Abstract

We introduce a temporal phase mixing model for a description of the frequency-doubling illusion (FDI). The model is generic in the sense that it can be set to refer to retinal ganglion cells, lateral geniculate cells, as well as simple cells in the primary visual cortex (V1). Model parameters, however, strongly suggest that the FDI originates in the cortex. The model shows how noise in the response phases of cells in V1, or in further processing of these phases, easily produces observed behavior of FDI onset as a function of spatiotemporal frequencies. It also shows how this noise can accommodate physiologically plausible spatial delays in comparing neural signals over a distance. The model offers an explanation for the disappearance of the FDI at sufficiently high spatial frequencies via increasingly correlated coding of neighboring grating stripes. Further, when the FDI is equated to vanishing perceptual discrimination between asynchronous contrast-reversal gratings, the model proposes the possibility that the FDI shows a resonance behavior at sufficiently high spatial frequencies, by which it is alternately perceived and not perceived in sequential temporal frequency bands.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Kelly, “Frequency doubling in visual responses,” J. Opt. Soc. Am. 56, 1628–1633 (1966).
    [CrossRef]
  2. W. Richards and T. Felton, “Spatial frequency doubling: retinal or central?” Vis. Res. 13, 2129–2137 (1973).
    [CrossRef]
  3. C. Tyler, “Observations on spatial-frequency doubling,” Perception 3, 81–86 (1974).
    [CrossRef]
  4. J. Kulikowski, “Apparent fineness of briefly presented gratings: balance between movement and pattern channels,” Vis. Res. 15, 673–680 (1975).
    [CrossRef]
  5. D. Kelly, “Nonlinear visual responses to flickering sinusoidal gratings,” J. Opt. Soc. Am. 71, 1051–1055 (1981).
    [CrossRef]
  6. A. Parker, “Shifts in perceived periodicity induced by temporal modulation and their influence on the spatial frequency tuning of two aftereffects,” Vis. Res. 21, 1739–1747 (1981).
    [CrossRef]
  7. A. Parker, “The effects of temporal modulation on the perceived spatial structure of sine wave gratings,” Perception 12, 663–682 (1983).
    [CrossRef]
  8. T. Maddess and W. Severt, “Testing for glaucoma with the spatial frequency-doubling illusion,” Vis. Res. 39, 4258–4273 (1999).
    [CrossRef]
  9. K. Vallam, I. Pataridis, and A. Metha, “Frequency doubling illusion under scotopic illumination and in peripheral vision,” Invest. Ophthalmol. Vis. Sci. 48, 3413–3418 (2007).
    [CrossRef]
  10. Y. Rosli, S. Bedford, and T. Maddess, “Low spatial-frequency channels and the spatial frequency doubling illusion,” Invest. Ophthalmol. Vis. Sci. 50, 1956–1963 (2009).
    [CrossRef]
  11. T. Maddess and G. Henry, “Performance of nonlinear visual units in ocular hypertension and glaucoma,” Clin Vision Sci 7, 371–383 (1992).
  12. C. Johnson and S. Samuels, “Screening for glaucomatous visual field loss with frequency-doubling perimetry,” Invest. Ophthalmol. Vis. Sci. 38, 413–425 (1997).
  13. L. Racette, F. Medeiros, L. Zangwill, D. Ng, R. Weinreb, and P. Sample, “Diagnostic accuracy of the matrix 24-2 and original n-30 frequency-doubling technology tests compared with standard automated perimetry,” Investig. Ophthalmol. Vis. Sci. 49, 954–960 (2008).
    [CrossRef]
  14. H. Sun, M. Dul, and W. Swanson, “Linearity can account for the similarity among conventional, frequency-doubling, and Gabor-based perimetric tests in the glaucomatous macula,” Optometry Vision Sci. 83, E455–E465 (2006).
    [CrossRef]
  15. C. Clement, I. Goldberg, P. Healey, and S. Graham, “Humphrey matrix frequency doubling perimetry for detection of visual-field defects in open-angle glaucoma,” British J. Ophthalmol. 93, 582–588 (2009).
    [CrossRef]
  16. A. Anderson and C. Johnson, “Mechanisms isolated by frequency-doubling technology perimetry,” Invest. Ophthalmol. Vis. Sci. 43, 398–401 (2002).
  17. M. Aghdaee and P. Cavanagh, “Temporal limits of long-range phase discrimination across the visual field,” Vis. Res. 47, 2156–2163 (2007).
    [CrossRef]
  18. J. Wielaard and P. Sajda, “Extraclassical phenomena and short-range connectivity in V1,” Cereb. Cortex 16, 1531–1545 (2006).
    [CrossRef]
  19. T. Maddess, “Frequency-doubling technology and parasol cells,” Invest. Ophthalmol. Vis. Sci. 52, 3759 (2011).
    [CrossRef]
  20. W. Swanson, H. Sun, B. Lee, and D. Cao, “Author response: frequency-doubling technology and parasol cells,” Invest. Ophthalmol. Vis. Sci. 52, 3759–3760 (2011).
    [CrossRef]
  21. T. Maddess, J. Hemmi, and A. James, “Evidence for spatial aliasing effects in the Y-like cells of the magnocellular visual pathway,” Vis. Res. 38, 1843–1859 (1998).
    [CrossRef]
  22. A. White, H. Sun, W. Swanson, and B. Lee, “An examination of physiological mechanisms underlying the frequency-doubling illusion,” Invest. Ophthalmol. Vis. Sci. 43, 3590–3599 (2002).
  23. W. Swanson, H. Sun, B. Lee, and D. Cao, “Responses of primate retinal ganglion cells to perimetric stimuli,” Investig. Ophthalmol. Vis. Sci. 52, 764–771 (2011).
    [CrossRef]
  24. J. Movshon, I. Thompson, and D. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. 283, 53–77 (1978).
  25. J. Movshon, I. Thompson, and D. Tolhurst, “Receptive field organization of complex cells in the cat’s striate cortex,” J. Physiol. 283, 79–99 (1978).
  26. R. De Valois, D. Albrecht, and L. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vis. Res. 22, 545–559 (1982).
    [CrossRef]
  27. H. Spitzer and S. Hochstein, “Simple- and complex-cell response dependencies on stimulation parameters,” J. Neurophysiol. 53, 1244–1265 (1985).
  28. R. Reid, R. Soodak, and R. Shapley, “Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex,” J. Neurophysiol. 66, 505–529 (1991).
  29. B. Skottun, R. De Valois, D. Grosof, J. Movshon, D. Albrecht, and A. Bonds, “Classification of simple and complex cells on the basis of response modulation,” Vis. Res. 31, 1078–1086 (1991).
  30. J. Wielaard, M. Shelley, D. McLaughlin, and R. Shapley, “How simple cells are made in a nonlinear network model of the visual cortex,” J. Neurosci. 21, 5203–5211 (2001).
  31. K. Vallam and A. Metha, “Spatial structure of the frequency doubling illusion,” Vis. Res. 47, 1732–1744 (2007).
    [CrossRef]
  32. K. Vallam and A. Metha, “The relationship between temporal phase discrimination ability and the frequency doubling illusion,” J. Vis. 7(14):17, 1–11 (2007).
    [CrossRef]
  33. M. Hawken, R. Shapley, and D. Grosof, “Temporal-frequency selectivity in monkey visual cortex,” Vis. Neurosci. 13, 477–492 (1996).
    [CrossRef]
  34. M. Schmolesky, Y. Wang, D. Hanes, K. Thomson, S. Leutgeb, J. Schall, and A. Leventhal, “Signal timing across the macaque visual system,” J. Neurophysiol. 79, 3272–3278 (1998).
  35. V. Lamme and P. Roelfsema, “The distinct modes of vision offered by feedforward and recurrent processing,” Trends Neurosci. 23, 571–579 (2000).
    [CrossRef]
  36. F. Mechler and J. Victor, “Comparison of thresholds for high-speed drifting Vernier and a matched temporal phase-discrimination task,” Vis. Res. 40, 1839–1855 (2000).
    [CrossRef]
  37. J. Victor and M. Conte, “Temporal phase discrimination depends critically on separation,” Vis. Res. 42, 2063–2071 (2002).
    [CrossRef]
  38. J. Rovamo and A. Raninen, “Critical flicker frequency and M-scaling of stimulus size and retinal illuminance,” Vis. Res. 24, 1127–1131 (1984).
    [CrossRef]
  39. T. Andrews, L. White, D. Binder, and D. Purves, “Temporal events in cyclopean vision,” Proc. Natl. Acad. Sci. U.S.A. 93, 3689–3692 (1996).
    [CrossRef]
  40. W. Van de Grind, O. Grüsser, and H. Lunkenheimer, Handbook of Sensory Physiology, R. Jung, ed. (Springer, 1973), Vol. VII/3, pp. 431–573.
  41. G. Westheimer and S. McKee, “Perception of temporal order in adjacent visual stimuli,” Vis. Res. 17, 887–892 (1977).
    [CrossRef]
  42. S. He, P. Cavanagh, and J. Intriligator, “Attentional resolution,” Trends Cogn. Sci. 1, 115–121 (1997).
    [CrossRef]
  43. D. Rogers-Ramachandra and V. Ramachandran, “Psychophysical evidence for boundary and surface systems in human vision,” Vis. Res. 38, 71–77 (1998).
    [CrossRef]
  44. J. Forte, J. Hogben, and J. Ross, “Spatial limitations of temporal segmentation,” Vis. Res. 39, 4052–4061 (1999).
    [CrossRef]
  45. A. Holcombe, “Spatial limitations of temporal segmentation,” Trends Cogn. Sci. 13, 216–221 (2009).
    [CrossRef]
  46. R. De Valois, M. Webster, K. De Valois, and B. Lingelbach, “Temporal properties of brightness and color induction,” Vis. Res. 26, 887–897 (1986).
    [CrossRef]
  47. I. Motoyoshi, “The role of spatial interactions in perceptual synchrony,” J. Vis. 4(5):1, 352–361 (2004).
    [CrossRef]
  48. P. Cavanagh, “Attention-based motion perception,” Science 257, 1563–1565 (1992).
    [CrossRef]
  49. Z. Lu and G. Sperling, “Three-systems theory of human visual motion perception: review and update,” J. Opt. Soc. Am. A 18, 2331–2370 (2001).
    [CrossRef]
  50. F. Verstraten, P. Cavanagh, and A. Labianca, “Limits of attentive tracking reveal temporal properties of attention,” Vis. Res. 40, 3651–3664 (2000).
    [CrossRef]
  51. L. Battelli, P. Cavanagh, P. Martini, and J. Barton, “Bilateral deficits of transient visual attention in right parietal patients,” Brain 126, 2164–2174 (2003).
    [CrossRef]
  52. O. Grüsser and T. Landis, Visual Agnosias and Other Disturbances of Visual Perception and Cognition (Macmillan, 1991).
  53. M. Fahle, “Figure-ground discrimination from temporal information,” Proc. R. Soc. B 254, 199–203 (1993).
    [CrossRef]
  54. U. Leonards, W. Singer, and M. Fahle, “The influence of temporal phase differences on texture segmentation,” Vis. Res. 36, 2689–2697 (1996).
    [CrossRef]
  55. F. Kandil and M. Fahle, “Purely temporal figure-ground segregation,” Eur. J. Neurosci. 13, 2004–2008 (2001).
    [CrossRef]

