Abstract

To determine the linear, unadapted responses of the cone pathways, we have measured the critical fusion frequency (CFF) for green (555-nm) and red (642-nm) flicker as a function of retinal illuminance. Both functions obeyed the Ferry–Porter law (CFF proportional to log illuminance) to high accuracy over a ≥5-log-unit range. In both foveola and periphery the CFF/illuminance functions were significantly steeper for green light than for red light. The peripheral 555-nm function had an average slope 1.26 times the average slope of the 642-nm function. An additive model of flicker detection could not account for the observed differences in slope. A threshold independence model, in which detection is based on the most sensitive mechanism, accurately fits the data. Whichever model is assumed, the presence of different slopes for the two wavelength flicker conditions strongly implies that the R- and G-cone pathways have different temporal properties. The occurrence of steeper CFF/illuminance slopes in response to green light implies that the linear (near-CFF) response of the G-cone pathways is inherently faster than that of the R-cone pathways at both retinal loci. These differences in R- and G-cone-mediated temporal properties complicate the fundamental concept of luminance and invalidate it for precise application over the full illuminance range.

© 1992 Optical Society of America

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  81. This empirical treatment of the data is not arbitrary. It is similar to a solution of the linear component of the Hodgkin–Huxley equation82 applied to photoreceptor dynamics, an n-pole filter of the form F(s)=A(n-1)!/(T+s)n, where sis complex frequency, nis the number of poles, and Aand Tare constants. The time constant Tis inversely proportional to the Ferry–Porter slope. This filter equation was fitted to the 555- and 642-nm data of Figs. 2 and 3, with n= 9 and with Tvalues derived from the average Ferry–Porter slopes in each case. Taking the inverse Laplace transform of the resulting frequency responses yields the nine-pole linear impulse responses shown in the left-hand portion of Fig. 8.
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  83. The use of the terms “direct” and “indirect” here seem to be somewhat anachronistic and misleading. Direct methods refer to brightness matches between spatially segregated fields that are, for practical purposes, not changing in time. Flicker photometry is termed an indirect method because the fields being equated are spatially contiguous but alternate in time. This distinction seems artificial. It is traditional to think of stimuli unchanging in time as probes of a single point on a temporal continuum. Wyszecki and Stiles55 suggest the use of the term “flicker brightness” to refer to that which is matched in indirect (flicker) methods of photometry. We might propose that stimuli matched by this method be called “equimodulant.” The concept of equimodulance explicitly includes a dependence on the temporal parameters of the stimuli but may be extended to zero frequency (i.e., the temporal domain of so-called direct measures).
  84. Kaiser85 has recently proposed the term “sensation luminance” or “s luminance” when an individual subject’s spectral sensitivity (as determined by HFP, for example) is the basis of a light measurement. The term “luminance” would be reserved strictly for the photometric units based on the CIE photopic luminous efficiency function. A well-calibrated photometer can measure luminance; however, s luminance, which is inherently subject dependent, must be measured by a suitable (i.e., one in which additivity holds) psychophysical technique. Thus, for example, a 570-nm reference stimulus at 10 cd/m2can be matched by HFP (or minimum distinct border) to a series of test spectral stimuli. These will then all be at the same s luminance for that subject, in this case 10 Ives/m2 (the unit Kaiser proposed for s luminances).Although the concept of s luminance is a sensible one, it does not solve the problem that we are addressing here, namely, that for an individual subject the shape of the spectral-sensitivity curve itself varies with the temporal frequency (and the mean retinal illuminance) used to measure it, because of the underlying differences between R- and G-cone temporal properties. Thus two stimuli that have been matched at 10 Ives/m2at a low temporal frequency will not match at a high frequency.
  85. P. K. Kaiser, “Sensation luminance: a new name to distinguish CIE luminance from luminance dependent on an individual’s spectral sensitivity,” Vision Res. 28, 455–456 (1988).
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  89. There are many methodological and empirical issues (e.g., retinal locus, temporal and spatial extent of the stimuli, isolation of scotopic versus photopic measures, threshold-measurement techniques, definition of standard observer) that require careful discussion when one is formulating a standardized protocol for absolute threshold measurements. However, such a discussion is beyond the scope of this paper.
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    [CrossRef]

1992 (1)

S. Yamamoto, P. Gouras, C. J. MacKay, R. Lopez, “The cone ERG to focal and fullfield stimuli,” Invest. Ophthalmol. Vis. Sci. Suppl. 33, 836 (1992).

