Abstract

We created a sequential ideal-observer model that could address the question, How much of letter identification performance and its change with eccentricity can be accounted for by preneural factors? The ideal-observer model takes into account preneural factors including the stimulus rendering properties of a CRT display, the optical imaging quality of the eye, and photon capture and sampling characteristics of the cones. We validated the formulation of the model by comparing its performance on simple psychophysical tasks with that of previous sequential ideal-observer models. The model was used to study properties of the image rendering of letters. For example, the model’s identification of high-resolution letters (i.e., many pixels per letter), but not low-resolution letters, is largely immune to changes in pixel width. We compared human and ideal-observer letter-identification acuity for the lowercase alphabet at 0°, 5°, and 20° retinal eccentricity. Acuity of the ideal observer for high-contrast letters is approximately seven times better than that of the human observers at 0°. Acuity decreased with eccentricity more rapidly for human observers than for the ideal observer such that the thresholds differed by a factor of 50 at 20°. A decrease in stimulus duration from 100 to 33 ms resulted in no decrease in relative threshold size between the human and ideal observers at all eccentricities, indicating that humans effectively integrate stimulus information over this range. Decreasing contrast from 75% to 25%, however, reduced the difference in acuities twofold at all eccentricities between humans and the ideal-observer model, consistent with the presence a compressive nonlinearity only in the human observers. The gap between human and ideal acuity in central vision means that there are substantial limitations in human letter recognition beyond the stage of photoreceptor sampling. The increasing performance gap between human and ideal-observer performance with eccentricity implicates an increasing role of neural limitations with eccentricity in limiting human letter identification.

© 2002 Optical Society of America

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2001 (2)

G. E. Legge, J. S. Mansfield, S. T. L. Chung, “Psychophysics of reading XX. Linking letter recognition to reading speed in central and peripheral vision,” Vision Res. 41, 725–743 (2001).
[CrossRef] [PubMed]

W. Seiple, K. Holopigian, Y. Shnayder, J. P. Szlyk, “Duration thresholds for target detection and identification in the peripheral visual field,” Optom. Vision Sci. 78, 169–176 (2001).
[CrossRef]

2000 (2)

1999 (3)

R. S. Anderson, L. N. Thibos, “Relationship between acuity for gratings and for tumbling-E letters in peripheral vision,” J. Opt. Soc. Am. A 16, 2321–2333 (1999).
[CrossRef]

A. Roorda, D. R. Williams, “The arrangement of the three cone classes in the living human eye,” Nature 397, 520–522 (1999).
[CrossRef] [PubMed]

A. Guirao, P. Artal, “Off-axis monochromatic aberrations estimated from double pass measurements in the human eye,” Vision Res. 39, 207–217 (1999).
[CrossRef] [PubMed]

1998 (1)

S. T. L. Chung, J. S. Mansfield, G. E. Legge, “Psychophysics of reading XVIII. The effect of print size on reading speed in normal peripheral vision,” Vision Res. 38, 2949–2962 (1998).
[CrossRef] [PubMed]

1997 (3)

K. R. Alexander, W. Xie, D. J. Derlacki, “Visual acuity and contrast sensitivity for individual Sloan letters,” Vision Res. 37, 813–819 (1997).
[CrossRef] [PubMed]

G. E. Legge, S. J. Ahn, T. S. Klitz, A. Luebker, “Psychophysics of reading XVI. The visual span in normal and low vision,” Vision Res. 37, 1999–2010 (1997).
[CrossRef] [PubMed]

C. M. Cicerone, S. Otake, “Color-opponent sites: individual variability and changes with retinal eccentricity,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S454 (1997).

1996 (4)

P. D. Gowdy, S. Otake, C. M. Cicerone, “The spatial arrangement of L and M cones in the living human eye,” Vision Res. Suppl. 37, S448 (1996).

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

S. Marcos, R. Navarro, P. Artal, “Coherent imaging of the cone mosaic in the living human eye,” J. Opt. Soc. Am. A 13, 897–905 (1996).
[CrossRef]

A. M. McKendrick, N. A. Brennan, “Distribution of astigmatism in the adult population,” J. Opt. Soc. Am. A 13, 206–214 (1996).
[CrossRef]

1995 (3)

P. Artal, I. Iglesias, N. López-Gil, D. G. Green, “Double-pass measurements of the retinal-image quality with unequal entrance and exit pupil sizes and the reversibility of the eye’s optical system,” J. Opt. Soc. Am. A 12, 2358–2366 (1995).
[CrossRef]

B. S. Tjan, W. L. Braje, G. E. Legge, D. Kersten, “Human efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3069 (1995).
[CrossRef] [PubMed]

K. R. Aggarwala, S. Nowbotsing, P. B. Kruger, “Accom-modation to monochromatic and white-light targets,” Invest. Ophthalmol. Visual Sci. 36, 2695–2705 (1995).

