Abstract

Psychometric functions were determined concurrently for detection of simple gratings (luminance sinusoidally modulated with spatial frequency ƒ) and complex gratings (luminance modulated by the sum of two sinusoids, with frequencies ƒ and ƒ′). Results were used to test the hypothesis that the two components of a complex grating may be detected independently. In an extensive experiment with ƒ = 14 cycles/deg, the independence hypothesis was consistently rejected only when ƒ/ƒ′ = 5/4 or 4/5, but rarely rejected when the value of ƒ/ƒ′ lay outside this range. In other experiments, ƒ was between 1.9 and 22.4 cycles/deg. All results are compatible with the assumption that the human visual system contains sensory channels, each selectively sensitive to different narrow ranges of spatial frequencies, whose outputs are detected independently.

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  1. O. H. Schade, J. Opt. Soc. Am. 46, 721 (1956).
  2. H. deLange, J. Opt. Soc. Am. 48, 777 (1958).
  3. J. G. Robson, J. Opt. Soc. Am. 56, 1141 (1966).
  4. F. Ratliff, M1ach Bands: Quantitative Studies on Neural Networks in the Retina (Holden-Day, San Francisco, 1965).
  5. F. W. Campbell and J. G. Robson, J. Physiol. (London) 197, 551 (1968).
  6. C. Enroth-Cugell and J. G. Robson, J. Physiol (London) 187, 517 (1966).
  7. F. W. Campbell, G. F. Cooper, J. G. Robson, and M. B. Sachs, J. Physiol. (London) 204, 120 (1969).
  8. A. Pantle and R. Sekuler, Science 162, 1146 (1968).
  9. C. Blakemore and F. W. Campbell, J. Physiol (London) 203, 237 (1969).
  10. C. Blakemore and P. Sutton, Science 166, 245 (1969).
  11. Whenever ƒ/ƒ′ can be expressed as a ratio of odd integers, then there is some value of (ø-ø′) for which the largest peak-to-trough difference in the input complex waveform will be equal to exactly 2L0(m+m′). The corresponding peak-to-trough value for the output of the single channel (assuming a symmetrical spread function) will be proportional to (am+am′). Hence, for a peak-to-trough detector, the functions G and G′ in Eq. (3) are linear in m and m′, respectively. For other values of ƒ/ƒ′, the largest peak-to-trough difference in the luminance waveform will be less than 2L0(m+m′) no matter what the phase of the component sinusoids.
  12. D. J. Finney, Probit Analysis (Cambridge U. P., England, 1964), Appendix II.
  13. A. M. Mood and F. A. Graybill, Introduction to the Theory of Statistics. 2nd ed. (McGraw-Hill, New York, 1963), Ch. 12.
  14. R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 833 (1965).
  15. F. W. Campbell, G. F. Cooper, and C. Enroth-Cugell, J. Physiol (London) 203, 223 (1969).
  16. F. W. Campbell, J. Nachmias, and J. Jukes, J. Opt. Soc. Am. 60, 555 (1970).
  17. N. Graham and J. Nachmias, Vision Res. 11, 251 (1971).
  18. R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover, New York, 1958).
  19. D. D. McCracken and W. S. Dorn, Numerical Methods and Fortran Programming (Wiley, New York, 1964), Ch. 5.

Blackman, R. B.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover, New York, 1958).

Blakemore, C.

C. Blakemore and P. Sutton, Science 166, 245 (1969).

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

Campbell, F. W.

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

F. W. Campbell, G. F. Cooper, J. G. Robson, and M. B. Sachs, J. Physiol. (London) 204, 120 (1969).

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

F. W. Campbell, J. Nachmias, and J. Jukes, J. Opt. Soc. Am. 60, 555 (1970).

F. W. Campbell, G. F. Cooper, and C. Enroth-Cugell, J. Physiol (London) 203, 223 (1969).

Cooper, G. F.

F. W. Campbell, G. F. Cooper, and C. Enroth-Cugell, J. Physiol (London) 203, 223 (1969).

F. W. Campbell, G. F. Cooper, J. G. Robson, and M. B. Sachs, J. Physiol. (London) 204, 120 (1969).

deLange, H.

H. deLange, J. Opt. Soc. Am. 48, 777 (1958).

Dorn, W. S.

D. D. McCracken and W. S. Dorn, Numerical Methods and Fortran Programming (Wiley, New York, 1964), Ch. 5.

Enroth-Cugell, C.