1991 (1)

A. Raninen, R. Franssila, J. Rovamo, “Critical flicker frequency to red targets as a function of luminance and flux across the human visual field,” Vision Res. 31, 1875–1881 (1991).
[CrossRef] [PubMed]

1990 (3)

1989 (7)

V. C. Smith, B. B. Lee, J. Pokorny, P. R. Martin, A. Vallberg, “Response of macaque ganglion cells to change in the phase of two flickering lights,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 323 (1989).

P. R. Martin, J. Pokorny, V. C. Smith, B. B. Lee, A. Vallberg, “Sensitivity of macaque ganglion cells to luminance and chromatic flicker,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 323 (1989).

B. B. Lee, P. R. Martin, A. Vallberg, “A non-linear summation of M- and L-cone inputs to phasic retinal ganglion cells of the macaque,”J. Neurosci. 9, 1433–1442 (1989).
[PubMed]

B. B. Lee, P. R. Martin, A. Vallberg, “Sensitivity of macaque retinal ganglion cells to chromatic and luminance flicker,”J. Physiol. (London) 414, 223–243 (1989).

S. S. Grigsby, C. R. Ingling, “An explanation of the phase shift between R- and G-mechanisms,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 322 (1989).

B. B. Lee, P. R. Martin, P. K. Kaiser, A. Vallberg, “The physiological basis of the minimum distinct border (MDB),” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 323 (1989).

T. Yeh, V. C. Smith, J. Pokorny, “The effect of background luminance on cone sensitivity functions,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 2077–2086 (1989).

1988 (2)

B. B. Lee, P. R. Martin, A. Vallberg, “The physiological basis of heterochromatic flicker photometry demonstrated in the ganglion cells of the macaque retina,”J. Physiol. (London) 404, 323–347 (1988).

P. K. Kaiser, “Sensation luminance: a new name to distinguish CIE luminance from luminance dependent on an individual’s spectral sensitivity,” Vision Res. 28, 455–456 (1988).
[CrossRef]

1987 (4)

C. W. Tyler, “Analysis of visual modulation sensitivity. III. Meridional variations in peripheral flicker sensitivity,” J. Opt. Soc. Am. A 4, 1612–1619 (1987).
[CrossRef] [PubMed]

J. L. Schnapf, T. W. Kraft, D. A. Baylor, “Spectral sensitivity of human cone photoreceptors,” Nature (London) 325, 439–441 (1987).
[CrossRef]

R. D. Hamer, C. W. Tyler, “The linear impulse response of cone pathways: variations with retinal locus,” Invest. Ophthalmol. Vis. Sci. Suppl. 28, 232 (1987).

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Chromatic suppression of cone inputs to the luminance flicker mechanism,” Vision Res. 27, 1113–1137 (1987).
[CrossRef] [PubMed]

1986 (4)

C. W. Tyler, R. D. Hamer, “The jurisdiction of the Ferry–Porter law,” Invest. Ophthalmol. Vis. Sci. Suppl. 27, 72 (1986).

E. N. Pugh, W. H. Cobbs, “Visual transduction in vertebrate rods and cones: a tale of two transmitters, calcium and cyclic GMP,” Vision Res. 26, 1613–1643 (1986).
[CrossRef] [PubMed]

N. J. Coletta, A. J. Adams, “Spatial extent of rod–cone and cone–cone interactions for flicker detection,” Vision Res. 26, 917–925 (1986).
[CrossRef]

A. Gorea, C. W. Tyler, “New look at Bloch’s law for contrast,” J. Opt. Soc. Am. A 3, 52–611986.
[CrossRef] [PubMed]

1985 (3)

C. W. Tyler, “Analysis of visual modulation sensitivity. II. Peripheral retina and the role of photoreceptor dimensions,” J. Opt. Soc. Am. A 2, 393 (1985).
[CrossRef] [PubMed]

F. A. Abraham, M. Alpern, D. B. Kirk, “Electroretinograms evoked by sinusoidal excitation of human cones,”J. Physiol. (London) 363, 135–150 (1985).

