Abstract

Contrast masking was studied psychophysically. A two-alternative forced-choice procedure was used to measure contrast thresholds for 2.0 cpd sine-wave gratings in the presence of masking sine-wave gratings. Thresholds were measured for 11 masker contrasts spanning three log units, and seven masker frequencies ranging ± one octave from the signal frequency. Corresponding measurements were made for gratings with horizontal widths of 0.75° (narrow fields) and 6.0° (wide fields). For high contrast maskers at all frequencies, signal thresholds were related to masking contrast by power functions with exponents near 0.6. For a range of low masking contrasts, signal thresholds were reduced by the masker. For the wide fields, high contrast masking tuning functions peaked at the signal frequency, were slightly asymmetric, and had approximately invariant half maximum frequencies that lie 3/4 octave below and 1 octave above the signal frequency. The corresponding low contrast tuning functions exhibited peak threshold reduction at the signal frequency, with half-minimum frequencies at roughly ± 0.25 octaves. For the narrow fields, the masking tuning functions were much broader at both low and high masking contrasts. A masking model is presented that encompasses contrast detection, discrimination, and masking phenomena. Central constructs of the model include a linear spatial frequency filter, a nonlinear transducer, and a process of spatial pooling that acts at low contrasts only.

© 1980 Optical Society of America

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  1. R. Fox, "Visual masking," in Handbook of Sensory Physiology. VIII. Perception, edited by R. Held, H. W. Leibowitz, and H.-L. Teuber (Springer-Verlag, Berlin, 1978).
  2. J. Nachmias and R. V. Sansbury, "Grating contrast: discrimination may be better than detection," Vision Res. 14, 1039–1042 (1974).
  3. C. F. Stromeyer, III and S. Klein, "Spatial frequency channels in human vision as asymmetric (edge) mechanisms," Vision Res. 14, 1409–1420 (1974).
  4. J. M. Foley and G. E. Legge, "Contrast detection and near-threshold discrimination in human vision," Vision Res. (in press).
  5. D. M. Green, An Introduction to Hearing (Lawrence Erlbaum Associates, Hillsdale, New Jersey, 1976).
  6. U. Greis and R. Röhler, "Untersuchung der subjektiven Detailerkennbarkeit mit Hilfe der Ortsfrequenzfilterung," Opt. Acta 17, 515–526 (1970).
  7. C. F. Stromeyer, III and B. Julesz, "Spatial frequency masking in vision: critical bands and spread of masking," J. Opt. Soc. Am. 62, 1221–1232 (1972).
  8. A. Pantle, Visual Information Processing of Complex Imagery (Aerospace Medical Research Laboratory Report AMRL-TR-74–43, 1974).
  9. G. E. Legge, "Sustained and transient mechanisms in human vision: temporal and spatial properties," Vision Res. 18, 69–81 (1978).
  10. G. E. Legge, "Spatial frequency masking in human vision: binocular interactions," J. Opt. Soc. Am. 69, 838–847 (1979).
  11. A. Pantle and R. Sekuler, "Size detecting mechanisms in human vision," Science 162, 1146–1148 (1968).
  12. C. Blakemore and F. W. Campbell, "On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images," J. Physiol. (London) 203, 237–260 (1969).
  13. K. K. De Valois, "Spatial frequency adaptation can enhance contrast sensitivity," Vision Res. 17, 1057–1065 (1977).
  14. M. B. Sachs, J. Nachmias, and J. G. Robson, "Spatial frequency channels in human vision," J. Opt. Soc. Am. 61, 1176–1186 (1971).
  15. R. F. Quick, Jr. and T. Reichert, "Spatial frequency selectivity in contrast detection," Vision Res. 15, 637–643 (1975).
  16. C. F. Stromeyer, III and S. Klein, "Evidence against narrow-band spatial frequency channels in human vision: the detectability of frequency-modulated gratings," Vision Res. 15, 899–910 (1975).
  17. N. Graham, "Visual detection of aperiodic spatial stimuli by probability summation among narrow-band channels," Vision Res. 17, 637–652 (1977).
  18. R. F. Quick, Jr., W. W. Mullins, and T. A. Reichert, "Spatial summation effects on two-component grating thresholds," J. Opt. Soc. Am. 68, 116–121 (1978).
  19. D. J. Tolhurst, "Adaptation to square-wave gratings: inhibition between spatial frequency channels in the human visual system," J. Physiol. (London) 226, 231–48 (1972).
  20. R. S. Dealy and D. J. Tolhurst, "Is spatial frequency adaptation an aftereffect of prolonged inhibition?" J. Physiol. (London) 241, 261–270 (1974).
  21. C. F. Stromeyer, III, S. Klein, and C. E. Sternheim, "Is spatial adaptation caused by prolonged inhibition?" Vision Res. 17, 603–606 (1977).
  22. D. J. Tolhurst, "Separate channels for the analysis of the shape and the movement of a moving visual stimulus," J. Physiol. (London) 231, 385–402 (1973).
  23. F. W. Campbell and D. G. Green, "Optical and retinal factors affecting visual resolution," J. Physiol. (London) 181, 576–593 (1965).
  24. G. B. Wetherill and H. Levitt, "Sequential estimation of points on a psychometric function," Br. J. Math. Stat. Psychol. 18, 1–10 (1965).
  25. C. Blakemore and J. Nachmias, "The orientation specificity of two visual aftereffects," J. Physiol. (London) 213, 157–174 (1971).
  26. C. Blakemore, J. P. J. Muncey, and R. Ridley, "Stimulus specificity in the human visual system," Vision Res. 13, 1915–1931 (1973).
  27. F. W. Campbell and J. J. Kulikowski, "Orientational selectivity of the human visual system," J. Physiol. (London) 187, 437–445 (1966).
  28. I. Bodis-Wollner, C. D. Hendley, and J. J. Kulikowski, "Electro-physiological and psychophysical responses to modulation of contrast of a grating pattern," Perception 1, 341–349 (1972).
  29. D. J. Tolhurst and L. P. Barfield, "Interactions between spatial frequency channels," Vision Res. 18, 951–958 (1978).
  30. G. E. Legge, "In search of Weber's law for contrast discrimination," Suppl. Invest. Ophthalmol. Vis. Sci. 19, 43 (1980).
  31. I. Bodis-Wollner, C. D. Hendley, and M. Tajfel, "Contrast-modulation thresholds as a function of spatial frequency," J. Opt. Soc. Am. 63, 1297 (1973).
  32. J. J. Kulikowski, "Effective contrast constancy and linearity of contrast sensation," Vision Res. 16, 1419–1432 (1976).
  33. J. J. Kulikowski and A. Gorea, "Complete adaptation to pattern stimuli: a necessary and sufficient condition for Weber's law for contrast," Vision Res. 18, 1223–1227 (1978).
  34. J. Nachmias and E. C. Kocher, "Visual detection and discrimination of luminance increments," J. Opt. Soc. Am. 69, 382–389 (1970).
  35. T. E. Cohn, L. N. Thibos, and R. N. Kleinstein, "Detectability of a luminance increment," J. Opt. Soc. Am. 64, 1321–1327 (1974).
  36. G. E. Legge, "Space domain properties of a spatial frequency channel in human vision," Vision Res. 18, 959–969 (1978).
  37. J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge, and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).
  38. J. Nachmias and A. Weber, "Discrimination of simple and complex gratings," Vision Res. 15, 217–223 (1975).
