Abstract

Although the retinal image is typically polychromatic, few studies have examined polychromatic image quality in the human eye. We begin with a conceptual framework including the formulation of a psychophysical linking hypothesis that underlies the utility of image quality metrics based on the polychromatic point-spread function. We then outline strategies for computing polychromatic point-spread functions of the eye when monochromatic aberrations are known for only a single wavelength. Implementation problems and solutions for this strategy are described. Polychromatic image quality is largely unaffected by wavelength-dependent diffraction and higher-order chromatic aberration. However, accuracy is found to depend critically upon spectral sampling. Using typical aberrations from the Indiana Aberration Study, we assessed through-focus image quality for model eyes with and without chromatic aberrations using a polychromatic metric called the visual Strehl ratio. In the presence of typical levels of monochromatic aberrations, the effect of longitudinal chromatic aberration is greatly reduced. The effect of typical levels of transverse chromatic aberration is virtually eliminated in the presence of longitudinal chromatic aberration and monochromatic aberrations. Clinical value and limitations of the method are discussed.

© 2008 Optical Society of America

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2007 (1)

2006 (4)

E. J. Fernández, A. Unterhuber, B. Považay, B. Hermann, P. Artal, and W. Drexler, “Chromatic aberration correction of the human eye for retinal imaging in the near infrared,” Opt. Express 14, 6213-6225 (2006).
[CrossRef] [PubMed]

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. Vision Sci. 83, 635-640 (2006).
[CrossRef]

S. Ravikumar, A. Bradley, and L. N. Thibos, “Do monochromatic aberrations protect the eye against chromatic blur?” Invest. Ophthalmol. Visual Sci. 47, E-Abstract 1505 (2006).

T. Yamaguchi, K. Negishi, T. Noda, K. Fujiiki, K. Tsubota, and K. Ohnuma, “Differences in wavefront aberrations in different wavelengths,” Invest. Ophthalmol. Visual Sci. 47, E-Abstract 1199 (2006).

2005 (2)

S. Ravikumar, A. Bradley, and L. N. Thibos, “Influence of environmental color on refraction and polychromatic image quality,” J. Vision 5, 81-81 (2005).
[CrossRef]

L. Chen, B. Singer, A. Guirao, J. Porter, and D. R. Williams, “Image metrics for predicting subjective image quality,” Optom. Vision Sci. 82, 358-369 (2005).
[CrossRef]

2004 (4)

J. D. Marsack, L. N. Thibos, and R. A. Applegate, “Metrics of optical quality derived from wave aberrations predict visual performance,” J. Vision 4, 322-328 (2004).
[CrossRef]

X. Cheng, A. Bradley, and L. N. Thibos, “Predicting subjective judgment of best focus with objective image quality metrics,” J. Vision 4, 310-321 (2004).
[CrossRef]

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of methods to predict the results of subjective refraction from monochromatic wavefront aberration maps,” J. Vision 4, 329-351 (2004).

C. E. Campbell, “Improving visual function diagnostic metrics with the use of higher-order aberration information from the eye,” J. Refract. Surg. 20, S495-503 (2004).
[PubMed]

2003 (2)

A. Guirao and D. Williams, “A method to predict refractive errors from wave aberration data,” Optom. Vision Sci. 80, 36-42 (2003).
[CrossRef]

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26-35 (2003).
[CrossRef]

2002 (7)

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652-660 (2002).
[PubMed]

L. N. Thibos, A. Bradley, and X. Hong, “A statistical model of the aberration structure of normal, well-corrected eyes,” Ophthalmic Physiol. Opt. 22, 427-433 (2002).
[CrossRef] [PubMed]

J. S. McLellan, S. Marcos, P. M. Prieto, and S. A. Burns, “Imperfect optics may be the eye's defence against chromatic blur,” Nature 417, 174-176 (2002).
[CrossRef] [PubMed]

