Abstract

Modulation sensitivity was measured as a function of the relative phase of two equiluminous chromatic sources (564 and 625 nm) for temporal frequencies ranging from 1 to 40 Hz. Measurements were made at a retinal illuminance of 900 Td, with a 2° field metameric to approximately 600 nm. For most frequencies, the phase of least sensitivity was other than 180°, indicating the existence of a luminance response to antiphase modulation. Additional data sets examined the effects of field size (0.5°–8°) and mean chromaticity (583–610 nm). Variation in field size, chromaticity, and photometric setting had little effect on the phase of least sensitivity. The data were fitted by using vector summation between luminance and chromatic responses; the modulation-sensitivity functions that resulted from this analysis agreed with those of earlier studies.

© 1987 Optical Society of America

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References

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  1. R. M. Boynton, Human Color Vision (Holt, New York, 1979).
  2. H. deLange, “Research into the dynamic nature of the human fovea-cortex systems with intermittent and modulated light. II. Phase shift in brightness and delay in color perception,”J. Opt. Soc. Am. 48, 784–789 (1958).
    [Crossref]
  3. P. L. Walraven, H. J. Leebeek, “Phase shift of alternating coloured stimuli,” Doc. Opthalmol. 18, 56–71 (1964).
    [Crossref]
  4. J. J. Vos, P. L. Walraven, “Phase shift in the perception of sinusiodally modulated light at low luminances,” in Performance of the Eye at Low Luminances: Proceedings of the Colloquium in Delft 1965, M.A. Bauman, J. J. Vos, eds. (Excerpta Medica Foundation, New York, 1966), pp. 91–103.
  5. M. W. von Grunau, “Lateral interactions and rod intrusion in color flicker,” Vision Res. 17, 911–916 (1977).
    [Crossref] [PubMed]
  6. W. B. Cushman, J. Z. Levinson, “Phase shift in red and green counterphase flicker at high temporal frequencies,”J. Opt. Soc. Am. 73, 1557–1561 (1983).
    [Crossref]
  7. V. C. Smith, R. W. Bowen, J. Pokorny, “Threshold temporal integration of chromatic stimuli,” Vision Res. 24, 653–659 (1984).
    [Crossref] [PubMed]
  8. D. T. Lindsey, J. Pokorny, V. C. Smith, “Phase-dependent sensitivity to heterochromatic flicker,” J. Opt. Soc. Am. A. 3, 921–927 (1986).
    [Crossref] [PubMed]
  9. R. F. Quick, “A vector-magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
    [Crossref] [PubMed]
  10. W. H. Swanson, T. Ueno, V. C. Smith, J. Pokorny, “Temporal modulation sensitivity and pulse detection thresholds for chromatic and luminance perturbations,” J. Opt. Soc. Am. A 4, 1992–2005 (1987).
    [Crossref]
  11. The reported phase axes were obtained by performing this analysis, using differences in the logarithms of the modulations. When the analysis was performed by using linear differences of the modulations, phase axes were within 2° of the reported values, with the following exceptions: 5° higher for subject WS at 1 Hz, 5° higher for subject RV at 10 Hz, 5° lower for subject RS at 16 Hz, 8° lower for subject WS at 5 Hz, 12° higher for subject RS at 4 Hz, and 15° lower for subject RV at 4 Hz.
  12. The phase of least sensitivity for a given cosine template is directly related to the phase shift. With a phase shift of θ, the chromatic response is smallest for a relative phase of θ, and the luminance response is smallest for a relative phase of θ− 180°. The more sensitive cosine template determines threshold for all relative phases, except those near its phase of minimum response, so the phase of least sensitivity is determined by the more sensitive channel.
  13. We followed the convention of Cushman and Levinson,6 who used the term “green-leads-red,” to refer to the shift in response onset from a relative phase of 180°. For our stimuli, the term “green-leads-red” refers to relative phases from −160° to 0°, and “red-leads-green” refers to relative phases from 0° to 180°.
  14. Data were not gathered at 40 Hz for the 0.5° field nor for the 2° fields metameric to 610 and 583 nm, since flicker could not be detected with the maximum available modulation under these conditions.
  15. For observer WS, the luminance modulation-sensitivity function shown was derived previously from data gathered on the same apparatus; see Ref. 10. The remaining modulation-sensitivity functions were derived in the same manner from the values obtained for sensitivities of the luminance and chromatic cosine templates. First, a digital impulse-response function was derived by using the method of Stork and Falk.21 This digital function was then fitted with an analytic function. The analytic modulation-sensitivity function is the Fourier transform of this analytic impulse-response function. For chromatic sensitivities, the, analytical functions were five-stage linear filters; for luminance sensitivities the analytical functions were differences of two five-stage linear filters (response of the second filter was delayed by a latency). The parameters for these functions are shown in Table 3.
  16. Reviewed by A. B. Watson, “Temporal sensitivity,” in Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds., Vol. I of Sensory Process and Perception (Wiley, New York, 1986), Chap. 6.
  17. J. J. Wisowaty, “Estimates for the temporal response characteristics of chromatic pathways,”J. Opt. Soc. Am. 71, 970–977 (1981).
    [Crossref] [PubMed]
  18. C. Noorlander, M. J. G. Heuts, J. J. Koenderink, “Sensitivity to spatiotemporal combined luminance and chromaticity contrast,” J. Opt, Soc: Am. 71, 453–459 (1981).
    [Crossref]
  19. D. H. Kelly, D. van Norren, “Two-band model of heterochromatic flicker,”J. Opt. Soc. Am. 67, 1081–1091 (1977).
    [Crossref] [PubMed]
  20. G. J. C. van der Horst, “Chromatic flicker,”J. Opt. Soc. Am. 59, 1213–1217 (1969).
    [Crossref] [PubMed]
  21. D. G. Stork, D. S. Falk, “Temporal impulse responses from flicker sensitivities,” J. Opt. Soc. Am. A 4, 1130–1135 (1987). The computer program was kindly provided by David Stork.
    [Crossref] [PubMed]

