Abstract

Our purpose is to develop a computational approach that jointly assesses the impact of stimulus luminance and pupil size on visual quality. We compared traditional optical measures of image quality and those that incorporate the impact of retinal illuminance dependent neural contrast sensitivity. Visually weighted image quality was calculated for a presbyopic model eye with representative levels of chromatic and monochromatic aberrations as pupil diameter was varied from 7 to 1 mm, stimulus luminance varied from 2000 to 0.1  cd/m2, and defocus varied from 0 to 2 diopters. The model included the effects of quantal fluctuations on neural contrast sensitivity. We tested the model’s predictions for five cycles per degree gratings by measuring contrast sensitivity at 5  cyc/deg. Unlike the traditional Strehl ratio and the visually weighted area under the modulation transfer function, the visual Strehl ratio derived from the optical transfer function was able to capture the combined impact of optics and quantal noise on visual quality. In a well-focused eye, provided retinal illuminance is held constant as pupil size varies, visual image quality scales approximately as the square root of illuminance because of quantum fluctuations, but optimum pupil size is essentially independent of retinal illuminance and quantum fluctuations. Conversely, when stimulus luminance is held constant (and therefore illuminance varies with pupil size), optimum pupil size increases as luminance decreases, thereby compensating partially for increased quantum fluctuations. However, in the presence of 1 and 2 diopters of defocus and at high photopic levels where Weber’s law operates, optical aberrations and diffraction dominate image quality and pupil optimization. Similar behavior was observed in human observers viewing sinusoidal gratings. Optimum pupil size increases as stimulus luminance drops for the well-focused eye, and the benefits of small pupils for improving defocused image quality remain throughout the photopic and mesopic ranges. However, restricting pupils to <2  mm will cause significant reductions in the best focus vision at low photopic and mesopic luminances.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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  7. S. B. Laughlin, “Retinal information capacity and the function of the pupil,” Ophthalmic Physiolog. Opt. 12, 161–164 (1992).
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  10. L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 329–351 (2004).
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  17. A. K. Dexl, O. Seyeddain, W. Riha, M. Hohensinn, T. Ruckl, W. Hitzl, and G. Grabner, “Reading performance after implantation of a modified corneal inlay design for the surgical correction of presbyopia: 1-year follow-up,” Am. J. Ophthalmol. 153, 994–1001 (2012).
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  20. N. L. Himebaugh, L. N. Thibos, A. Bradley, G. Wilson, and C. G. Begley, “Predicting optical effects of tear film break up on retinal image quality using the Shack–Hartmann aberrometer and computational optical modeling,” Adv. Exp. Med. Biol. 506, 1141–1147 (2002).
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    [Crossref]
  30. L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
    [Crossref]
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  32. R. Xu, A. Bradley, N. Lopez-Gil, and L. N. Thibos, “Modelling the effects of secondary spherical aberration on refractive error, image quality and depth of focus,” Ophthal. Physiolog. Opt. 35, 28–38 (2015).
    [Crossref]
  33. X. Cheng, A. Bradley, and L. N. Thibos, “Predicting subjective judgment of best focus with objective image quality metrics,” J. Vis. 4(4), 310 (2004).
    [Crossref]
  34. A. Ravikumar, E. J. Sarver, and R. A. Applegate, “Change in visual acuity is highly correlated with change in six image quality metrics independent of wavefront error and/or pupil diameter,” J. Vis. 12(10), 11 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  41. A. B. Watson and D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Precept. Psychophys. 33, 113–120 (1983).
    [Crossref]
  42. H. A. Anderson, G. Hentz, A. Glasser, K. K. Stuebing, and R. E. Manny, “Minus-lens-stimulated accommodative amplitude decreases sigmoidally with age: a study of objectively measured accommodative amplitudes from age 3,” Invest. Ophthalmol. Visual Sci. 49, 2919–2926 (2008).
    [Crossref]
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    [Crossref]
  44. A. Hickenbotham, P. Tiruveedhula, and A. Roorda, “Comparison of spherical aberration and small-pupil profiles in improving depth of focus for presbyopic corrections,” J. Cataract Refractive Surg. 38, 2071–2079 (2012).
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    [Crossref]
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    [Crossref]
  48. R. L. Woods, A. Bradley, and D. A. Atchison, “Consequences of monocular diplopia for the contrast sensitivity function,” Vis. Res. 36, 3587–3596 (1996).
    [Crossref]
  49. S. Ravikumar, A. Bradley, and L. Thibos, “Phase changes induced by optical aberrations degrade letter and face acuity,” J. Vis. 10(14), 18 (2010).
    [Crossref]
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    [Crossref]
  52. D. G. Pelli and L. C. Applegate, “The visual requirements of mobility,” Perception 14, 19–29 (1985).
    [Crossref]
  53. J. S. Pan and G. P. Bingham, “With an eye to low vision: optic flow enables perception despite image blur,” Optom. Vis. Sci. 90, 1119–1127 (2013).
    [Crossref]

2016 (2)

R. Xu, L. Thibos, and A. Bradley, “Effect of target luminance on optimum pupil diameter for presbyopic eyes,” Optom. Vis. Sci. 93, 1409–1419 (2016).
[Crossref]

R. Xu, D. Gil, M. Dibas, W. Hare, and A. Bradley, “The effect of light level and small pupils on presbyopic reading performance,” Invest. Ophthalmol. Visual Sci. 57, 5656–5664 (2016).
[Crossref]

2015 (1)

R. Xu, A. Bradley, N. Lopez-Gil, and L. N. Thibos, “Modelling the effects of secondary spherical aberration on refractive error, image quality and depth of focus,” Ophthal. Physiolog. Opt. 35, 28–38 (2015).
[Crossref]

2014 (2)

A. Bradley, J. Nam, R. Xu, L. Harman, and L. Thibos, “Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality,” Ophthalmic Physiolog. Opt. 34, 331–345 (2014).
[Crossref]

A. Bradley, R. Xu, L. Thibos, G. Marin, and M. Hernandez, “Influence of spherical aberration, stimulus spatial frequency, and pupil apodisation on subjective refractions,” Ophthalmic Physiolog. Opt. 34, 309–320 (2014).
[Crossref]