M. A. Webster, M. A. Georgeson, and S. M. Webster, “Neural adjustments to image blur,” Nat. Neurosci. 5, 839-840 (2002).
[CrossRef] [PubMed]

G. Y. Yoon and D. R. Williams, “Visual performance after correcting the monochromatic and chromatic aberrations of the eye,” J. Opt. Soc. Am. A 19, 266-275 (2002).
[CrossRef]

S. M. C. Nascimento, F. Ferreira, and D. H. Foster, “Statistics of spatial cone-excitation ratios in natural scenes,” J. Opt. Soc. Am. A 19, 1484-1490 (2002).
[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]

2001 (1)

S. Marcos, S. Barbero, L. Llorente, and J. Merayo-Lloves, “Optical response to LASIK surgery for myopia from total and corneal aberration measurements,” Invest. Ophthalmol. Visual Sci. 42, 3349-3356 (2001).

1999 (1)

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

1997 (2)

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548-556 (1997).
[CrossRef]

D. A. Atchison, W. N. Charman, and R. L. Woods, “Subjective depth-of-focus of the eye,” Optom. Vision Sci. 74, 511-520 (1997).
[CrossRef]

1995 (1)

1994 (2)

1993 (1)

P. B. Kruger, S. Mathews, K. R. Aggarwala, and N. Sanchez, “Chromatic aberration and ocular focus: Fincham revisited,” Vision Res. 33, 1397-1411 (1993).
[CrossRef] [PubMed]

1992 (2)

1991 (1)

L. N. Thibos, A. Bradley, and X. X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vision Sci. 68, 599-607 (1991).
[CrossRef]

1990 (2)

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

P. G. J. Barten, “Evaluation of subjective image quality with the square-root integral method,” J. Opt. Soc. Am. A 7, 2024-2031 (1990).
[CrossRef]

1988 (1)

P. A. Howarth, X. Zhang, A. Bradley, D. L. Still, and L. N. Thibos, “Does the chromatic aberration of the eye vary with age?” Vision Res. 5, 2087-2092 (1988).

1986 (1)

P. A. Howarth and A. Bradley, “The longitudinal chromatic aberration of the human eye, and its correction,” Vision Res. 26, 361-366 (1986).
[CrossRef] [PubMed]

1985 (1)

K. T. Mullen, “The contrast sensitivity of human colour vision to red-green and blue-yellow chromatic gratings.,” J. Physiol. (London) 359, 381-400 (1985).

1977 (1)

W. N. Charman and H. Whitefoot, “Pupil diameter and the depth-of-field of the human eye as measured by laser speckle,” Opt. Acta 24, 1211-1216 (1977).
[CrossRef]

1974 (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]

R. Barnden, “Calculation of axial polychromatic optical transfer function,” Opt. Acta 21, 981-1003 (1974).
[CrossRef]

1973 (1)

1972 (1)

E. M. Granger and K. N. Cupery, “An optical merit function (SQF) which correlates with subjective image judgements,” Photograph. Sci. Eng. 16, 221-230 (1972).

1967 (1)

F. W. Campbell and R. W. Gubisch, “The effect of chromatic aberration on visual acuity,” J. Physiol. (London) 192, 345-358 (1967).

1965 (1)

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

1964 (1)

1962 (1)

1957 (2)

G. T. Di Francia, “Modern trends in the evaluation of optical images,” J. Opt. Soc. Am. 47, 507 (1957).
[CrossRef]

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta 4, 157-164 (1957).
[CrossRef]

1955 (1)

P. B. Fellgett and E. H. Linfoot, “On assessment of optical images,” Philos. Trans. R. Soc. London, Ser. A 247, 369-407 (1955).
[CrossRef]

Aggarwala, K. R.

P. B. Kruger, S. Mathews, K. R. Aggarwala, and N. Sanchez, “Chromatic aberration and ocular focus: Fincham revisited,” Vision Res. 33, 1397-1411 (1993).
[CrossRef] [PubMed]

Applegate, R. A.

