Abstract

We used diffraction modulation transfer functions and model eyes to predict the effect of defocus on the contrast sensitivity function (CSF) and compared these predictions with previously published experimental data. Using the principle that optically induced changes in the modulation transfer function should be paralleled by identical changes in the CSF, we used the modulation transfer function calculations with the best-focus CSF measurements to predict the defocused CSF. An aberration-free model predicted the effects of defocus well when the CSF was measured with small pupils (e.g., 2 mm) but not with larger pupils (6–8 mm). When the model included average aberrations, prediction of the defocused CSF with large pupils was better but remained inaccurate, failing, in particular, to reflect differences between individual subjects. Inclusion of measured aberrations for individual subjects provided accurate predictions in the shape of the monochromatic CSF of two of three subjects with hyperopic defocus and good predictions of the polychromatic CSF of two subjects with hyperopic defocus. Prediction of the effects of myopic defocus by use of measured individual aberrations of one subject were less successful. Hence a diffraction optics model can provide good predictions of the effects of defocus on the human CSF, given that one has knowledge of the individual ocular aberrations. These predictions are dependent on the quality of the aberration measurements.

© 1998 Optical Society of America

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1997 (1)

1996 (3)

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

R. L. Woods, A. Bradley, D. A. Atchison, “Monocular diplopia caused by aberrations and defocus,” Vision Res. 36, 3597–3606 (1996).
[CrossRef] [PubMed]

L. J. Bour, P. Apkarian, “Selective broad-band spatial frequency loss in contrast sensitivity functions,” Invest. Ophthalmol. Visual Sci. 37, 2475–2484 (1996).

1995 (2)

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

M. J. Collins, C. F. Wildsoet, D. A. Atchison, “Monochromatic aberrations and myopia,” Vision Res. 35, 1157–1163 (1995).
[CrossRef] [PubMed]

1994 (2)

1993 (2)

1992 (1)

1990 (2)

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]

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

1987 (3)

C. D. Kay, J. D. Morrison, “A quantitative investigation into the effects of pupil diameter and defocus on contrast sensitivity for an extended range of spatial frequencies in natural and homatropinized eyes,” Ophthalmic Physiol. Opt. 7, 21–30 (1987).
[CrossRef] [PubMed]

G. E. Legge, K. T. Mullen, G. C. Woo, F. W. Campbell, “Tolerance to visual defocus,” J. Opt. Soc. Am. A 5, 851–863 (1987).
[CrossRef]

P. Apkarian, R. Tijssen, H. Spekreijse, D. Regan, “Origin of notches in CSF: optical or neural?” Invest. Ophthalmol. Visual Sci. 28, 607–612 (1987).

1985 (1)

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

1984 (1)

D. A. Atchison, “Visual optics in man,” Aust. J. Optom. 67, 141–150 (1984).

1982 (1)

G. Smith, “Ocular defocus, spurious resolution and contrast reversal,” Ophthalmic Physiol. Opt. 2, 5–23 (1982).
[PubMed]

1979 (1)

W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
[PubMed]

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]

1971 (1)

J. Macdonald, “The calculation of the optical transfer function,” Opt. Acta 18, 269–290 (1971).
[CrossRef]

1966 (2)

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. (London) 186, 558–578 (1966).

F. W. Campbell, D. G. Green, “Optical factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1966).

1965 (1)

1963 (1)

T. C. A. Jenkins, “Aberrations of the human eye and their effects on vision. Part 1,” Br. J. Physiol. Opt. 20, 59–91 (1963).
[PubMed]

1959 (1)

R. Leinhos, “Die Alterabhängigkeit des Augenpupillendurchmessers,” Optik 16, 669–671 (1959).

1956 (1)

1955 (1)

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. Phys. Soc. London Sect. A 231, 91–103 (1955).
[CrossRef]

1952 (1)

1950 (1)

J. E. Birren, R. C. Casperson, J. Botwinick, “Age changes in pupil size,” J. Gerontol. 5, 216–224 (1950).
[CrossRef] [PubMed]

1949 (1)

1933 (1)

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the light pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Apkarian, P.

L. J. Bour, P. Apkarian, “Selective broad-band spatial frequency loss in contrast sensitivity functions,” Invest. Ophthalmol. Visual Sci. 37, 2475–2484 (1996).

