Abstract

We have measured the sensitivity of the visual system to temporal modulation with unpredictable, aperiodic signals. We used three kinds of stimulation, (i) a band-limited gaussian random signal, (ii) a passband-limited gaussian random signal, (iii) a periodically quenched random signal. The sensitivity to stimulation with random signals can be predicted from the sensitivity of the visual system to periodic temporal signals. The sensitivity to random signals with narrow frequency bands at high frequencies is governed by the pseudoflash phenomenon. If the bandwidth is such that the signal contains less than two independent samples per second, the psychometric curve follows from the amplitude distribution of the random signal. If the signal contains a larger number of independent samples per second, the psychometric curves are as steep as they are for sine-wave stimulation. If the De Lange characteristic is the envelope of the sensitivity characteristics of independent channels, sensitive to specific frequency bands, then these experiments permit us to estimate the bandwidth of the most-sensitive channel.

© 1974 Optical Society of America

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References

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  1. C. Blakemore and F. W. Campbell, J. Physiol. (Lond.) 203, 237 (1969).
  2. R. A. Smith, Vision Res. 10, 275 (1970).
    [CrossRef] [PubMed]
  3. R. A. Smith, J. Physiol. (Lond.) 216, 531 (1971).
  4. A. Pantle, Vision Res. 11, 943 (1971).
    [CrossRef] [PubMed]
  5. D. H. Kelly, J. Opt. Soc. Am. 52, 89 (1962).
    [CrossRef] [PubMed]
  6. D. G. Green, Vision Res. 9, 591 (1969).
    [CrossRef] [PubMed]
  7. G. A. Korn, Random-Process Simulation and Measurements (McGraw-Hill, New York, 1966).
  8. By a random telegraph wave we mean an analog signal that can take on only two separate values and that switches back and forth between these two values at random moments of time.
  9. J. Levinson, Science 160, 21 (1968).
    [CrossRef] [PubMed]
  10. J. A. Decker, Appl. Opt. 9, 1392 (1970).
    [CrossRef] [PubMed]
  11. H. F. Harmuth, Transmission of Information by Orthogonal Functions (Springer, Berlin, 1970).
    [CrossRef]
  12. H. L. van Trees, Detection, Estimation, and Modulation Theory, Part I (Wiley, New York, 1968), p. 197.

1971 (2)

R. A. Smith, J. Physiol. (Lond.) 216, 531 (1971).

A. Pantle, Vision Res. 11, 943 (1971).
[CrossRef] [PubMed]

1970 (2)

1969 (2)

D. G. Green, Vision Res. 9, 591 (1969).
[CrossRef] [PubMed]

C. Blakemore and F. W. Campbell, J. Physiol. (Lond.) 203, 237 (1969).

1968 (1)

J. Levinson, Science 160, 21 (1968).
[CrossRef] [PubMed]

1962 (1)

Blakemore, C.

C. Blakemore and F. W. Campbell, J. Physiol. (Lond.) 203, 237 (1969).

Campbell, F. W.

C. Blakemore and F. W. Campbell, J. Physiol. (Lond.) 203, 237 (1969).

Decker, J. A.

Green, D. G.

D. G. Green, Vision Res. 9, 591 (1969).
[CrossRef] [PubMed]

Harmuth, H. F.

H. F. Harmuth, Transmission of Information by Orthogonal Functions (Springer, Berlin, 1970).
[CrossRef]

Kelly, D. H.

Korn, G. A.

G. A. Korn, Random-Process Simulation and Measurements (McGraw-Hill, New York, 1966).

Levinson, J.

J. Levinson, Science 160, 21 (1968).
[CrossRef] [PubMed]

Pantle, A.

A. Pantle, Vision Res. 11, 943 (1971).
[CrossRef] [PubMed]

Smith, R. A.

R. A. Smith, J. Physiol. (Lond.) 216, 531 (1971).

R. A. Smith, Vision Res. 10, 275 (1970).
[CrossRef] [PubMed]

van Trees, H. L.