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. Vision Sci. 83, 635-640 (2006).
[CrossRef]

J. D. Marsack, L. N. Thibos, and R. A. Applegate, “Metrics of optical quality derived from wave aberrations predict visual performance,” J. Vision 4, 322-328 (2004).
[CrossRef]

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of methods to predict the results of subjective refraction from monochromatic wavefront aberration maps,” J. Vision 4, 329-351 (2004).

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652-660 (2002).
[PubMed]

R. R. Krueger, R. A. Applegate, and S. M. MacRae, Wavefront Customized Visual Correction: The Quest for Super Vision II (Slack, Inc., 2004).

Artal, P.

Atchison, D. A.

D. A. Atchison, W. N. Charman, and R. L. Woods, “Subjective depth-of-focus of the eye,” Optom. Vision Sci. 74, 511-520 (1997).
[CrossRef]

Barbero, S.

S. Marcos, S. Barbero, L. Llorente, and J. Merayo-Lloves, “Optical response to LASIK surgery for myopia from total and corneal aberration measurements,” Invest. Ophthalmol. Visual Sci. 42, 3349-3356 (2001).

Barnden, R.

R. Barnden, “Calculation of axial polychromatic optical transfer function,” Opt. Acta 21, 981-1003 (1974).
[CrossRef]

Barten, P. G. J.

Benny, Y.

Bille, J. F.

Bradley, A.

S. Ravikumar, A. Bradley, and L. N. Thibos, “Do monochromatic aberrations protect the eye against chromatic blur?” Invest. Ophthalmol. Visual Sci. 47, E-Abstract 1505 (2006).

S. Ravikumar, A. Bradley, and L. N. Thibos, “Influence of environmental color on refraction and polychromatic image quality,” J. Vision 5, 81-81 (2005).
[CrossRef]

X. Cheng, A. Bradley, and L. N. Thibos, “Predicting subjective judgment of best focus with objective image quality metrics,” J. Vision 4, 310-321 (2004).
[CrossRef]

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of methods to predict the results of subjective refraction from monochromatic wavefront aberration maps,” J. Vision 4, 329-351 (2004).

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]

L. N. Thibos, A. Bradley, and X. Hong, “A statistical model of the aberration structure of normal, well-corrected eyes,” Ophthalmic Physiol. Opt. 22, 427-433 (2002).
[CrossRef] [PubMed]

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548-556 (1997).
[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] [PubMed]

L. N. Thibos, A. Bradley, and X. X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vision Sci. 68, 599-607 (1991).
[CrossRef]

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

P. A. Howarth, X. Zhang, A. Bradley, D. L. Still, and L. N. Thibos, “Does the chromatic aberration of the eye vary with age?” Vision Res. 5, 2087-2092 (1988).

P. A. Howarth and A. Bradley, “The longitudinal chromatic aberration of the human eye, and its correction,” Vision Res. 26, 361-366 (1986).
[CrossRef] [PubMed]

L. N. Thibos and A. Bradley, “Chromatic aberration and its impact on vision,” in Wavefront Customized Visual Correction: The Quest for Super Vision II, R.R.Krueger, R.A.Applegate, and S.M.MacRae, eds. (Slack, 2004), pp. 91-99.

L. N. Thibos and A. Bradley, “Modeling the refractive and neuro-sensor systems of the eye,” in Visual Instrumentation: Optical Design and EngineeringPrinciples, P.Mouroulis, ed. (McGraw-Hill, 1999), pp. 101-159.

Brimm, B.

Brindley, G. S.

G. S. Brindley, Physiology of the Retina and Visual Pathway, 2nd ed. (Arnold, 1970), p. 315.

Burns, S. A.