2013 (2)

J. S. Pan and G. P. Bingham, “With an eye to low vision: optic flow enables perception despite image blur,” Optom. Vis. Sci. 90, 1119–1127 (2013).
[Crossref]

A. Ravikumar, J. D. Marsack, H. E. Bedell, Y. Shi, and R. A. Applegate, “Change in visual acuity is well correlated with change in image-quality metrics for both normal and keratoconic wavefront errors,” J. Vis. 13(13), 28 (2013).
[Crossref]

2012 (5)

S. Garcia-Lazaro, T. Ferrer-Blasco, and H. Radhakrishnan, “Visual function through 4 contact lens-based pinhole systems for presbyopia,” J. Cataract Refractive Surg. 38, 858–865 (2012).
[Crossref]

A. K. Dexl, O. Seyeddain, W. Riha, M. Hohensinn, T. Ruckl, W. Hitzl, and G. Grabner, “Reading performance after implantation of a modified corneal inlay design for the surgical correction of presbyopia: 1-year follow-up,” Am. J. Ophthalmol. 153, 994–1001 (2012).
[Crossref]

A. Hickenbotham, P. Tiruveedhula, and A. Roorda, “Comparison of spherical aberration and small-pupil profiles in improving depth of focus for presbyopic corrections,” J. Cataract Refractive Surg. 38, 2071–2079 (2012).
[Crossref]

A. Ravikumar, E. J. Sarver, and R. A. Applegate, “Change in visual acuity is highly correlated with change in six image quality metrics independent of wavefront error and/or pupil diameter,” J. Vis. 12(10), 11 (2012).
[Crossref]

A. B. Watson and J. I. Yellott, “A unified formula for light-adapted pupil size,” J. Vis. 12(10), 12 (2012).
[Crossref]

2010 (3)

M. Kilintari, A. Pallikaris, N. Tsiklis, and H. S. Ginis, “Evaluation of image quality metrics for the prediction of subjective best focus,” Optom. Vis. Sci. 87, 183–189 (2010).
[Crossref]

X. Cheng, A. Bradley, S. Ravikumar, and L. N. Thibos, “Visual impact of Zernike and Seidel forms of monochromatic aberrations,” Optom. Vis. Sci. 87, 300–312 (2010).
[Crossref]

S. Ravikumar, A. Bradley, and L. Thibos, “Phase changes induced by optical aberrations degrade letter and face acuity,” J. Vis. 10(14), 18 (2010).
[Crossref]

2008 (2)

H. A. Anderson, G. Hentz, A. Glasser, K. K. Stuebing, and R. E. Manny, “Minus-lens-stimulated accommodative amplitude decreases sigmoidally with age: a study of objectively measured accommodative amplitudes from age 3,” Invest. Ophthalmol. Visual Sci. 49, 2919–2926 (2008).
[Crossref]

S. Ravikumar, L. N. Thibos, and A. Bradley, “Calculation of retinal image quality for polychromatic light,” J. Opt. Soc. Am. A 25, 2395–2407 (2008).
[Crossref]

2007 (1)

D. M. Win-Hall, L. A. Ostrin, S. Kasthurirangan, and A. Glasser, “Objective accommodation measurement with the Grand Seiko and Hartinger coincidence refractometer,” Optom. Vis. Sci. 84, 879–887 (2007).
[Crossref]

2006 (1)

R. A. Applegate, J. D. Marsack, and L. N. Thibos, “Metrics of retinal image quality predict visual performance in eyes with 20/17 or better visual acuity,” Optom. Vis. Sci. 83, 635–640 (2006).
[Crossref]

2004 (2)

X. Cheng, A. Bradley, and L. N. Thibos, “Predicting subjective judgment of best focus with objective image quality metrics,” J. Vis. 4(4), 310 (2004).
[Crossref]

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 329–351 (2004).
[Crossref]

2003 (1)

P. Artal, A. Guirao, E. Berrio, P. Piers, and S. Norrby, “Optical aberrations and the aging eye,” Int. Ophthalmol. Clin. 43, 63–77 (2003).
[Crossref]

2002 (5)

2001 (1)

J. S. McLellan, S. Marcos, and S. A. Burns, “Age-related changes in monochromatic wave aberrations of the human eye,” Invest. Ophthalmol. Visual Sci. 42, 1390–1395 (2001).

1996 (2)

M. Bach, “The Freiburg visual acuity test—automatic measurement of visual acuity,” Optom. Vis. Sci. 73, 49–53 (1996).
[Crossref]

R. L. Woods, A. Bradley, and D. A. Atchison, “Consequences of monocular diplopia for the contrast sensitivity function,” Vis. Res. 36, 3587–3596 (1996).
[Crossref]

1994 (3)

B. Winn, D. Whitaker, D. B. Elliott, and N. J. Phillips, “Factors affecting light-adapted pupil size in normal human subjects,” Invest. Ophthalmol. Vis. Sci. 35, 1132–1137 (1994).

J. Rovamo, J. Mustonen, and R. Nasanen, “Modelling contrast sensitivity as a function of retinal illuminance and grating area,” Vis. Res. 34, 1301–1314 (1994).
[Crossref]

P. Artal and 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]

1992 (2)

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
[Crossref]

S. B. Laughlin, “Retinal information capacity and the function of the pupil,” Ophthalmic Physiolog. Opt. 12, 161–164 (1992).
[Crossref]

1990 (1)

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

1987 (1)

M. S. Banks, W. S. Geisler, and P. J. Bennett, “The physical limits of grating visibility,” Vis. Res. 27, 1915–1924 (1987).
[Crossref]

1985 (1)

D. G. Pelli and L. C. Applegate, “The visual requirements of mobility,” Perception 14, 19–29 (1985).
[Crossref]

1983 (1)

A. B. Watson and D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Precept. Psychophys. 33, 113–120 (1983).
[Crossref]

1982 (1)

G. Smith, “Angular diameter of defocus blur discs,” Am. J. Optom. Physiolog. Opt. 59, 885–889 (1982).
[Crossref]

1979 (2)

