Abstract

This paper reports an unexpected visual phenomenon. When a wide, photopic stimulus field is sinusoidally modulated in both space and time, over a certain frequency range the apparent spatial frequency of the stimulus is doubled. In its original form, the (deLange) flicker-fusion model which has been accepted by the author and others cannot account for this result. But it can be explained by assuming that there is a second (low-pass) filtering operation which follows the nonlinear (brightness) response of the visual system, rather than preceding it. If this hypothesis is correct, then the frequency-doubling effect is the result of neural mechanisms which are more central than the locus of flicker fusion.

© 1966 Optical Society of America

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References

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  1. H. deLange, thesis, Technical University, Delft, Holland (1957).
  2. H. deLange, J. Opt. Soc. Am. 48, 777 (1958).
    [Crossref]
  3. D. H. Kelly, J. Opt. Soc. Am. 51, 422 (1961).
    [Crossref] [PubMed]
  4. O. H. Schade, J. Opt. Soc. Am. 46, 721 (1956).
    [Crossref] [PubMed]
  5. D. G. Green and F. W. Campbell, J. Opt. Soc. Am. 55, 1154 (1965).
    [Crossref]
  6. D. H. Kelly, J. Opt. Soc. Am. 50, 1115 (1960).
    [Crossref] [PubMed]
  7. Final Technical Report on Contract No. DA-44-009-AMC-453 (T), 27 May 1966 (Vidya Report No. 221).
  8. J. G. Robson (private communication).
  9. D. H. Kelly, M. E. Lynch, and D. S. Ross, J. Opt. Soc. Am. 48, 858 (1958).
    [Crossref]
  10. J. Levinson and L. D. Harmon, Kybernetic 1, 107 (1961).
    [Crossref]
  11. D. H. Kelly, J. Opt. Soc. Am. 51, 747 (1961).
    [Crossref]
  12. D. H. Kelly, Doc. Ophthalmol. 18, 16 (1964).
    [Crossref]

1965 (1)

1964 (1)

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

1961 (3)

1960 (1)

1958 (2)

1956 (1)

Doc. Ophthalmol. (1)

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

J. Opt. Soc. Am. (7)

Kybernetic (1)

J. Levinson and L. D. Harmon, Kybernetic 1, 107 (1961).
[Crossref]

Other (3)

H. deLange, thesis, Technical University, Delft, Holland (1957).

Final Technical Report on Contract No. DA-44-009-AMC-453 (T), 27 May 1966 (Vidya Report No. 221).

J. G. Robson (private communication).

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Figures (8)

Fig. 1
Fig. 1

Photograph of the CRT stimulator, showing the experimenter’s controls at the right, and the Green’s Refractor at the left of the main rack.

Fig. 2
Fig. 2

Perspective view of three-dimensional spatiotemporal threshold surface, constructed from preliminary data.

Fig. 3
Fig. 3

Subjective brightness of a static sinusoidal pattern of moderate contrast.

Fig. 4
Fig. 4

Schematic diagram of the deLange model discussed in the text.

Fig. 5
Fig. 5

Approximate map of subjective phenomena encountered at various spatial and temporal frequencies. The plotted points represent the 100% modulation contour at an adaptation level of 100 mL (all stimuli to the right and above this curve are indistinguishable from an unmodulated uniform field).

Fig. 6
Fig. 6

Two-dimensional deLange model with additional stage to account for spatial frequency-doubling.

Fig. 7
Fig. 7

Successive spatial patterns at the output of the nonlinear stage, and the double-frequency pattern resulting from temporal integration.

Fig. 8
Fig. 8

Hypothetical scheme for spatial integration which would yield temporal frequency doubling.

Tables (1)

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Table I Deflection parameters of spiral scan with constant angular velocity.

Equations (16)

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s ( x ) = 1 + m cos α x
r ( x ) = log s ( x ) ,
r ( x ) = log ( 1 + m cos α x ) = m cos α x 1 2 m 2 cos 2 α x + 1 3 m 3 cos 3 α x
s ( x , t ) = 1 + m ( cos α x ) ( cos ω t ) ,
r ( x , t ) = log [ 1 + m ( cos α x ) ( cos ω t ) ] = m ( cos α x ) ( cos ω t ) 1 2 m 2 ( cos 2 α x ) ( cos 2 ω t ) + .
r ( x , 0 ) = m cos α x 1 2 m 2 cos 2 α x + 1 3 m 2 cos 3 α x
r ( x , π / ω ) = m cos α x 1 2 m 2 cos 2 α x 1 3 m 3 cos 3 α x ;
r ( x , 0 ) + r ( x , π / ω ) = m 2 cos 2 α x + e
m 2 cos 2 α x = 1 2 m 2 ( 1 + cos 2 α x ) ,
0 2 π / ω r ( x , t ) d t = ( π m 2 / 4 ω ) ( 1 + cos 2 α x ) + e .
s ( 0 , t ) = 1 + cos ω t
s ( π / α , t ) = 1 cos ω t ,
r ( 0 , t ) = log ( 1 + m cos ω t )
r ( π / α , t ) = log ( 1 m cos ω t ) .
r ( 0 , t ) + r ( π / α , t ) = m 2 cos 2 ω t + e
m 2 cos 2 ω t = 1 2 m 2 ( 1 + cos 2 ω t ) ,