J. S. McLellan, S. Marcos, P. M. Prieto, and S. A. Burns, “Imperfect optics may be the eye's defence against chromatic blur,” Nature 417, 174-176 (2002).
[CrossRef] [PubMed]

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

Campbell, C. E.

C. E. Campbell, “Improving visual function diagnostic metrics with the use of higher-order aberration information from the eye,” J. Refract. Surg. 20, S495-503 (2004).
[PubMed]

Campbell, F. W.

F. W. Campbell and R. W. Gubisch, “The effect of chromatic aberration on visual acuity,” J. Physiol. (London) 192, 345-358 (1967).

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

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta 4, 157-164 (1957).
[CrossRef]

Charman, W. N.

D. A. Atchison, W. N. Charman, and R. L. Woods, “Subjective depth-of-focus of the eye,” Optom. Vision Sci. 74, 511-520 (1997).
[CrossRef]

W. N. Charman and H. Whitefoot, “Pupil diameter and the depth-of-field of the human eye as measured by laser speckle,” Opt. Acta 24, 1211-1216 (1977).
[CrossRef]

Chen, L.

L. Chen, B. Singer, A. Guirao, J. Porter, and D. R. Williams, “Image metrics for predicting subjective image quality,” Optom. Vision Sci. 82, 358-369 (2005).
[CrossRef]

Cheng, X.

X. Cheng, A. Bradley, and L. N. Thibos, “Predicting subjective judgment of best focus with objective image quality metrics,” J. Vision 4, 310-321 (2004).
[CrossRef]

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Appl. Opt. (1)

Invest. Ophthalmol. Visual Sci. (3)

S. Marcos, S. Barbero, L. Llorente, and J. Merayo-Lloves, “Optical response to LASIK surgery for myopia from total and corneal aberration measurements,” Invest. Ophthalmol. Visual Sci. 42, 3349-3356 (2001).

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J. Physiol. (London) (3)

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J. Refract. Surg. (2)

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652-660 (2002).
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J. D. Marsack, L. N. Thibos, and R. A. Applegate, “Metrics of optical quality derived from wave aberrations predict visual performance,” J. Vision 4, 322-328 (2004).
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S. Ravikumar, A. Bradley, and L. N. Thibos, “Influence of environmental color on refraction and polychromatic image quality,” J. Vision 5, 81-81 (2005).
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Nat. Neurosci. (1)

M. A. Webster, M. A. Georgeson, and S. M. Webster, “Neural adjustments to image blur,” Nat. Neurosci. 5, 839-840 (2002).
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Nature (1)

J. S. McLellan, S. Marcos, P. M. Prieto, and S. A. Burns, “Imperfect optics may be the eye's defence against chromatic blur,” Nature 417, 174-176 (2002).
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Ophthalmic Physiol. Opt. (1)

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L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548-556 (1997).
[CrossRef]

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26-35 (2003).
[CrossRef]

L. Chen, B. Singer, A. Guirao, J. Porter, and D. R. Williams, “Image metrics for predicting subjective image quality,” Optom. Vision Sci. 82, 358-369 (2005).
[CrossRef]

L. N. Thibos, A. Bradley, and X. X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vision Sci. 68, 599-607 (1991).
[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. Vision Sci. 83, 635-640 (2006).
[CrossRef]

Philos. Trans. R. Soc. London, Ser. A (1)

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[CrossRef]

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Vision Res. (5)

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[CrossRef] [PubMed]

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[CrossRef]

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Other (10)

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[CrossRef]

L. N. Thibos and A. Bradley, “Modeling the refractive and neuro-sensor systems of the eye,” in Visual Instrumentation: Optical Design and EngineeringPrinciples, P.Mouroulis, ed. (McGraw-Hill, 1999), pp. 101-159.

L. N. Thibos and A. Bradley, “Chromatic aberration and its impact on vision,” in Wavefront Customized Visual Correction: The Quest for Super Vision II, R.R.Krueger, R.A.Applegate, and S.M.MacRae, eds. (Slack, 2004), pp. 91-99.