D. A. Atchison, G. Smith, and N. Efron, “The effect of pupil size on visual acuity in uncorrected and corrected myopia,” Am. J. Optom. Physiolog. Opt. 56, 315–323 (1979).
[Crossref]

L. N. Thibos, W. R. Levick, and T. E. Cohn, “Receiver operating characteristic curves for Poisson signals,” Biol. Cybern. 33, 57–61 (1979).
[Crossref]

1975 (3)

A. T. Bahill, M. R. Clark, and L. Stark, “The main sequence, a tool for studying human eye movements,” Math. Biosci. 24, 191–204 (1975).
[Crossref]

J. Tucker and W. N. Charman, “The depth-of-focus of the human eye for Snellen letters,” Am. J. Optom. Physiolog. Opt. 52, 3–21 (1975).
[Crossref]

J. M. Woodhouse, “The effect of pupil size on grating detection at various contrast levels,” Vis. Res. 15, 645–648 (1975).
[Crossref]

1974 (2)

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

T. E. Cohn, L. N. Thibos, and R. N. Kleinstein, “Detectability of a luminance increment,” J. Opt. Soc. Am. 64, 1321–1327 (1974).
[Crossref]

1972 (1)

A. Van Meeteren and J. J. Vos, “Resolution and contrast sensitivity at low luminances,” Vis. Res. 12, 825–833 (1972).
[Crossref]

1967 (1)

1965 (1)

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

1960 (1)

F. W. Campbell and A. H. Gregory, “Effect of size of pupil on visual acuity,” Nature 187, 1121–1123 (1960).
[Crossref]

1943 (1)

H. L. de Vries, “The quantum character of light and its bearing upon threshold of vision, the differential sensitivity and visual acuity of the eye,” Physica 10, 553–564 (1943).
[Crossref]

Anderson, H. A.

H. A. Anderson, G. Hentz, A. Glasser, K. K. Stuebing, and R. E. Manny, “Minus-lens-stimulated accommodative amplitude decreases sigmoidally with age: a study of objectively measured accommodative amplitudes from age 3,” Invest. Ophthalmol. Visual Sci. 49, 2919–2926 (2008).
[Crossref]

Applegate, L. C.

D. G. Pelli and L. C. Applegate, “The visual requirements of mobility,” Perception 14, 19–29 (1985).
[Crossref]

Applegate, R. A.

A. Ravikumar, J. D. Marsack, H. E. Bedell, Y. Shi, and R. A. Applegate, “Change in visual acuity is well correlated with change in image-quality metrics for both normal and keratoconic wavefront errors,” J. Vis. 13(13), 28 (2013).
[Crossref]

A. Ravikumar, E. J. Sarver, and R. A. Applegate, “Change in visual acuity is highly correlated with change in six image quality metrics independent of wavefront error and/or pupil diameter,” J. Vis. 12(10), 11 (2012).
[Crossref]

R. A. Applegate, J. D. Marsack, and L. N. Thibos, “Metrics of retinal image quality predict visual performance in eyes with 20/17 or better visual acuity,” Optom. Vis. Sci. 83, 635–640 (2006).
[Crossref]

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 329–351 (2004).
[Crossref]

Artal, P.

P. Artal, A. Guirao, E. Berrio, P. Piers, and S. Norrby, “Optical aberrations and the aging eye,” Int. Ophthalmol. Clin. 43, 63–77 (2003).
[Crossref]

P. Artal and 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]

Atchison, D. A.

R. L. Woods, A. Bradley, and D. A. Atchison, “Consequences of monocular diplopia for the contrast sensitivity function,” Vis. Res. 36, 3587–3596 (1996).
[Crossref]

D. A. Atchison, G. Smith, and N. Efron, “The effect of pupil size on visual acuity in uncorrected and corrected myopia,” Am. J. Optom. Physiolog. Opt. 56, 315–323 (1979).
[Crossref]

Bach, M.

M. Bach, “The Freiburg visual acuity test—automatic measurement of visual acuity,” Optom. Vis. Sci. 73, 49–53 (1996).
[Crossref]

Bahill, A. T.

A. T. Bahill, M. R. Clark, and L. Stark, “The main sequence, a tool for studying human eye movements,” Math. Biosci. 24, 191–204 (1975).
[Crossref]

Banks, M. S.

M. S. Banks, W. S. Geisler, and P. J. Bennett, “The physical limits of grating visibility,” Vis. Res. 27, 1915–1924 (1987).
[Crossref]

Bedell, H. E.

A. Ravikumar, J. D. Marsack, H. E. Bedell, Y. Shi, and R. A. Applegate, “Change in visual acuity is well correlated with change in image-quality metrics for both normal and keratoconic wavefront errors,” J. Vis. 13(13), 28 (2013).
[Crossref]

Begley, C. G.

N. L. Himebaugh, L. N. Thibos, A. Bradley, G. Wilson, and C. G. Begley, “Predicting optical effects of tear film break up on retinal image quality using the Shack–Hartmann aberrometer and computational optical modeling,” Adv. Exp. Med. Biol. 506, 1141–1147 (2002).
[Crossref]

Bennett, P. J.

M. S. Banks, W. S. Geisler, and P. J. Bennett, “The physical limits of grating visibility,” Vis. Res. 27, 1915–1924 (1987).
[Crossref]

Berrio, E.

P. Artal, A. Guirao, E. Berrio, P. Piers, and S. Norrby, “Optical aberrations and the aging eye,” Int. Ophthalmol. Clin. 43, 63–77 (2003).
[Crossref]

Bingham, G. P.

J. S. Pan and G. P. Bingham, “With an eye to low vision: optic flow enables perception despite image blur,” Optom. Vis. Sci. 90, 1119–1127 (2013).
[Crossref]

Bouman, M. A.

Bradley, A.