L. J. Bour, P. Apkarian, “Segmented refraction of the crystalline lens as a prerequisite for the occurrence of monocular polyplopia, increased depth of focus, and contrast sensitivity function notches,” J. Opt. Soc. Am. A 11, 2769–2776 (1994).
[CrossRef]

P. Apkarian, R. Tijssen, H. Spekreijse, D. Regan, “Origin of notches in CSF: optical or neural?” Invest. Ophthalmol. Visual Sci. 28, 607–612 (1987).

Applegate, R. A.

Atchison, D. A.

R. L. Woods, A. Bradley, D. A. Atchison, “Monocular diplopia caused by aberrations and defocus,” Vision Res. 36, 3597–3606 (1996).
[CrossRef] [PubMed]

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

M. J. Collins, C. F. Wildsoet, D. A. Atchison, “Monochromatic aberrations and myopia,” Vision Res. 35, 1157–1163 (1995).
[CrossRef] [PubMed]

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

D. A. Atchison, “Visual optics in man,” Aust. J. Optom. 67, 141–150 (1984).

D. A. Atchison, R. L. Woods, A. Bradley, “Predicting variations in visual performance caused by optical defects,” in Vision Science and Its Applications, Vol. 1 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 226–229.

G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, New York, 1997), pp. 675–677.

Bille, J. F.

Birren, J. E.

J. E. Birren, R. C. Casperson, J. Botwinick, “Age changes in pupil size,” J. Gerontol. 5, 216–224 (1950).
[CrossRef] [PubMed]

Botwinick, J.

J. E. Birren, R. C. Casperson, J. Botwinick, “Age changes in pupil size,” J. Gerontol. 5, 216–224 (1950).
[CrossRef] [PubMed]

Bour, L. J.

Bradley, A.

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

R. L. Woods, A. Bradley, D. A. Atchison, “Monocular diplopia caused by aberrations and defocus,” Vision Res. 36, 3597–3606 (1996).
[CrossRef] [PubMed]

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

D. A. Atchison, R. L. Woods, A. Bradley, “Predicting variations in visual performance caused by optical defects,” in Vision Science and Its Applications, Vol. 1 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 226–229.

Campbell, F. W.

G. E. Legge, K. T. Mullen, G. C. Woo, F. W. Campbell, “Tolerance to visual defocus,” J. Opt. Soc. Am. A 5, 851–863 (1987).
[CrossRef]

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. (London) 186, 558–578 (1966).

F. W. Campbell, D. G. Green, “Optical factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1966).

D. G. Green, F. W. Campbell, “Effect of focus on the visual response to a sinusoidally modulated spatial stimulus,” J. Opt. Soc. Am. 55, 1154–1157 (1965).
[CrossRef]

Campbell, M. C. W.

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

Casperson, R. C.

J. E. Birren, R. C. Casperson, J. Botwinick, “Age changes in pupil size,” J. Gerontol. 5, 216–224 (1950).
[CrossRef] [PubMed]

Charman, W. N.

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

W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
[PubMed]

Christensen, J.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Collins, M. J.

M. J. Collins, C. F. Wildsoet, D. A. Atchison, “Monochromatic aberrations and myopia,” Vision Res. 35, 1157–1163 (1995).
[CrossRef] [PubMed]

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Crawford, B. H.

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the light pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

De Groot, S. G.

Gebhard, J. W.

Goelz, S.

Green, D. G.

F. W. Campbell, D. G. Green, “Optical factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1966).

D. G. Green, F. W. Campbell, “Effect of focus on the visual response to a sinusoidally modulated spatial stimulus,” J. Opt. Soc. Am. 55, 1154–1157 (1965).
[CrossRef]

Grimm, B.

Gubisch, R. W.

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. (London) 186, 558–578 (1966).

Harrison, E. M.

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

Hopkins, H. H.

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. Phys. Soc. London Sect. A 231, 91–103 (1955).
[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, B.

Howland, H. C.

Ivanoff, A.

Jenkins, T. C. A.

T. C. A. Jenkins, “Aberrations of the human eye and their effects on vision. Part 1,” Br. J. Physiol. Opt. 20, 59–91 (1963).
[PubMed]

Kay, C. D.

C. D. Kay, J. D. Morrison, “A quantitative investigation into the effects of pupil diameter and defocus on contrast sensitivity for an extended range of spatial frequencies in natural and homatropinized eyes,” Ophthalmic Physiol. Opt. 7, 21–30 (1987).
[CrossRef] [PubMed]

Koomen, M.

Lakshminarayanan, V.

Legge, G. E.