2011 (3)

T. Maddess, “Frequency-doubling technology and parasol cells,” Invest. Ophthalmol. Vis. Sci. 52, 3759 (2011).
[CrossRef]

W. Swanson, H. Sun, B. Lee, and D. Cao, “Author response: frequency-doubling technology and parasol cells,” Invest. Ophthalmol. Vis. Sci. 52, 3759–3760 (2011).
[CrossRef]

W. Swanson, H. Sun, B. Lee, and D. Cao, “Responses of primate retinal ganglion cells to perimetric stimuli,” Investig. Ophthalmol. Vis. Sci. 52, 764–771 (2011).
[CrossRef]

2009 (3)

Y. Rosli, S. Bedford, and T. Maddess, “Low spatial-frequency channels and the spatial frequency doubling illusion,” Invest. Ophthalmol. Vis. Sci. 50, 1956–1963 (2009).
[CrossRef]

C. Clement, I. Goldberg, P. Healey, and S. Graham, “Humphrey matrix frequency doubling perimetry for detection of visual-field defects in open-angle glaucoma,” British J. Ophthalmol. 93, 582–588 (2009).
[CrossRef]

A. Holcombe, “Spatial limitations of temporal segmentation,” Trends Cogn. Sci. 13, 216–221 (2009).
[CrossRef]

2008 (1)

L. Racette, F. Medeiros, L. Zangwill, D. Ng, R. Weinreb, and P. Sample, “Diagnostic accuracy of the matrix 24-2 and original n-30 frequency-doubling technology tests compared with standard automated perimetry,” Investig. Ophthalmol. Vis. Sci. 49, 954–960 (2008).
[CrossRef]

2007 (4)

K. Vallam, I. Pataridis, and A. Metha, “Frequency doubling illusion under scotopic illumination and in peripheral vision,” Invest. Ophthalmol. Vis. Sci. 48, 3413–3418 (2007).
[CrossRef]

M. Aghdaee and P. Cavanagh, “Temporal limits of long-range phase discrimination across the visual field,” Vis. Res. 47, 2156–2163 (2007).
[CrossRef]

K. Vallam and A. Metha, “Spatial structure of the frequency doubling illusion,” Vis. Res. 47, 1732–1744 (2007).
[CrossRef]

K. Vallam and A. Metha, “The relationship between temporal phase discrimination ability and the frequency doubling illusion,” J. Vis. 7(14):17, 1–11 (2007).
[CrossRef]

2006 (2)

J. Wielaard and P. Sajda, “Extraclassical phenomena and short-range connectivity in V1,” Cereb. Cortex 16, 1531–1545 (2006).
[CrossRef]

H. Sun, M. Dul, and W. Swanson, “Linearity can account for the similarity among conventional, frequency-doubling, and Gabor-based perimetric tests in the glaucomatous macula,” Optometry Vision Sci. 83, E455–E465 (2006).
[CrossRef]

2004 (1)

I. Motoyoshi, “The role of spatial interactions in perceptual synchrony,” J. Vis. 4(5):1, 352–361 (2004).
[CrossRef]

2003 (1)

L. Battelli, P. Cavanagh, P. Martini, and J. Barton, “Bilateral deficits of transient visual attention in right parietal patients,” Brain 126, 2164–2174 (2003).
[CrossRef]

2002 (3)

J. Victor and M. Conte, “Temporal phase discrimination depends critically on separation,” Vis. Res. 42, 2063–2071 (2002).
[CrossRef]

A. Anderson and C. Johnson, “Mechanisms isolated by frequency-doubling technology perimetry,” Invest. Ophthalmol. Vis. Sci. 43, 398–401 (2002).

A. White, H. Sun, W. Swanson, and B. Lee, “An examination of physiological mechanisms underlying the frequency-doubling illusion,” Invest. Ophthalmol. Vis. Sci. 43, 3590–3599 (2002).

2001 (3)

J. Wielaard, M. Shelley, D. McLaughlin, and R. Shapley, “How simple cells are made in a nonlinear network model of the visual cortex,” J. Neurosci. 21, 5203–5211 (2001).

Z. Lu and G. Sperling, “Three-systems theory of human visual motion perception: review and update,” J. Opt. Soc. Am. A 18, 2331–2370 (2001).
[CrossRef]

F. Kandil and M. Fahle, “Purely temporal figure-ground segregation,” Eur. J. Neurosci. 13, 2004–2008 (2001).
[CrossRef]

2000 (3)

F. Verstraten, P. Cavanagh, and A. Labianca, “Limits of attentive tracking reveal temporal properties of attention,” Vis. Res. 40, 3651–3664 (2000).
[CrossRef]

V. Lamme and P. Roelfsema, “The distinct modes of vision offered by feedforward and recurrent processing,” Trends Neurosci. 23, 571–579 (2000).
[CrossRef]

F. Mechler and J. Victor, “Comparison of thresholds for high-speed drifting Vernier and a matched temporal phase-discrimination task,” Vis. Res. 40, 1839–1855 (2000).
[CrossRef]

1999 (2)

T. Maddess and W. Severt, “Testing for glaucoma with the spatial frequency-doubling illusion,” Vis. Res. 39, 4258–4273 (1999).
[CrossRef]

J. Forte, J. Hogben, and J. Ross, “Spatial limitations of temporal segmentation,” Vis. Res. 39, 4052–4061 (1999).
[CrossRef]

1998 (3)

D. Rogers-Ramachandra and V. Ramachandran, “Psychophysical evidence for boundary and surface systems in human vision,” Vis. Res. 38, 71–77 (1998).
[CrossRef]

M. Schmolesky, Y. Wang, D. Hanes, K. Thomson, S. Leutgeb, J. Schall, and A. Leventhal, “Signal timing across the macaque visual system,” J. Neurophysiol. 79, 3272–3278 (1998).

T. Maddess, J. Hemmi, and A. James, “Evidence for spatial aliasing effects in the Y-like cells of the magnocellular visual pathway,” Vis. Res. 38, 1843–1859 (1998).
[CrossRef]

1997 (2)

C. Johnson and S. Samuels, “Screening for glaucomatous visual field loss with frequency-doubling perimetry,” Invest. Ophthalmol. Vis. Sci. 38, 413–425 (1997).

S. He, P. Cavanagh, and J. Intriligator, “Attentional resolution,” Trends Cogn. Sci. 1, 115–121 (1997).
[CrossRef]

1996 (3)

T. Andrews, L. White, D. Binder, and D. Purves, “Temporal events in cyclopean vision,” Proc. Natl. Acad. Sci. U.S.A. 93, 3689–3692 (1996).
[CrossRef]

U. Leonards, W. Singer, and M. Fahle, “The influence of temporal phase differences on texture segmentation,” Vis. Res. 36, 2689–2697 (1996).
[CrossRef]

M. Hawken, R. Shapley, and D. Grosof, “Temporal-frequency selectivity in monkey visual cortex,” Vis. Neurosci. 13, 477–492 (1996).
[CrossRef]

1993 (1)

M. Fahle, “Figure-ground discrimination from temporal information,” Proc. R. Soc. B 254, 199–203 (1993).
[CrossRef]

1992 (2)

P. Cavanagh, “Attention-based motion perception,” Science 257, 1563–1565 (1992).
[CrossRef]

T. Maddess and G. Henry, “Performance of nonlinear visual units in ocular hypertension and glaucoma,” Clin Vision Sci 7, 371–383 (1992).