1987 (2)

1986 (1)

D. T. Lindsey, J. Pokorny, V. C. Smith, “Phase-dependent sensitivity to heterochromatic flicker,” J. Opt. Soc. Am. A. 3, 921–927 (1986).
[Crossref] [PubMed]

1984 (1)

V. C. Smith, R. W. Bowen, J. Pokorny, “Threshold temporal integration of chromatic stimuli,” Vision Res. 24, 653–659 (1984).
[Crossref] [PubMed]

1983 (1)

1981 (2)

J. J. Wisowaty, “Estimates for the temporal response characteristics of chromatic pathways,”J. Opt. Soc. Am. 71, 970–977 (1981).
[Crossref] [PubMed]

C. Noorlander, M. J. G. Heuts, J. J. Koenderink, “Sensitivity to spatiotemporal combined luminance and chromaticity contrast,” J. Opt, Soc: Am. 71, 453–459 (1981).
[Crossref]

1977 (2)

D. H. Kelly, D. van Norren, “Two-band model of heterochromatic flicker,”J. Opt. Soc. Am. 67, 1081–1091 (1977).
[Crossref] [PubMed]

M. W. von Grunau, “Lateral interactions and rod intrusion in color flicker,” Vision Res. 17, 911–916 (1977).
[Crossref] [PubMed]

1974 (1)

R. F. Quick, “A vector-magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
[Crossref] [PubMed]

1969 (1)

1964 (1)

P. L. Walraven, H. J. Leebeek, “Phase shift of alternating coloured stimuli,” Doc. Opthalmol. 18, 56–71 (1964).
[Crossref]

1958 (1)

Bowen, R. W.

V. C. Smith, R. W. Bowen, J. Pokorny, “Threshold temporal integration of chromatic stimuli,” Vision Res. 24, 653–659 (1984).
[Crossref] [PubMed]

Boynton, R. M.

