and a computer-generated set of optotypes at different scales corresponding to different VA values. The cortical image representation is based on a set of Gabor filters and on the neural contrast threshold. Then the Bayesian pattern recognition process is applied to the different optotypes sets, and the returned VA is the one for which the number of correct answers is above threshold.

Fig. 2
Fig. 2

Plot of the NTF (inverse of neural contrast threshold) and the three frequency Gabor channels considered in the current version of the model. (Each frequency channel contains four orientation channels).

Fig. 3
Fig. 3

Illustration of the stages of the model. The input chart and the wave aberration are shown in the upper row. The retinal optical image, the result of the recognition, and the resulting visual acuity are shown the middle row (√ and × mean correct or wrong answers, respectively). The reduced alphabet of 18 characters used in the recognition process is displayed at the bottom.  

Fig. 4
Fig. 4

Predicted visual acuity for different defocus values for subject RN in both monochromatic (solid curve) and polychromatic (dotted curve) light. Circles represent average experimental VA (polychromatic) from four runs of the experiment, with error bars corresponding to the standard deviation. Predicted grating detection acuity is also included (dashed curve).

Fig. 5
Fig. 5

Comparison of predicted VA in a patient before (solid curves) and after (dashed curves) LASIK refractive surgery, for 3.5- (upper panel) and 6.5- (lower panel) mm pupil diameters. The predicted VA suffers a slight decrease after surgery.

Fig. 6
Fig. 6

Predicted VA for a perfect eye in which all aberrations have been corrected, for 3.5- (solid curve) and 6.5- (dotted curve) mm pupil diameters.

Fig. 7
Fig. 7

Comparison of the VA predicted in polychromatic light by the multichannel model (solid curve) and by the global model (dotted curve). The circles show the average experimental VA. The error bars on the global model predictions correspond to the standard deviation in the predicted values VA from five different noise realizations.

Equations (19)

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

P(ξ, η)=T(ξ, η)exp-i2π nλ W(ξ, η),
W(ξ, η)k=135ckzk(ξ/Rp, η/Rp).
T(ξ, η)=exp-ρ2 (ξ2+η2)circ(ξ2+η2, R),
OTF(u, v)=P(ξ/λ, η/λ)  P(ξ/λ, η/λ),
I(x, y)=FT-1[FT[O(x, y)]OTF(u, v)],
Zd=DR24,
oi(x)=[h(x)*c(x)]*gi(x)+ηi(x)hici(x-ui)+ηi(x),i=1,, Nc
p(c,{hi, ui}|{oi})=Kp({oi}|c,{hi, ui})p(c)p({hi, u}),
p(c,{hi, ui}|{oi})=Kp({oi}|c,{hi, ui})p(c),
(cˆ,{h^i,u^i})=argmax(c,{hi,ui}) p({oi}|c,{hi, ui})p(c),
p({oi}|c,{hi, ui})=i=1Ncxpηi(oi(x)-hici(x-ui)).
p(c,{hi, ui}|{oi})i=1Ncxpηi(oi(x)-hici(x-ui))×j=1Nδ(c-cj),
p(c=cj,{hi,ui}|{oi})
i=1Ncxpηi(oi(x)-hicij(x-ui)).
Eij=x[oi(x)-hicij(x-ui)]2.
Pj=max{p(c=cj{hi, ui}|{oi})}exp12σ2i=1Nch^ijcorrij(u^ij).
Eij=x[oi(x)]2+(hi)2x[cij(x)]2-2hixoi(x)cij(x-ui).
Eijhi=2hiKij-2 xoi(x)cij(x-ui)=0,
Eijui=2hixoi(x) cij(x-ui)ui=0.

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