  39. R. V. Sansbury, Some Properties of Spatial Channels Revealed by Pulsed Simultaneous Masking, Ph.D. dissertation, Dept. of Psychology, University of Pennsylvania, Philadelphia, 1974 (unpublished).
  40. J. Hoekstra, D. P. J. van der Goot, G. van den Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns," Vision Res. 14, 365–368 (1974).
  41. R. L. Savoy and J. J. McCann, "Visibility of low-spatial-frequency sine-wave targets: dependence on number of cycles," J. Opt. Soc. Am. 65, 343–350 (1975).
  42. O. Estevez and C. R. Cavonius, "Low-frequency attenuation in the detection of gratings: sorting out the artifacts," Vision Res. 16, 497–500 (1976).
  43. J. J. McCann, R. L. Savoy, and J. A. Hall, Jr., "Visibility of lowfrequency sine-wave targets: dependence on number of cycles and surround parameters," Vision Res. 18, 891–894 (1978).
  44. W. J. McGill and J. P. Goldberg, "A study of the near-miss involving Weber's law and pure tone intensity discrimination," Percept. Psychophys. 7, 105–109 (1968).
  45. J. H. Hall and M. M. Sondhi, "Detection threshold for a two-tone complex," J. Acoust. Soc. Am. 62, 636–640 (1977).
  46. J. P. Thomas, "Model for function of receptive fields in human vision," Psychol. Rev. 77, 121–134 (1970).
  47. I. D. G. Macleod and A. Rosenfeld, "The visibility of gratings: spatial frequency channels or bar detecting units?" Vision Res. 14, 909–15 (1974).
  48. H. R. Wilson and J. R. Bergen, "A four mechanism model for threshold spatial vision," Vision Res. 19, 19–32 (1979).
  49. The spatial frequency sensitivity function of Fig. 8(a) will be identified with the linear filter. Extrapolation of the fitted straight line toward 0 cpd (uniform field) suggests little sensitivity to mean luminance.
  50. In Eq. (4), let x′ = x − x0. Then: r0(f) = C-∞ cos2πf(x′ + x0)S(x′)dx′ = C-∞ (cos2πfx′ cos2πfx0 - sin2πfx′ sin2πfx0)S(x′)dx′ = C cos2πfx0-∞ cos2πfxS(x′)dx′ - C sin2πfx0-∞-∞ sin2πfxS(x′)dx′. Assuming S is even-symmetric and finite, the second term is 0, and we are left with Eq. (5).
  51. The only restriction upon Eq. (6) is that the spatial sensitivity function S(x) be center-symmetric and finite. All "phase effects" due to the position of the detector are accounted for by the factor cos2πƒx0.
  52. R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).
  53. J. J. Koenderink, M. A. Bouman, A. E. Bueno de Mesquita, and S. Slappendell, "Perimetry of contrast detection thresholds of moving spatial sinewave patterns. I. The near peripheral visual field," J. Opt. Soc. Am. 68, 845–849 (1978).
  54. H. R. Wilson and S. C. Giese, "Threshold visibility of frequency gradient patterns," Vision Res. 17, 1177–1190 (1977).
  55. Fechner (see Boring,56 Chap. 14) derived a sensory magnitude function from discrimination data. If the effects of spatial pooling are ignored, Fechner's technique may be used to derive the transducer function F from the discrimination functions in Figs. 2 or 4. The discrimination function is proportional to the reciprocal of the derivative of F.
  56. E. G. Boring, A History of Experimental Psychology (Appleton-Century-Crofts, New York, 1957).
  57. If the constant variance assumption is relaxed, the transducer function cannot be inferred directly from forced-choice data. Information concerning the dependence of noise variance on contrast could be obtained from other psychophysical procedures, such as the "bootstrap" procedure of Nachmias and Kocher.34 With this information in hand, a corrected form of the transducer function could be computed. Changes in variance with contrast would not be expected to affect the shape of the channel sensitivity function, Fig. 8(a). There exists little evidence concerning the dependence of variance on stimulus contrast. Paired comparison data of Foley and Legge4 indicate small changes in variance over a range of low contrasts. Further discussion of the effects of relaxing the constant variance assumption is given by Nachmias and Sansbury.2
  58. N. Graham and B. E. Rogowitz, "Spatial pooling properties deduced from the detectability of FM and quasi-AM gratings: a reanalysis," Vision Res. 16, 1021–1026 (1976).
  59. P. E. King-Smith and J. J. Kulikowski, "The detection of gratings by independent activation of line detectors," J. Physiol. (London) 247, 237–271 (1975).
  60. H. Mostafavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Vision Res. 16, 957–968 (1976).
  61. H. R. Wilson, "Quantitative prediction of line spread function measurements: implications for channel bandwidths," Vision Res. 18, 493–496 (1978).
  62. H. R. Wilson, "Quantitative characterization of two types of linespread function near the fovea," Vision Res. 18, 971–981 (1978).
  63. C. F. Stromeyer, III has pointed out an interesting property of the contrast discrimination data of Fig. 6. If the narrow field data points are moved downward by a factor of 2 and to the left by a factor of 2, they are very nearly superimposed upon the wide field data. This result means that contrast sensitivity for the narrow field stimuli is a factor of 2 lower than contrast sensitivity for the wide field stimuli.
  64. If the sampling density is doubled, center-symmetric detectors will be included that are located at zero crossings of the signal. Since these detectors will be insensitive to the signal, they will add only noise, resulting in a small reduction in the improvement of sensitivity due to spatial pooling. The effect upon the masking model is to elevate slightly its predictions for wide field masking at low contrasts [Fig. 6, dashed curve, and Fig. 10(a)]. Refinement of the masking model to include signal-dependent noise and/or odd-symmetric receptive fields would reduce such sampling effects.
  65. If spatial pooling and spectral effects are ignored, a logarithmic transducer results in Weber's law for discrimination, and masking tuning functions that match the shape of the linear filter function. If the nonlinearity is a power function with exponent n, the properties of masking will depend on the value of n. (i) For 0 < n < 1, there is threshold elevation and the masking tuning functions are broader than the filter function. (ii) For n = 1, signal thresholds are unaffected by the masker. (iii) For 1 < n < 2, masking produces facilitation, but the tuning functions are broader than the filter function. (iv) For n > 2, masking produces facilitation and the tuning functions are narrower than the filter function.
  66. G. J. Burton, "Evidence for nonlinear response processes in the human visual system from measurements of the thresholds of spatial beat frequencies," Vision Res. 13, 1211–1225 (1973).
  67. F. W. Campbell and J. G. Robson, "Applications of Fourier analysis to the visibility of gratings," J. Physiol. (London) 197, 551–566 (1968).
  68. F. W. Campbell, R. H. S. Carpenter, and J. Z. Levinson, "Visibility of aperiodic patterns compared with that of sinusoidal gratings," J. Physiol. (London) 204, 283–298 (1969).
  69. M. Hines, "Line spread function variation near the fovea," Vision Res. 16, 567–572 (1976).