1991 (2)

R. Reid, R. Soodak, and R. Shapley, “Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex,” J. Neurophysiol. 66, 505–529 (1991).

B. Skottun, R. De Valois, D. Grosof, J. Movshon, D. Albrecht, and A. Bonds, “Classification of simple and complex cells on the basis of response modulation,” Vis. Res. 31, 1078–1086 (1991).

1986 (1)

R. De Valois, M. Webster, K. De Valois, and B. Lingelbach, “Temporal properties of brightness and color induction,” Vis. Res. 26, 887–897 (1986).
[CrossRef]

1985 (1)

H. Spitzer and S. Hochstein, “Simple- and complex-cell response dependencies on stimulation parameters,” J. Neurophysiol. 53, 1244–1265 (1985).

1984 (1)

J. Rovamo and A. Raninen, “Critical flicker frequency and M-scaling of stimulus size and retinal illuminance,” Vis. Res. 24, 1127–1131 (1984).
[CrossRef]

1983 (1)

A. Parker, “The effects of temporal modulation on the perceived spatial structure of sine wave gratings,” Perception 12, 663–682 (1983).
[CrossRef]

1982 (1)

R. De Valois, D. Albrecht, and L. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vis. Res. 22, 545–559 (1982).
[CrossRef]

1981 (2)

D. Kelly, “Nonlinear visual responses to flickering sinusoidal gratings,” J. Opt. Soc. Am. 71, 1051–1055 (1981).
[CrossRef]

A. Parker, “Shifts in perceived periodicity induced by temporal modulation and their influence on the spatial frequency tuning of two aftereffects,” Vis. Res. 21, 1739–1747 (1981).
[CrossRef]

1978 (2)

J. Movshon, I. Thompson, and D. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. 283, 53–77 (1978).

J. Movshon, I. Thompson, and D. Tolhurst, “Receptive field organization of complex cells in the cat’s striate cortex,” J. Physiol. 283, 79–99 (1978).

1977 (1)

G. Westheimer and S. McKee, “Perception of temporal order in adjacent visual stimuli,” Vis. Res. 17, 887–892 (1977).
[CrossRef]

1975 (1)

J. Kulikowski, “Apparent fineness of briefly presented gratings: balance between movement and pattern channels,” Vis. Res. 15, 673–680 (1975).
[CrossRef]

1974 (1)

C. Tyler, “Observations on spatial-frequency doubling,” Perception 3, 81–86 (1974).
[CrossRef]

1973 (1)

W. Richards and T. Felton, “Spatial frequency doubling: retinal or central?” Vis. Res. 13, 2129–2137 (1973).
[CrossRef]

1966 (1)

Aghdaee, M.

M. Aghdaee and P. Cavanagh, “Temporal limits of long-range phase discrimination across the visual field,” Vis. Res. 47, 2156–2163 (2007).
[CrossRef]

Albrecht, D.

B. Skottun, R. De Valois, D. Grosof, J. Movshon, D. Albrecht, and A. Bonds, “Classification of simple and complex cells on the basis of response modulation,” Vis. Res. 31, 1078–1086 (1991).

R. De Valois, D. Albrecht, and L. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vis. Res. 22, 545–559 (1982).
[CrossRef]

Anderson, A.

A. Anderson and C. Johnson, “Mechanisms isolated by frequency-doubling technology perimetry,” Invest. Ophthalmol. Vis. Sci. 43, 398–401 (2002).

Andrews, T.

T. Andrews, L. White, D. Binder, and D. Purves, “Temporal events in cyclopean vision,” Proc. Natl. Acad. Sci. U.S.A. 93, 3689–3692 (1996).
[CrossRef]

Barton, J.

L. Battelli, P. Cavanagh, P. Martini, and J. Barton, “Bilateral deficits of transient visual attention in right parietal patients,” Brain 126, 2164–2174 (2003).
[CrossRef]

Battelli, L.

L. Battelli, P. Cavanagh, P. Martini, and J. Barton, “Bilateral deficits of transient visual attention in right parietal patients,” Brain 126, 2164–2174 (2003).
[CrossRef]

Bedford, S.

Y. Rosli, S. Bedford, and T. Maddess, “Low spatial-frequency channels and the spatial frequency doubling illusion,” Invest. Ophthalmol. Vis. Sci. 50, 1956–1963 (2009).
[CrossRef]

Binder, D.

T. Andrews, L. White, D. Binder, and D. Purves, “Temporal events in cyclopean vision,” Proc. Natl. Acad. Sci. U.S.A. 93, 3689–3692 (1996).
[CrossRef]

Bonds, A.

B. Skottun, R. De Valois, D. Grosof, J. Movshon, D. Albrecht, and A. Bonds, “Classification of simple and complex cells on the basis of response modulation,” Vis. Res. 31, 1078–1086 (1991).

Cao, D.

W. Swanson, H. Sun, B. Lee, and D. Cao, “Responses of primate retinal ganglion cells to perimetric stimuli,” Investig. Ophthalmol. Vis. Sci. 52, 764–771 (2011).
[CrossRef]

W. Swanson, H. Sun, B. Lee, and D. Cao, “Author response: frequency-doubling technology and parasol cells,” Invest. Ophthalmol. Vis. Sci. 52, 3759–3760 (2011).
[CrossRef]

Cavanagh, P.

M. Aghdaee and P. Cavanagh, “Temporal limits of long-range phase discrimination across the visual field,” Vis. Res. 47, 2156–2163 (2007).
[CrossRef]

L. Battelli, P. Cavanagh, P. Martini, and J. Barton, “Bilateral deficits of transient visual attention in right parietal patients,” Brain 126, 2164–2174 (2003).
[CrossRef]

F. Verstraten, P. Cavanagh, and A. Labianca, “Limits of attentive tracking reveal temporal properties of attention,” Vis. Res. 40, 3651–3664 (2000).
[CrossRef]

S. He, P. Cavanagh, and J. Intriligator, “Attentional resolution,” Trends Cogn. Sci. 1, 115–121 (1997).
[CrossRef]

P. Cavanagh, “Attention-based motion perception,” Science 257, 1563–1565 (1992).
[CrossRef]

Clement, C.

C. Clement, I. Goldberg, P. Healey, and S. Graham, “Humphrey matrix frequency doubling perimetry for detection of visual-field defects in open-angle glaucoma,” British J. Ophthalmol. 93, 582–588 (2009).
[CrossRef]

Conte, M.

J. Victor and M. Conte, “Temporal phase discrimination depends critically on separation,” Vis. Res. 42, 2063–2071 (2002).
[CrossRef]

De Valois, K.

R. De Valois, M. Webster, K. De Valois, and B. Lingelbach, “Temporal properties of brightness and color induction,” Vis. Res. 26, 887–897 (1986).
[CrossRef]

De Valois, R.

B. Skottun, R. De Valois, D. Grosof, J. Movshon, D. Albrecht, and A. Bonds, “Classification of simple and complex cells on the basis of response modulation,” Vis. Res. 31, 1078–1086 (1991).

R. De Valois, M. Webster, K. De Valois, and B. Lingelbach, “Temporal properties of brightness and color induction,” Vis. Res. 26, 887–897 (1986).
[CrossRef]

R. De Valois, D. Albrecht, and L. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vis. Res. 22, 545–559 (1982).
[CrossRef]

Dul, M.

H. Sun, M. Dul, and W. Swanson, “Linearity can account for the similarity among conventional, frequency-doubling, and Gabor-based perimetric tests in the glaucomatous macula,” Optometry Vision Sci. 83, E455–E465 (2006).
[CrossRef]

Fahle, M.

F. Kandil and M. Fahle, “Purely temporal figure-ground segregation,” Eur. J. Neurosci. 13, 2004–2008 (2001).
[CrossRef]

U. Leonards, W. Singer, and M. Fahle, “The influence of temporal phase differences on texture segmentation,” Vis. Res. 36, 2689–2697 (1996).
[CrossRef]

M. Fahle, “Figure-ground discrimination from temporal information,” Proc. R. Soc. B 254, 199–203 (1993).
[CrossRef]

Felton, T.

W. Richards and T. Felton, “Spatial frequency doubling: retinal or central?” Vis. Res. 13, 2129–2137 (1973).
[CrossRef]

Forte, J.

J. Forte, J. Hogben, and J. Ross, “Spatial limitations of temporal segmentation,” Vis. Res. 39, 4052–4061 (1999).
[CrossRef]

Goldberg, I.

C. Clement, I. Goldberg, P. Healey, and S. Graham, “Humphrey matrix frequency doubling perimetry for detection of visual-field defects in open-angle glaucoma,” British J. Ophthalmol. 93, 582–588 (2009).
[CrossRef]

Graham, S.

C. Clement, I. Goldberg, P. Healey, and S. Graham, “Humphrey matrix frequency doubling perimetry for detection of visual-field defects in open-angle glaucoma,” British J. Ophthalmol. 93, 582–588 (2009).
[CrossRef]

Grosof, D.