R. Xu, D. Gil, M. Dibas, W. Hare, and A. Bradley, “The effect of light level and small pupils on presbyopic reading performance,” Invest. Ophthalmol. Visual Sci. 57, 5656–5664 (2016).
[Crossref]

R. Xu, L. Thibos, and A. Bradley, “Effect of target luminance on optimum pupil diameter for presbyopic eyes,” Optom. Vis. Sci. 93, 1409–1419 (2016).
[Crossref]

R. Xu, A. Bradley, N. Lopez-Gil, and L. N. Thibos, “Modelling the effects of secondary spherical aberration on refractive error, image quality and depth of focus,” Ophthal. Physiolog. Opt. 35, 28–38 (2015).
[Crossref]

A. Bradley, R. Xu, L. Thibos, G. Marin, and M. Hernandez, “Influence of spherical aberration, stimulus spatial frequency, and pupil apodisation on subjective refractions,” Ophthalmic Physiolog. Opt. 34, 309–320 (2014).
[Crossref]

A. Bradley, J. Nam, R. Xu, L. Harman, and L. Thibos, “Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality,” Ophthalmic Physiolog. Opt. 34, 331–345 (2014).
[Crossref]

S. Ravikumar, A. Bradley, and L. Thibos, “Phase changes induced by optical aberrations degrade letter and face acuity,” J. Vis. 10(14), 18 (2010).
[Crossref]

X. Cheng, A. Bradley, S. Ravikumar, and L. N. Thibos, “Visual impact of Zernike and Seidel forms of monochromatic aberrations,” Optom. Vis. Sci. 87, 300–312 (2010).
[Crossref]

S. Ravikumar, L. N. Thibos, and A. Bradley, “Calculation of retinal image quality for polychromatic light,” J. Opt. Soc. Am. A 25, 2395–2407 (2008).
[Crossref]

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 329–351 (2004).
[Crossref]

X. Cheng, A. Bradley, and L. N. Thibos, “Predicting subjective judgment of best focus with objective image quality metrics,” J. Vis. 4(4), 310 (2004).
[Crossref]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19, 2329–2348 (2002).
[Crossref]

N. L. Himebaugh, L. N. Thibos, A. Bradley, G. Wilson, and C. G. Begley, “Predicting optical effects of tear film break up on retinal image quality using the Shack–Hartmann aberrometer and computational optical modeling,” Adv. Exp. Med. Biol. 506, 1141–1147 (2002).
[Crossref]

R. L. Woods, A. Bradley, and D. A. Atchison, “Consequences of monocular diplopia for the contrast sensitivity function,” Vis. Res. 36, 3587–3596 (1996).
[Crossref]

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
[Crossref]

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

Burns, S. A.

J. S. McLellan, S. Marcos, and S. A. Burns, “Age-related changes in monochromatic wave aberrations of the human eye,” Invest. Ophthalmol. Visual Sci. 42, 1390–1395 (2001).

Campbell, F. W.

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

F. W. Campbell and A. H. Gregory, “Effect of size of pupil on visual acuity,” Nature 187, 1121–1123 (1960).
[Crossref]

Charman, W. N.

J. Tucker and W. N. Charman, “The depth-of-focus of the human eye for Snellen letters,” Am. J. Optom. Physiolog. Opt. 52, 3–21 (1975).
[Crossref]

Cheng, X.

X. Cheng, A. Bradley, S. Ravikumar, and L. N. Thibos, “Visual impact of Zernike and Seidel forms of monochromatic aberrations,” Optom. Vis. Sci. 87, 300–312 (2010).
[Crossref]

X. Cheng, A. Bradley, and L. N. Thibos, “Predicting subjective judgment of best focus with objective image quality metrics,” J. Vis. 4(4), 310 (2004).
[Crossref]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19, 2329–2348 (2002).
[Crossref]

Clark, M. R.

A. T. Bahill, M. R. Clark, and L. Stark, “The main sequence, a tool for studying human eye movements,” Math. Biosci. 24, 191–204 (1975).
[Crossref]

Cohn, T. E.

L. N. Thibos, W. R. Levick, and T. E. Cohn, “Receiver operating characteristic curves for Poisson signals,” Biol. Cybern. 33, 57–61 (1979).
[Crossref]

T. E. Cohn, L. N. Thibos, and R. N. Kleinstein, “Detectability of a luminance increment,” J. Opt. Soc. Am. 64, 1321–1327 (1974).
[Crossref]

Cox, I. G.

de Vries, H. L.

H. L. de Vries, “The quantum character of light and its bearing upon threshold of vision, the differential sensitivity and visual acuity of the eye,” Physica 10, 553–564 (1943).
[Crossref]

Dexl, A. K.

A. K. Dexl, O. Seyeddain, W. Riha, M. Hohensinn, T. Ruckl, W. Hitzl, and G. Grabner, “Reading performance after implantation of a modified corneal inlay design for the surgical correction of presbyopia: 1-year follow-up,” Am. J. Ophthalmol. 153, 994–1001 (2012).
[Crossref]

Dibas, M.

R. Xu, D. Gil, M. Dibas, W. Hare, and A. Bradley, “The effect of light level and small pupils on presbyopic reading performance,” Invest. Ophthalmol. Visual Sci. 57, 5656–5664 (2016).
[Crossref]

Efron, N.

D. A. Atchison, G. Smith, and N. Efron, “The effect of pupil size on visual acuity in uncorrected and corrected myopia,” Am. J. Optom. Physiolog. Opt. 56, 315–323 (1979).
[Crossref]

Elliott, D. B.

B. Winn, D. Whitaker, D. B. Elliott, and N. J. Phillips, “Factors affecting light-adapted pupil size in normal human subjects,” Invest. Ophthalmol. Vis. Sci. 35, 1132–1137 (1994).

Ferrer-Blasco, T.

S. Garcia-Lazaro, T. Ferrer-Blasco, and H. Radhakrishnan, “Visual function through 4 contact lens-based pinhole systems for presbyopia,” J. Cataract Refractive Surg. 38, 858–865 (2012).
[Crossref]

Garcia-Lazaro, S.

S. Garcia-Lazaro, T. Ferrer-Blasco, and H. Radhakrishnan, “Visual function through 4 contact lens-based pinhole systems for presbyopia,” J. Cataract Refractive Surg. 38, 858–865 (2012).
[Crossref]

Geisler, W. S.

M. S. Banks, W. S. Geisler, and P. J. Bennett, “The physical limits of grating visibility,” Vis. Res. 27, 1915–1924 (1987).
[Crossref]

Gil, D.