R. W. Nygaard, T. E. Frumkes, “Frequency dependence in scotopic flicker sensitivity,” Vision Res.115–127 (1985).
[CrossRef] [PubMed]

1984 (1)

P. Lennie, “Temporal modulation sensitivities of red- and green-cone-sensitive systems in dichromats,” Vision Res. 24, 1995–1999 (1984).
[CrossRef]

1983 (1)

P. H. Schiller, C. L. Colby, “The responses of single cells in the lateral geniculate nucleus of the rhesus monkey to color and luminance contrast,” Vision Res. 23, 1631–1641 (1983).
[CrossRef] [PubMed]

1982 (1)

J. D. Conner, “The temporal properties of rod vision.” J. Physiol. (London) 332, 139–155, 1982.

1981 (1)

1980 (2)

J. J. Wisowaty, R. M. Boynton, “Temporal modulation sensitivity of the blue mechanism: measurements made without chromatic adaptation,” Vision Res. 20, 895–909 (1980).
[CrossRef] [PubMed]

F. W. Fitzke, R. W. Massof, “Absolute cone thresholds derived from the Ferry–Porter law,” Invest. Ophthalmol. Vis. Sci. Suppl. 19, 212 (1980).

1979 (3)

J. Rovamo, V. Virsu, “An estimation and application of the human cortical magnification factor,” Exp. Brain Res. 37, 495–510 (1979).
[CrossRef] [PubMed]

O. D. Creutzfeldt, B. B. Lee, A. Elephandt, “A quantitative study of chromatic organisation and receptive fields of cells in the lateral geniculate body of the rhesus monkey,” Exp. Brain Res. 35, 527–545 (1979).
[CrossRef] [PubMed]

A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979).
[CrossRef] [PubMed]

1978 (3)

F. M. de Monasterio, “Properties of concentrically organized X and Y ganglion cells of macaque retina,”J. Neurophysiol. 41, 1394–1417 (1978).
[PubMed]

C. M. Cicerone, D. G. Green, “Relative modulation sensitivities of the red and green color mechanisms,” Vision Res. 18, 1593–1598 (1978).
[CrossRef] [PubMed]

C. R. Ingling, B. H.-P. Tsou, T. J. Gast, S. A. Burns, J. O. Emerick, L. Riesenberg, “The achromatic channel—I. The non-linearity of minimum-border and flicker matches,” Vis. Res. 18, 379–390 (1978).
[CrossRef]

1977 (1)

1976 (1)

1975 (4)

R. M. Boynton, W. S. Baron, “Sinusoidal flicker characteristics of primate cones in response to heterochromatic stimuli,”J. Opt. Soc. Am. 65, 1091–1100 (1975).
[CrossRef] [PubMed]

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

O. Estevez, C. R. Cavonius, “Flicker sensitivity of the human red and green color mechanisms,” Vision Res. 15, 879–881 (1975).
[CrossRef] [PubMed]

C. R. Cavonius, O. Estevez, “Sensitivity of human color mechanisms to gratings and flicker,”J. Opt. Soc. Am. 65, 966–968 (1975).
[CrossRef] [PubMed]

1974 (3)

O. Estevez, H. Spekreijse, “A spectral compensation method for determining the flicker characteristics of the human colour mechanisms,” Vision Res. 14, 823–830 (1974).
[CrossRef] [PubMed]

D. A. Baylor, A. L. Hodgkin, T. D. Lamb, “The electrical response of turtle cones to flashes and steps of light,”J. Physiol. (London) 242, 685–727 (1974).