1994 (1)

J. A. Solomon, D. G. Pelli, “The visual filter mediating letter identification,” Nature 369, 395–397 (1994).
[CrossRef] [PubMed]

1993 (3)

1992 (3)

K. Donner, “Noise and the absolute thresholds of cone and rod vision,” Vision Res. 32, 853–866 (1992).
[CrossRef] [PubMed]

J. L. Nerger, C. M. Cicerone, “The ratio of L cones to M cones in the human parafoveal retina,” Vision Res. 32, 879–888 (1992).
[CrossRef] [PubMed]

C. A. Curcio, K. R. Sloan, “Packing geometry of human cone photoreceptors: variation with eccentricity and evidence for local anisotropy,” Visual Neurosci. 9, 169–180 (1992).
[CrossRef]

1991 (3)

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with antiblue opsin,” J. Comp. Neurol. 312, 610–624 (1991).
[CrossRef] [PubMed]

D. H. Foster, W. F. Bischof, “Thresholds from psychometric functions: Superiority of bootstrap to incremental and probit variance estimators,” Psychol. Bull. 109, 152–159 (1991).
[CrossRef]

M. S. Banks, A. B. Sekuler, S. J. Anderson, “Peripheral spatial vision: limits imposed by optics, photoreceptors, and receptor pooling,” J. Opt. Soc. Am. A 8, 1775–1787 (1991).
[CrossRef] [PubMed]

1990 (5)

C. A. Curcio, K. A. Allen, “Topography of ganglion cells in human retina,” J. Comp. Neurol. 300, 5–25 (1990).
[CrossRef] [PubMed]

L. T. Maloney, “Confidence intervals for the parameters of psychometric functions,” Percept. Psychophys. 47, 127–134 (1990).
[CrossRef] [PubMed]

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

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

H. Wässle, “Retinal ganglion cell density and cortical magnification factor in the primate,” Vision Res. 30, 1897–1911 (1990).
[CrossRef] [PubMed]

1989 (6)

J. M. White, D. S. Loshin, “Grating acuity overestimates Snellen acuity in patients with age-related maculopathy,” Optom. Vision Sci. 66, 751–755 (1989).
[CrossRef]

C. A. Curcio, K. R. Sloan, D. Meyers, “Computer methods for sampling, reconstruction, display and analysis of retinal whole mounts,” Vision Res. 29, 529–540 (1989).
[CrossRef] [PubMed]

W. S. Geisler, “Sequential ideal-observer analysis of visual discriminations,” Psychol. Rev. 96, 267–314 (1989).
[CrossRef] [PubMed]

A. M. Jacobs, T. A. Nazir, O. Heller, “Perception of lowercase letters in peripheral vision: a discrimination matrix based on saccade latencies,” Percept. Psychophys. 46, 95–102 (1989).
[CrossRef] [PubMed]

C. M. Cicerone, J. L. Nerger, “The relative numbers of long-wavelength-sensitive to middle-wavelength-sensitive cones in the human fovea centralis,” Vision Res. 29, 115–128 (1989).
[CrossRef] [PubMed]

H. E. Blanchard, A. Pollatsek, K. Rayner, “The acquisition of parafoveal word information in reading,” Percept. Psychophys. 46, 85–94 (1989).
[CrossRef] [PubMed]

1988 (1)

1987 (3)

1986 (3)

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

W. S. Geisler, D. B. Hamilton, “Sampling-theory analysis of spatial vision,” J. Opt. Soc. Am. A 3, 62–70 (1986).
[CrossRef] [PubMed]

P. B. Kruger, J. Pola, “Stimuli for accommodation: blur, chromatic aberration and size,” Vision Res. 26, 957–971 (1986).
[CrossRef] [PubMed]

1985 (2)

G. E. Legge, G. S. Rubin, D. G. Pelli, M. M. Schleske, “Psychophysics of reading II. Low vision,” Vision Res. 25, 253–266 (1985).
[CrossRef]

W. S. Geisler, K. D. Davila, “Ideal discriminators in spatial vision: two-point stimuli,” J. Opt. Soc. Am. A 2, 1483–1497 (1985).
[CrossRef] [PubMed]

1984 (1)

1980 (1)

1979 (1)

K. Rayner, J. H. Bertera, “Reading without a fovea,” Science 206, 468–469 (1979).
[CrossRef] [PubMed]

1975 (1)

M. Millodot, C. A. Johnson, A. Lamont, H. W. Leibowitz, “Effect of dioptrics on peripheral visual acuity,” Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

1974 (3)

S. M. Anstis, “A chart demonstrating variations in acuity with retinal position,” Vision Res. 14, 589–592 (1974).
[CrossRef] [PubMed]

N. Drasdo, C. W. Fowler, “Non-linear projection of the retinal image in a wide-angle schematic eye,” Br. J. Ophthamol. 58, 709–714 (1974).
[CrossRef]

W. Lotmar, T. Lotmar, “Peripheral astigmatism in the human eye: experimental data and theoretical model predictions,” J. Opt. Soc. Am. 64, 510–513 (1974).
[CrossRef] [PubMed]

1973 (1)

R. M. Steinman, G. M. Haddad, A. A. Skavenski, D. Wyman, “Miniature eye movements,” Science 181, 810–819 (1973).
[CrossRef] [PubMed]

1971 (1)

H. Bouma, “Visual recognition of isolated lower-case letters,” Vision Res. 11, 459–474 (1971).
[CrossRef] [PubMed]

1968 (1)

L. L. Sloan, “The photopic acuity-luminance function with special reference to parafoveal vision,” Vision Res. 8, 901–911 (1968).
[CrossRef] [PubMed]

1966 (1)

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

1941 (1)

E. Ludvigh, “Extrafoveal visual acuity as measured with Snellen test-letters,” Am. J. Ophthalmol. 24, 303–310 (1941).

1912 (1)

B. E. Roethlein, “The relative legibility of different faces of printing types,” Am. J. Psychol. 23, 1–36 (1912).
[CrossRef]

1888 (1)

E. C. Sanford, “The relative legibility of the small letters,” Am. J. Psychol. 1, 402–435 (1888).
[CrossRef]

Aggarwala, K. R.