1980

G. E. Legge, "In search of Weber's law for contrast discrimination," Suppl. Invest. Ophthalmol. Vis. Sci. 19, 43 (1980).

1979

H. R. Wilson and J. R. Bergen, "A four mechanism model for threshold spatial vision," Vision Res. 19, 19–32 (1979).

G. E. Legge, "Spatial frequency masking in human vision: binocular interactions," J. Opt. Soc. Am. 69, 838–847 (1979).

1978

J. J. Koenderink, M. A. Bouman, A. E. Bueno de Mesquita, and S. Slappendell, "Perimetry of contrast detection thresholds of moving spatial sinewave patterns. I. The near peripheral visual field," J. Opt. Soc. Am. 68, 845–849 (1978).

R. F. Quick, Jr., W. W. Mullins, and T. A. Reichert, "Spatial summation effects on two-component grating thresholds," J. Opt. Soc. Am. 68, 116–121 (1978).

H. R. Wilson, "Quantitative prediction of line spread function measurements: implications for channel bandwidths," Vision Res. 18, 493–496 (1978).

H. R. Wilson, "Quantitative characterization of two types of linespread function near the fovea," Vision Res. 18, 971–981 (1978).

G. E. Legge, "Sustained and transient mechanisms in human vision: temporal and spatial properties," Vision Res. 18, 69–81 (1978).

D. J. Tolhurst and L. P. Barfield, "Interactions between spatial frequency channels," Vision Res. 18, 951–958 (1978).

J. J. Kulikowski and A. Gorea, "Complete adaptation to pattern stimuli: a necessary and sufficient condition for Weber's law for contrast," Vision Res. 18, 1223–1227 (1978).

G. E. Legge, "Space domain properties of a spatial frequency channel in human vision," Vision Res. 18, 959–969 (1978).

J. J. McCann, R. L. Savoy, and J. A. Hall, Jr., "Visibility of lowfrequency sine-wave targets: dependence on number of cycles and surround parameters," Vision Res. 18, 891–894 (1978).

1977

J. H. Hall and M. M. Sondhi, "Detection threshold for a two-tone complex," J. Acoust. Soc. Am. 62, 636–640 (1977).

K. K. De Valois, "Spatial frequency adaptation can enhance contrast sensitivity," Vision Res. 17, 1057–1065 (1977).

N. Graham, "Visual detection of aperiodic spatial stimuli by probability summation among narrow-band channels," Vision Res. 17, 637–652 (1977).

C. F. Stromeyer, III, S. Klein, and C. E. Sternheim, "Is spatial adaptation caused by prolonged inhibition?" Vision Res. 17, 603–606 (1977).

H. R. Wilson and S. C. Giese, "Threshold visibility of frequency gradient patterns," Vision Res. 17, 1177–1190 (1977).

1976

N. Graham and B. E. Rogowitz, "Spatial pooling properties deduced from the detectability of FM and quasi-AM gratings: a reanalysis," Vision Res. 16, 1021–1026 (1976).

H. Mostafavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Vision Res. 16, 957–968 (1976).

M. Hines, "Line spread function variation near the fovea," Vision Res. 16, 567–572 (1976).

O. Estevez and C. R. Cavonius, "Low-frequency attenuation in the detection of gratings: sorting out the artifacts," Vision Res. 16, 497–500 (1976).

J. J. Kulikowski, "Effective contrast constancy and linearity of contrast sensation," Vision Res. 16, 1419–1432 (1976).

1975

R. F. Quick, Jr. and T. Reichert, "Spatial frequency selectivity in contrast detection," Vision Res. 15, 637–643 (1975).

C. F. Stromeyer, III and S. Klein, "Evidence against narrow-band spatial frequency channels in human vision: the detectability of frequency-modulated gratings," Vision Res. 15, 899–910 (1975).

J. Nachmias and A. Weber, "Discrimination of simple and complex gratings," Vision Res. 15, 217–223 (1975).

P. E. King-Smith and J. J. Kulikowski, "The detection of gratings by independent activation of line detectors," J. Physiol. (London) 247, 237–271 (1975).

R. L. Savoy and J. J. McCann, "Visibility of low-spatial-frequency sine-wave targets: dependence on number of cycles," J. Opt. Soc. Am. 65, 343–350 (1975).

1974

T. E. Cohn, L. N. Thibos, and R. N. Kleinstein, "Detectability of a luminance increment," J. Opt. Soc. Am. 64, 1321–1327 (1974).

A. Pantle, Visual Information Processing of Complex Imagery (Aerospace Medical Research Laboratory Report AMRL-TR-74–43, 1974).

I. D. G. Macleod and A. Rosenfeld, "The visibility of gratings: spatial frequency channels or bar detecting units?" Vision Res. 14, 909–15 (1974).

R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).

J. Hoekstra, D. P. J. van der Goot, G. van den Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns," Vision Res. 14, 365–368 (1974).

J. Nachmias and R. V. Sansbury, "Grating contrast: discrimination may be better than detection," Vision Res. 14, 1039–1042 (1974).

C. F. Stromeyer, III and S. Klein, "Spatial frequency channels in human vision as asymmetric (edge) mechanisms," Vision Res. 14, 1409–1420 (1974).

R. S. Dealy and D. J. Tolhurst, "Is spatial frequency adaptation an aftereffect of prolonged inhibition?" J. Physiol. (London) 241, 261–270 (1974).