G. E. Legge, K. T. Mullen, G. C. Woo, F. W. Campbell, “Tolerance to visual defocus,” J. Opt. Soc. Am. A 5, 851–863 (1987).
[CrossRef]

Leinhos, R.

R. Leinhos, “Die Alterabhängigkeit des Augenpupillendurchmessers,” Optik 16, 669–671 (1959).

Liang, J.

Macdonald, J.

J. Macdonald, “The calculation of the optical transfer function,” Opt. Acta 18, 269–290 (1971).
[CrossRef]

Morrison, J. D.

C. D. Kay, J. D. Morrison, “A quantitative investigation into the effects of pupil diameter and defocus on contrast sensitivity for an extended range of spatial frequencies in natural and homatropinized eyes,” Ophthalmic Physiol. Opt. 7, 21–30 (1987).
[CrossRef] [PubMed]

Mullen, K. T.

G. E. Legge, K. T. Mullen, G. C. Woo, F. W. Campbell, “Tolerance to visual defocus,” J. Opt. Soc. Am. A 5, 851–863 (1987).
[CrossRef]

Regan, D.

P. Apkarian, R. Tijssen, H. Spekreijse, D. Regan, “Origin of notches in CSF: optical or neural?” Invest. Ophthalmol. Visual Sci. 28, 607–612 (1987).

Scolnik, R.

Simonet, P.

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

Smith, G.

G. Smith, “Ocular defocus, spurious resolution and contrast reversal,” Ophthalmic Physiol. Opt. 2, 5–23 (1982).
[PubMed]

G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, New York, 1997), pp. 675–677.

Spekreijse, H.

P. Apkarian, R. Tijssen, H. Spekreijse, D. Regan, “Origin of notches in CSF: optical or neural?” Invest. Ophthalmol. Visual Sci. 28, 607–612 (1987).

Stiles, W. S.

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the light pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

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]

Thibos, L. N.

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

Tijssen, R.

P. Apkarian, R. Tijssen, H. Spekreijse, D. Regan, “Origin of notches in CSF: optical or neural?” Invest. Ophthalmol. Visual Sci. 28, 607–612 (1987).

Tousey, R.

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]

Walsh, G.

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

Waterworth, M. D.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Wildsoet, C. F.

M. J. Collins, C. F. Wildsoet, D. A. Atchison, “Monochromatic aberrations and myopia,” Vision Res. 35, 1157–1163 (1995).
[CrossRef] [PubMed]

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Williams, D. R.

Woo, G. C.

G. E. Legge, K. T. Mullen, G. C. Woo, F. W. Campbell, “Tolerance to visual defocus,” J. Opt. Soc. Am. A 5, 851–863 (1987).
[CrossRef]

Woods, R. L.

R. L. Woods, A. Bradley, D. A. Atchison, “Monocular diplopia caused by aberrations and defocus,” Vision Res. 36, 3597–3606 (1996).
[CrossRef] [PubMed]

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

R. L. Woods, “Reliability of visual performance measurement under optical degradation,” Ophthalmic Physiol. Opt. 13, 143–150 (1993).
[CrossRef] [PubMed]

D. A. Atchison, R. L. Woods, A. Bradley, “Predicting variations in visual performance caused by optical defects,” in Vision Science and Its Applications, Vol. 1 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 226–229.

Ye, M.

Zhang, X.

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

Appl. Opt. (1)

Aust. J. Optom. (1)

D. A. Atchison, “Visual optics in man,” Aust. J. Optom. 67, 141–150 (1984).

Br. J. Physiol. Opt. (2)

W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
[PubMed]

T. C. A. Jenkins, “Aberrations of the human eye and their effects on vision. Part 1,” Br. J. Physiol. Opt. 20, 59–91 (1963).
[PubMed]

Invest. Ophthalmol. Visual Sci. (2)

P. Apkarian, R. Tijssen, H. Spekreijse, D. Regan, “Origin of notches in CSF: optical or neural?” Invest. Ophthalmol. Visual Sci. 28, 607–612 (1987).