R. Xu, D. Gil, M. Dibas, W. Hare, and A. Bradley, “The effect of light level and small pupils on presbyopic reading performance,” Invest. Ophthalmol. Visual Sci. 57, 5656–5664 (2016).
[Crossref]

Ginis, H. S.

M. Kilintari, A. Pallikaris, N. Tsiklis, and H. S. Ginis, “Evaluation of image quality metrics for the prediction of subjective best focus,” Optom. Vis. Sci. 87, 183–189 (2010).
[Crossref]

Glasser, A.

H. A. Anderson, G. Hentz, A. Glasser, K. K. Stuebing, and R. E. Manny, “Minus-lens-stimulated accommodative amplitude decreases sigmoidally with age: a study of objectively measured accommodative amplitudes from age 3,” Invest. Ophthalmol. Visual Sci. 49, 2919–2926 (2008).
[Crossref]

D. M. Win-Hall, L. A. Ostrin, S. Kasthurirangan, and A. Glasser, “Objective accommodation measurement with the Grand Seiko and Hartinger coincidence refractometer,” Optom. Vis. Sci. 84, 879–887 (2007).
[Crossref]

Grabner, G.

A. K. Dexl, O. Seyeddain, W. Riha, M. Hohensinn, T. Ruckl, W. Hitzl, and G. Grabner, “Reading performance after implantation of a modified corneal inlay design for the surgical correction of presbyopia: 1-year follow-up,” Am. J. Ophthalmol. 153, 994–1001 (2012).
[Crossref]

Green, D. G.

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

Gregory, A. H.

F. W. Campbell and A. H. Gregory, “Effect of size of pupil on visual acuity,” Nature 187, 1121–1123 (1960).
[Crossref]

Guirao, A.

Hare, W.

R. Xu, D. Gil, M. Dibas, W. Hare, and A. Bradley, “The effect of light level and small pupils on presbyopic reading performance,” Invest. Ophthalmol. Visual Sci. 57, 5656–5664 (2016).
[Crossref]

Harman, L.

A. Bradley, J. Nam, R. Xu, L. Harman, and L. Thibos, “Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality,” Ophthalmic Physiolog. Opt. 34, 331–345 (2014).
[Crossref]

Hentz, G.

H. A. Anderson, G. Hentz, A. Glasser, K. K. Stuebing, and R. E. Manny, “Minus-lens-stimulated accommodative amplitude decreases sigmoidally with age: a study of objectively measured accommodative amplitudes from age 3,” Invest. Ophthalmol. Visual Sci. 49, 2919–2926 (2008).
[Crossref]

Hernandez, M.

A. Bradley, R. Xu, L. Thibos, G. Marin, and M. Hernandez, “Influence of spherical aberration, stimulus spatial frequency, and pupil apodisation on subjective refractions,” Ophthalmic Physiolog. Opt. 34, 309–320 (2014).
[Crossref]

Hickenbotham, A.

A. Hickenbotham, P. Tiruveedhula, and A. Roorda, “Comparison of spherical aberration and small-pupil profiles in improving depth of focus for presbyopic corrections,” J. Cataract Refractive Surg. 38, 2071–2079 (2012).
[Crossref]

Himebaugh, N. L.

N. L. Himebaugh, L. N. Thibos, A. Bradley, G. Wilson, and C. G. Begley, “Predicting optical effects of tear film break up on retinal image quality using the Shack–Hartmann aberrometer and computational optical modeling,” Adv. Exp. Med. Biol. 506, 1141–1147 (2002).
[Crossref]

Hitzl, W.

A. K. Dexl, O. Seyeddain, W. Riha, M. Hohensinn, T. Ruckl, W. Hitzl, and G. Grabner, “Reading performance after implantation of a modified corneal inlay design for the surgical correction of presbyopia: 1-year follow-up,” Am. J. Ophthalmol. 153, 994–1001 (2012).
[Crossref]

Hohensinn, M.

A. K. Dexl, O. Seyeddain, W. Riha, M. Hohensinn, T. Ruckl, W. Hitzl, and G. Grabner, “Reading performance after implantation of a modified corneal inlay design for the surgical correction of presbyopia: 1-year follow-up,” Am. J. Ophthalmol. 153, 994–1001 (2012).
[Crossref]

Hong, X.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 329–351 (2004).
[Crossref]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19, 2329–2348 (2002).
[Crossref]

Howarth, P. A.

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

Kasthurirangan, S.

D. M. Win-Hall, L. A. Ostrin, S. Kasthurirangan, and A. Glasser, “Objective accommodation measurement with the Grand Seiko and Hartinger coincidence refractometer,” Optom. Vis. Sci. 84, 879–887 (2007).
[Crossref]

Kilintari, M.

M. Kilintari, A. Pallikaris, N. Tsiklis, and H. S. Ginis, “Evaluation of image quality metrics for the prediction of subjective best focus,” Optom. Vis. Sci. 87, 183–189 (2010).
[Crossref]

Kleinstein, R. N.

Laughlin, S. B.

S. B. Laughlin, “Retinal information capacity and the function of the pupil,” Ophthalmic Physiolog. Opt. 12, 161–164 (1992).
[Crossref]

Levick, W. R.

L. N. Thibos, W. R. Levick, and T. E. Cohn, “Receiver operating characteristic curves for Poisson signals,” Biol. Cybern. 33, 57–61 (1979).
[Crossref]

Lopez-Gil, N.

R. Xu, A. Bradley, N. Lopez-Gil, and L. N. Thibos, “Modelling the effects of secondary spherical aberration on refractive error, image quality and depth of focus,” Ophthal. Physiolog. Opt. 35, 28–38 (2015).
[Crossref]

Manny, R. E.

H. A. Anderson, G. Hentz, A. Glasser, K. K. Stuebing, and R. E. Manny, “Minus-lens-stimulated accommodative amplitude decreases sigmoidally with age: a study of objectively measured accommodative amplitudes from age 3,” Invest. Ophthalmol. Visual Sci. 49, 2919–2926 (2008).
[Crossref]

Marcos, S.

J. S. McLellan, S. Marcos, and S. A. Burns, “Age-related changes in monochromatic wave aberrations of the human eye,” Invest. Ophthalmol. Visual Sci. 42, 1390–1395 (2001).