1973

C. Blakemore, J. P. J. Muncey, and R. Ridley, "Stimulus specificity in the human visual system," Vision Res. 13, 1915–1931 (1973).

D. J. Tolhurst, "Separate channels for the analysis of the shape and the movement of a moving visual stimulus," J. Physiol. (London) 231, 385–402 (1973).

I. Bodis-Wollner, C. D. Hendley, and M. Tajfel, "Contrast-modulation thresholds as a function of spatial frequency," J. Opt. Soc. Am. 63, 1297 (1973).

J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge, and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).

G. J. Burton, "Evidence for nonlinear response processes in the human visual system from measurements of the thresholds of spatial beat frequencies," Vision Res. 13, 1211–1225 (1973).

1972

C. F. Stromeyer, III and B. Julesz, "Spatial frequency masking in vision: critical bands and spread of masking," J. Opt. Soc. Am. 62, 1221–1232 (1972).

I. Bodis-Wollner, C. D. Hendley, and J. J. Kulikowski, "Electro-physiological and psychophysical responses to modulation of contrast of a grating pattern," Perception 1, 341–349 (1972).

D. J. Tolhurst, "Adaptation to square-wave gratings: inhibition between spatial frequency channels in the human visual system," J. Physiol. (London) 226, 231–48 (1972).

1971

C. Blakemore and J. Nachmias, "The orientation specificity of two visual aftereffects," J. Physiol. (London) 213, 157–174 (1971).

M. B. Sachs, J. Nachmias, and J. G. Robson, "Spatial frequency channels in human vision," J. Opt. Soc. Am. 61, 1176–1186 (1971).

1970

J. Nachmias and E. C. Kocher, "Visual detection and discrimination of luminance increments," J. Opt. Soc. Am. 69, 382–389 (1970).

J. P. Thomas, "Model for function of receptive fields in human vision," Psychol. Rev. 77, 121–134 (1970).

U. Greis and R. Röhler, "Untersuchung der subjektiven Detailerkennbarkeit mit Hilfe der Ortsfrequenzfilterung," Opt. Acta 17, 515–526 (1970).

1969

C. Blakemore and F. W. Campbell, "On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images," J. Physiol. (London) 203, 237–260 (1969).

F. W. Campbell, R. H. S. Carpenter, and J. Z. Levinson, "Visibility of aperiodic patterns compared with that of sinusoidal gratings," J. Physiol. (London) 204, 283–298 (1969).

1968

F. W. Campbell and J. G. Robson, "Applications of Fourier analysis to the visibility of gratings," J. Physiol. (London) 197, 551–566 (1968).

A. Pantle and R. Sekuler, "Size detecting mechanisms in human vision," Science 162, 1146–1148 (1968).

W. J. McGill and J. P. Goldberg, "A study of the near-miss involving Weber's law and pure tone intensity discrimination," Percept. Psychophys. 7, 105–109 (1968).

1966

F. W. Campbell and J. J. Kulikowski, "Orientational selectivity of the human visual system," J. Physiol. (London) 187, 437–445 (1966).

1965

F. W. Campbell and D. G. Green, "Optical and retinal factors affecting visual resolution," J. Physiol. (London) 181, 576–593 (1965).

G. B. Wetherill and H. Levitt, "Sequential estimation of points on a psychometric function," Br. J. Math. Stat. Psychol. 18, 1–10 (1965).

Barfield, L. P.

D. J. Tolhurst and L. P. Barfield, "Interactions between spatial frequency channels," Vision Res. 18, 951–958 (1978).

Bergen, J. R.

H. R. Wilson and J. R. Bergen, "A four mechanism model for threshold spatial vision," Vision Res. 19, 19–32 (1979).

Bilsen, F. A.

J. Hoekstra, D. P. J. van der Goot, G. van den Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns," Vision Res. 14, 365–368 (1974).

Blakemore, C.

C. Blakemore, J. P. J. Muncey, and R. Ridley, "Stimulus specificity in the human visual system," Vision Res. 13, 1915–1931 (1973).

C. Blakemore and J. Nachmias, "The orientation specificity of two visual aftereffects," J. Physiol. (London) 213, 157–174 (1971).

C. Blakemore and F. W. Campbell, "On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images," J. Physiol. (London) 203, 237–260 (1969).

Bodis-Wollner, I.

I. Bodis-Wollner, C. D. Hendley, and M. Tajfel, "Contrast-modulation thresholds as a function of spatial frequency," J. Opt. Soc. Am. 63, 1297 (1973).

I. Bodis-Wollner, C. D. Hendley, and J. J. Kulikowski, "Electro-physiological and psychophysical responses to modulation of contrast of a grating pattern," Perception 1, 341–349 (1972).

Boring, E. G.

E. G. Boring, A History of Experimental Psychology (Appleton-Century-Crofts, New York, 1957).

Bouman, M. A.

Burton, G. J.

G. J. Burton, "Evidence for nonlinear response processes in the human visual system from measurements of the thresholds of spatial beat frequencies," Vision Res. 13, 1211–1225 (1973).

Campbell, F. W.

C. Blakemore and F. W. Campbell, "On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images," J. Physiol. (London) 203, 237–260 (1969).

F. W. Campbell, R. H. S. Carpenter, and J. Z. Levinson, "Visibility of aperiodic patterns compared with that of sinusoidal gratings," J. Physiol. (London) 204, 283–298 (1969).

F. W. Campbell and J. G. Robson, "Applications of Fourier analysis to the visibility of gratings," J. Physiol. (London) 197, 551–566 (1968).

F. W. Campbell and J. J. Kulikowski, "Orientational selectivity of the human visual system," J. Physiol. (London) 187, 437–445 (1966).

F. W. Campbell and D. G. Green, "Optical and retinal factors affecting visual resolution," J. Physiol. (London) 181, 576–593 (1965).

Carpenter, R. H. S.

F. W. Campbell, R. H. S. Carpenter, and J. Z. Levinson, "Visibility of aperiodic patterns compared with that of sinusoidal gratings," J. Physiol. (London) 204, 283–298 (1969).

Cavonius, C. R.

O. Estevez and C. R. Cavonius, "Low-frequency attenuation in the detection of gratings: sorting out the artifacts," Vision Res. 16, 497–500 (1976).

R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).

Cohn, T. E.

de Mesquita, A. E. Bueno

De Valois, K. K.

K. K. De Valois, "Spatial frequency adaptation can enhance contrast sensitivity," Vision Res. 17, 1057–1065 (1977).

Dealy, R. S.