R. M. Boynton, Human Color Vision (Holt, New York, 1979).

Cushman, W. B.

deLange, H.

Falk, D. S.

Heuts, M. J. G.

C. Noorlander, M. J. G. Heuts, J. J. Koenderink, “Sensitivity to spatiotemporal combined luminance and chromaticity contrast,” J. Opt, Soc: Am. 71, 453–459 (1981).
[Crossref]

Kelly, D. H.

Koenderink, J. J.

C. Noorlander, M. J. G. Heuts, J. J. Koenderink, “Sensitivity to spatiotemporal combined luminance and chromaticity contrast,” J. Opt, Soc: Am. 71, 453–459 (1981).
[Crossref]

Leebeek, H. J.

P. L. Walraven, H. J. Leebeek, “Phase shift of alternating coloured stimuli,” Doc. Opthalmol. 18, 56–71 (1964).
[Crossref]

Levinson, J. Z.

Lindsey, D. T.

D. T. Lindsey, J. Pokorny, V. C. Smith, “Phase-dependent sensitivity to heterochromatic flicker,” J. Opt. Soc. Am. A. 3, 921–927 (1986).
[Crossref] [PubMed]

Noorlander, C.

C. Noorlander, M. J. G. Heuts, J. J. Koenderink, “Sensitivity to spatiotemporal combined luminance and chromaticity contrast,” J. Opt, Soc: Am. 71, 453–459 (1981).
[Crossref]

Pokorny, J.

W. H. Swanson, T. Ueno, V. C. Smith, J. Pokorny, “Temporal modulation sensitivity and pulse detection thresholds for chromatic and luminance perturbations,” J. Opt. Soc. Am. A 4, 1992–2005 (1987).
[Crossref]

D. T. Lindsey, J. Pokorny, V. C. Smith, “Phase-dependent sensitivity to heterochromatic flicker,” J. Opt. Soc. Am. A. 3, 921–927 (1986).
[Crossref] [PubMed]

V. C. Smith, R. W. Bowen, J. Pokorny, “Threshold temporal integration of chromatic stimuli,” Vision Res. 24, 653–659 (1984).
[Crossref] [PubMed]

Quick, R. F.

R. F. Quick, “A vector-magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
[Crossref] [PubMed]

Smith, V. C.

W. H. Swanson, T. Ueno, V. C. Smith, J. Pokorny, “Temporal modulation sensitivity and pulse detection thresholds for chromatic and luminance perturbations,” J. Opt. Soc. Am. A 4, 1992–2005 (1987).
[Crossref]

D. T. Lindsey, J. Pokorny, V. C. Smith, “Phase-dependent sensitivity to heterochromatic flicker,” J. Opt. Soc. Am. A. 3, 921–927 (1986).
[Crossref] [PubMed]

V. C. Smith, R. W. Bowen, J. Pokorny, “Threshold temporal integration of chromatic stimuli,” Vision Res. 24, 653–659 (1984).
[Crossref] [PubMed]

Stork, D. G.

Swanson, W. H.

Ueno, T.

van der Horst, G. J. C.

van Norren, D.

von Grunau, M. W.

M. W. von Grunau, “Lateral interactions and rod intrusion in color flicker,” Vision Res. 17, 911–916 (1977).
[Crossref] [PubMed]

Vos, J. J.

J. J. Vos, P. L. Walraven, “Phase shift in the perception of sinusiodally modulated light at low luminances,” in Performance of the Eye at Low Luminances: Proceedings of the Colloquium in Delft 1965, M.A. Bauman, J. J. Vos, eds. (Excerpta Medica Foundation, New York, 1966), pp. 91–103.

Walraven, P. L.