Marin, G.

A. Bradley, R. Xu, L. Thibos, G. Marin, and M. Hernandez, “Influence of spherical aberration, stimulus spatial frequency, and pupil apodisation on subjective refractions,” Ophthalmic Physiolog. Opt. 34, 309–320 (2014).
[Crossref]

Marsack, J. D.

A. Ravikumar, J. D. Marsack, H. E. Bedell, Y. Shi, and R. A. Applegate, “Change in visual acuity is well correlated with change in image-quality metrics for both normal and keratoconic wavefront errors,” J. Vis. 13(13), 28 (2013).
[Crossref]

R. A. Applegate, J. D. Marsack, and L. N. Thibos, “Metrics of retinal image quality predict visual performance in eyes with 20/17 or better visual acuity,” Optom. Vis. Sci. 83, 635–640 (2006).
[Crossref]

McLellan, J. S.

J. S. McLellan, S. Marcos, and S. A. Burns, “Age-related changes in monochromatic wave aberrations of the human eye,” Invest. Ophthalmol. Visual Sci. 42, 1390–1395 (2001).

Mustonen, J.

J. Rovamo, J. Mustonen, and R. Nasanen, “Modelling contrast sensitivity as a function of retinal illuminance and grating area,” Vis. Res. 34, 1301–1314 (1994).
[Crossref]

Nam, J.

A. Bradley, J. Nam, R. Xu, L. Harman, and L. Thibos, “Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality,” Ophthalmic Physiolog. Opt. 34, 331–345 (2014).
[Crossref]

Nasanen, R.

J. Rovamo, J. Mustonen, and R. Nasanen, “Modelling contrast sensitivity as a function of retinal illuminance and grating area,” Vis. Res. 34, 1301–1314 (1994).
[Crossref]

Navarro, R.

Norrby, S.

P. Artal, A. Guirao, E. Berrio, P. Piers, and S. Norrby, “Optical aberrations and the aging eye,” Int. Ophthalmol. Clin. 43, 63–77 (2003).
[Crossref]

Ostrin, L. A.

D. M. Win-Hall, L. A. Ostrin, S. Kasthurirangan, and A. Glasser, “Objective accommodation measurement with the Grand Seiko and Hartinger coincidence refractometer,” Optom. Vis. Sci. 84, 879–887 (2007).
[Crossref]

Pallikaris, A.

M. Kilintari, A. Pallikaris, N. Tsiklis, and H. S. Ginis, “Evaluation of image quality metrics for the prediction of subjective best focus,” Optom. Vis. Sci. 87, 183–189 (2010).
[Crossref]

Pan, J. S.

J. S. Pan and G. P. Bingham, “With an eye to low vision: optic flow enables perception despite image blur,” Optom. Vis. Sci. 90, 1119–1127 (2013).
[Crossref]

Pelli, D. G.

D. G. Pelli and L. C. Applegate, “The visual requirements of mobility,” Perception 14, 19–29 (1985).
[Crossref]

A. B. Watson and D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Precept. Psychophys. 33, 113–120 (1983).
[Crossref]

Phillips, N. J.

B. Winn, D. Whitaker, D. B. Elliott, and N. J. Phillips, “Factors affecting light-adapted pupil size in normal human subjects,” Invest. Ophthalmol. Vis. Sci. 35, 1132–1137 (1994).

Piers, P.

P. Artal, A. Guirao, E. Berrio, P. Piers, and S. Norrby, “Optical aberrations and the aging eye,” Int. Ophthalmol. Clin. 43, 63–77 (2003).
[Crossref]

Porter, J.

Powell, R.

R. Powell, The Hertzsprung Russell Diagram, An Atlas of the Universe (2006), http://www.atlasoftheuniverse.com/hr.html .

Radhakrishnan, H.

S. Garcia-Lazaro, T. Ferrer-Blasco, and H. Radhakrishnan, “Visual function through 4 contact lens-based pinhole systems for presbyopia,” J. Cataract Refractive Surg. 38, 858–865 (2012).
[Crossref]

Ravikumar, A.

A. Ravikumar, J. D. Marsack, H. E. Bedell, Y. Shi, and R. A. Applegate, “Change in visual acuity is well correlated with change in image-quality metrics for both normal and keratoconic wavefront errors,” J. Vis. 13(13), 28 (2013).
[Crossref]

A. Ravikumar, E. J. Sarver, and R. A. Applegate, “Change in visual acuity is highly correlated with change in six image quality metrics independent of wavefront error and/or pupil diameter,” J. Vis. 12(10), 11 (2012).
[Crossref]

Ravikumar, S.

S. Ravikumar, A. Bradley, and L. Thibos, “Phase changes induced by optical aberrations degrade letter and face acuity,” J. Vis. 10(14), 18 (2010).
[Crossref]

X. Cheng, A. Bradley, S. Ravikumar, and L. N. Thibos, “Visual impact of Zernike and Seidel forms of monochromatic aberrations,” Optom. Vis. Sci. 87, 300–312 (2010).
[Crossref]

S. Ravikumar, L. N. Thibos, and A. Bradley, “Calculation of retinal image quality for polychromatic light,” J. Opt. Soc. Am. A 25, 2395–2407 (2008).
[Crossref]

Riha, W.

A. K. Dexl, O. Seyeddain, W. Riha, M. Hohensinn, T. Ruckl, W. Hitzl, and G. Grabner, “Reading performance after implantation of a modified corneal inlay design for the surgical correction of presbyopia: 1-year follow-up,” Am. J. Ophthalmol. 153, 994–1001 (2012).
[Crossref]

Roorda, A.

A. Hickenbotham, P. Tiruveedhula, and A. Roorda, “Comparison of spherical aberration and small-pupil profiles in improving depth of focus for presbyopic corrections,” J. Cataract Refractive Surg. 38, 2071–2079 (2012).
[Crossref]

Rovamo, J.

J. Rovamo, J. Mustonen, and R. Nasanen, “Modelling contrast sensitivity as a function of retinal illuminance and grating area,” Vis. Res. 34, 1301–1314 (1994).
[Crossref]

Ruckl, T.