M. Hawken, R. Shapley, and D. Grosof, “Temporal-frequency selectivity in monkey visual cortex,” Vis. Neurosci. 13, 477–492 (1996).
[CrossRef]

B. Skottun, R. De Valois, D. Grosof, J. Movshon, D. Albrecht, and A. Bonds, “Classification of simple and complex cells on the basis of response modulation,” Vis. Res. 31, 1078–1086 (1991).

Grüsser, O.

W. Van de Grind, O. Grüsser, and H. Lunkenheimer, Handbook of Sensory Physiology, R. Jung, ed. (Springer, 1973), Vol. VII/3, pp. 431–573.

O. Grüsser and T. Landis, Visual Agnosias and Other Disturbances of Visual Perception and Cognition (Macmillan, 1991).

Hanes, D.

M. Schmolesky, Y. Wang, D. Hanes, K. Thomson, S. Leutgeb, J. Schall, and A. Leventhal, “Signal timing across the macaque visual system,” J. Neurophysiol. 79, 3272–3278 (1998).

Hawken, M.

M. Hawken, R. Shapley, and D. Grosof, “Temporal-frequency selectivity in monkey visual cortex,” Vis. Neurosci. 13, 477–492 (1996).
[CrossRef]

He, S.

S. He, P. Cavanagh, and J. Intriligator, “Attentional resolution,” Trends Cogn. Sci. 1, 115–121 (1997).
[CrossRef]

Healey, P.

C. Clement, I. Goldberg, P. Healey, and S. Graham, “Humphrey matrix frequency doubling perimetry for detection of visual-field defects in open-angle glaucoma,” British J. Ophthalmol. 93, 582–588 (2009).
[CrossRef]

Hemmi, J.

T. Maddess, J. Hemmi, and A. James, “Evidence for spatial aliasing effects in the Y-like cells of the magnocellular visual pathway,” Vis. Res. 38, 1843–1859 (1998).
[CrossRef]

Henry, G.

T. Maddess and G. Henry, “Performance of nonlinear visual units in ocular hypertension and glaucoma,” Clin Vision Sci 7, 371–383 (1992).

Hochstein, S.

H. Spitzer and S. Hochstein, “Simple- and complex-cell response dependencies on stimulation parameters,” J. Neurophysiol. 53, 1244–1265 (1985).

Hogben, J.

J. Forte, J. Hogben, and J. Ross, “Spatial limitations of temporal segmentation,” Vis. Res. 39, 4052–4061 (1999).
[CrossRef]

Holcombe, A.

A. Holcombe, “Spatial limitations of temporal segmentation,” Trends Cogn. Sci. 13, 216–221 (2009).
[CrossRef]

Intriligator, J.

S. He, P. Cavanagh, and J. Intriligator, “Attentional resolution,” Trends Cogn. Sci. 1, 115–121 (1997).
[CrossRef]

James, A.

T. Maddess, J. Hemmi, and A. James, “Evidence for spatial aliasing effects in the Y-like cells of the magnocellular visual pathway,” Vis. Res. 38, 1843–1859 (1998).
[CrossRef]

Johnson, C.

A. Anderson and C. Johnson, “Mechanisms isolated by frequency-doubling technology perimetry,” Invest. Ophthalmol. Vis. Sci. 43, 398–401 (2002).

C. Johnson and S. Samuels, “Screening for glaucomatous visual field loss with frequency-doubling perimetry,” Invest. Ophthalmol. Vis. Sci. 38, 413–425 (1997).

Kandil, F.

F. Kandil and M. Fahle, “Purely temporal figure-ground segregation,” Eur. J. Neurosci. 13, 2004–2008 (2001).
[CrossRef]

Kelly, D.

Kulikowski, J.

J. Kulikowski, “Apparent fineness of briefly presented gratings: balance between movement and pattern channels,” Vis. Res. 15, 673–680 (1975).
[CrossRef]

Labianca, A.

F. Verstraten, P. Cavanagh, and A. Labianca, “Limits of attentive tracking reveal temporal properties of attention,” Vis. Res. 40, 3651–3664 (2000).
[CrossRef]

Lamme, V.

V. Lamme and P. Roelfsema, “The distinct modes of vision offered by feedforward and recurrent processing,” Trends Neurosci. 23, 571–579 (2000).
[CrossRef]

Landis, T.

O. Grüsser and T. Landis, Visual Agnosias and Other Disturbances of Visual Perception and Cognition (Macmillan, 1991).

Lee, B.

W. Swanson, H. Sun, B. Lee, and D. Cao, “Responses of primate retinal ganglion cells to perimetric stimuli,” Investig. Ophthalmol. Vis. Sci. 52, 764–771 (2011).
[CrossRef]

W. Swanson, H. Sun, B. Lee, and D. Cao, “Author response: frequency-doubling technology and parasol cells,” Invest. Ophthalmol. Vis. Sci. 52, 3759–3760 (2011).
[CrossRef]

A. White, H. Sun, W. Swanson, and B. Lee, “An examination of physiological mechanisms underlying the frequency-doubling illusion,” Invest. Ophthalmol. Vis. Sci. 43, 3590–3599 (2002).

Leonards, U.

U. Leonards, W. Singer, and M. Fahle, “The influence of temporal phase differences on texture segmentation,” Vis. Res. 36, 2689–2697 (1996).
[CrossRef]

Leutgeb, S.

M. Schmolesky, Y. Wang, D. Hanes, K. Thomson, S. Leutgeb, J. Schall, and A. Leventhal, “Signal timing across the macaque visual system,” J. Neurophysiol. 79, 3272–3278 (1998).

Leventhal, A.

M. Schmolesky, Y. Wang, D. Hanes, K. Thomson, S. Leutgeb, J. Schall, and A. Leventhal, “Signal timing across the macaque visual system,” J. Neurophysiol. 79, 3272–3278 (1998).

Lingelbach, B.

R. De Valois, M. Webster, K. De Valois, and B. Lingelbach, “Temporal properties of brightness and color induction,” Vis. Res. 26, 887–897 (1986).
[CrossRef]

Lu, Z.

Lunkenheimer, H.

W. Van de Grind, O. Grüsser, and H. Lunkenheimer, Handbook of Sensory Physiology, R. Jung, ed. (Springer, 1973), Vol. VII/3, pp. 431–573.

Maddess, T.

T. Maddess, “Frequency-doubling technology and parasol cells,” Invest. Ophthalmol. Vis. Sci. 52, 3759 (2011).
[CrossRef]

Y. Rosli, S. Bedford, and T. Maddess, “Low spatial-frequency channels and the spatial frequency doubling illusion,” Invest. Ophthalmol. Vis. Sci. 50, 1956–1963 (2009).
[CrossRef]

T. Maddess and W. Severt, “Testing for glaucoma with the spatial frequency-doubling illusion,” Vis. Res. 39, 4258–4273 (1999).
[CrossRef]

T. Maddess, J. Hemmi, and A. James, “Evidence for spatial aliasing effects in the Y-like cells of the magnocellular visual pathway,” Vis. Res. 38, 1843–1859 (1998).
[CrossRef]

T. Maddess and G. Henry, “Performance of nonlinear visual units in ocular hypertension and glaucoma,” Clin Vision Sci 7, 371–383 (1992).

Martini, P.

L. Battelli, P. Cavanagh, P. Martini, and J. Barton, “Bilateral deficits of transient visual attention in right parietal patients,” Brain 126, 2164–2174 (2003).
[CrossRef]

McKee, S.

G. Westheimer and S. McKee, “Perception of temporal order in adjacent visual stimuli,” Vis. Res. 17, 887–892 (1977).
[CrossRef]

McLaughlin, D.

J. Wielaard, M. Shelley, D. McLaughlin, and R. Shapley, “How simple cells are made in a nonlinear network model of the visual cortex,” J. Neurosci. 21, 5203–5211 (2001).

Mechler, F.

F. Mechler and J. Victor, “Comparison of thresholds for high-speed drifting Vernier and a matched temporal phase-discrimination task,” Vis. Res. 40, 1839–1855 (2000).
[CrossRef]

Medeiros, F.

L. Racette, F. Medeiros, L. Zangwill, D. Ng, R. Weinreb, and P. Sample, “Diagnostic accuracy of the matrix 24-2 and original n-30 frequency-doubling technology tests compared with standard automated perimetry,” Investig. Ophthalmol. Vis. Sci. 49, 954–960 (2008).
[CrossRef]

Metha, A.

K. Vallam, I. Pataridis, and A. Metha, “Frequency doubling illusion under scotopic illumination and in peripheral vision,” Invest. Ophthalmol. Vis. Sci. 48, 3413–3418 (2007).
[CrossRef]

K. Vallam and A. Metha, “Spatial structure of the frequency doubling illusion,” Vis. Res. 47, 1732–1744 (2007).
[CrossRef]

K. Vallam and A. Metha, “The relationship between temporal phase discrimination ability and the frequency doubling illusion,” J. Vis. 7(14):17, 1–11 (2007).
[CrossRef]

Motoyoshi, I.

I. Motoyoshi, “The role of spatial interactions in perceptual synchrony,” J. Vis. 4(5):1, 352–361 (2004).
[CrossRef]

Movshon, J.