R. S. Dealy and D. J. Tolhurst, "Is spatial frequency adaptation an aftereffect of prolonged inhibition?" J. Physiol. (London) 241, 261–270 (1974).

Estevez, O.

O. Estevez and C. R. Cavonius, "Low-frequency attenuation in the detection of gratings: sorting out the artifacts," Vision Res. 16, 497–500 (1976).

Foley, J. M.

J. M. Foley and G. E. Legge, "Contrast detection and near-threshold discrimination in human vision," Vision Res. (in press).

Fox, R.

R. Fox, "Visual masking," in Handbook of Sensory Physiology. VIII. Perception, edited by R. Held, H. W. Leibowitz, and H.-L. Teuber (Springer-Verlag, Berlin, 1978).

Giese, S. C.

H. R. Wilson and S. C. Giese, "Threshold visibility of frequency gradient patterns," Vision Res. 17, 1177–1190 (1977).

Goldberg, J. P.

W. J. McGill and J. P. Goldberg, "A study of the near-miss involving Weber's law and pure tone intensity discrimination," Percept. Psychophys. 7, 105–109 (1968).

Gorea, A.

J. J. Kulikowski and A. Gorea, "Complete adaptation to pattern stimuli: a necessary and sufficient condition for Weber's law for contrast," Vision Res. 18, 1223–1227 (1978).

Graham, N.

N. Graham, "Visual detection of aperiodic spatial stimuli by probability summation among narrow-band channels," Vision Res. 17, 637–652 (1977).

N. Graham and B. E. Rogowitz, "Spatial pooling properties deduced from the detectability of FM and quasi-AM gratings: a reanalysis," Vision Res. 16, 1021–1026 (1976).

Green, D. G.

F. W. Campbell and D. G. Green, "Optical and retinal factors affecting visual resolution," J. Physiol. (London) 181, 576–593 (1965).

Green, D. M.

D. M. Green, An Introduction to Hearing (Lawrence Erlbaum Associates, Hillsdale, New Jersey, 1976).

Greis, U.

U. Greis and R. Röhler, "Untersuchung der subjektiven Detailerkennbarkeit mit Hilfe der Ortsfrequenzfilterung," Opt. Acta 17, 515–526 (1970).

Hall, J. H.

J. H. Hall and M. M. Sondhi, "Detection threshold for a two-tone complex," J. Acoust. Soc. Am. 62, 636–640 (1977).

Hall, Jr., J. A.

J. J. McCann, R. L. Savoy, and J. A. Hall, Jr., "Visibility of lowfrequency sine-wave targets: dependence on number of cycles and surround parameters," Vision Res. 18, 891–894 (1978).

Hendley, C. D.

I. Bodis-Wollner, C. D. Hendley, and M. Tajfel, "Contrast-modulation thresholds as a function of spatial frequency," J. Opt. Soc. Am. 63, 1297 (1973).

I. Bodis-Wollner, C. D. Hendley, and J. J. Kulikowski, "Electro-physiological and psychophysical responses to modulation of contrast of a grating pattern," Perception 1, 341–349 (1972).

Hilz, R.

R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).

Hines, M.

M. Hines, "Line spread function variation near the fovea," Vision Res. 16, 567–572 (1976).

Hoekstra, J.

J. Hoekstra, D. P. J. van der Goot, G. van den Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns," Vision Res. 14, 365–368 (1974).

Julesz, B.

King-Smith, P. E.

P. E. King-Smith and J. J. Kulikowski, "The detection of gratings by independent activation of line detectors," J. Physiol. (London) 247, 237–271 (1975).

J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge, and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).

Klein, S.

C. F. Stromeyer, III, S. Klein, and C. E. Sternheim, "Is spatial adaptation caused by prolonged inhibition?" Vision Res. 17, 603–606 (1977).

C. F. Stromeyer, III and S. Klein, "Evidence against narrow-band spatial frequency channels in human vision: the detectability of frequency-modulated gratings," Vision Res. 15, 899–910 (1975).

C. F. Stromeyer, III and S. Klein, "Spatial frequency channels in human vision as asymmetric (edge) mechanisms," Vision Res. 14, 1409–1420 (1974).

Kleinstein, R. N.

Kocher, E. C.

J. Nachmias and E. C. Kocher, "Visual detection and discrimination of luminance increments," J. Opt. Soc. Am. 69, 382–389 (1970).

Koenderink, J. J.

Kulikowski, J. J.

J. J. Kulikowski and A. Gorea, "Complete adaptation to pattern stimuli: a necessary and sufficient condition for Weber's law for contrast," Vision Res. 18, 1223–1227 (1978).

J. J. Kulikowski, "Effective contrast constancy and linearity of contrast sensation," Vision Res. 16, 1419–1432 (1976).

P. E. King-Smith and J. J. Kulikowski, "The detection of gratings by independent activation of line detectors," J. Physiol. (London) 247, 237–271 (1975).

J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge, and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).

I. Bodis-Wollner, C. D. Hendley, and J. J. Kulikowski, "Electro-physiological and psychophysical responses to modulation of contrast of a grating pattern," Perception 1, 341–349 (1972).

F. W. Campbell and J. J. Kulikowski, "Orientational selectivity of the human visual system," J. Physiol. (London) 187, 437–445 (1966).

Legge, G. E.

G. E. Legge, "In search of Weber's law for contrast discrimination," Suppl. Invest. Ophthalmol. Vis. Sci. 19, 43 (1980).

G. E. Legge, "Spatial frequency masking in human vision: binocular interactions," J. Opt. Soc. Am. 69, 838–847 (1979).

G. E. Legge, "Space domain properties of a spatial frequency channel in human vision," Vision Res. 18, 959–969 (1978).

G. E. Legge, "Sustained and transient mechanisms in human vision: temporal and spatial properties," Vision Res. 18, 69–81 (1978).

J. M. Foley and G. E. Legge, "Contrast detection and near-threshold discrimination in human vision," Vision Res. (in press).

Levinson, J. Z.

F. W. Campbell, R. H. S. Carpenter, and J. Z. Levinson, "Visibility of aperiodic patterns compared with that of sinusoidal gratings," J. Physiol. (London) 204, 283–298 (1969).

Levitt, H.

G. B. Wetherill and H. Levitt, "Sequential estimation of points on a psychometric function," Br. J. Math. Stat. Psychol. 18, 1–10 (1965).

Macleod, I. D. G.

I. D. G. Macleod and A. Rosenfeld, "The visibility of gratings: spatial frequency channels or bar detecting units?" Vision Res. 14, 909–15 (1974).

McCann, J. J.