A. K. Dexl, O. Seyeddain, W. Riha, M. Hohensinn, T. Ruckl, W. Hitzl, and G. Grabner, “Reading performance after implantation of a modified corneal inlay design for the surgical correction of presbyopia: 1-year follow-up,” Am. J. Ophthalmol. 153, 994–1001 (2012).
[Crossref]

Sarver, E. J.

A. Ravikumar, E. J. Sarver, and R. A. Applegate, “Change in visual acuity is highly correlated with change in six image quality metrics independent of wavefront error and/or pupil diameter,” J. Vis. 12(10), 11 (2012).
[Crossref]

Schwiegerling, J.

Seyeddain, O.

A. K. Dexl, O. Seyeddain, W. Riha, M. Hohensinn, T. Ruckl, W. Hitzl, and G. Grabner, “Reading performance after implantation of a modified corneal inlay design for the surgical correction of presbyopia: 1-year follow-up,” Am. J. Ophthalmol. 153, 994–1001 (2012).
[Crossref]

Shi, Y.

A. Ravikumar, J. D. Marsack, H. E. Bedell, Y. Shi, and R. A. Applegate, “Change in visual acuity is well correlated with change in image-quality metrics for both normal and keratoconic wavefront errors,” J. Vis. 13(13), 28 (2013).
[Crossref]

Smith, G.

G. Smith, “Angular diameter of defocus blur discs,” Am. J. Optom. Physiolog. Opt. 59, 885–889 (1982).
[Crossref]

D. A. Atchison, G. Smith, and N. Efron, “The effect of pupil size on visual acuity in uncorrected and corrected myopia,” Am. J. Optom. Physiolog. Opt. 56, 315–323 (1979).
[Crossref]

Stark, L.

A. T. Bahill, M. R. Clark, and L. Stark, “The main sequence, a tool for studying human eye movements,” Math. Biosci. 24, 191–204 (1975).
[Crossref]

Still, D. L.

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

Stuebing, K. K.

H. A. Anderson, G. Hentz, A. Glasser, K. K. Stuebing, and R. E. Manny, “Minus-lens-stimulated accommodative amplitude decreases sigmoidally with age: a study of objectively measured accommodative amplitudes from age 3,” Invest. Ophthalmol. Visual Sci. 49, 2919–2926 (2008).
[Crossref]

Thibos, L.

R. Xu, L. Thibos, and A. Bradley, “Effect of target luminance on optimum pupil diameter for presbyopic eyes,” Optom. Vis. Sci. 93, 1409–1419 (2016).
[Crossref]

A. Bradley, R. Xu, L. Thibos, G. Marin, and M. Hernandez, “Influence of spherical aberration, stimulus spatial frequency, and pupil apodisation on subjective refractions,” Ophthalmic Physiolog. Opt. 34, 309–320 (2014).
[Crossref]

A. Bradley, J. Nam, R. Xu, L. Harman, and L. Thibos, “Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality,” Ophthalmic Physiolog. Opt. 34, 331–345 (2014).
[Crossref]

S. Ravikumar, A. Bradley, and L. Thibos, “Phase changes induced by optical aberrations degrade letter and face acuity,” J. Vis. 10(14), 18 (2010).
[Crossref]

Thibos, L. N.

R. Xu, A. Bradley, N. Lopez-Gil, and L. N. Thibos, “Modelling the effects of secondary spherical aberration on refractive error, image quality and depth of focus,” Ophthal. Physiolog. Opt. 35, 28–38 (2015).
[Crossref]

X. Cheng, A. Bradley, S. Ravikumar, and L. N. Thibos, “Visual impact of Zernike and Seidel forms of monochromatic aberrations,” Optom. Vis. Sci. 87, 300–312 (2010).
[Crossref]

S. Ravikumar, L. N. Thibos, and A. Bradley, “Calculation of retinal image quality for polychromatic light,” J. Opt. Soc. Am. A 25, 2395–2407 (2008).
[Crossref]

R. A. Applegate, J. D. Marsack, and L. N. Thibos, “Metrics of retinal image quality predict visual performance in eyes with 20/17 or better visual acuity,” Optom. Vis. Sci. 83, 635–640 (2006).
[Crossref]

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 329–351 (2004).
[Crossref]

X. Cheng, A. Bradley, and L. N. Thibos, “Predicting subjective judgment of best focus with objective image quality metrics,” J. Vis. 4(4), 310 (2004).
[Crossref]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19, 2329–2348 (2002).
[Crossref]

N. L. Himebaugh, L. N. Thibos, A. Bradley, G. Wilson, and C. G. Begley, “Predicting optical effects of tear film break up on retinal image quality using the Shack–Hartmann aberrometer and computational optical modeling,” Adv. Exp. Med. Biol. 506, 1141–1147 (2002).
[Crossref]

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
[Crossref]

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

L. N. Thibos, W. R. Levick, and T. E. Cohn, “Receiver operating characteristic curves for Poisson signals,” Biol. Cybern. 33, 57–61 (1979).
[Crossref]

T. E. Cohn, L. N. Thibos, and R. N. Kleinstein, “Detectability of a luminance increment,” J. Opt. Soc. Am. 64, 1321–1327 (1974).
[Crossref]

Tiruveedhula, P.

A. Hickenbotham, P. Tiruveedhula, and A. Roorda, “Comparison of spherical aberration and small-pupil profiles in improving depth of focus for presbyopic corrections,” J. Cataract Refractive Surg. 38, 2071–2079 (2012).
[Crossref]

Tsiklis, N.

M. Kilintari, A. Pallikaris, N. Tsiklis, and H. S. Ginis, “Evaluation of image quality metrics for the prediction of subjective best focus,” Optom. Vis. Sci. 87, 183–189 (2010).
[Crossref]

Tucker, J.

J. Tucker and W. N. Charman, “The depth-of-focus of the human eye for Snellen letters,” Am. J. Optom. Physiolog. Opt. 52, 3–21 (1975).
[Crossref]

Van Meeteren, A.

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

A. Van Meeteren and J. J. Vos, “Resolution and contrast sensitivity at low luminances,” Vis. Res. 12, 825–833 (1972).
[Crossref]

Van Nes, F. L.

Vos, J. J.

