Abstract

The number of cycles in a low-frequency sinusoidal display is a crucial variable in determining the visibility of the display. In particular, the threshold contrast is essentially independent of spatial frequency for these displays. We have extended the above experiments, using more cycles and a variety of targets and observer tasks. The results confirm previous findings; they also show that the type of target or task has little influence. For low-frequency sinusoids that contain up to about 3 cycles, the threshold contrast is determined by the number of cycles. For high-number-of-cycles targets with spatial frequencies above 6–10 cycles per degree, visibility is predominantly dependent on the spatial frequency. The results suggest that the low-frequency decrease in reported MTF’s is due to the decrease of the number of cycles used in determining them.

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  1. J. J. McCann, R. L. Savoy, J. A. Hall, Jr., and J. J. Scarpetti, Vision Res. 14, 917 (1974).
  2. A sine wave of limited extent possesses spectral energy over a range of spatial frequencies that includes the nominal frequency. So, strictly, it is incorrect to speak of, for example, a 3-cycle-per-degree sine wave when we mean a truncated sine wave with a nominal spatial frequency of 3 cycles per degree. However, because we will be referring to truncated sine waves throughout this paper, it will frequently be convenient to use the looser terminology.
  3. J. Hoekstra, D. P. J. van der Goot, G. van den Brink, and F. A. Bilsen, Vision Res. 14, 364 (1974).
  4. O. H. Schade, Sr., J. Opt. Soc. Am. 46, 721 (1956).
  5. J. J. DePalma and E. M. Lowry, J. Opt. Soc. Am. 52, 328 (1962).
  6. M. Davidson, J. Opt. Soc. Am. 58, 1300 (1968).
  7. F. W. Campbell and J. G. Robson, J. Physiol. 197, 551 (1968).
  8. We found that, with our apparatus, a 1-cycle target had the same threshold whether the left-hand edge was equal to the average liminance (sine phase) or the maximum luminance (cosine phase) of the sinusoidal region. Kelly (Ref. 9) showed that the edge created by a cosine phase target can determine threshold in the no-plateau condition. In our experiments, however, the edge between the mirror and the tube face never completely disappeared, so subjects could not use the creation of an edge as their principal cue for threshold; they needed to perceive some form.
  9. D. H. Kelly, J. Opt. Soc. Am. 60, 98 (1970).
  10. The definition of bandwidth used in this discussion is width at half-power. For targets with a fixed w, this bandwidth and the peak value of the transform undergo negligible change as n changes except when n is very close to zero. In that case, overlap with the transform component centered at -ƒ makes a significant contribution. However, there is only a 10% change of the height of the peak of the transform of the ½-cycle target, the lowest number of cycles used in our experiments.
  11. M. Davidson and J. A. Whiteside, J. Opt. Soc. Am. 61, 530 (1971).
  12. C. Blakemore and F. W. Campbell, J. Physiol. 203, 237 (1969).
  13. F. W. Campbell, G. F. Cooper, and C. Enroth-Cugell, J. Physiol. 203, 223 (1969).
  14. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Bilsen, F. A.

J. Hoekstra, D. P. J. van der Goot, G. van den Brink, and F. A. Bilsen, Vision Res. 14, 364 (1974).

Blakemore, C.

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

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Campbell, F. W.

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

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

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

Cooper, G. F.

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

Davidson, M.

M. Davidson, J. Opt. Soc. Am. 58, 1300 (1968).

M. Davidson and J. A. Whiteside, J. Opt. Soc. Am. 61, 530 (1971).

DePalma, J. J.

J. J. DePalma and E. M. Lowry, J. Opt. Soc. Am. 52, 328 (1962).

Enroth-Cugell, C.

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

Hall, Jr., J. A.

J. J. McCann, R. L. Savoy, J. A. Hall, Jr., and J. J. Scarpetti, Vision Res. 14, 917 (1974).

Hoekstra, J.

J. Hoekstra, D. P. J. van der Goot, G. van den Brink, and F. A. Bilsen, Vision Res. 14, 364 (1974).

Kelly, D. H.

D. H. Kelly, J. Opt. Soc. Am. 60, 98 (1970).

Lowry, E. M.

J. J. DePalma and E. M. Lowry, J. Opt. Soc. Am. 52, 328 (1962).

McCann, J. J.

J. J. McCann, R. L. Savoy, J. A. Hall, Jr., and J. J. Scarpetti, Vision Res. 14, 917 (1974).

Robson, J. G.

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

Savoy, R. L.

J. J. McCann, R. L. Savoy, J. A. Hall, Jr., and J. J. Scarpetti, Vision Res. 14, 917 (1974).

Scarpetti, J. J.

J. J. McCann, R. L. Savoy, J. A. Hall, Jr., and J. J. Scarpetti, Vision Res. 14, 917 (1974).

Schade, Sr., O. H.

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

van der Brink, G.

J. Hoekstra, D. P. J. van der Goot, G. van den Brink, and F. A. Bilsen, Vision Res. 14, 364 (1974).

van der Goot, D. P. J.

J. Hoekstra, D. P. J. van der Goot, G. van den Brink, and F. A. Bilsen, Vision Res. 14, 364 (1974).

Whiteside, J. A.

M. Davidson and J. A. Whiteside, J. Opt. Soc. Am. 61, 530 (1971).

Other (14)

J. J. McCann, R. L. Savoy, J. A. Hall, Jr., and J. J. Scarpetti, Vision Res. 14, 917 (1974).

A sine wave of limited extent possesses spectral energy over a range of spatial frequencies that includes the nominal frequency. So, strictly, it is incorrect to speak of, for example, a 3-cycle-per-degree sine wave when we mean a truncated sine wave with a nominal spatial frequency of 3 cycles per degree. However, because we will be referring to truncated sine waves throughout this paper, it will frequently be convenient to use the looser terminology.

J. Hoekstra, D. P. J. van der Goot, G. van den Brink, and F. A. Bilsen, Vision Res. 14, 364 (1974).

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

J. J. DePalma and E. M. Lowry, J. Opt. Soc. Am. 52, 328 (1962).

M. Davidson, J. Opt. Soc. Am. 58, 1300 (1968).

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

We found that, with our apparatus, a 1-cycle target had the same threshold whether the left-hand edge was equal to the average liminance (sine phase) or the maximum luminance (cosine phase) of the sinusoidal region. Kelly (Ref. 9) showed that the edge created by a cosine phase target can determine threshold in the no-plateau condition. In our experiments, however, the edge between the mirror and the tube face never completely disappeared, so subjects could not use the creation of an edge as their principal cue for threshold; they needed to perceive some form.

D. H. Kelly, J. Opt. Soc. Am. 60, 98 (1970).

The definition of bandwidth used in this discussion is width at half-power. For targets with a fixed w, this bandwidth and the peak value of the transform undergo negligible change as n changes except when n is very close to zero. In that case, overlap with the transform component centered at -ƒ makes a significant contribution. However, there is only a 10% change of the height of the peak of the transform of the ½-cycle target, the lowest number of cycles used in our experiments.

M. Davidson and J. A. Whiteside, J. Opt. Soc. Am. 61, 530 (1971).

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

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

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

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