P. L. Walraven, H. J. Leebeek, “Phase shift of alternating coloured stimuli,” Doc. Opthalmol. 18, 56–71 (1964).
[Crossref]

J. J. Vos, P. L. Walraven, “Phase shift in the perception of sinusiodally modulated light at low luminances,” in Performance of the Eye at Low Luminances: Proceedings of the Colloquium in Delft 1965, M.A. Bauman, J. J. Vos, eds. (Excerpta Medica Foundation, New York, 1966), pp. 91–103.

Watson, A. B.

Reviewed by A. B. Watson, “Temporal sensitivity,” in Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds., Vol. I of Sensory Process and Perception (Wiley, New York, 1986), Chap. 6.

Wisowaty, J. J.

Doc. Opthalmol. (1)

P. L. Walraven, H. J. Leebeek, “Phase shift of alternating coloured stimuli,” Doc. Opthalmol. 18, 56–71 (1964).
[Crossref]

J. Opt, Soc: Am. (1)

C. Noorlander, M. J. G. Heuts, J. J. Koenderink, “Sensitivity to spatiotemporal combined luminance and chromaticity contrast,” J. Opt, Soc: Am. 71, 453–459 (1981).
[Crossref]

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. A. (1)

D. T. Lindsey, J. Pokorny, V. C. Smith, “Phase-dependent sensitivity to heterochromatic flicker,” J. Opt. Soc. Am. A. 3, 921–927 (1986).
[Crossref] [PubMed]

Kybernetik (1)

R. F. Quick, “A vector-magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
[Crossref] [PubMed]

Vision Res. (2)

V. C. Smith, R. W. Bowen, J. Pokorny, “Threshold temporal integration of chromatic stimuli,” Vision Res. 24, 653–659 (1984).
[Crossref] [PubMed]

M. W. von Grunau, “Lateral interactions and rod intrusion in color flicker,” Vision Res. 17, 911–916 (1977).
[Crossref] [PubMed]

Other (8)

R. M. Boynton, Human Color Vision (Holt, New York, 1979).

J. J. Vos, P. L. Walraven, “Phase shift in the perception of sinusiodally modulated light at low luminances,” in Performance of the Eye at Low Luminances: Proceedings of the Colloquium in Delft 1965, M.A. Bauman, J. J. Vos, eds. (Excerpta Medica Foundation, New York, 1966), pp. 91–103.

The reported phase axes were obtained by performing this analysis, using differences in the logarithms of the modulations. When the analysis was performed by using linear differences of the modulations, phase axes were within 2° of the reported values, with the following exceptions: 5° higher for subject WS at 1 Hz, 5° higher for subject RV at 10 Hz, 5° lower for subject RS at 16 Hz, 8° lower for subject WS at 5 Hz, 12° higher for subject RS at 4 Hz, and 15° lower for subject RV at 4 Hz.

The phase of least sensitivity for a given cosine template is directly related to the phase shift. With a phase shift of θ, the chromatic response is smallest for a relative phase of θ, and the luminance response is smallest for a relative phase of θ− 180°. The more sensitive cosine template determines threshold for all relative phases, except those near its phase of minimum response, so the phase of least sensitivity is determined by the more sensitive channel.

We followed the convention of Cushman and Levinson,6 who used the term “green-leads-red,” to refer to the shift in response onset from a relative phase of 180°. For our stimuli, the term “green-leads-red” refers to relative phases from −160° to 0°, and “red-leads-green” refers to relative phases from 0° to 180°.

Data were not gathered at 40 Hz for the 0.5° field nor for the 2° fields metameric to 610 and 583 nm, since flicker could not be detected with the maximum available modulation under these conditions.

For observer WS, the luminance modulation-sensitivity function shown was derived previously from data gathered on the same apparatus; see Ref. 10. The remaining modulation-sensitivity functions were derived in the same manner from the values obtained for sensitivities of the luminance and chromatic cosine templates. First, a digital impulse-response function was derived by using the method of Stork and Falk.21 This digital function was then fitted with an analytic function. The analytic modulation-sensitivity function is the Fourier transform of this analytic impulse-response function. For chromatic sensitivities, the, analytical functions were five-stage linear filters; for luminance sensitivities the analytical functions were differences of two five-stage linear filters (response of the second filter was delayed by a latency). The parameters for these functions are shown in Table 3.