K. R. Aggarwala, S. Nowbotsing, P. B. Kruger, “Accom-modation to monochromatic and white-light targets,” Invest. Ophthalmol. Visual Sci. 36, 2695–2705 (1995).

Ahn, S. J.

G. E. Legge, S. J. Ahn, T. S. Klitz, A. Luebker, “Psychophysics of reading XVI. The visual span in normal and low vision,” Vision Res. 37, 1999–2010 (1997).
[CrossRef] [PubMed]

Alexander, K. R.

K. R. Alexander, W. Xie, D. J. Derlacki, “Visual acuity and contrast sensitivity for individual Sloan letters,” Vision Res. 37, 813–819 (1997).
[CrossRef] [PubMed]

K. R. Alexander, D. J. Derlacki, G. A. Fishman, J. P. Szlyk, “Temporal properties of letter identification in retinitis pigmentosa,” J. Opt. Soc. Am. A 10, 1631–1636 (1993).
[CrossRef] [PubMed]

Allen, K. A.

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with antiblue opsin,” J. Comp. Neurol. 312, 610–624 (1991).
[CrossRef] [PubMed]

C. A. Curcio, K. A. Allen, “Topography of ganglion cells in human retina,” J. Comp. Neurol. 300, 5–25 (1990).
[CrossRef] [PubMed]

Anderson, R. S.

Anderson, S. J.

Anstis, S. M.

S. M. Anstis, “A chart demonstrating variations in acuity with retinal position,” Vision Res. 14, 589–592 (1974).
[CrossRef] [PubMed]

Artal, P.

Banks, M. S.

Beckmann, P. J.

P. J. Beckmann, “Preneural limitations to identification performance in central and peripheral vision,” Ph.D. dissertation (University of Minnesota, Minneapolis, Minn., 1998).

Bennett, P. J.

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

Bertera, J. H.

K. Rayner, J. H. Bertera, “Reading without a fovea,” Science 206, 468–469 (1979).
[CrossRef] [PubMed]

Bescos, J.

Bischof, W. F.

D. H. Foster, W. F. Bischof, “Thresholds from psychometric functions: Superiority of bootstrap to incremental and probit variance estimators,” Psychol. Bull. 109, 152–159 (1991).
[CrossRef]

Blanchard, H. E.

H. E. Blanchard, A. Pollatsek, K. Rayner, “The acquisition of parafoveal word information in reading,” Percept. Psychophys. 46, 85–94 (1989).
[CrossRef] [PubMed]

Bouma, H.

H. Bouma, “Visual recognition of isolated lower-case letters,” Vision Res. 11, 459–474 (1971).
[CrossRef] [PubMed]

Bradley, 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]

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

Brainard, D. H.

D. H. Brainard, A. Roorda, Y. Yamauchi, J. B. Calderone, A. Metha, M. Neitz, J. Neitz, D. R. Williams, G. H. Jacobs, “Function consequences of the relative numbers of L and M cones,” J. Opt. Soc. Am. A 17, 607–614 (2000).
[CrossRef]

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

Braje, W. L.

B. S. Tjan, W. L. Braje, G. E. Legge, D. Kersten, “Human efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3069 (1995).
[CrossRef] [PubMed]

Brennan, N. A.

Calderone, J. B.

Campbell, F. W.

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

Carrion-Carire, V.

Charman, W. N.

W. N. Charman, “Optics of the human eye,” in Vision and Visual Dysfunction, Vol. 1, Visual Optics and Instrumentation, W. N. Charman, ed. (Macmillan, London, 1991), pp. 1–26.

Chen, B.

B. Chen, W. Makous, D. R. Williams, “Serial spatial filters in vision,” Vision Res. 33, 413–427 (1993).
[CrossRef] [PubMed]

Chung, S. T. L.

G. E. Legge, J. S. Mansfield, S. T. L. Chung, “Psychophysics of reading XX. Linking letter recognition to reading speed in central and peripheral vision,” Vision Res. 41, 725–743 (2001).
[CrossRef] [PubMed]

S. T. L. Chung, J. S. Mansfield, G. E. Legge, “Psychophysics of reading XVIII. The effect of print size on reading speed in normal peripheral vision,” Vision Res. 38, 2949–2962 (1998).
[CrossRef] [PubMed]

Cicerone, C. M.

S. Otake, P. D. Gowdy, C. M. Cicerone, “The spatial arrangement of L and M cones in the peripheral human retina,” Vision Res. 40, 677–693 (2000).
[CrossRef] [PubMed]

C. M. Cicerone, S. Otake, “Color-opponent sites: individual variability and changes with retinal eccentricity,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S454 (1997).

P. D. Gowdy, S. Otake, C. M. Cicerone, “The spatial arrangement of L and M cones in the living human eye,” Vision Res. Suppl. 37, S448 (1996).

J. L. Nerger, C. M. Cicerone, “The ratio of L cones to M cones in the human parafoveal retina,” Vision Res. 32, 879–888 (1992).
[CrossRef] [PubMed]

C. M. Cicerone, J. L. Nerger, “The relative numbers of long-wavelength-sensitive to middle-wavelength-sensitive cones in the human fovea centralis,” Vision Res. 29, 115–128 (1989).
[CrossRef] [PubMed]

Cowan, W.

W. Cowan, “Displays for vision research,” in Handbook of Optics. Vol. I: Fundamentals, Techniques, and Design, M. Bass, ed. (McGraw-Hill, New York, 1995), pp. 27.1–27.44.