F. W. Campbell, G. F. Cooper, and C. Enroth-Cugell, J. Physiol (London) 203, 223 (1969).

C. Enroth-Cugell and J. G. Robson, J. Physiol (London) 187, 517 (1966).

Finney, D. J.

D. J. Finney, Probit Analysis (Cambridge U. P., England, 1964), Appendix II.

Graham, N.

N. Graham and J. Nachmias, Vision Res. 11, 251 (1971).

Graybill, F. A.

A. M. Mood and F. A. Graybill, Introduction to the Theory of Statistics. 2nd ed. (McGraw-Hill, New York, 1963), Ch. 12.

Jukes, J.

F. W. Campbell, J. Nachmias, and J. Jukes, J. Opt. Soc. Am. 60, 555 (1970).

McCracken, D. D.

D. D. McCracken and W. S. Dorn, Numerical Methods and Fortran Programming (Wiley, New York, 1964), Ch. 5.

Mood, A. M.

A. M. Mood and F. A. Graybill, Introduction to the Theory of Statistics. 2nd ed. (McGraw-Hill, New York, 1963), Ch. 12.

Nachmias, J.

F. W. Campbell, J. Nachmias, and J. Jukes, J. Opt. Soc. Am. 60, 555 (1970).

N. Graham and J. Nachmias, Vision Res. 11, 251 (1971).

Pantle, A.

A. Pantle and R. Sekuler, Science 162, 1146 (1968).

Ratliff, F.

F. Ratliff, M1ach Bands: Quantitative Studies on Neural Networks in the Retina (Holden-Day, San Francisco, 1965).

Robson, J. G.

F. W. Campbell, G. F. Cooper, J. G. Robson, and M. B. Sachs, J. Physiol. (London) 204, 120 (1969).

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

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

C. Enroth-Cugell and J. G. Robson, J. Physiol (London) 187, 517 (1966).

Rodieck, R. W.

R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 833 (1965).

Sachs, M. B.

F. W. Campbell, G. F. Cooper, J. G. Robson, and M. B. Sachs, J. Physiol. (London) 204, 120 (1969).

Schade, O. H.

O. H. Schade, J. Opt. Soc. Am. 46, 721 (1956).

Sekuler, R.

A. Pantle and R. Sekuler, Science 162, 1146 (1968).

Stone, J.

R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 833 (1965).

Sutton, P.

C. Blakemore and P. Sutton, Science 166, 245 (1969).

Tukey, J. W.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover, New York, 1958).

Other

O. H. Schade, J. Opt. Soc. Am. 46, 721 (1956).

H. deLange, J. Opt. Soc. Am. 48, 777 (1958).

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

F. Ratliff, M1ach Bands: Quantitative Studies on Neural Networks in the Retina (Holden-Day, San Francisco, 1965).

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

C. Enroth-Cugell and J. G. Robson, J. Physiol (London) 187, 517 (1966).

F. W. Campbell, G. F. Cooper, J. G. Robson, and M. B. Sachs, J. Physiol. (London) 204, 120 (1969).

A. Pantle and R. Sekuler, Science 162, 1146 (1968).

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

C. Blakemore and P. Sutton, Science 166, 245 (1969).

Whenever ƒ/ƒ′ can be expressed as a ratio of odd integers, then there is some value of (ø-ø′) for which the largest peak-to-trough difference in the input complex waveform will be equal to exactly 2L0(m+m′). The corresponding peak-to-trough value for the output of the single channel (assuming a symmetrical spread function) will be proportional to (am+am′). Hence, for a peak-to-trough detector, the functions G and G′ in Eq. (3) are linear in m and m′, respectively. For other values of ƒ/ƒ′, the largest peak-to-trough difference in the luminance waveform will be less than 2L0(m+m′) no matter what the phase of the component sinusoids.

D. J. Finney, Probit Analysis (Cambridge U. P., England, 1964), Appendix II.

A. M. Mood and F. A. Graybill, Introduction to the Theory of Statistics. 2nd ed. (McGraw-Hill, New York, 1963), Ch. 12.

R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 833 (1965).

F. W. Campbell, G. F. Cooper, and C. Enroth-Cugell, J. Physiol (London) 203, 223 (1969).

F. W. Campbell, J. Nachmias, and J. Jukes, J. Opt. Soc. Am. 60, 555 (1970).

N. Graham and J. Nachmias, Vision Res. 11, 251 (1971).

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover, New York, 1958).

D. D. McCracken and W. S. Dorn, Numerical Methods and Fortran Programming (Wiley, New York, 1964), Ch. 5.

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