B. Skottun, R. De Valois, D. Grosof, J. Movshon, D. Albrecht, and A. Bonds, “Classification of simple and complex cells on the basis of response modulation,” Vis. Res. 31, 1078–1086 (1991).

J. Movshon, I. Thompson, and D. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. 283, 53–77 (1978).

J. Movshon, I. Thompson, and D. Tolhurst, “Receptive field organization of complex cells in the cat’s striate cortex,” J. Physiol. 283, 79–99 (1978).

Ng, D.

L. Racette, F. Medeiros, L. Zangwill, D. Ng, R. Weinreb, and P. Sample, “Diagnostic accuracy of the matrix 24-2 and original n-30 frequency-doubling technology tests compared with standard automated perimetry,” Investig. Ophthalmol. Vis. Sci. 49, 954–960 (2008).
[CrossRef]

Parker, A.

A. Parker, “The effects of temporal modulation on the perceived spatial structure of sine wave gratings,” Perception 12, 663–682 (1983).
[CrossRef]

A. Parker, “Shifts in perceived periodicity induced by temporal modulation and their influence on the spatial frequency tuning of two aftereffects,” Vis. Res. 21, 1739–1747 (1981).
[CrossRef]

Pataridis, I.

K. Vallam, I. Pataridis, and A. Metha, “Frequency doubling illusion under scotopic illumination and in peripheral vision,” Invest. Ophthalmol. Vis. Sci. 48, 3413–3418 (2007).
[CrossRef]

Purves, D.

T. Andrews, L. White, D. Binder, and D. Purves, “Temporal events in cyclopean vision,” Proc. Natl. Acad. Sci. U.S.A. 93, 3689–3692 (1996).
[CrossRef]

Racette, L.

L. Racette, F. Medeiros, L. Zangwill, D. Ng, R. Weinreb, and P. Sample, “Diagnostic accuracy of the matrix 24-2 and original n-30 frequency-doubling technology tests compared with standard automated perimetry,” Investig. Ophthalmol. Vis. Sci. 49, 954–960 (2008).
[CrossRef]

Ramachandran, V.

D. Rogers-Ramachandra and V. Ramachandran, “Psychophysical evidence for boundary and surface systems in human vision,” Vis. Res. 38, 71–77 (1998).
[CrossRef]

Raninen, A.

J. Rovamo and A. Raninen, “Critical flicker frequency and M-scaling of stimulus size and retinal illuminance,” Vis. Res. 24, 1127–1131 (1984).
[CrossRef]

Reid, R.

R. Reid, R. Soodak, and R. Shapley, “Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex,” J. Neurophysiol. 66, 505–529 (1991).

Richards, W.

W. Richards and T. Felton, “Spatial frequency doubling: retinal or central?” Vis. Res. 13, 2129–2137 (1973).
[CrossRef]

Roelfsema, P.

V. Lamme and P. Roelfsema, “The distinct modes of vision offered by feedforward and recurrent processing,” Trends Neurosci. 23, 571–579 (2000).
[CrossRef]

Rogers-Ramachandra, D.

D. Rogers-Ramachandra and V. Ramachandran, “Psychophysical evidence for boundary and surface systems in human vision,” Vis. Res. 38, 71–77 (1998).
[CrossRef]

Rosli, Y.

Y. Rosli, S. Bedford, and T. Maddess, “Low spatial-frequency channels and the spatial frequency doubling illusion,” Invest. Ophthalmol. Vis. Sci. 50, 1956–1963 (2009).
[CrossRef]

Ross, J.

J. Forte, J. Hogben, and J. Ross, “Spatial limitations of temporal segmentation,” Vis. Res. 39, 4052–4061 (1999).
[CrossRef]

Rovamo, J.

J. Rovamo and A. Raninen, “Critical flicker frequency and M-scaling of stimulus size and retinal illuminance,” Vis. Res. 24, 1127–1131 (1984).
[CrossRef]

Sajda, P.

J. Wielaard and P. Sajda, “Extraclassical phenomena and short-range connectivity in V1,” Cereb. Cortex 16, 1531–1545 (2006).
[CrossRef]

Sample, P.

L. Racette, F. Medeiros, L. Zangwill, D. Ng, R. Weinreb, and P. Sample, “Diagnostic accuracy of the matrix 24-2 and original n-30 frequency-doubling technology tests compared with standard automated perimetry,” Investig. Ophthalmol. Vis. Sci. 49, 954–960 (2008).
[CrossRef]

Samuels, S.

C. Johnson and S. Samuels, “Screening for glaucomatous visual field loss with frequency-doubling perimetry,” Invest. Ophthalmol. Vis. Sci. 38, 413–425 (1997).

Schall, J.

M. Schmolesky, Y. Wang, D. Hanes, K. Thomson, S. Leutgeb, J. Schall, and A. Leventhal, “Signal timing across the macaque visual system,” J. Neurophysiol. 79, 3272–3278 (1998).

Schmolesky, M.

M. Schmolesky, Y. Wang, D. Hanes, K. Thomson, S. Leutgeb, J. Schall, and A. Leventhal, “Signal timing across the macaque visual system,” J. Neurophysiol. 79, 3272–3278 (1998).

Severt, W.

T. Maddess and W. Severt, “Testing for glaucoma with the spatial frequency-doubling illusion,” Vis. Res. 39, 4258–4273 (1999).
[CrossRef]

Shapley, R.

J. Wielaard, M. Shelley, D. McLaughlin, and R. Shapley, “How simple cells are made in a nonlinear network model of the visual cortex,” J. Neurosci. 21, 5203–5211 (2001).

M. Hawken, R. Shapley, and D. Grosof, “Temporal-frequency selectivity in monkey visual cortex,” Vis. Neurosci. 13, 477–492 (1996).
[CrossRef]

R. Reid, R. Soodak, and R. Shapley, “Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex,” J. Neurophysiol. 66, 505–529 (1991).

Shelley, M.

J. Wielaard, M. Shelley, D. McLaughlin, and R. Shapley, “How simple cells are made in a nonlinear network model of the visual cortex,” J. Neurosci. 21, 5203–5211 (2001).

Singer, W.

U. Leonards, W. Singer, and M. Fahle, “The influence of temporal phase differences on texture segmentation,” Vis. Res. 36, 2689–2697 (1996).
[CrossRef]

Skottun, B.

B. Skottun, R. De Valois, D. Grosof, J. Movshon, D. Albrecht, and A. Bonds, “Classification of simple and complex cells on the basis of response modulation,” Vis. Res. 31, 1078–1086 (1991).

Soodak, R.

R. Reid, R. Soodak, and R. Shapley, “Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex,” J. Neurophysiol. 66, 505–529 (1991).

Sperling, G.

Spitzer, H.

H. Spitzer and S. Hochstein, “Simple- and complex-cell response dependencies on stimulation parameters,” J. Neurophysiol. 53, 1244–1265 (1985).

Sun, H.

W. Swanson, H. Sun, B. Lee, and D. Cao, “Author response: frequency-doubling technology and parasol cells,” Invest. Ophthalmol. Vis. Sci. 52, 3759–3760 (2011).
[CrossRef]

W. Swanson, H. Sun, B. Lee, and D. Cao, “Responses of primate retinal ganglion cells to perimetric stimuli,” Investig. Ophthalmol. Vis. Sci. 52, 764–771 (2011).
[CrossRef]

H. Sun, M. Dul, and W. Swanson, “Linearity can account for the similarity among conventional, frequency-doubling, and Gabor-based perimetric tests in the glaucomatous macula,” Optometry Vision Sci. 83, E455–E465 (2006).
[CrossRef]

A. White, H. Sun, W. Swanson, and B. Lee, “An examination of physiological mechanisms underlying the frequency-doubling illusion,” Invest. Ophthalmol. Vis. Sci. 43, 3590–3599 (2002).

Swanson, W.

W. Swanson, H. Sun, B. Lee, and D. Cao, “Responses of primate retinal ganglion cells to perimetric stimuli,” Investig. Ophthalmol. Vis. Sci. 52, 764–771 (2011).
[CrossRef]

W. Swanson, H. Sun, B. Lee, and D. Cao, “Author response: frequency-doubling technology and parasol cells,” Invest. Ophthalmol. Vis. Sci. 52, 3759–3760 (2011).
[CrossRef]

H. Sun, M. Dul, and W. Swanson, “Linearity can account for the similarity among conventional, frequency-doubling, and Gabor-based perimetric tests in the glaucomatous macula,” Optometry Vision Sci. 83, E455–E465 (2006).
[CrossRef]

A. White, H. Sun, W. Swanson, and B. Lee, “An examination of physiological mechanisms underlying the frequency-doubling illusion,” Invest. Ophthalmol. Vis. Sci. 43, 3590–3599 (2002).

Thompson, I.

J. Movshon, I. Thompson, and D. Tolhurst, “Receptive field organization of complex cells in the cat’s striate cortex,” J. Physiol. 283, 79–99 (1978).

J. Movshon, I. Thompson, and D. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. 283, 53–77 (1978).

Thomson, K.

M. Schmolesky, Y. Wang, D. Hanes, K. Thomson, S. Leutgeb, J. Schall, and A. Leventhal, “Signal timing across the macaque visual system,” J. Neurophysiol. 79, 3272–3278 (1998).