Curcio, C. A.

C. A. Curcio, K. R. Sloan, “Packing geometry of human cone photoreceptors: variation with eccentricity and evidence for local anisotropy,” Visual Neurosci. 9, 169–180 (1992).
[CrossRef]

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with antiblue opsin,” J. Comp. Neurol. 312, 610–624 (1991).
[CrossRef] [PubMed]

C. A. Curcio, K. A. Allen, “Topography of ganglion cells in human retina,” J. Comp. Neurol. 300, 5–25 (1990).
[CrossRef] [PubMed]

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

C. A. Curcio, K. R. Sloan, D. Meyers, “Computer methods for sampling, reconstruction, display and analysis of retinal whole mounts,” Vision Res. 29, 529–540 (1989).
[CrossRef] [PubMed]

C. A. Curcio, University of Alabama at Birmingham; 700 South 18th Street, Room H20; Birmingham, Alabama 35294-0009 (personal communication, October6, 1993).

Davila, K. D.

Derlacki, D. J.

K. R. Alexander, W. Xie, D. J. Derlacki, “Visual acuity and contrast sensitivity for individual Sloan letters,” Vision Res. 37, 813–819 (1997).
[CrossRef] [PubMed]

K. R. Alexander, D. J. Derlacki, G. A. Fishman, J. P. Szlyk, “Temporal properties of letter identification in retinitis pigmentosa,” J. Opt. Soc. Am. A 10, 1631–1636 (1993).
[CrossRef] [PubMed]

Donner, K.

K. Donner, “Noise and the absolute thresholds of cone and rod vision,” Vision Res. 32, 853–866 (1992).
[CrossRef] [PubMed]

Drasdo, N.

N. Drasdo, C. W. Fowler, “Non-linear projection of the retinal image in a wide-angle schematic eye,” Br. J. Ophthamol. 58, 709–714 (1974).
[CrossRef]

Fishman, G. A.

Foley, J. M.

Foster, D. H.

D. H. Foster, W. F. Bischof, “Thresholds from psychometric functions: Superiority of bootstrap to incremental and probit variance estimators,” Psychol. Bull. 109, 152–159 (1991).
[CrossRef]

Fowler, C. W.

N. Drasdo, C. W. Fowler, “Non-linear projection of the retinal image in a wide-angle schematic eye,” Br. J. Ophthamol. 58, 709–714 (1974).
[CrossRef]

Geisler, W. S.

Gonzalez, R. C.

J. T. Tou, R. C. Gonzalez, Pattern Recognition Principles (Addison-Wesley, Reading, Mass., 1974).

Gowdy, P. D.

S. Otake, P. D. Gowdy, C. M. Cicerone, “The spatial arrangement of L and M cones in the peripheral human retina,” Vision Res. 40, 677–693 (2000).
[CrossRef] [PubMed]

P. D. Gowdy, S. Otake, C. M. Cicerone, “The spatial arrangement of L and M cones in the living human eye,” Vision Res. Suppl. 37, S448 (1996).

Green, D. G.

Gubisch, R. W.

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

Guirao, A.

A. Guirao, P. Artal, “Off-axis monochromatic aberrations estimated from double pass measurements in the human eye,” Vision Res. 39, 207–217 (1999).
[CrossRef] [PubMed]

Haddad, G. M.

R. M. Steinman, G. M. Haddad, A. A. Skavenski, D. Wyman, “Miniature eye movements,” Science 181, 810–819 (1973).
[CrossRef] [PubMed]

Hamilton, D. B.

Heller, O.

A. M. Jacobs, T. A. Nazir, O. Heller, “Perception of lowercase letters in peripheral vision: a discrimination matrix based on saccade latencies,” Percept. Psychophys. 46, 95–102 (1989).
[CrossRef] [PubMed]

Hendrickson, A. E.

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

Holopigian, K.

W. Seiple, K. Holopigian, Y. Shnayder, J. P. Szlyk, “Duration thresholds for target detection and identification in the peripheral visual field,” Optom. Vision Sci. 78, 169–176 (2001).
[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]

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

Hurley, J. B.

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with antiblue opsin,” J. Comp. Neurol. 312, 610–624 (1991).
[CrossRef] [PubMed]

Iglesias, I.

Jacobs, A. M.

A. M. Jacobs, T. A. Nazir, O. Heller, “Perception of lowercase letters in peripheral vision: a discrimination matrix based on saccade latencies,” Percept. Psychophys. 46, 95–102 (1989).
[CrossRef] [PubMed]

Jacobs, G. H.

Jacobs, J. C.

F. L. van Nes, J. C. Jacobs, “The effect of contrast on letter and word recognition,” IPO Ann. Prog. Rep.16, 72–80 (1981).

Johnson, C. A.

M. Millodot, C. A. Johnson, A. Lamont, H. W. Leibowitz, “Effect of dioptrics on peripheral visual acuity,” Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

Kalina, R. E.

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

Kersten, D.

B. S. Tjan, W. L. Braje, G. E. Legge, D. Kersten, “Human efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3069 (1995).
[CrossRef] [PubMed]

Klitz, T. S.

G. E. Legge, S. J. Ahn, T. S. Klitz, A. Luebker, “Psychophysics of reading XVI. The visual span in normal and low vision,” Vision Res. 37, 1999–2010 (1997).
[CrossRef] [PubMed]

Klock, I. B.