R. R. Shannon, The Art and Science of Optical Design (Cambridge U. Press, 1997).

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J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, 1950).

L. N. Thibos, “From wavefronts to refractions,” in Adaptive Optics for Vision Science, J.Porter, H.Queener, K.Thorn, and R.Awwal, eds. (Wiley, 2006), pp. 331-362.

R. R. Krueger, R. A. Applegate, and S. M. MacRae, Wavefront Customized Visual Correction: The Quest for Super Vision II (Slack, Inc., 2004).

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Figures (13)

Fig. 1
Fig. 1

Experimental paradigm for determining whether two dissimilar retinal images have the same quality. This paradigm embodies the psychophysical linking hypothesis that retinal images of equal quality lead to equal performance on visual tasks.

Fig. 2
Fig. 2

Graphical interpretation of text Eq. (1) for computing the polychromatic PSF as the sum of luminance-weighted monochromatic PSFs. For each wavelength in the source spectrum, a monochromatic PSF is computed from monochromatic aberrations plus the focal shift associated with LCA and the lateral displacement associated with TCA; The diagram shows three such PSFs schematically as blur disks of varying diameter. The luminance weighting of each blur disk is given by the height of the source spectrum curve shown below the LCA curve.

Fig. 3
Fig. 3

Polychromatic images calculated using the PSF poly approach, with LCA of the Indiana model eye. Wavelength in focus was 589 nm , and pupil diameter was 4 mm . RED, GRN, and BLU letters were constructed using typical R, G, and B phosphor spectra, respectively. The WHT images were generated with equal amounts of energy in the R, G, and B layers. In (a), a chromatically aberrated image was computed using a single PSF poly developed using a uniform white spectral weighting function. The image in (b) is generated as the linear sum of the R, G, and B images, each generated separately with a PSF poly spectrally weighted by the R, G, or B phosphor spectrum, respectively. (Note: The faded out appearance of the BLU layer is due to luminance scaling relative to WHT. A full color version is available in the online publication.)

Fig. 4
Fig. 4

Geometry of the aberrated reduced eye. Optical path differences between the marginal and the central rays vary with wavelength because the refractive index of the ocular medium varies with wavelength.

Fig. 5
Fig. 5

(Top) Validation of OPD method described in the text for computing LCA of the Indiana reduced eye for which defocus coefficient c 2 0 = 0 at the emmetropic wavelength ( 589 nm ) . (Bottom) Chromatic variation of Zernike spherical aberration with wavelength. Pupil diameter = 5 mm .

Fig. 6
Fig. 6

Two schemes for sampling the pupil function. (Left) Circular pupil is represented by an N × N square matrix of sample points. (Right) Pupil of the same diameter is sampled by the variable number N λ min λ rows and columns. Sample points outside the pupil circle are set to zero in both schemes to produce an N × N square matrix of sample values for all wavelengths. Note that the number of sample points inside the pupil circle varies with wavelength in the scheme on the right but is fixed in the scheme on the left.

Fig. 7
Fig. 7

Examples of commensurate, unit volume, monochromatic diffraction-limited PSFs computed using the variable sampling scheme of Fig. 6. Wavelengths are 400 nm (circles), 600 nm (squares), and 800 nm (diamonds). Note the agreement of sample locations for all three wavelengths.

Fig. 8
Fig. 8

Effect of wavelength sampling interval on polychromatic PSFs. In each panel, results are shown for spectral sampling at 50, 10, and 1 nm intervals (dashed curve, open circle, and continuous curve, respectively). The top two panels describe results for a model eye exhibiting LCA but otherwise aberration free for a D65 white source and a 5-mm-diameter pupil. In the top panel results are shown for an eye well focused at 400 nm , and sampled at 400 nm (see text), while the middle panel shows the case for an eye focused at 550 nm and sampled at 425 nm and at increments of 50, 10, and 1 nm up to 725 nm . The bottom panel repeats the analysis in the middle panel for an eye with typical levels of monochromatic aberrations. The inset in (a) shows the full shape of the 50 nm case over a 30 arcmin width.