Thorell, L.

R. De Valois, D. Albrecht, and L. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vis. Res. 22, 545–559 (1982).
[CrossRef]

Tolhurst, D.

J. Movshon, I. Thompson, and D. Tolhurst, “Receptive field organization of complex cells in the cat’s striate cortex,” J. Physiol. 283, 79–99 (1978).

J. Movshon, I. Thompson, and D. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. 283, 53–77 (1978).

Tyler, C.

C. Tyler, “Observations on spatial-frequency doubling,” Perception 3, 81–86 (1974).
[CrossRef]

Vallam, K.

K. Vallam, I. Pataridis, and A. Metha, “Frequency doubling illusion under scotopic illumination and in peripheral vision,” Invest. Ophthalmol. Vis. Sci. 48, 3413–3418 (2007).
[CrossRef]

K. Vallam and A. Metha, “The relationship between temporal phase discrimination ability and the frequency doubling illusion,” J. Vis. 7(14):17, 1–11 (2007).
[CrossRef]

K. Vallam and A. Metha, “Spatial structure of the frequency doubling illusion,” Vis. Res. 47, 1732–1744 (2007).
[CrossRef]

Van de Grind, W.

W. Van de Grind, O. Grüsser, and H. Lunkenheimer, Handbook of Sensory Physiology, R. Jung, ed. (Springer, 1973), Vol. VII/3, pp. 431–573.

Verstraten, F.

F. Verstraten, P. Cavanagh, and A. Labianca, “Limits of attentive tracking reveal temporal properties of attention,” Vis. Res. 40, 3651–3664 (2000).
[CrossRef]

Victor, J.

J. Victor and M. Conte, “Temporal phase discrimination depends critically on separation,” Vis. Res. 42, 2063–2071 (2002).
[CrossRef]

F. Mechler and J. Victor, “Comparison of thresholds for high-speed drifting Vernier and a matched temporal phase-discrimination task,” Vis. Res. 40, 1839–1855 (2000).
[CrossRef]

Wang, Y.

M. Schmolesky, Y. Wang, D. Hanes, K. Thomson, S. Leutgeb, J. Schall, and A. Leventhal, “Signal timing across the macaque visual system,” J. Neurophysiol. 79, 3272–3278 (1998).

Webster, M.

R. De Valois, M. Webster, K. De Valois, and B. Lingelbach, “Temporal properties of brightness and color induction,” Vis. Res. 26, 887–897 (1986).
[CrossRef]

Weinreb, R.

L. Racette, F. Medeiros, L. Zangwill, D. Ng, R. Weinreb, and P. Sample, “Diagnostic accuracy of the matrix 24-2 and original n-30 frequency-doubling technology tests compared with standard automated perimetry,” Investig. Ophthalmol. Vis. Sci. 49, 954–960 (2008).
[CrossRef]

Westheimer, G.

G. Westheimer and S. McKee, “Perception of temporal order in adjacent visual stimuli,” Vis. Res. 17, 887–892 (1977).
[CrossRef]

White, A.

A. White, H. Sun, W. Swanson, and B. Lee, “An examination of physiological mechanisms underlying the frequency-doubling illusion,” Invest. Ophthalmol. Vis. Sci. 43, 3590–3599 (2002).

White, L.

T. Andrews, L. White, D. Binder, and D. Purves, “Temporal events in cyclopean vision,” Proc. Natl. Acad. Sci. U.S.A. 93, 3689–3692 (1996).
[CrossRef]

Wielaard, J.

J. Wielaard and P. Sajda, “Extraclassical phenomena and short-range connectivity in V1,” Cereb. Cortex 16, 1531–1545 (2006).
[CrossRef]

J. Wielaard, M. Shelley, D. McLaughlin, and R. Shapley, “How simple cells are made in a nonlinear network model of the visual cortex,” J. Neurosci. 21, 5203–5211 (2001).

Zangwill, L.

L. Racette, F. Medeiros, L. Zangwill, D. Ng, R. Weinreb, and P. Sample, “Diagnostic accuracy of the matrix 24-2 and original n-30 frequency-doubling technology tests compared with standard automated perimetry,” Investig. Ophthalmol. Vis. Sci. 49, 954–960 (2008).
[CrossRef]

Brain (1)

L. Battelli, P. Cavanagh, P. Martini, and J. Barton, “Bilateral deficits of transient visual attention in right parietal patients,” Brain 126, 2164–2174 (2003).
[CrossRef]

British J. Ophthalmol. (1)

C. Clement, I. Goldberg, P. Healey, and S. Graham, “Humphrey matrix frequency doubling perimetry for detection of visual-field defects in open-angle glaucoma,” British J. Ophthalmol. 93, 582–588 (2009).
[CrossRef]

Cereb. Cortex (1)

J. Wielaard and P. Sajda, “Extraclassical phenomena and short-range connectivity in V1,” Cereb. Cortex 16, 1531–1545 (2006).
[CrossRef]

Clin Vision Sci (1)

T. Maddess and G. Henry, “Performance of nonlinear visual units in ocular hypertension and glaucoma,” Clin Vision Sci 7, 371–383 (1992).

Eur. J. Neurosci. (1)

F. Kandil and M. Fahle, “Purely temporal figure-ground segregation,” Eur. J. Neurosci. 13, 2004–2008 (2001).
[CrossRef]

Invest. Ophthalmol. Vis. Sci. (7)

C. Johnson and S. Samuels, “Screening for glaucomatous visual field loss with frequency-doubling perimetry,” Invest. Ophthalmol. Vis. Sci. 38, 413–425 (1997).

A. Anderson and C. Johnson, “Mechanisms isolated by frequency-doubling technology perimetry,” Invest. Ophthalmol. Vis. Sci. 43, 398–401 (2002).

K. Vallam, I. Pataridis, and A. Metha, “Frequency doubling illusion under scotopic illumination and in peripheral vision,” Invest. Ophthalmol. Vis. Sci. 48, 3413–3418 (2007).
[CrossRef]

Y. Rosli, S. Bedford, and T. Maddess, “Low spatial-frequency channels and the spatial frequency doubling illusion,” Invest. Ophthalmol. Vis. Sci. 50, 1956–1963 (2009).
[CrossRef]

T. Maddess, “Frequency-doubling technology and parasol cells,” Invest. Ophthalmol. Vis. Sci. 52, 3759 (2011).
[CrossRef]

W. Swanson, H. Sun, B. Lee, and D. Cao, “Author response: frequency-doubling technology and parasol cells,” Invest. Ophthalmol. Vis. Sci. 52, 3759–3760 (2011).
[CrossRef]

A. White, H. Sun, W. Swanson, and B. Lee, “An examination of physiological mechanisms underlying the frequency-doubling illusion,” Invest. Ophthalmol. Vis. Sci. 43, 3590–3599 (2002).

Investig. Ophthalmol. Vis. Sci. (2)

W. Swanson, H. Sun, B. Lee, and D. Cao, “Responses of primate retinal ganglion cells to perimetric stimuli,” Investig. Ophthalmol. Vis. Sci. 52, 764–771 (2011).
[CrossRef]

L. Racette, F. Medeiros, L. Zangwill, D. Ng, R. Weinreb, and P. Sample, “Diagnostic accuracy of the matrix 24-2 and original n-30 frequency-doubling technology tests compared with standard automated perimetry,” Investig. Ophthalmol. Vis. Sci. 49, 954–960 (2008).
[CrossRef]

J. Neurophysiol. (3)

H. Spitzer and S. Hochstein, “Simple- and complex-cell response dependencies on stimulation parameters,” J. Neurophysiol. 53, 1244–1265 (1985).

R. Reid, R. Soodak, and R. Shapley, “Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex,” J. Neurophysiol. 66, 505–529 (1991).

M. Schmolesky, Y. Wang, D. Hanes, K. Thomson, S. Leutgeb, J. Schall, and A. Leventhal, “Signal timing across the macaque visual system,” J. Neurophysiol. 79, 3272–3278 (1998).

J. Neurosci. (1)

J. Wielaard, M. Shelley, D. McLaughlin, and R. Shapley, “How simple cells are made in a nonlinear network model of the visual cortex,” J. Neurosci. 21, 5203–5211 (2001).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Physiol. (2)

J. Movshon, I. Thompson, and D. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. 283, 53–77 (1978).

J. Movshon, I. Thompson, and D. Tolhurst, “Receptive field organization of complex cells in the cat’s striate cortex,” J. Physiol. 283, 79–99 (1978).