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with antiblue opsin,” J. Comp. Neurol. 312, 610–624 (1991).
[CrossRef] [PubMed]

Kruger, P. B.

K. R. Aggarwala, S. Nowbotsing, P. B. Kruger, “Accom-modation to monochromatic and white-light targets,” Invest. Ophthalmol. Visual Sci. 36, 2695–2705 (1995).

P. B. Kruger, J. Pola, “Stimuli for accommodation: blur, chromatic aberration and size,” Vision Res. 26, 957–971 (1986).
[CrossRef] [PubMed]

Lamont, A.

M. Millodot, C. A. Johnson, A. Lamont, H. W. Leibowitz, “Effect of dioptrics on peripheral visual acuity,” Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

Lannery, B. P.

W. H. Press, B. P. Lannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, New York, 1988).

Legge, G. E.

G. E. Legge, J. S. Mansfield, S. T. L. Chung, “Psychophysics of reading XX. Linking letter recognition to reading speed in central and peripheral vision,” Vision Res. 41, 725–743 (2001).
[CrossRef] [PubMed]

S. T. L. Chung, J. S. Mansfield, G. E. Legge, “Psychophysics of reading XVIII. The effect of print size on reading speed in normal peripheral vision,” Vision Res. 38, 2949–2962 (1998).
[CrossRef] [PubMed]

G. E. Legge, S. J. Ahn, T. S. Klitz, A. Luebker, “Psychophysics of reading XVI. The visual span in normal and low vision,” Vision Res. 37, 1999–2010 (1997).
[CrossRef] [PubMed]

B. S. Tjan, W. L. Braje, G. E. Legge, D. Kersten, “Human efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3069 (1995).
[CrossRef] [PubMed]

G. E. Legge, G. S. Rubin, D. G. Pelli, M. M. Schleske, “Psychophysics of reading II. Low vision,” Vision Res. 25, 253–266 (1985).
[CrossRef]

G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1471 (1980).
[CrossRef] [PubMed]

Leibowitz, H. W.

M. Millodot, C. A. Johnson, A. Lamont, H. W. Leibowitz, “Effect of dioptrics on peripheral visual acuity,” Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

Lerea, C. L.

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with antiblue opsin,” J. Comp. Neurol. 312, 610–624 (1991).
[CrossRef] [PubMed]

Levine, M. W.

López-Gil, N.

Loshin, D. S.

J. M. White, D. S. Loshin, “Grating acuity overestimates Snellen acuity in patients with age-related maculopathy,” Optom. Vision Sci. 66, 751–755 (1989).
[CrossRef]

Lotmar, T.

Lotmar, W.

Ludvigh, E.

E. Ludvigh, “Extrafoveal visual acuity as measured with Snellen test-letters,” Am. J. Ophthalmol. 24, 303–310 (1941).

Luebker, A.

G. E. Legge, S. J. Ahn, T. S. Klitz, A. Luebker, “Psychophysics of reading XVI. The visual span in normal and low vision,” Vision Res. 37, 1999–2010 (1997).
[CrossRef] [PubMed]

Makous, W.

B. Chen, W. Makous, D. R. Williams, “Serial spatial filters in vision,” Vision Res. 33, 413–427 (1993).
[CrossRef] [PubMed]

Maloney, L. T.

L. T. Maloney, “Confidence intervals for the parameters of psychometric functions,” Percept. Psychophys. 47, 127–134 (1990).
[CrossRef] [PubMed]

Mansfield, J. S.

G. E. Legge, J. S. Mansfield, S. T. L. Chung, “Psychophysics of reading XX. Linking letter recognition to reading speed in central and peripheral vision,” Vision Res. 41, 725–743 (2001).
[CrossRef] [PubMed]

S. T. L. Chung, J. S. Mansfield, G. E. Legge, “Psychophysics of reading XVIII. The effect of print size on reading speed in normal peripheral vision,” Vision Res. 38, 2949–2962 (1998).
[CrossRef] [PubMed]

Marcos, S.

McKendrick, A. M.

McMahon, M. J.

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

Metha, A.

Meyers, D.

C. A. Curcio, K. R. Sloan, D. Meyers, “Computer methods for sampling, reconstruction, display and analysis of retinal whole mounts,” Vision Res. 29, 529–540 (1989).
[CrossRef] [PubMed]

Milam, A. H.

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with antiblue opsin,” J. Comp. Neurol. 312, 610–624 (1991).
[CrossRef] [PubMed]

Millodot, M.

M. Millodot, C. A. Johnson, A. Lamont, H. W. Leibowitz, “Effect of dioptrics on peripheral visual acuity,” Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

Navarro, R.

Nazir, T. A.

A. M. Jacobs, T. A. Nazir, O. Heller, “Perception of lowercase letters in peripheral vision: a discrimination matrix based on saccade latencies,” Percept. Psychophys. 46, 95–102 (1989).
[CrossRef] [PubMed]

Neitz, J.

Neitz, M.

Nerger, J. L.

J. L. Nerger, C. M. Cicerone, “The ratio of L cones to M cones in the human parafoveal retina,” Vision Res. 32, 879–888 (1992).
[CrossRef] [PubMed]

C. M. Cicerone, J. L. Nerger, “The relative numbers of long-wavelength-sensitive to middle-wavelength-sensitive cones in the human fovea centralis,” Vision Res. 29, 115–128 (1989).
[CrossRef] [PubMed]

Nowbotsing, S.