Reviewed by A. B. Watson, “Temporal sensitivity,” in Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds., Vol. I of Sensory Process and Perception (Wiley, New York, 1986), Chap. 6.

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Figures (5)

Fig. 1
Fig. 1

Predictions for modulation threshold as a function of the relative phase difference of the two LED’s. Data shown are for frequencies from 1 to 40 Hz, with a 900-Td 2° field metameric to approximately 600 nm. Curves drawn through the data were derived by using the model of Lindsey et al.8 Left-hand panel shows data for subject WS, middle panel shows data for subject RS, and right-hand panel shows data for subject RV. For clarity, the data for each frequency were scaled vertically by the following additive scaling factors: 0.1 (2 Hz), 0.2 (2.8 Hz), 0.3 (4 Hz), 0.4 (5 Hz), 0.5 (6.2 Hz), 0.6 (8 Hz), 0.7 (10 Hz), 0.8 (13.3 Hz), 0.9 (16 Hz), 1.0 (20 Hz), 1.0 (26.7 Hz for subjects WS and RS), 1.1 (26.7 Hz for subject RV), 0.6 (40 Hz for subjects WS and RS), 0.9 (40 Hz for subject RV).

Fig. 2
Fig. 2

Phase of least sensitivity as a function of temporal frequency. Left panel shows values for three observers with a 2°, 600-nm field. Middle panel shows values for observer WS with 600-nm fields of 0.5°, 2°, and 8°. Right panel shows values for observer WS with 2° fields metameric to 583, 600, and 610 nm.

Fig. 3
Fig. 3

Values obtained for sensitivities of the luminance and chromatic cosine templates as a functions of frequency, with analytic modulation-sensitivity functions derived using the method of Swanson et al.10 Values for the parameters used to generate these functions are given in Table 2. Filled symbols are values for cosine-template sensitivities, and solid lines are the modulation-sensitivity functions for the luminance channel. Open symbols are scaling factors, and dashed lines are the modulation-sensitivity functions for the chromatic channel. Left panel is for subject WS, middle panel is for subject RS, and right panel is for subject RV.

Fig. 4
Fig. 4

Modulation threshold as a function of relative phase for observer WS at 8 Hz with a 600-nm 2° field. Filled circles are median data for a normal photometric setting, open circles are for a 0.2-log unit increase in the radiance of the 625-nm LED, and open squares are for a 0.2-log unit decrease.

Fig. 5
Fig. 5

Phase of least sensitivity as a function of temporal frequency: values from three studies. Triangles connected by solid lines show the average values for our three observers with a 900-Td 2° 600-nm field. Circles connected by dotted lines show the average values for the three observers of Cushman and Levinson6 for a 340-Td field. Squares connected by dashed lines show the average values for the two observers of Lindsey et al.8 for a 100-Td field.

Tables (3)

Tables Icon

Table 1 Modulation Thresholds for 13 Frequencies and 18 Relative Phasesa

Tables Icon

Table 2 Parameters Used to Generate the Predictions Shown in Fig. 1 for Our Three Observersa

Tables Icon

Table 3 Parameters for Modulation-Sensitivity Functions Shown in Fig. 3a

Equations (3)

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L ( t ) = L + [ M cos θ / 2 ] { sin [ ( f t / 360 ) - ( θ / 2 ) ] } ,
C ( t ) = C + [ M cos θ / 2 ] { cos [ ( f t / 360 ) - ( θ / 2 ) ] } ,
M = 1 / ( { cos 2 [ ( θ - ϕ ) / 2 ] / M L T 2 + sin 2 [ ( θ - ϕ ) / 2 ] M C T 2 } 0.5 ) ,

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