J. Vis. (2)

I. Motoyoshi, “The role of spatial interactions in perceptual synchrony,” J. Vis. 4(5):1, 352–361 (2004).
[CrossRef]

K. Vallam and A. Metha, “The relationship between temporal phase discrimination ability and the frequency doubling illusion,” J. Vis. 7(14):17, 1–11 (2007).
[CrossRef]

Optometry Vision Sci. (1)

H. Sun, M. Dul, and W. Swanson, “Linearity can account for the similarity among conventional, frequency-doubling, and Gabor-based perimetric tests in the glaucomatous macula,” Optometry Vision Sci. 83, E455–E465 (2006).
[CrossRef]

Perception (2)

A. Parker, “The effects of temporal modulation on the perceived spatial structure of sine wave gratings,” Perception 12, 663–682 (1983).
[CrossRef]

C. Tyler, “Observations on spatial-frequency doubling,” Perception 3, 81–86 (1974).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

T. Andrews, L. White, D. Binder, and D. Purves, “Temporal events in cyclopean vision,” Proc. Natl. Acad. Sci. U.S.A. 93, 3689–3692 (1996).
[CrossRef]

Proc. R. Soc. B (1)

M. Fahle, “Figure-ground discrimination from temporal information,” Proc. R. Soc. B 254, 199–203 (1993).
[CrossRef]

Science (1)

P. Cavanagh, “Attention-based motion perception,” Science 257, 1563–1565 (1992).
[CrossRef]

Trends Cogn. Sci. (2)

S. He, P. Cavanagh, and J. Intriligator, “Attentional resolution,” Trends Cogn. Sci. 1, 115–121 (1997).
[CrossRef]

A. Holcombe, “Spatial limitations of temporal segmentation,” Trends Cogn. Sci. 13, 216–221 (2009).
[CrossRef]

Trends Neurosci. (1)

V. Lamme and P. Roelfsema, “The distinct modes of vision offered by feedforward and recurrent processing,” Trends Neurosci. 23, 571–579 (2000).
[CrossRef]

Vis. Neurosci. (1)

M. Hawken, R. Shapley, and D. Grosof, “Temporal-frequency selectivity in monkey visual cortex,” Vis. Neurosci. 13, 477–492 (1996).
[CrossRef]

Vis. Res. (18)

R. De Valois, M. Webster, K. De Valois, and B. Lingelbach, “Temporal properties of brightness and color induction,” Vis. Res. 26, 887–897 (1986).
[CrossRef]

D. Rogers-Ramachandra and V. Ramachandran, “Psychophysical evidence for boundary and surface systems in human vision,” Vis. Res. 38, 71–77 (1998).
[CrossRef]

J. Forte, J. Hogben, and J. Ross, “Spatial limitations of temporal segmentation,” Vis. Res. 39, 4052–4061 (1999).
[CrossRef]

F. Verstraten, P. Cavanagh, and A. Labianca, “Limits of attentive tracking reveal temporal properties of attention,” Vis. Res. 40, 3651–3664 (2000).
[CrossRef]

U. Leonards, W. Singer, and M. Fahle, “The influence of temporal phase differences on texture segmentation,” Vis. Res. 36, 2689–2697 (1996).
[CrossRef]

G. Westheimer and S. McKee, “Perception of temporal order in adjacent visual stimuli,” Vis. Res. 17, 887–892 (1977).
[CrossRef]

F. Mechler and J. Victor, “Comparison of thresholds for high-speed drifting Vernier and a matched temporal phase-discrimination task,” Vis. Res. 40, 1839–1855 (2000).
[CrossRef]

J. Victor and M. Conte, “Temporal phase discrimination depends critically on separation,” Vis. Res. 42, 2063–2071 (2002).
[CrossRef]

J. Rovamo and A. Raninen, “Critical flicker frequency and M-scaling of stimulus size and retinal illuminance,” Vis. Res. 24, 1127–1131 (1984).
[CrossRef]

K. Vallam and A. Metha, “Spatial structure of the frequency doubling illusion,” Vis. Res. 47, 1732–1744 (2007).
[CrossRef]

B. Skottun, R. De Valois, D. Grosof, J. Movshon, D. Albrecht, and A. Bonds, “Classification of simple and complex cells on the basis of response modulation,” Vis. Res. 31, 1078–1086 (1991).

R. De Valois, D. Albrecht, and L. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vis. Res. 22, 545–559 (1982).
[CrossRef]

T. Maddess, J. Hemmi, and A. James, “Evidence for spatial aliasing effects in the Y-like cells of the magnocellular visual pathway,” Vis. Res. 38, 1843–1859 (1998).
[CrossRef]

J. Kulikowski, “Apparent fineness of briefly presented gratings: balance between movement and pattern channels,” Vis. Res. 15, 673–680 (1975).
[CrossRef]

W. Richards and T. Felton, “Spatial frequency doubling: retinal or central?” Vis. Res. 13, 2129–2137 (1973).
[CrossRef]

T. Maddess and W. Severt, “Testing for glaucoma with the spatial frequency-doubling illusion,” Vis. Res. 39, 4258–4273 (1999).
[CrossRef]

A. Parker, “Shifts in perceived periodicity induced by temporal modulation and their influence on the spatial frequency tuning of two aftereffects,” Vis. Res. 21, 1739–1747 (1981).
[CrossRef]

M. Aghdaee and P. Cavanagh, “Temporal limits of long-range phase discrimination across the visual field,” Vis. Res. 47, 2156–2163 (2007).
[CrossRef]

Other (2)

O. Grüsser and T. Landis, Visual Agnosias and Other Disturbances of Visual Perception and Cognition (Macmillan, 1991).

W. Van de Grind, O. Grüsser, and H. Lunkenheimer, Handbook of Sensory Physiology, R. Jung, ed. (Springer, 1973), Vol. VII/3, pp. 431–573.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1.
Fig. 1.

A Schematic depiction of the human perception of a contrast-reversal grating stimulus with spatial frequency k and temporal frequency ω reproduced from data in Kelly’s 1966 paper [1]. The illusion occurs for spatial frequencies below about 2 cpd and sets in when the temporal frequency surpasses 10–30 Hz, depending on the spatial frequency; note their linear proportionality. The dashed curve is constructed from published experimental data for two asynchronously flickering disks [17], and it marks the threshold for discrimination between the two disks when they are at a distance x=0.5/k apart. B Distributions of the phase of the first Fourier components of the simulated spike trains of cells in a large-scale model of macaque V1 [18] for a contrast-reversal grating stimulus of 2 cpd and temporal frequencies of 8 (solid curves) and 24 Hz (dashed curves). Spikes were collected for 0.625 s from a stationary part of the spike trains. Distributions are shown for simple cells (black) and complex cells (gray). For both cell types, we have a good phase separation at 8 Hz while this has vanished at 24 Hz.

Fig. 2.
Fig. 2.

A Schematic temporal response profiles of type I and type II simple cells in V1 for a contrast-reversal grating in the quasi-linear regime aibi(ε) and small temporal frequency ω. B Response of a type I cell (i) as a function of grating phase k⃗·x⃗ and time. For a type II cell (j), the pattern would look the same for small ω but with a horizontal shift close to one column and a vertical shift of ψj(k⃗)ψi(k⃗).

Fig. 3.
Fig. 3.

Plot of the measures c(ω) (dashed black), b(ω) (solid black) for the FDI, and the minimal errors εc,min(2)(ω,π) (dashed blue) εb,min(2)(ω,π) (solid blue) for discrimination between a contrast-reversal grating s and its contrast inverse s (asynchronous contrast-reversal gratings). The thin blue curves are the corresponding minimal errors εc,min(4), εb,min(4), and εb,min(8) as indicated. A little before ϑ=1, the conditions become favorable for perception of the FDI and for loss of discrimination between the asynchronous gratings. Note also the resonance behavior beyond ϑ=1, particularly in the probability for discrimination between the asynchronous gratings (minimal errors). Resonances become stronger when more phases (bright and dark stripes) are recruited for discrimination between the gratings.

Fig. 4.
Fig. 4.

Marginal distributions pI0(θ) (dashed) and pII0(θ) (solid) and some examples of the correlation function g2(θ1,θ2) when band correlations are introduced in the distribution P(θ1,θ2)=pI(θ1)pII(θ2) as in Eq. (40). Plots are for ϑ=1.25, which is just after onset of the FDI. For block correlations, the distributions and correlation function are similar, except for the absence of the slanted parts.

Fig. 5.
Fig. 5.

Plots of the continuous and binary measures c and b (black curves), and minimal errors εmin(2)(ω,1/2) (red curves) for the two different types of correlations, band and block correlations. Note the crucial difference between c(ω), d(ω) (black dashed) and c(k,ω), d(k,ω) (solid black). The former were obtained for the correlated distribution, while the latter were computed for the uncorrected remainder [as in Eq. (41)]. The same was done for minimal errors. Note, however, that contrary to the c and b measures, there is little difference between the correlated minimal errors (dashed red) and uncorrelated minimal errors (solid red). Outer panels show a virtually ideal perception of the FDI with c(k,ω),d(k,ω)1/2 and c(ω)=d(ω)=1. Also, the central panels show a clear FDI perception albeit less ideal than the outer panels. The short-dashed horizontal lines indicate the margin for likely FDI perception in terms of c(k,ω), d(k,ω) (compare Fig. 3).

Fig. 6.
Fig. 6.

Binary correlations gn(0,0) as a function of temporal frequency (ϑ) and temporal phase (Ψ) for band and block correlations. Note the stark difference between g2 for these types of correlations. The reason is the invariance of the correlation recipe for band correlations in two dimensions under an arbitrary shift in Ψ. The block-correlations recipe does not have this symmetry. Band correlations also lack this symmetry in higher dimensions, and the binary block and band correlations g3 and g4 are seen to be qualitatively similar.

Fig. 7.
Fig. 7.