K. R. Aggarwala, S. Nowbotsing, P. B. Kruger, “Accom-modation to monochromatic and white-light targets,” Invest. Ophthalmol. Visual Sci. 36, 2695–2705 (1995).

Otake, S.

S. Otake, P. D. Gowdy, C. M. Cicerone, “The spatial arrangement of L and M cones in the peripheral human retina,” Vision Res. 40, 677–693 (2000).
[CrossRef] [PubMed]

C. M. Cicerone, S. Otake, “Color-opponent sites: individual variability and changes with retinal eccentricity,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S454 (1997).

P. D. Gowdy, S. Otake, C. M. Cicerone, “The spatial arrangement of L and M cones in the living human eye,” Vision Res. Suppl. 37, S448 (1996).

Pelli, D. G.

J. A. Solomon, D. G. Pelli, “The visual filter mediating letter identification,” Nature 369, 395–397 (1994).
[CrossRef] [PubMed]

G. E. Legge, G. S. Rubin, D. G. Pelli, M. M. Schleske, “Psychophysics of reading II. Low vision,” Vision Res. 25, 253–266 (1985).
[CrossRef]

D. G. Pelli, “The quantum efficiency of vision,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, 1990), pp. 3–24.

Pola, J.

P. B. Kruger, J. Pola, “Stimuli for accommodation: blur, chromatic aberration and size,” Vision Res. 26, 957–971 (1986).
[CrossRef] [PubMed]

Pollatsek, A.

H. E. Blanchard, A. Pollatsek, K. Rayner, “The acquisition of parafoveal word information in reading,” Percept. Psychophys. 46, 85–94 (1989).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, B. P. Lannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, New York, 1988).

Rayner, K.

H. E. Blanchard, A. Pollatsek, K. Rayner, “The acquisition of parafoveal word information in reading,” Percept. Psychophys. 46, 85–94 (1989).
[CrossRef] [PubMed]

K. Rayner, J. H. Bertera, “Reading without a fovea,” Science 206, 468–469 (1979).
[CrossRef] [PubMed]

Roethlein, B. E.

B. E. Roethlein, “The relative legibility of different faces of printing types,” Am. J. Psychol. 23, 1–36 (1912).
[CrossRef]

Roorda, A.

Rubin, G. S.

G. E. Legge, G. S. Rubin, D. G. Pelli, M. M. Schleske, “Psychophysics of reading II. Low vision,” Vision Res. 25, 253–266 (1985).
[CrossRef]

Sanford, E. C.

E. C. Sanford, “The relative legibility of the small letters,” Am. J. Psychol. 1, 402–435 (1888).
[CrossRef]

Santamari´a, J.

Schleske, M. M.

G. E. Legge, G. S. Rubin, D. G. Pelli, M. M. Schleske, “Psychophysics of reading II. Low vision,” Vision Res. 25, 253–266 (1985).
[CrossRef]

Seiple, W.

W. Seiple, K. Holopigian, Y. Shnayder, J. P. Szlyk, “Duration thresholds for target detection and identification in the peripheral visual field,” Optom. Vision Sci. 78, 169–176 (2001).
[CrossRef]

Sekuler, A. B.

Shnayder, Y.

W. Seiple, K. Holopigian, Y. Shnayder, J. P. Szlyk, “Duration thresholds for target detection and identification in the peripheral visual field,” Optom. Vision Sci. 78, 169–176 (2001).
[CrossRef]

Skavenski, A. A.

R. M. Steinman, G. M. Haddad, A. A. Skavenski, D. Wyman, “Miniature eye movements,” Science 181, 810–819 (1973).
[CrossRef] [PubMed]

Sloan, K. R.

C. A. Curcio, K. R. Sloan, “Packing geometry of human cone photoreceptors: variation with eccentricity and evidence for local anisotropy,” Visual Neurosci. 9, 169–180 (1992).
[CrossRef]

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C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1990).
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C. A. Curcio, K. R. Sloan, D. Meyers, “Computer methods for sampling, reconstruction, display and analysis of retinal whole mounts,” Vision Res. 29, 529–540 (1989).
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W. Seiple, K. Holopigian, Y. Shnayder, J. P. Szlyk, “Duration thresholds for target detection and identification in the peripheral visual field,” Optom. Vision Sci. 78, 169–176 (2001).
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D. H. Brainard, A. Roorda, Y. Yamauchi, J. B. Calderone, A. Metha, M. Neitz, J. Neitz, D. R. Williams, G. H. Jacobs, “Function consequences of the relative numbers of L and M cones,” J. Opt. Soc. Am. A 17, 607–614 (2000).
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B. Chen, W. Makous, D. R. Williams, “Serial spatial filters in vision,” Vision Res. 33, 413–427 (1993).
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R. M. Steinman, G. M. Haddad, A. A. Skavenski, D. Wyman, “Miniature eye movements,” Science 181, 810–819 (1973).
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B. Chen, W. Makous, D. R. Williams, “Serial spatial filters in vision,” Vision Res. 33, 413–427 (1993).
[CrossRef] [PubMed]

K. R. Alexander, W. Xie, D. J. Derlacki, “Visual acuity and contrast sensitivity for individual Sloan letters,” Vision Res. 37, 813–819 (1997).
[CrossRef] [PubMed]

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Other (26)

W. N. Charman, “Optics of the human eye,” in Vision and Visual Dysfunction, Vol. 1, Visual Optics and Instrumentation, W. N. Charman, ed. (Macmillan, London, 1991), pp. 1–26.

