Abstract

The effects of spatial patterns on the sine-wave flicker sensitivity are explored with sharp and blurred edges, circular and rectilinear targets having various flickering and nonflickering areas, and gratings of various spatial frequencies with adjacent bars flickering in opposite phases. The results are consistent with pattern responses studied electro-physiologically by Spekreijse, Riggs, and others. Pattern effects (as opposed to area effects) are confined to frequencies below 10 Hz, and can be explained in terms of the temporal characteristics of lateral inhibition. Earlier differences between the flicker data of deLange and those of Kelly are resolved on this basis, and a response function is calculated for the cross-connecting filters of the inhibiting network.

© 1969 Optical Society of America

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References

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  1. D. H. Kelly, J. Opt. Soc. Am. 49, 730 (1959).
    [CrossRef] [PubMed]
  2. H. deLange, J. Opt. Soc. Am. 48, 777 (1958).
    [CrossRef]
  3. D. H. Kelly, J. Opt. Soc. Am.Soc. Am. 51, 422 (1961).
    [CrossRef]
  4. D. H. Kelly, Doc. Ophthalmol. 18, 16 (1964).
    [CrossRef]
  5. D. H. Kelly, J. Opt. Soc. Am. 51, 747 (1961).
    [CrossRef]
  6. D. C. West, Opt. Acta 15, 317 (1968).
    [CrossRef]
  7. D. C. West, Vision Res. 8, 719 (1968).
    [CrossRef] [PubMed]
  8. U. T. Keesey, J. Opt. Soc. Am. 58, 728A (1968).Also see Ref. 4, p. 19.
  9. G. W. Hughes and L. Maffei, J. Neurophysiol. 29, 333 (1966).
    [PubMed]
  10. F. Ratliff, B. W. Knight, J. Toyoda, and H. K. Hartline, Science 158, 392 (1967).
    [CrossRef] [PubMed]
  11. L. Maffei and R. E. Poppele, Vision Res. 8, 229 (1968).
    [CrossRef] [PubMed]
  12. J. G. Robson, J. Opt. Soc. Am. 56, 1141 (1966).
    [CrossRef]
  13. D. H. Kelly, J. Opt. Soc. Am. 58, 728A (1968).
  14. L. A. Riggs, E. P. Johnson, and A. M. L. Schick, Science 144, 567 (1964).
    [CrossRef]
  15. L. H. van der Tweel and H. Spekreijse, in The Clinical Value of Electroretinography, ISCERG Symposium, Ghent 1966 (Karger, New York–Basel, 1968), p. 83.
  16. D. H. Kelly, J. Opt. Soc. Am. 56, 1628 (1966).
    [CrossRef]
  17. J. Levinson, Doc. Opthalmol. 18, 36 (1964).
    [CrossRef]
  18. F. W. Campbell and J. G. Robson, J. Physiol. (London) 197, 551 (1968).
  19. D. H. Hubel and T. N. Wiesel, J. Physiol. (London) 154, 572 (1960).
  20. H. Spekreijse, thesis, University of Amsterdam, Netherlands (1966).
  21. E. P. Johnson, L. A. Riggs, and A. M. L. Schick, in Clinical Eleclrorelinography Symposium, 1964, Vision Res. Suppl. 1 (1966), p. 75.
  22. For a comparative discussion of various neural-network models, see F. Ratliff, Mach Bands (Holden–Day, Inc., San Francisco, 1965).
  23. An arbitrary phase assumption of some kind is necessary, since we have only amplitude data. This one avoids the necessity of assuming any specific phase function, but is more realistic than assuming that φ = 0 (which would lead to the same result). However, the phase lag may be small in both channels (at the low frequencies we are considering), so that any difference would cause only a second-order error of this assumption. (Otherwise, perhaps it would not yield such a plausible amplitude response.)
  24. D. H. Kelly, J. Opt. Soc. Am. 52, 89 (1962).
    [CrossRef] [PubMed]

1968 (6)

D. C. West, Opt. Acta 15, 317 (1968).
[CrossRef]

D. C. West, Vision Res. 8, 719 (1968).
[CrossRef] [PubMed]

U. T. Keesey, J. Opt. Soc. Am. 58, 728A (1968).Also see Ref. 4, p. 19.

L. Maffei and R. E. Poppele, Vision Res. 8, 229 (1968).
[CrossRef] [PubMed]

F. W. Campbell and J. G. Robson, J. Physiol. (London) 197, 551 (1968).

D. H. Kelly, J. Opt. Soc. Am. 58, 728A (1968).

1967 (1)

F. Ratliff, B. W. Knight, J. Toyoda, and H. K. Hartline, Science 158, 392 (1967).
[CrossRef] [PubMed]

1966 (4)

E. P. Johnson, L. A. Riggs, and A. M. L. Schick, in Clinical Eleclrorelinography Symposium, 1964, Vision Res. Suppl. 1 (1966), p. 75.