J. J. McCann, R. L. Savoy, and J. A. Hall, Jr., "Visibility of lowfrequency sine-wave targets: dependence on number of cycles and surround parameters," Vision Res. 18, 891–894 (1978).

R. L. Savoy and J. J. McCann, "Visibility of low-spatial-frequency sine-wave targets: dependence on number of cycles," J. Opt. Soc. Am. 65, 343–350 (1975).

McGill, W. J.

W. J. McGill and J. P. Goldberg, "A study of the near-miss involving Weber's law and pure tone intensity discrimination," Percept. Psychophys. 7, 105–109 (1968).

Mostafavi, H.

H. Mostafavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Vision Res. 16, 957–968 (1976).

Mullins, W. W.

Muncey, J. P. J.

C. Blakemore, J. P. J. Muncey, and R. Ridley, "Stimulus specificity in the human visual system," Vision Res. 13, 1915–1931 (1973).

Nachmias, J.

J. Nachmias and A. Weber, "Discrimination of simple and complex gratings," Vision Res. 15, 217–223 (1975).

J. Nachmias and R. V. Sansbury, "Grating contrast: discrimination may be better than detection," Vision Res. 14, 1039–1042 (1974).

M. B. Sachs, J. Nachmias, and J. G. Robson, "Spatial frequency channels in human vision," J. Opt. Soc. Am. 61, 1176–1186 (1971).

C. Blakemore and J. Nachmias, "The orientation specificity of two visual aftereffects," J. Physiol. (London) 213, 157–174 (1971).

J. Nachmias and E. C. Kocher, "Visual detection and discrimination of luminance increments," J. Opt. Soc. Am. 69, 382–389 (1970).

Pantle, A.

A. Pantle, Visual Information Processing of Complex Imagery (Aerospace Medical Research Laboratory Report AMRL-TR-74–43, 1974).

A. Pantle and R. Sekuler, "Size detecting mechanisms in human vision," Science 162, 1146–1148 (1968).

Quick, Jr., R. F.

R. F. Quick, Jr., W. W. Mullins, and T. A. Reichert, "Spatial summation effects on two-component grating thresholds," J. Opt. Soc. Am. 68, 116–121 (1978).

R. F. Quick, Jr. and T. Reichert, "Spatial frequency selectivity in contrast detection," Vision Res. 15, 637–643 (1975).

Reichert, T.

R. F. Quick, Jr. and T. Reichert, "Spatial frequency selectivity in contrast detection," Vision Res. 15, 637–643 (1975).

Reichert, T. A.

Ridley, R.

C. Blakemore, J. P. J. Muncey, and R. Ridley, "Stimulus specificity in the human visual system," Vision Res. 13, 1915–1931 (1973).

Robson, J. G.

M. B. Sachs, J. Nachmias, and J. G. Robson, "Spatial frequency channels in human vision," J. Opt. Soc. Am. 61, 1176–1186 (1971).

F. W. Campbell and J. G. Robson, "Applications of Fourier analysis to the visibility of gratings," J. Physiol. (London) 197, 551–566 (1968).

Rogowitz, B. E.

N. Graham and B. E. Rogowitz, "Spatial pooling properties deduced from the detectability of FM and quasi-AM gratings: a reanalysis," Vision Res. 16, 1021–1026 (1976).

Röhler, R.

U. Greis and R. Röhler, "Untersuchung der subjektiven Detailerkennbarkeit mit Hilfe der Ortsfrequenzfilterung," Opt. Acta 17, 515–526 (1970).

Rosenfeld, A.

I. D. G. Macleod and A. Rosenfeld, "The visibility of gratings: spatial frequency channels or bar detecting units?" Vision Res. 14, 909–15 (1974).

Sachs, M. B.

Sakrison, D. J.

H. Mostafavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Vision Res. 16, 957–968 (1976).

Sansbury, R. V.

J. Nachmias and R. V. Sansbury, "Grating contrast: discrimination may be better than detection," Vision Res. 14, 1039–1042 (1974).

R. V. Sansbury, Some Properties of Spatial Channels Revealed by Pulsed Simultaneous Masking, Ph.D. dissertation, Dept. of Psychology, University of Pennsylvania, Philadelphia, 1974 (unpublished).

Savoy, R. L.

J. J. McCann, R. L. Savoy, and J. A. Hall, Jr., "Visibility of lowfrequency sine-wave targets: dependence on number of cycles and surround parameters," Vision Res. 18, 891–894 (1978).

R. L. Savoy and J. J. McCann, "Visibility of low-spatial-frequency sine-wave targets: dependence on number of cycles," J. Opt. Soc. Am. 65, 343–350 (1975).

Sekuler, R.

A. Pantle and R. Sekuler, "Size detecting mechanisms in human vision," Science 162, 1146–1148 (1968).

Slappendell, S.

Sondhi, M. M.

J. H. Hall and M. M. Sondhi, "Detection threshold for a two-tone complex," J. Acoust. Soc. Am. 62, 636–640 (1977).

Sternheim, C. E.

C. F. Stromeyer, III, S. Klein, and C. E. Sternheim, "Is spatial adaptation caused by prolonged inhibition?" Vision Res. 17, 603–606 (1977).

Stromeyer, III, C. F.

C. F. Stromeyer, III, S. Klein, and C. E. Sternheim, "Is spatial adaptation caused by prolonged inhibition?" Vision Res. 17, 603–606 (1977).

C. F. Stromeyer, III and S. Klein, "Evidence against narrow-band spatial frequency channels in human vision: the detectability of frequency-modulated gratings," Vision Res. 15, 899–910 (1975).

C. F. Stromeyer, III and S. Klein, "Spatial frequency channels in human vision as asymmetric (edge) mechanisms," Vision Res. 14, 1409–1420 (1974).

C. F. Stromeyer, III and B. Julesz, "Spatial frequency masking in vision: critical bands and spread of masking," J. Opt. Soc. Am. 62, 1221–1232 (1972).

C. F. Stromeyer, III has pointed out an interesting property of the contrast discrimination data of Fig. 6. If the narrow field data points are moved downward by a factor of 2 and to the left by a factor of 2, they are very nearly superimposed upon the wide field data. This result means that contrast sensitivity for the narrow field stimuli is a factor of 2 lower than contrast sensitivity for the wide field stimuli.

Tajfel, M.

I. Bodis-Wollner, C. D. Hendley, and M. Tajfel, "Contrast-modulation thresholds as a function of spatial frequency," J. Opt. Soc. Am. 63, 1297 (1973).

Thibos, L. N.

Thomas, J. P.

J. P. Thomas, "Model for function of receptive fields in human vision," Psychol. Rev. 77, 121–134 (1970).

Tolhurst, D. J.