Each cone class is assumed to have a fixed probability of absorption for all quanta entering its aperture, based on the wavelength of the light and the cone class. Some evidence of individual differences in the photopigment density, at least near the fovea,63exists. This difference, however, is not incorporated into the model. Instead, a peak absorption probability of 50% is assumed in the calculations.

G. Wyszecki, W. S. Stiles, Color Science, 2nd ed. (Wiley, New York, 1982).

Psychophysical studies of cone vision66have shown that quantum noise follows Poisson statistics in the dark-adapted human eye.

The Gabor patch was rendered as a 101×101 pixel bitmap representing a cosinusoidal horizontal grating modulated by a 2D circular half-cosine envelope. The half-cosine spanned 7.5 periods of the underlying grating. Each period of the grating was rendered across 12.5 pixels. The spatial frequency of the grating was changed by changing the viewing distance and keeping the rendering of the grating the same. The amplitude of the grating modulation of the background was changed for each distance until the model performed at threshold level.

The cutoff due to diffraction is 110 cpd for a 4-mm pupil. It is reasonable to expect the 4-mm pupil diameter represented in the current model to exhibit a cutoff higher than that of the 1.5-mm pupil used by Banks but lower than the theoretical diffraction limit due to aberrations.

J. T. Tou, R. C. Gonzalez, Pattern Recognition Principles (Addison-Wesley, Reading, Mass., 1974).

F. L. van Nes, J. C. Jacobs, “The effect of contrast on letter and word recognition,” IPO Ann. Prog. Rep.16, 72–80 (1981).

Postscript™ assigns an origin within its definition for each letter. Within each x-height size, the origin of the letters was in the same location, trial to trial. Alternative rules for aligning stimulus letters on the screen could influence performance of the ideal observer; for instance, in an extreme case in which the 26 letters were presented at distinct, nonoverlapping regions of the screen, the ideal-observer’s performance would be significantly improved. The method used here, however, resulted in substantial overlap between the letter images.

B. S. Tjan, “Ideal observer analysis of object recognition,” Ph.D. dissertation (University of Minnesota, Minneapolis, Minn., 1996).

W. H. Press, B. P. Lannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, New York, 1988).

This presentation time was chosen because it was the shortest reliable presentation time possible with the software and hardware used in the experiment.

The model uses the field scale values of 282, 277, and 262 μm/deg at 0°, 5°, and 20° eccentricity to determine the size of the stimulus image on the retina. These field scales have been calculated by using the Drasdo49wide-field schematic eye following Curcio.50

The PSF includes the effects of defocus, chromatic aberration, diffraction, and scatter. For our study the reported modulation transfer function values of Navarro et al.4were used to estimate the PSF. The horizontal and vertical cross sections of the PSF were each modeled as the sum of two Gaussians. Fitting the PSF with Gaussians provided a straightforward computation of the retinal image of a 2D Gaussian pixel. The area under the PSF was normalized to 1.0 while the relative contributions of these two Gaussians and their standard deviations were varied with eccentricity. In the simulations reported here, astigmatism was not included for the following reasons. Central astigmatism varies within the human population and between the eyes of individuals.45In addition, the effects of peripheral astigmatism are quite small within 20° of central vision.46The relationship between central and peripheral astigmatism initially appeared to vary in complex ways that differ significantly between individuals.4Artal and his colleagues, however, recently developed a technique that allows investigation of odd-order aberrations, including peripheral astigmatism.1,3They found that peripheral astigmatism and coma were most consistent between subjects but that peripheral defocus varied greatly between subjects. The position of Williams47and Guirao and Artal3is that the circle of least confusion remains unchanged at least out to 20°. This compromise condition of focus is the one included here.

Two parameters that affect the rendering of the letter on the display will be considered here: pixel pitchdefined as the physical separation between adjacent pixels, and pixel widthdefined as the standard deviation of the Gaussian pixel profile. The pixels are arranged on a rectangular grid.

W. Cowan, “Displays for vision research,” in Handbook of Optics. Vol. I: Fundamentals, Techniques, and Design, M. Bass, ed. (McGraw-Hill, New York, 1995), pp. 27.1–27.44.

The photoreceptors were positioned on a regular, triangular close-packed grid. Photons were captured by the photoreceptor if they fell anywhere in their physiologic aperture, which was taken to be a circle with a diameter equal to the cone spacing. The retinal image was sampled by this mosaic by multiplying it by the Fourier transform of a single cone, inverse transforming the result, and sampling the image at the known receptor sites.

Geisler derived a closed-form expression for the likelihood computed from the mean absorption counts for both of the alternatives.

Their study controlled the optical image quality of the eye across the visual field by using an external 1.5-mm pupil. They used such a pupil in the human experiments and represented the imaging in the model as diffraction limited.

G. Westheimer, “The eye as an optical instrument,” in Handbook of Perception and Human Performance. Vol. I. Sensory Processes and Perception, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), pp. 4-1–4-20.

The photoreceptors were positioned on a regular triangular mosaic at the densities found by Curcio and her colleagues,6and the aperture of the photoreceptor was taken as either the diameter of the inner segment or the outer segment of the receptor, with a photon taken as captured if it fell anywhere within the aperture. The isomerization rate was taken as eccentricity dependent.

The location of each cone is known exactly by the decision stage.

D. G. Pelli, “The quantum efficiency of vision,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, 1990), pp. 3–24.

C. A. Curcio, University of Alabama at Birmingham; 700 South 18th Street, Room H20; Birmingham, Alabama 35294-0009 (personal communication, October6, 1993).