Impression of the phase mixing model’s psychometric functions for discrimination between contrast-reversal gratings with temporal phase difference Ψ based on a variety of multiphase distributions. The distributions for two, three, and four phases were fully correlated, i.e., correlations between all phases following specified recipes. For the 2×2 case, the four-phase distribution was only pairwise correlated, i.e., phase correlations at each location but not between locations (grating stripes). Results are for ϑ=1.25 and for band (top) and block correlations (bottom). Plotted results are for correlated distributions (solid curves) and their independent residues (dash-dot curves) for continuous (black) and binary coding (gray).

Fig. 8.
Fig. 8.

Psychometric functions for the phase mixing model’s temporal phase discrimination of contrast-reversal gratings with a temporal phase lag Ψ as a function of temporal frequency ω=2πϑ/τ. Color-coded is the average maximum likelihood probability for correct discrimination 1εmin for binary and continuous phase coding. Results are for the block correlations for three particular choices of correlated phase distributions: (i) two correlated phases (top two rows), (ii) 2×2 correlated phases, where phases pertain to two different locations and are correlated at each location but not between locations (middle rows), and (iii) four fully correlated phases, where phases pertain to two different locations and are correlated at and between each location (two bottom rows). Corresponding independent residues are given in the first, third, and fifth rows, respectively. See text for an interpretation of these results in terms of the phase encoding of the grating and phase recruitment for the discrimination task. Upper and lower row results may be interpreted to correspond to the model’s small and large spatial frequency behavior, respectively. Discrimination threshold (75% chance for correct discrimination) is indicated by the thick white line. Note also the linear behavior of the discrimination threshold for small temporal frequencies.

Fig. 9.
Fig. 9.

Psychometric functions of the two-phase and four-phase results of Fig. 8 averaged over the temporal phase difference Ψ. Corresponding results for band correlations are also shown. Solid lines represent the two-phase results, dash-dot lines refer to the four-phase results for both continuous (black) and binary coding (gray). Shown are the results for the correlated distributions (lower row) as well as for their independent residues (top row). The model’s low spatial frequency behavior is given by the solid curves in the upper panels, whereas the high spatial frequency behavior corresponds to the dash-dot curves in the lower panels. Clearly, for high enough spatial frequency, the model on average is able to distinguish between contrast-reversal gratings with a random temporal phase lag for all temporal frequencies.

Fig. 10.
Fig. 10.

Temporal phase thresholds for our phase mixing model for block correlations (gray) and band correlations (black). A Results for the two-bar stimulus of [37] with a gap (dash dot) and without a gap (solid) between the bars. Also shown are the results when the gap is filled with a third bar with a phase centered between the phases of the end bars (dashed). Results are for one-phase (gap), two-phase (no gap), and four-phase (filled gap) distributions, where in the latter, the phases corresponding to the ends of the central bar are independent. Note that in that case, the discrimination threshold improves with respect to the no-gap threshold by about a factor of 2 for higher temporal frequencies. B Results for the two-bar stimulus of [37] with a gap and a similar four-bar stimulus where an identical bar of opposite contrast is added to each side. Thresholds are for two-phase distributions (two bars, dash dot) and four-phase distributions (four bars, solid), and our model predicts a decrease of the lower thresholds by at least a factor of 2 for intermediate and higher temporal frequencies.

Fig. 11.
Fig. 11.

A Measure c(k,ω) as a function of a widening of the phase distribution ϑ and a spatial delay kd/k. A spatial delay only influences the phase mixing for narrow distributions, i.e., small ϑ. For ϑ larger than 0.8, the delay effects are negligible. We must have c(k,ω)>2/3 for kd=0 for proper perception of contrast-reversal gratings at sufficiently low temporal frequencies. B For a perceptual model with fixed ϑ and in which mixing only occurs because of a spatial delay, this leads to FDI perception only being likely in narrow temporal frequency intervals, which is not in agreement with the experimental observation.

Equations (45)

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

ri(t)=[ai+bi(ε)sin(ωt+ϕi(ω))sin(k⃗·(x⃗x⃗i)+ψi(k⃗))]+.
Ri(x⃗x⃗0)s(x⃗)d2x>0,
f±,(x⃗,t)=[A±B(x⃗)sin(ωt+ϕ±,(x⃗,ω))]+,
B(x⃗)=R(y⃗x⃗)s(y⃗)d2y.
p(x⃗,t)L0+L1R(x⃗y⃗){f+,(y⃗,t)f,(y⃗,t)}d2y,
p(x⃗,t)L0+L1×d2yd2zsin(ωt+ϕ(y⃗,ω))R(x⃗y⃗)R(z⃗y⃗)s(z⃗).
p(x⃗,t)L0+L1×sin(ωt+ϕ0)d2keik⃗·x⃗R^*(k⃗)R^(k⃗)s^(k⃗),
p(x⃗,t)=L0+L1sin(ωt+ϕ0)sin(k⃗0·x⃗+ψ0),
p(x⃗,t)L0+L1sin(ωt+ϕ0)s(x⃗).
ϕ(x⃗,ω)=k⃗d·x⃗,
Δt=k⃗d·Δx⃗kdνd.
p(x⃗,t)L0+L1×Im{eiωtd2kei(k⃗k⃗d)·x⃗R^*(k⃗)R^(k⃗k⃗d)s^(k⃗)}.
R^*(k⃗)R^(k⃗k⃗d)S0>0.
Ri(x⃗)=ex⃗2/σi2cos(k⃗i·x⃗+ϕi),
p(x⃗,t)L0+L1sin(ωt+k⃗d·x⃗)s(x⃗).
p(x⃗,t)L0±L1{cos(ωt)cos(ωt±2k⃗0·x⃗)}.
s(x⃗)=ns^nenik⃗0·x⃗,
ω*=νdk*.
θI(II)(x)=arg02πnc/ωei(ωt+kdx)SI(II)(x,t)dt,
c(ω)=π/23π/2dρ02πdθIdθIIδ(|θIθII|ρ)Pω(θI,θII|s).
Pk,ω(n;m|s)=IndθIImdθIIPk,ω(θI+θ¯I;θII+θ¯I|s),
b(k,ω)=Pk,ω(0;1|s)+Pk,ω(1;0|s),
Pk,ω(θI,θII;θI,θII|s+Ψ)=Pk,ω(θIΨ,θIIΨ;θIΨ,θIIΨ|s).
εc,min(2)(ω,Ψ)=12dθIdθII×min{Pω(θI,θII|s),Pω(θIΨ,θIIΨ|s)},
εb,min(2)(ω,Ψ)=12n,mmin{Pω(n;m|s),Pω(n;m|s+Ψ)},
εb,min(2)(ω,π)=12n,mmin{Pω(n;m|s),Pω(n1;m1|s)},
pI(θ)=pI(θkd2k),
Pk,ω(θI,θII;θI,θII|s)=pI(θI)pI(θIkd2k)pII(θII)pII(θIIkd2k).
pI(θ)={μ+1ϑif|θθμ|<ϑ2μ2μϑelse,
pI(θ)={μ1ϑif|θθμ|<μ2ϑ2μϑelse,
c(ω)=(μϑ)2(93214wμ12wμ2)+μ(μ+1)ϑ2wμ2+H(18wn){(μϑ)2(73274wμ+92wμ2)+μ(μ+1)ϑ2(2wμ9wμ2)+(μ+1ϑ)24wμ2}+H(wn18){(μϑ)2(53234wμ+12wμ2)+μ(μ+1)ϑ2(18wμ2)+(μ+1ϑ)2(116+wμ)},
εc,min(2)(ω,π)=(μϑ)2(124wμ2)+μ(μ+1)ϑ24wμ2,
εc,min(2)(ω,π)=(μϑ)2(124wμ(12wμ))+(μ1)μϑ24wμ(13wμ)+(μ1ϑ)24wμ2.
Pω(0;0|s)=Pk,ω(1;1|s)=μ(ϑμ/2)2ϑ2,
Pω(0;1|s)={(ϑμ/2ϑ)2evenμ(μ2ϑ)2oddμ,
Pω(1;0|s)={(ϑμ/2ϑ)2oddμ(μ2ϑ)2evenμ.
b(ω)=μ(ϑμ/2)ϑ2.
εb,min(2)(ω,π)={1μ2ϑμ1/2<ϑμμ2ϑμ<ϑμ+1/2.
εb,min(4)(ω,π)={(1μ2ϑ)2(μϑ+1)μ1/2<ϑμ(μ2ϑ)2(3μϑ)μ<ϑμ+1/2.
Pω(θI,θII|s)={0ifθIθII<1/4n0pI(θI|s)pII(θII|s)else,
Pω(θI,θII|s)=pI0(θI|s)pII0(θII|s)+g2(θI,θII|s),
pI0(n|s)=n/2(n+1)/2dθIpI0(θI|s),
g2(n,m|s)=n/2(n+1)/2dθIm/2(m+1)/2dθIIg2(θI,θII|s),
εc,min(4)(ω,Ψ)=12dθIdθIIdθIdθII×min{B2,ω(θI,θII;θI,θII),B2,ω(θI,θII;θIΨ,θIIΨ)},
εc,min(4)(ω,Ψ)=12dθIdθIdθIdθI×min{B3,ω(θI;θI;θI;θI),B3,ω(θI;θIΨ/2;θIΨ/2;θIΨ)}.

Metrics