D. J. Tolhurst and L. P. Barfield, "Interactions between spatial frequency channels," Vision Res. 18, 951–958 (1978).

R. S. Dealy and D. J. Tolhurst, "Is spatial frequency adaptation an aftereffect of prolonged inhibition?" J. Physiol. (London) 241, 261–270 (1974).

D. J. Tolhurst, "Separate channels for the analysis of the shape and the movement of a moving visual stimulus," J. Physiol. (London) 231, 385–402 (1973).

D. J. Tolhurst, "Adaptation to square-wave gratings: inhibition between spatial frequency channels in the human visual system," J. Physiol. (London) 226, 231–48 (1972).

van den Brink, G.

J. Hoekstra, D. P. J. van der Goot, G. van den Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns," Vision Res. 14, 365–368 (1974).

van der Goot, D. P. J.

J. Hoekstra, D. P. J. van der Goot, G. van den Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns," Vision Res. 14, 365–368 (1974).

Weber, A.

J. Nachmias and A. Weber, "Discrimination of simple and complex gratings," Vision Res. 15, 217–223 (1975).

Wetherill, G. B.

G. B. Wetherill and H. Levitt, "Sequential estimation of points on a psychometric function," Br. J. Math. Stat. Psychol. 18, 1–10 (1965).

Wilson, H. R.

H. R. Wilson and J. R. Bergen, "A four mechanism model for threshold spatial vision," Vision Res. 19, 19–32 (1979).

H. R. Wilson, "Quantitative characterization of two types of linespread function near the fovea," Vision Res. 18, 971–981 (1978).

H. R. Wilson, "Quantitative prediction of line spread function measurements: implications for channel bandwidths," Vision Res. 18, 493–496 (1978).

H. R. Wilson and S. C. Giese, "Threshold visibility of frequency gradient patterns," Vision Res. 17, 1177–1190 (1977).

Br. J. Math. Stat. Psychol.

G. B. Wetherill and H. Levitt, "Sequential estimation of points on a psychometric function," Br. J. Math. Stat. Psychol. 18, 1–10 (1965).

J. Acoust. Soc. Am.

J. H. Hall and M. M. Sondhi, "Detection threshold for a two-tone complex," J. Acoust. Soc. Am. 62, 636–640 (1977).

J. Opt. Soc. Am.

J. Physiol.

C. Blakemore and J. Nachmias, "The orientation specificity of two visual aftereffects," J. Physiol. (London) 213, 157–174 (1971).

F. W. Campbell and J. J. Kulikowski, "Orientational selectivity of the human visual system," J. Physiol. (London) 187, 437–445 (1966).

D. J. Tolhurst, "Adaptation to square-wave gratings: inhibition between spatial frequency channels in the human visual system," J. Physiol. (London) 226, 231–48 (1972).

R. S. Dealy and D. J. Tolhurst, "Is spatial frequency adaptation an aftereffect of prolonged inhibition?" J. Physiol. (London) 241, 261–270 (1974).

D. J. Tolhurst, "Separate channels for the analysis of the shape and the movement of a moving visual stimulus," J. Physiol. (London) 231, 385–402 (1973).

F. W. Campbell and D. G. Green, "Optical and retinal factors affecting visual resolution," J. Physiol. (London) 181, 576–593 (1965).

C. Blakemore and F. W. Campbell, "On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images," J. Physiol. (London) 203, 237–260 (1969).

P. E. King-Smith and J. J. Kulikowski, "The detection of gratings by independent activation of line detectors," J. Physiol. (London) 247, 237–271 (1975).

F. W. Campbell and J. G. Robson, "Applications of Fourier analysis to the visibility of gratings," J. Physiol. (London) 197, 551–566 (1968).

F. W. Campbell, R. H. S. Carpenter, and J. Z. Levinson, "Visibility of aperiodic patterns compared with that of sinusoidal gratings," J. Physiol. (London) 204, 283–298 (1969).

Opt. Acta

U. Greis and R. Röhler, "Untersuchung der subjektiven Detailerkennbarkeit mit Hilfe der Ortsfrequenzfilterung," Opt. Acta 17, 515–526 (1970).

Percept. Psychophys.

W. J. McGill and J. P. Goldberg, "A study of the near-miss involving Weber's law and pure tone intensity discrimination," Percept. Psychophys. 7, 105–109 (1968).

Perception

I. Bodis-Wollner, C. D. Hendley, and J. J. Kulikowski, "Electro-physiological and psychophysical responses to modulation of contrast of a grating pattern," Perception 1, 341–349 (1972).

Psychol. Rev.

J. P. Thomas, "Model for function of receptive fields in human vision," Psychol. Rev. 77, 121–134 (1970).

Science

A. Pantle and R. Sekuler, "Size detecting mechanisms in human vision," Science 162, 1146–1148 (1968).

Suppl. Invest. Ophthalmol. Vis. Sci.

G. E. Legge, "In search of Weber's law for contrast discrimination," Suppl. Invest. Ophthalmol. Vis. Sci. 19, 43 (1980).

Vision Res.

N. Graham and B. E. Rogowitz, "Spatial pooling properties deduced from the detectability of FM and quasi-AM gratings: a reanalysis," Vision Res. 16, 1021–1026 (1976).

J. Hoekstra, D. P. J. van der Goot, G. van den Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns," Vision Res. 14, 365–368 (1974).

H. R. Wilson and S. C. Giese, "Threshold visibility of frequency gradient patterns," Vision Res. 17, 1177–1190 (1977).

K. K. De Valois, "Spatial frequency adaptation can enhance contrast sensitivity," Vision Res. 17, 1057–1065 (1977).

R. F. Quick, Jr. and T. Reichert, "Spatial frequency selectivity in contrast detection," Vision Res. 15, 637–643 (1975).

C. F. Stromeyer, III and S. Klein, "Evidence against narrow-band spatial frequency channels in human vision: the detectability of frequency-modulated gratings," Vision Res. 15, 899–910 (1975).

N. Graham, "Visual detection of aperiodic spatial stimuli by probability summation among narrow-band channels," Vision Res. 17, 637–652 (1977).

G. E. Legge, "Space domain properties of a spatial frequency channel in human vision," Vision Res. 18, 959–969 (1978).

J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge, and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).

J. Nachmias and A. Weber, "Discrimination of simple and complex gratings," Vision Res. 15, 217–223 (1975).

D. J. Tolhurst and L. P. Barfield, "Interactions between spatial frequency channels," Vision Res. 18, 951–958 (1978).

C. Blakemore, J. P. J. Muncey, and R. Ridley, "Stimulus specificity in the human visual system," Vision Res. 13, 1915–1931 (1973).