Tjan measured percent-correct identification performance as a function of SNR for letters of fixed size. Our work uses letters of fixed contrast and letters of varying size. It is possible, however, to build a bridge between these two approaches by noting that “signal” for the ideal observer used by Tjan is proportional to the square of letter x height for fixed contrast. Thus a factor of kincrease in SNR at threshold performance in Tjan’s analysis corresponds to a k0.5increase in letter size at fixed contrast and the same threshold level of performance. We used this method to calculate our estimates.

P. J. Beckmann, “Preneural limitations to identification performance in central and peripheral vision,” Ph.D. dissertation (University of Minnesota, Minneapolis, Minn., 1998).

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Figures (10)

Fig. 1
Fig. 1

Representations of the stimulus and the stages of the model that convert one representation to another.

Fig. 2
Fig. 2

PSFs used in the model are shown for 0°, 5°, and 20° eccentricity. They were derived from Navarro et al.4 by using a sum of two Gaussian functions. In addition, the data of Campbell and Gubisch2 for a 3.4-mm pupil in white light and the diffraction limit for a 4-mm pupil are shown. The curves shown have been normalized to a peak amplitude of 1.0 to emphasize the differences in their shapes.

Fig. 3
Fig. 3

Three synthetic cone mosaics at 0°, 5°, and 20° (left to right) with jitter. These mosaics were generated from the parameters in Table 3. S cones are the lightest gray and L cones the darkest, with M cones rendered at an intermediate level of gray. 25-μm bars are shown in the lower-right corner of each panel for reference.

Fig. 4
Fig. 4

Contrast-sensitivity performance of the model at 0°, 5°, and 20° eccentricity. The stimulus was a horizontal cosine grating modulated by a half-cosine envelope spanning 7.5 grating periods. The background luminance was 340 cd/m2 and the exposure duration was 100 ms, with 400 simulated trials per point. The CRT pixel spacing was 1/7 mm and the spatial standard deviation of the pixel luminance profile was 0.1 mm. Data from Banks et al.28 are shown for comparison.

Fig. 5
Fig. 5

Letter-identification performance as a function of visual size for letters of fixed physical size but different pixel profiles. (a) Letters rendered with 27 pixels over the height of a lowercase x. (b) Letters rendered with nine pixels over an x height, 100 simulated trials per point.

Fig. 6
Fig. 6

Proportion correct as a function of letter x height in arc minutes for four human participants and the ideal-observer model (IDEAL). Psychometric data are given for 100-ms presentations at Michelson contrast of 75%. Mean performance is plotted for the three data blocks at 0°, 5°, and 20° eccentricity. Weibull-function fits to the block means are shown. Standard deviation bars are shown when they are larger than the symbols.

Fig. 7
Fig. 7

Threshold letter size as a function of eccentricity for four human participants and the ideal-observer model. Standard deviations of the thresholds from resampling analysis are shown when they are larger than the symbol. The ideal-observer model data are shown at two different scales. The open squares show the data on the same scale as the human data (use the left-axis scale). The open circles show the data on an expanded scale to show detail (use the right-axis scale).

Fig. 8
Fig. 8

Change in threshold letter size with a decrease in contrast from 75% to 25% with exposure time of 100 ms. The ratio of low-contrast threshold letter size over high-contrast threshold letter size as a function of eccentricity for two human participants and the ideal-observer model is shown.

Fig. 9
Fig. 9

Change in threshold letter size with a decrease in exposure time from 100 to 33 ms with contrast of 75%. The ratio of 33-ms threshold letter size over 100-ms threshold letter size as a function of eccentricity for two human participants and the ideal-observer model is shown.

Fig. 10
Fig. 10

Change in threshold letter size under high-contrast, 100-ms exposure conditions. Threshold letter size normalized to that at 0° for four human participants and the ideal-observer model is shown. In addition, the normalized threshold letter size for the model, multiplied by the estimate of ganglion-cell pooling of Banks et al.28 is plotted.

Tables (5)

Tables Icon

Table 1 Aspects of Some of the Studies of Identification Performance in the Periphery or of Lowercase Letter Identification

Tables Icon

Table 2 Key Characteristics of the Current Model and Closely Related Earlier Models in the Literature

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Table 3 Optical and Retinal Parameters at 0°, 5°, and 20° Eccentricity Used in the Simulations

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Table 4 Participant Summary

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Table 5 Mean Weibull Slope Parameter (beta) and Threshold Letter Size (alpha) for the Three Experiments

Equations (12)

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π(σ)=1-{(25/26)*exp[-(σ/α)β]}
pixel(x, y)=pamp12π psd2exp-x2+y22 psd2.
psf(x, y)=12πpsfhsdpsfvsd×exp-x22psfhsd2+y22psfvsd2
retina(x, y)=pixel  psf=-+pixel[(x-η),(y-v)]psf(η, v)dηdv.
capture(x, y)=exp-x2+y22recepsd2.
transfer(x0, y0)=recepsd2shsvexp-x022sh2+y022sv2,
sh=(psd2+psfhsd2+recepsd2)1/2
sv=(psd2+psfvsd2+recepsd2)1/2.
Li=jp(mij|Zj).
li=ln(Li)=jln(p(mij|Zj).
ln[p(mij|Zj)]=mijZjexp(-mij)Zj!
li=ln[p(mij|Zj)]=ln12πmijexp-(Zj-mij)22mij=-0.5 ln(2π)-0.5 ln mij-(Zj-mij)22mij.

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