Fig. 9
Fig. 9

Left and right sides of this figure show profiles of the PSF and MTF, respectively, obtained using fixed diffraction (dotted curves) or with wavelength-dependent diffraction (solid curves). A reddish purple spectrum was used as the source [inset in panel (c) where the luminance spectrum is plotted as a function of wavelength in micrometers]. The top row shows the impact of wavelength-dependent diffraction for a diffraction-limited eye with a 2.5 mm pupil. The second row shows the same results in an eye with LCA alone. The third row shows results for an eye with lower-order and higher-order monochromatic and chromatic aberrations and a 5 mm pupil. The bottom row shows results for the same eye, but when 550 nm is focused paraxially. In MTF panel (a), the neural contrast threshold cutoff [58] is shown with an arrow.

Fig. 10
Fig. 10

Equal-energy white-light polychromatic OTF for a 5 mm pupil is compared to three monochromatic OTFs. Variable wavelength diffraction calculations were employed for these computations, and thus as wavelength changes, diffraction and LCA change. The model is diffraction limited at 550 nm .

Fig. 11
Fig. 11

Influence of monochromatic and chromatic aberrations on the metric VSOTF in individual eyes with higher-order aberrations as summarized in Table 1. For each monochromatically aberrated eye, VSOTF was calculated with no chromatic aberrations (unfilled bar), only LCA (dark bar), only TCA (backward-slash-patterned bar), and both LCA and TCA (forward-slash-patterned bar). VSOTF values are normalized to an eye that has no LCA and no TCA and is diffraction limited at 555 nm . Equal-energy white was used as the source spectrum.

Fig. 12
Fig. 12

Polychromatic image quality as a function of defocus for two monochromatic sources (500 and 670 nm ) and a flat-white spectrum. Pupil diameter = 5 mm ; 550 nm is the wavelength in focus. VSOTF was normalized to the diffraction-limited OTF for monochromatic light at 550 nm . VSOTF was calculated for an eye with no higher-order aberration (a) and one with typical levels of higher-order aberrations (b). In both panels of the figure, small dashed curves represent monochromatic analysis.

Fig. 13
Fig. 13

Depth of focus based on the VSOTF metric. Results show depth of focus in an unaberrated eye and mean and SD for the five typically aberrated eyes reported in Table 1 with successive addition of chromatic aberrations and for two different criteria (drop in VSOTF of 0.2 or 0.08).

Tables (1)

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Table 1 Vector of Zernike Third- and Fourth-Order Coefficients for Six Eyes (ANSI Nomenclature [48]) a

Equations (11)

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PSF poly ( x , y ) = S ( λ ) psf ( x , y , λ ) d λ .
OTF poly ( f x , f y ) = S ( λ ) otf ( f x , f y , λ ) d λ ,
Image = PSF 1 O 1 + PSF 2 O 2 .
Image = ( PSF 1 + PSF 2 ) ( O 1 + O 2 )
= PSF 1 O 1 + PSF 1 O 2 + PSF 2 O 1 + PSF 2 O 2 .
Image = PSF 1 S 1 O + PSF 2 S 2 O = ( PSF 1 S 1 + PSF 2 S 2 ) O .
Image = PSF poly O .
OPD ( Y ) = [ Y S ] + n [ S R ] [ Y Q ] n [ Q R ] = [ Q S ] n ( [ Q R ] [ S R ] ) .
OPD ( Y ) [ Q S ] n [ Q S ] cos θ ,
[ Q S ] OPD ( Y ) ( 1 n cos θ ) .
sampling interval = ( d λ ) [ N ( λ min λ ) ] = d ( N λ min ) .

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