A. Van Meeteren and J. J. Vos, “Resolution and contrast sensitivity at low luminances,” Vis. Res. 12, 825–833 (1972).
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Figures (9)

Fig. 1.
Fig. 1. Neural CSFs for different retinal illuminances (0.9, 9, 90, 500, 900, and 9000 td). Note the 900 and 9000 td superimpose.
Fig. 2.
Fig. 2. VSOTF is plotted as a function of pupil diameter for geometrical (red filled symbols) and WO (black open symbols) at fixed retinal illuminances of 900 td (A) and 0.9 td (B) for four optical scenarios: diffraction-limited optics (circles), monochromatic aberrations only (squares), chromatic aberrations only (triangles), and both monochromatic and chromatic aberrations (diamonds). Values of VSOTF are for the optimally focused eye normalized to the monochromatic diffraction-limited 3 mm pupil case.
Fig. 3.
Fig. 3. VSOTFs are plotted as a function of pupil diameter in mm for three fixed luminance levels: 2000 (black open circles), 10 (black open squares) and 1    cd / m 2 (black open triangles). For comparison, we also plot VSOTF at a fixed retinal illuminance level of 0.9 td (red thick line), and the SROTF is shown in blue filled squares.
Fig. 4.
Fig. 4. Sample through-focus plots of polychromatic area MTF (A) and (B) and VSOTF (C) and (D) are plotted for our presbyopic eye model for a series of pupil diameters (1 to 7 mm) for high photopic [ 1000    cd / m 2 , (A) and (C)] and low mesopic [ 0.1    cd / m 2 , (B) and (D)] luminances. Absolute metric values are normalized to the best polychromatic IQ at 7068 td ( 1000    cd / m 2 ) for a 3 mm pupil that generated denominators of 22.97 for area MTF, 900.51 for VSOTF.
Fig. 5.
Fig. 5. Impact of pupil size on VSOTF IQ is plotted for three defocus levels (0, 1 , and 2 diopters, black, blue, and red, respectively) and three luminance levels [1000 (A), 20 (B), and 0.1 (C) cd / m 2 ].
Fig. 6.
Fig. 6. Polychromatic VSOTF is plotted as a function of retinal illuminance in Trolands for three defocus levels: 0 D (A); 1    D  (B); and 2    D  (C). Retinal illuminance was manipulated by using five stimulus luminances (1000, 100, 10, 1, 0.1    cd / m 2 ), producing five sets of data for each defocus level. Also, retinal illuminance was varied by varying pupil size (1, 1.2, 1.6, 2, 3, 4, 5, 6, and 7 mm), which generated the sets of nine data points connected by lines. The red solid lines with a slope of + 0.5 and black dashed line with a slope of 0 represent the photon noise slope prediction and Weber’s law prediction, respectively. The right-most data point in each series is for the 7 mm pupils, and the left most data points for 1 mm pupils. A VSOTF equal to 1.0 is the maximum anticipated value obtained for well-focused retinal images of high retinal illuminance (7068 td) formed through an optimum (3 mm) pupil. The solid line with slope = 0.5 was fit by eye to the upper left-most symbols in each data set. This reference line serves as an outer envelope for the data, while simultaneously indicating the anticipated behavior of VSOTF in the de Vries–Rose domain, where photon noise causes CS to be proportional to the square root of retinal illuminance. The intersection of these two reference lines occurs at retinal illuminance = 500  td, which mirrors the transition illuminance (between 90 and 900 td) from Weber’s law to de Vries–Rose law reported in the literature [11,13].
Fig. 7.
Fig. 7. NVC computed at 5 cpd (A) and CS at 5 cpd (B) and (C) are plotted as a function of retinal illuminance for focused (black squares) and 2    D defocused (red triangles) grating stimuli, at three luminance levels (0.2, 20, 2000    cd / m 2 ) for a series of pupil diameters (see text for the detailed pupil sizes), illustrated as sets of data points connected by lines. Two lines with slopes of + 0.5 and 0 are photon noise and Weber’s law predictions, respectively. The range of retinal illuminance levels within each group in (A) sequentially reflects 10 varying pupil sizes (1, 1.2, 1.6, 2, 2.6, 3, 4, 5, 6, and 7 mm), and similarly eight pupil sizes (1, 1.3, 1.6, 2, 2.5, 3, 4, and 6 mm) for the first subject in (B) and nine pupil sizes (1, 1.3, 1.6, 2, 2.5, 3, 4, 6, and 7 mm) for the second subject in (C). The model simulation in (A) has a + 0.6    μm spherical aberration of a 7 mm pupil, which is close to the SA of our two presbyopic subjects [9].
Fig. 8.
Fig. 8. Effect of retinal illuminance on retinal IQ metric VSOTF for three optical models. Dashed reference line has slope 0.5 (pupil diameter = 3    mm ).
Fig. 9.
Fig. 9. Effect of luminance on retinal IQ metric VSOTF for 7 mm (blue filled circles), 1.6 mm (black open triangles), optimum pupils (blue open circles) and natural pupils (red filled squares) at six luminance levels (0.1, 1, 10, 20, 100, and 1000    cd / m 2 ). Natural pupil diameters were 7 mm, 7 mm, 6 mm, 6 mm, 5 mm, and 4 mm for 0.1, 1, 10, 20, 100, and 1000 cd / m 2 , respectively [26].

Tables (1)

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Table 1. Third- through Sixth-Order Zernike Aberration Coefficients (ANSI Standard Convention) for a 7 mm Pupil Used in Our Model a

Equations (4)

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VSOTF = NCSF L ( f x , f y ) · OTF Poly ( f x , f y ) d f x d f y NCSF 7 K T d ( f x , f y ) · OTF Ref ( f x , f y ) d f x d f y ,
AreaMTF = r MTF Poly ( ρ ) d ρ NT L ( ρ ) d ρ r MTF Ref ( ρ ) d ρ NT 7 K T d ( ρ ) d ρ ,
SROTF = OTF Poly ( f x , f y ) d f x d f y OTF Ref ( f x , f y ) d f x d f y .
NVC = NCSF L ( f ) · r MTF Poly ( f ) NCSF 7 K T d ( f ) · r MTF Ref ( f ) .

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