D. H. Kelly, J. Opt. Soc. Am. 56, 1628 (1966).
[CrossRef]

G. W. Hughes and L. Maffei, J. Neurophysiol. 29, 333 (1966).
[PubMed]

J. G. Robson, J. Opt. Soc. Am. 56, 1141 (1966).
[CrossRef]

1964 (3)

L. A. Riggs, E. P. Johnson, and A. M. L. Schick, Science 144, 567 (1964).
[CrossRef]

J. Levinson, Doc. Opthalmol. 18, 36 (1964).
[CrossRef]

D. H. Kelly, Doc. Ophthalmol. 18, 16 (1964).
[CrossRef]

1962 (1)

1961 (2)

D. H. Kelly, J. Opt. Soc. Am. 51, 747 (1961).
[CrossRef]

D. H. Kelly, J. Opt. Soc. Am.Soc. Am. 51, 422 (1961).
[CrossRef]

1960 (1)

D. H. Hubel and T. N. Wiesel, J. Physiol. (London) 154, 572 (1960).

1959 (1)

1958 (1)

Campbell, F. W.

F. W. Campbell and J. G. Robson, J. Physiol. (London) 197, 551 (1968).

deLange, H.

Hartline, H. K.

F. Ratliff, B. W. Knight, J. Toyoda, and H. K. Hartline, Science 158, 392 (1967).
[CrossRef] [PubMed]

Hubel, D. H.

D. H. Hubel and T. N. Wiesel, J. Physiol. (London) 154, 572 (1960).

Hughes, G. W.

G. W. Hughes and L. Maffei, J. Neurophysiol. 29, 333 (1966).
[PubMed]

Johnson, E. P.

E. P. Johnson, L. A. Riggs, and A. M. L. Schick, in Clinical Eleclrorelinography Symposium, 1964, Vision Res. Suppl. 1 (1966), p. 75.

L. A. Riggs, E. P. Johnson, and A. M. L. Schick, Science 144, 567 (1964).
[CrossRef]

Keesey, U. T.

U. T. Keesey, J. Opt. Soc. Am. 58, 728A (1968).Also see Ref. 4, p. 19.

Kelly, D. H.

Knight, B. W.

F. Ratliff, B. W. Knight, J. Toyoda, and H. K. Hartline, Science 158, 392 (1967).
[CrossRef] [PubMed]

Levinson, J.

J. Levinson, Doc. Opthalmol. 18, 36 (1964).
[CrossRef]

Maffei, L.

L. Maffei and R. E. Poppele, Vision Res. 8, 229 (1968).
[CrossRef] [PubMed]

G. W. Hughes and L. Maffei, J. Neurophysiol. 29, 333 (1966).
[PubMed]

Poppele, R. E.

L. Maffei and R. E. Poppele, Vision Res. 8, 229 (1968).
[CrossRef] [PubMed]

Ratliff, F.

F. Ratliff, B. W. Knight, J. Toyoda, and H. K. Hartline, Science 158, 392 (1967).
[CrossRef] [PubMed]

For a comparative discussion of various neural-network models, see F. Ratliff, Mach Bands (Holden–Day, Inc., San Francisco, 1965).

Riggs, L. A.

E. P. Johnson, L. A. Riggs, and A. M. L. Schick, in Clinical Eleclrorelinography Symposium, 1964, Vision Res. Suppl. 1 (1966), p. 75.

L. A. Riggs, E. P. Johnson, and A. M. L. Schick, Science 144, 567 (1964).
[CrossRef]

Robson, J. G.

F. W. Campbell and J. G. Robson, J. Physiol. (London) 197, 551 (1968).

J. G. Robson, J. Opt. Soc. Am. 56, 1141 (1966).
[CrossRef]

Schick, A. M. L.

E. P. Johnson, L. A. Riggs, and A. M. L. Schick, in Clinical Eleclrorelinography Symposium, 1964, Vision Res. Suppl. 1 (1966), p. 75.

L. A. Riggs, E. P. Johnson, and A. M. L. Schick, Science 144, 567 (1964).
[CrossRef]

Spekreijse, H.