D. H. Kelly, “Spatio-temporal frequency characteristics of color-vision mechanisms,”J. Opt. Soc. Am. 64, 983–990 (1974).
[CrossRef]

1973 (1)

1972 (4)

J. Pokorny, V. C. Smith, “Luminosity and CFF in deuteranopes and protanopes,”J. Opt. Soc. Am. 62, 111–117 (1972).
[CrossRef] [PubMed]

G. Wagner, R. M. Boynton, “Comparison of four methods of heterochromatic photometry,”J. Opt. Soc. Am. 62, 1508–1515 (1972).
[CrossRef] [PubMed]

R. M. Boynton, D. N. Whitten, “Selective chromatic adaptation in primate photoreceptors,” Vision Res. 12, 855–874 (1972).
[CrossRef] [PubMed]

M. H. Bornstein, L. E. Marks, “Photopic luminosity measured by the method of critical frequency,” Vision Res. 12, 2023–2033 (1972).
[CrossRef] [PubMed]

1971 (2)

J. J. Vos, P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971).
[CrossRef] [PubMed]

J. J. Vos, P. L. Walraven, “On the derivation of foveal receptor primaries,” Vision Res. 11, 795–818 (1971).
[CrossRef]

1969 (2)

D. H. Kelly, “Diffusion model of linear flicker responses,”J. Opt. Soc. Am. 59, 1665–1670 (1969).
[CrossRef] [PubMed]

D. G. Green, “Sinusoidal flicker characteristics of the color-sensitive mechanisms of the eye,” Vision Res. 9, 591–601 (1969).
[CrossRef] [PubMed]

1968 (1)

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
[CrossRef] [PubMed]

1966 (2)

R. L. DeValois, I. Abramov, G. H. Jacobs, “Analysis of response patterns of LGN cells,”J. Opt. Soc. Am. 56, 966–977 (1966).
[CrossRef]

G. S. Brindley, J. J. Du Croz, W. A. H. Rushton, “The flicker fusion frequency of the blue-sensitive mechanism of colour vision,”J. Physiol. (London) 183, 497–500 (1966).

1964 (2)

1963 (1)

1962 (1)

1961 (2)

D. H. Kelly, “Visual responses to time-dependent stimuli. I. Amplitude sensitivity measurements,”J. Opt. Soc. Am. 51, 422–429 (1961).
[CrossRef]

J. Levinson, L. D. Harmon, “Studies with artificial neurons, III. Mechanisms of flicker fusion,” Kybernetik 1, 107–117 (1961).
[CrossRef]

1958 (1)

1954 (1)

C. Landis, “Determinants of the critical flicker-fusion threshold,” Physiol. Rev. 34, 259–286 (1954).
[PubMed]

1952 (1)

A. Hodgkin, H. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,”J. Physiol. (London) 117, 500–544 (1952).

1949 (1)

W. S. Stiles, “Increment thresholds and the mechanisms of colour vision,” Doc. Ophthalmol. 3, 138–163 (1949).
[CrossRef] [PubMed]

1948 (1)

H. DeVries, “The luminosity curve of the eye as determined by measurement with the flicker photometer,” Physica 14, 319–348 (1948).
[CrossRef]

1939 (1)

W. S. Stiles, “The directional sensitivity of the retina and the spectral sensitivities of the rods and cones,” Proc. R. Soc. London Ser. B, 127, 64–105 (1939).
[CrossRef]

1936 (1)

S. Hecht, S. Schlaer, “Intermittent stimulation by light. V. The relation between intensity and critical frequency for different parts of the spectrum,”J. Gen. Physiol. 19, 965–979 (1936).
[CrossRef] [PubMed]

1935 (1)

G. Oesterberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophthalmol. Suppl. 6, 1–102 (1935).

1933 (1)

S. Hecht, C. D. Verrijp, “Intermittent stimulation by light. III. The relation between intensity and critical fusion frequency for different retinal locations,”J. Gen. Physiol. 17, 251–268 (1933).
[CrossRef] [PubMed]

1924 (1)

R. L. Wegel, C. E. Lane, “The auditory masking of one pure tone by another and its probable relation to the dynamics of the inner ear,” Phys. Rev. 23, 266–285 (1924).
[CrossRef]

1922 (1)

H. E. Ives, “A theory of intermittent vision,”J. Opt. Soc. Am. Rev. Sci. Instrum. 6, 343–361 (1922).
[CrossRef]

1912 (1)

H. E. Ives, “Studies in the photometry of lights of different colours. II. Spectral luminosity curves by the method of critical frequency,” Philos. Mag. 24, 352–370 (1912).