H. L. van Trees, Detection, Estimation, and Modulation Theory, Part I (Wiley, New York, 1968), p. 197.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Physiol. (Lond.) (2)

C. Blakemore and F. W. Campbell, J. Physiol. (Lond.) 203, 237 (1969).

R. A. Smith, J. Physiol. (Lond.) 216, 531 (1971).

Science (1)

J. Levinson, Science 160, 21 (1968).
[CrossRef] [PubMed]

Vision Res. (3)

A. Pantle, Vision Res. 11, 943 (1971).
[CrossRef] [PubMed]

R. A. Smith, Vision Res. 10, 275 (1970).
[CrossRef] [PubMed]

D. G. Green, Vision Res. 9, 591 (1969).
[CrossRef] [PubMed]

Other (4)

G. A. Korn, Random-Process Simulation and Measurements (McGraw-Hill, New York, 1966).

By a random telegraph wave we mean an analog signal that can take on only two separate values and that switches back and forth between these two values at random moments of time.

H. F. Harmuth, Transmission of Information by Orthogonal Functions (Springer, Berlin, 1970).
[CrossRef]

H. L. van Trees, Detection, Estimation, and Modulation Theory, Part I (Wiley, New York, 1968), p. 197.

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Figures (7)

FIG. 1
FIG. 1

Two samples of signals used as stimuli. T is the period of the time base. Broken curve, a sequency-band-limited gaussian signal. The sequency power of this signal is spread out uniformly over the sequency band from 0 to (1/T), it is zero outside this band. Solid curve, a sequency-band-pass gaussian signal. The sequency power of this signal is spread out uniformly over the sequency band from (8/T) to (9/T), it is zero outside this band. The amplitude distribution of both signals is gaussian.

FIG. 2
FIG. 2

The autocorrelation functions of the signals depicted in Fig. 1. T is the time-base period. The autocorrelation is zero for times greater than T, or smaller than −T. Broken curve, autocorrelation function of the sequency-band-limited gaussian signal depicted in Fig. 1 (broken curve); solid curve, autocorrelation function of the sequency-band-pass gaussian signal depicted in Fig. 1 (solid curve).

FIG. 3
FIG. 3

The cumulative Fourier power spectra of the signals depicted in Fig. 1. The frequency scale is in units of the reciprocal of the time-base period. Broken curve, the cumulative frequency power spectrum of the sequency-band-limited gaussian signal depicted in Fig. 1 (broken curve); solid curve, the cumulative frequency power spectrum of the sequency-band-pass gaussian signal depicted in Fig. 1 (solid curve).

FIG. 4
FIG. 4

Results of the band-limited random-signal experiment. The threshold modulation m in percent modulation depth is given as a function of the half-power band-limit frequency. The dots represent measurements with a gaussian signal. The asterisks represent measurements with a random telegraph wave (Ref. 8). The curves are theoretical (see Discussion). Subject J. K.

FIG. 5
FIG. 5

Results of the band-limited random-signal experiment. The threshold modulation m in percent modulation depth is given as a function of the half-power band-limit frequency. The dots represent measurements with a gaussian signal. The asterisks represent measurements with a random telegraph wave (Ref. 8). The curves are theoretical (see Discussion). Subject A. D.

FIG. 6
FIG. 6

Results of the band-pass-limited random-signal experiment. Subject J. K. Open circles, relative (half-power) frequency bandwidth 0.69; squares, relative frequency bandwidth 0.35; filled circles, relative frequency bandwidth 0.085; filled asterisks, square wave; open asterisks, periodically quenched square wave. The broken line has a slope of 45°. The curve is the De Lange characteristic measured with sine waves. The thresholds for sine-wave stimuli are plotted in terms of their relative effective value.

FIG. 7
FIG. 7

Results of the band-pass-limited random-signal experiment. Subject A. D. Open circles, relative (half-power) frequency bandwidth 0.69; squares, relative frequency bandwidth 0.35; filled circles, relative frequency bandwidth 0.085; filled asterisks, square wave; open asterisks, periodically quenched square wave. The broken line has a slope of 45°. The curve is the De Lange characteristic measured with sine waves. The thresholds for sine-wave stimuli are plotted in terms of their relative effective value.

Equations (1)

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g ( t ) = ( n - 1 ) T n T f ( t ) d t             for n T < t < ( n + 1 ) T ,