H. Spekreijse, thesis, University of Amsterdam, Netherlands (1966).

L. H. van der Tweel and H. Spekreijse, in The Clinical Value of Electroretinography, ISCERG Symposium, Ghent 1966 (Karger, New York–Basel, 1968), p. 83.

Toyoda, J.

F. Ratliff, B. W. Knight, J. Toyoda, and H. K. Hartline, Science 158, 392 (1967).
[CrossRef] [PubMed]

van der Tweel, L. H.

L. H. van der Tweel and H. Spekreijse, in The Clinical Value of Electroretinography, ISCERG Symposium, Ghent 1966 (Karger, New York–Basel, 1968), p. 83.

West, D. C.

D. C. West, Opt. Acta 15, 317 (1968).
[CrossRef]

D. C. West, Vision Res. 8, 719 (1968).
[CrossRef] [PubMed]

Wiesel, T. N.

D. H. Hubel and T. N. Wiesel, J. Physiol. (London) 154, 572 (1960).

Clinical Eleclrorelinography Symposium, 1964 (1)

E. P. Johnson, L. A. Riggs, and A. M. L. Schick, in Clinical Eleclrorelinography Symposium, 1964, Vision Res. Suppl. 1 (1966), p. 75.

Doc. Ophthalmol. (1)

D. H. Kelly, Doc. Ophthalmol. 18, 16 (1964).
[CrossRef]

Doc. Opthalmol. (1)

J. Levinson, Doc. Opthalmol. 18, 36 (1964).
[CrossRef]

J. Neurophysiol. (1)

G. W. Hughes and L. Maffei, J. Neurophysiol. 29, 333 (1966).
[PubMed]

J. Opt. Soc. Am. (8)

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

D. H. Kelly, J. Opt. Soc. Am.Soc. Am. 51, 422 (1961).
[CrossRef]

J. Physiol. (London) (2)

F. W. Campbell and J. G. Robson, J. Physiol. (London) 197, 551 (1968).

D. H. Hubel and T. N. Wiesel, J. Physiol. (London) 154, 572 (1960).

Opt. Acta (1)

D. C. West, Opt. Acta 15, 317 (1968).
[CrossRef]

Science (2)

F. Ratliff, B. W. Knight, J. Toyoda, and H. K. Hartline, Science 158, 392 (1967).
[CrossRef] [PubMed]

L. A. Riggs, E. P. Johnson, and A. M. L. Schick, Science 144, 567 (1964).
[CrossRef]

Vision Res. (2)

L. Maffei and R. E. Poppele, Vision Res. 8, 229 (1968).
[CrossRef] [PubMed]

D. C. West, Vision Res. 8, 719 (1968).
[CrossRef] [PubMed]

Other (4)

H. Spekreijse, thesis, University of Amsterdam, Netherlands (1966).

For a comparative discussion of various neural-network models, see F. Ratliff, Mach Bands (Holden–Day, Inc., San Francisco, 1965).

An arbitrary phase assumption of some kind is necessary, since we have only amplitude data. This one avoids the necessity of assuming any specific phase function, but is more realistic than assuming that φ = 0 (which would lead to the same result). However, the phase lag may be small in both channels (at the low frequencies we are considering), so that any difference would cause only a second-order error of this assumption. (Otherwise, perhaps it would not yield such a plausible amplitude response.)

L. H. van der Tweel and H. Spekreijse, in The Clinical Value of Electroretinography, ISCERG Symposium, Ghent 1966 (Karger, New York–Basel, 1968), p. 83.

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Figures (13)

F. 1
F. 1

Sine-wave modulation thresholds for circular fields: 3° flickering spot with 16° steady surround (filled circles) vs uniformly flickering 16° circular field (open circles). Binocular viewing at 25 cm, 120 mL, 2.3-mm artificial pupils. Subject KE.

F. 2
F. 2

Sine-wave modulation thresholds for circular fields: 3° flickering spot with 16° steady surround; sharp CRT display (filled circles) vs blurred display (open circles). Scanning-spot diam for blurred display is 0.5°. Other conditions same as Fig. 1.

F. 3
F. 3

Modulation thresholds for circular fields: (a) 3° flickering spot with 16° counterphase flickering surround (open squares); (b) 3° flickering spot with 16° steady surround (filled circles); and (c) 0.5° flickering single-edged annulus, 3° edge (as shown in inset) with 2° spot and 16° surround both steady (open triangles). Filled squares show ratio of curve (a) to curve (b). Other conditions same as Fig. 1.