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Figures (7)

Fig. 1
Fig. 1

(a) MTF’s for theoretical eyes with 6-mm-diameter pupils. Results are shown for (i) ±2-D defocus in the absence of aberration, (ii) -2-D defocus relative to the in-focus condition combined with +0.9-D primary longitudinal spherical aberration (LSA; +3.68 waves at 550 mm) at the edge of the pupil, and (iii) +2-D defocus relative to the in-focus condition combined with +0.9-D primary LSA (+3.68 waves at 605 mm) at the edge of a 6-mm-diameter pupil. The in-focus condition for (ii) and (iii) is actually a defocus of -0.27-D (-2.2 waves) defocus at the edge of the pupil to give the best image quality at 20 cycles per degree (c/deg) object spatial frequency, chosen to be representative of the high spatial frequencies that are expected to be important during refraction procedures. A Stiles–Crawford effect coefficient of p=0.12 is used to obtain the MTF’s. (b) MTF’s for theoretical eyes with three waves of primary coma (along the horizontal direction) in addition to +0.9-D primary spherical aberration and -2-D defocus. Results are shown for both horizontal and vertical orientations of the sinusoidal object. Other details are the same as in (a).

Fig. 2
Fig. 2

CSF’s for subject DG2 for both in-focus (circles) and +2-D defocus (squares) conditions with a 2-mm pupil. The stimulus was a P1 phosphor. The CSF predicted for +2-D defocus (solid curve) on the basis of polychromatic MTF’s is also shown (these are affected by longitudinal chromatic aberration but not other aberrations). The arrows indicate the spatial frequencies at which notches occurred in the measured CSF for +2-D defocus. RMSE=0.48 log unit.

Fig. 3
Fig. 3

CSF’s for subjects9 for both in-focus (circles) and +0.75-D defocus (squares) conditions. The CSF’s predicted for +0.75-D defocus on the basis of aberration-free, polychromatic MTF’s (solid curve) and on the basis of average aberration, polychromatic MTF’s (dashed curve) are also shown. (a) Subject C2 with 3-mm pupil; (b) subject C1 with dilated pupil, which we assumed to be 8 mm. The arrow indicates the spatial frequency at which a notch occurred in the measured CSF for +0.75-D defocus.

Fig. 4
Fig. 4

Measured monochromatic CSF’s for in-focus and -2-D defocus, and monochromatic CSF for -2-D defocus predicted from the in-focus CSF and individual-based aberration MTF’s. The arrows indicate the spatial frequencies at which notches occurred in the measured CSF for -2-D defocus. (a) Subject AB, (b) subject DAA, (c) subject RLW.

Fig. 5
Fig. 5

Measured polychromatic CSF’s for in-focus (0-D) and -2-D defocus, and polychromatic CSF for -2-D defocus predicted from the in-focus CSF and the individual-based aberration MTF’s. The arrows indicate the spatial frequencies at which notches occurred in the measured CSF for -2-D defocus. (a) Subject AB, (b) subject RLW.

Fig. 6
Fig. 6

Results for subject DAA.7 Measured monochromatic CSF’s for +2-D defocus. The first CSF prediction (solid curve) was based on the individual-based aberration MTF’s as previously described. The second (dashed curve) was based on the aberration data for the in-focus condition combined with an additional defocus term (A1=+14.88 waves). The arrows indicate the spatial frequencies at which notches occurred in the measured CSF for +2-D defocus.

Fig. 7
Fig. 7

Results for subject DAA.7 Measured monochromatic CSF’s for -2-D defocus, and monochromatic CSF’s for -2-D defocus predicted from both diffraction optics (solid curve) and geometrical-optics (dashed curve) models.

Tables (2)

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Table 1 Wave Aberration Coefficientsa Derived from Subjects in the Study by Woods et al.b

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Table 2 Comparison of the Perceived Contrast Minima (c/deg) in a Star Pattern Measureda and Predicted by Our Aberration-Free and Average Aberration Models

Equations (14)

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

f(x, y)=M(x, y)exp[i2πW(x, y)].
W(x, y)=A0x+A1(x2+y2)+A2(x2+y2)x+A3(x2+y2)2+A4(x2+y2)2x+A5(x2+y2)3.
M(x, y)=exp{-p/2[(x2+y2)h2]},
Ax(λ)=Ax(λref)λrefλ,
A1(λ)=A1(λ)-Cλh22λ.
A1=Lh22λ,
W=W40h4,
A3=0.04545h4.
T(X)=B0+B1X+B2X2+B3X3+B4X4+B5X5,
W(x)=A0x+A1x2+A2x3+A3x4+A4x5+A5x6,
A0=-B0h/(Rλ),A1=-B1h2/(2Rλ),
A2=-B2h3/(3Rλ),A3=-B3h4/(4Rλ),
A4=-B4h5/5Rλ),A5=-B5h6/(6Rλ),
RMSE=(Cm-Cp)2n-1,

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