C. F. Stromeyer, III, S. Klein, and C. E. Sternheim, "Is spatial adaptation caused by prolonged inhibition?" Vision Res. 17, 603–606 (1977).

J. J. Kulikowski, "Effective contrast constancy and linearity of contrast sensation," Vision Res. 16, 1419–1432 (1976).

J. J. Kulikowski and A. Gorea, "Complete adaptation to pattern stimuli: a necessary and sufficient condition for Weber's law for contrast," Vision Res. 18, 1223–1227 (1978).

J. Nachmias and R. V. Sansbury, "Grating contrast: discrimination may be better than detection," Vision Res. 14, 1039–1042 (1974).

C. F. Stromeyer, III and S. Klein, "Spatial frequency channels in human vision as asymmetric (edge) mechanisms," Vision Res. 14, 1409–1420 (1974).

I. D. G. Macleod and A. Rosenfeld, "The visibility of gratings: spatial frequency channels or bar detecting units?" Vision Res. 14, 909–15 (1974).

H. R. Wilson and J. R. Bergen, "A four mechanism model for threshold spatial vision," Vision Res. 19, 19–32 (1979).

G. J. Burton, "Evidence for nonlinear response processes in the human visual system from measurements of the thresholds of spatial beat frequencies," Vision Res. 13, 1211–1225 (1973).

R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).

M. Hines, "Line spread function variation near the fovea," Vision Res. 16, 567–572 (1976).

O. Estevez and C. R. Cavonius, "Low-frequency attenuation in the detection of gratings: sorting out the artifacts," Vision Res. 16, 497–500 (1976).

J. J. McCann, R. L. Savoy, and J. A. Hall, Jr., "Visibility of lowfrequency sine-wave targets: dependence on number of cycles and surround parameters," Vision Res. 18, 891–894 (1978).

H. Mostafavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Vision Res. 16, 957–968 (1976).

H. R. Wilson, "Quantitative prediction of line spread function measurements: implications for channel bandwidths," Vision Res. 18, 493–496 (1978).

H. R. Wilson, "Quantitative characterization of two types of linespread function near the fovea," Vision Res. 18, 971–981 (1978).

G. E. Legge, "Sustained and transient mechanisms in human vision: temporal and spatial properties," Vision Res. 18, 69–81 (1978).

Other

C. F. Stromeyer, III has pointed out an interesting property of the contrast discrimination data of Fig. 6. If the narrow field data points are moved downward by a factor of 2 and to the left by a factor of 2, they are very nearly superimposed upon the wide field data. This result means that contrast sensitivity for the narrow field stimuli is a factor of 2 lower than contrast sensitivity for the wide field stimuli.

If the sampling density is doubled, center-symmetric detectors will be included that are located at zero crossings of the signal. Since these detectors will be insensitive to the signal, they will add only noise, resulting in a small reduction in the improvement of sensitivity due to spatial pooling. The effect upon the masking model is to elevate slightly its predictions for wide field masking at low contrasts [Fig. 6, dashed curve, and Fig. 10(a)]. Refinement of the masking model to include signal-dependent noise and/or odd-symmetric receptive fields would reduce such sampling effects.

If spatial pooling and spectral effects are ignored, a logarithmic transducer results in Weber's law for discrimination, and masking tuning functions that match the shape of the linear filter function. If the nonlinearity is a power function with exponent n, the properties of masking will depend on the value of n. (i) For 0 < n < 1, there is threshold elevation and the masking tuning functions are broader than the filter function. (ii) For n = 1, signal thresholds are unaffected by the masker. (iii) For 1 < n < 2, masking produces facilitation, but the tuning functions are broader than the filter function. (iv) For n > 2, masking produces facilitation and the tuning functions are narrower than the filter function.

A. Pantle, Visual Information Processing of Complex Imagery (Aerospace Medical Research Laboratory Report AMRL-TR-74–43, 1974).

The spatial frequency sensitivity function of Fig. 8(a) will be identified with the linear filter. Extrapolation of the fitted straight line toward 0 cpd (uniform field) suggests little sensitivity to mean luminance.

In Eq. (4), let x′ = x − x0. Then: r0(f) = C-∞ cos2πf(x′ + x0)S(x′)dx′ = C-∞ (cos2πfx′ cos2πfx0 - sin2πfx′ sin2πfx0)S(x′)dx′ = C cos2πfx0-∞ cos2πfxS(x′)dx′ - C sin2πfx0-∞-∞ sin2πfxS(x′)dx′. Assuming S is even-symmetric and finite, the second term is 0, and we are left with Eq. (5).

The only restriction upon Eq. (6) is that the spatial sensitivity function S(x) be center-symmetric and finite. All "phase effects" due to the position of the detector are accounted for by the factor cos2πƒx0.

J. M. Foley and G. E. Legge, "Contrast detection and near-threshold discrimination in human vision," Vision Res. (in press).

D. M. Green, An Introduction to Hearing (Lawrence Erlbaum Associates, Hillsdale, New Jersey, 1976).

R. Fox, "Visual masking," in Handbook of Sensory Physiology. VIII. Perception, edited by R. Held, H. W. Leibowitz, and H.-L. Teuber (Springer-Verlag, Berlin, 1978).

R. V. Sansbury, Some Properties of Spatial Channels Revealed by Pulsed Simultaneous Masking, Ph.D. dissertation, Dept. of Psychology, University of Pennsylvania, Philadelphia, 1974 (unpublished).

Fechner (see Boring,56 Chap. 14) derived a sensory magnitude function from discrimination data. If the effects of spatial pooling are ignored, Fechner's technique may be used to derive the transducer function F from the discrimination functions in Figs. 2 or 4. The discrimination function is proportional to the reciprocal of the derivative of F.

E. G. Boring, A History of Experimental Psychology (Appleton-Century-Crofts, New York, 1957).

If the constant variance assumption is relaxed, the transducer function cannot be inferred directly from forced-choice data. Information concerning the dependence of noise variance on contrast could be obtained from other psychophysical procedures, such as the "bootstrap" procedure of Nachmias and Kocher.34 With this information in hand, a corrected form of the transducer function could be computed. Changes in variance with contrast would not be expected to affect the shape of the channel sensitivity function, Fig. 8(a). There exists little evidence concerning the dependence of variance on stimulus contrast. Paired comparison data of Foley and Legge4 indicate small changes in variance over a range of low contrasts. Further discussion of the effects of relaxing the constant variance assumption is given by Nachmias and Sansbury.2

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