F. 4
F. 4

Wide-field (16°) flicker curve from Fig. 1 (solid curve, open circles) compared with (a) counterphase, (b) blurred spot, and (c) annulus curves from Figs. 2 and 3 (dashed lines). Note that the wide-field data fit the counterphase curve at high frequencies, but fit the other two at low frequencies. Same conditions as in previous figures.

F. 5
F. 5

Sine-wave modulation thresholds for rectangular flickering field, 16° wide by 8° high, with one rectilinear, vertical, sharp counterphase edge (filled squares) or blurred counterphase edge (open squares), in center of field. Scanning-spot diam for blurred display is 0.5°. Binocular viewing at 25 cm, 120 mL, 2.3-mm artificial pupils. Subject KE.

F. 6
F. 6

1-Hz sine-wave flicker thresholds for 16°×8° rectilinear, counterphase gratings, with vertical bars of various spatial frequencies. Filled squares represent square-wave grating patterns; open circles, sine-wave grating patterns. Display sharply focused. Other conditions same as in Fig. 5. (Note maximum sensitivity at 2 cycles/deg, corresponding to 15′ arc between flicker nodes.)

F. 7
F. 7

Sine-wave flicker curves for the three (16°×8°, rectilinear, counterphase) square-wave gratings indicated by arrows in Fig. 6: 15′ bars (open squares), 1° bars (open triangles), and 2° bars (filled circles). The sharp-edge curve from Fig. 5 is also shown for comparison (dashed line). Other conditions as in Fig. 6.

F. 8
F. 8

Sine-wave flicker curves for the three (16°×8°, rectilinear, counterphase) sine-wave gratings indicated by arrows in Fig. 6:2 cycles/deg (open squares), 0.5 cycle/deg (open triangles), and 0.25 cycle/deg (filled circles). The blurred-edge curve from Fig. 5 is also shown for comparison (dashed line). Other conditions as in Fig. 6.

F. 9
F. 9

Maximum (open circles) and minimum (filled squares) modulation thresholds obtained with rectilinear targets at 120 mL (1500 td). Maximum thresholds (mU) for uniformly flickering 16°×8° field; minimum thresholds (mC) for 15′ counterphase bars (replotted from Fig. 7). Both single-edge curves from Fig. 5 are also shown for comparison (dashed lines)—(a) sharp edge, (b) 0.5° blurred edge. Other conditions same as in Fig. 6. (The dotted curve,|G|, at the bottom of the figure represents a hypothetical inhibitory response function calculated from mU/mC; see text.)

F. 10
F. 10

Diagram of two identical interacting channels of a simplified, non-regressive model of lateral inhibition. Each channel consists of a log converter, an all-pass phase-shifter, a subtractor, and the initially unknown filter G, cross connected as shown. (Because the subtractor removes dc components, the log converter has no effect when m≪1; see Appendix.)

F. 11
F. 11

Same as Fig. 9, but with adaptation level reduced to 1.2 mL (15 td). Note decreased |G|. Also shown for comparison are flicker thresholds for 30′ counterphase bars (open squares); see text.

F. 12
F. 12

1-Hz sine-wave flicker thresholds for 16°×8°, rectilinear, counterphase, square-wave gratings of various bar widths, but with same adaptation level as Fig. 11 (1.2 mL). The corresponding 120-mL curve from Fig. 6 is shown for comparison (dashed line). Note uniform decrease of sensitivity for all targets. (Arrows indicate possible shift of maximum from 15′ to 30′ bars.)

F. 13
F. 13

Same as Fig. 9, but with subject DK. A sharp-edge, counter-phase curve for this subject, comparable to Fig. 5, is also included (open triangles).

Equations (11)

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| G | = ( m U m C ) / ( m U + m C ) = ( R 1 ) / ( R + 1 ) , where R = m U / m C .
f ( t ) = B ( 1 + m e j ω t ) ,
log f = log B + m e j ω t 1 2 m 2 e 2 j ω t + 1 3 m 3 e 3 j ω t .
H ( ω ) = m U e j ( ω t + φ ) G m U e j ω t = m U e j ω t ( e j φ G ) ,
H = m U e j ( ω t + φ ) ( 1 | G ( ω ) | ) .
| H | = const = m U ( 1 | G ( ω ) | ) .
f ( t ) = B ( 1 m e j ω t ) ,
H ( ω ) = m C e j ω t ( e j φ + G ) ,
| H | = const = m C ( 1 + | G ( ω ) | ) .
R = m U / m C = ( 1 + | G | ) / ( 1 | G | ) .
| G ( ω ) | = ( R 1 ) / ( R + 1 ) = ( m U m C ) / ( m U + m C ) .