1902 (1)

T. C. Porter, “Contributions to the study of flicker,” Proc. R. Soc. London Ser. A 70, 313–329 (1902).
[CrossRef]

Abraham, F. A.

F. A. Abraham, M. Alpern, D. B. Kirk, “Electroretinograms evoked by sinusoidal excitation of human cones,”J. Physiol. (London) 363, 135–150 (1985).

Abramov, I.

Adams, A. J.

N. J. Coletta, A. J. Adams, “Spatial extent of rod–cone and cone–cone interactions for flicker detection,” Vision Res. 26, 917–925 (1986).
[CrossRef]

Alexander, J. V.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
[CrossRef] [PubMed]

Alpern, M.

F. A. Abraham, M. Alpern, D. B. Kirk, “Electroretinograms evoked by sinusoidal excitation of human cones,”J. Physiol. (London) 363, 135–150 (1985).

Baron, W. S.

Baylor, D. A.

J. L. Schnapf, B. J. Nunn, M. Meister, D. A. Baylor, “Visual transduction in cones of the monkey Macaca fascicularis,” J. Physiol. (London) 427, 681–713 (1990).

J. L. Schnapf, T. W. Kraft, D. A. Baylor, “Spectral sensitivity of human cone photoreceptors,” Nature (London) 325, 439–441 (1987).
[CrossRef]

D. A. Baylor, A. L. Hodgkin, T. D. Lamb, “The electrical response of turtle cones to flashes and steps of light,”J. Physiol. (London) 242, 685–727 (1974).

Bornstein, M. H.

M. H. Bornstein, L. E. Marks, “Photopic luminosity measured by the method of critical frequency,” Vision Res. 12, 2023–2033 (1972).
[CrossRef] [PubMed]

Boynton, R. M.

J. J. Wisowaty, R. M. Boynton, “Temporal modulation sensitivity of the blue mechanism: measurements made without chromatic adaptation,” Vision Res. 20, 895–909 (1980).
[CrossRef] [PubMed]

R. M. Boynton, W. S. Baron, “Sinusoidal flicker characteristics of primate cones in response to heterochromatic stimuli,”J. Opt. Soc. Am. 65, 1091–1100 (1975).
[CrossRef] [PubMed]

G. Wagner, R. M. Boynton, “Comparison of four methods of heterochromatic photometry,”J. Opt. Soc. Am. 62, 1508–1515 (1972).
[CrossRef] [PubMed]

R. M. Boynton, D. N. Whitten, “Selective chromatic adaptation in primate photoreceptors,” Vision Res. 12, 855–874 (1972).
[CrossRef] [PubMed]

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

Brindley, G. S.

G. S. Brindley, J. J. Du Croz, W. A. H. Rushton, “The flicker fusion frequency of the blue-sensitive mechanism of colour vision,”J. Physiol. (London) 183, 497–500 (1966).

Burns, S. A.

C. R. Ingling, B. H.-P. Tsou, T. J. Gast, S. A. Burns, J. O. Emerick, L. Riesenberg, “The achromatic channel—I. The non-linearity of minimum-border and flicker matches,” Vis. Res. 18, 379–390 (1978).
[CrossRef]

Carden, D.

Cavonius, C. R.

C. R. Cavonius, O. Estevez, “Sensitivity of human color mechanisms to gratings and flicker,”J. Opt. Soc. Am. 65, 966–968 (1975).
[CrossRef] [PubMed]

O. Estevez, C. R. Cavonius, “Flicker sensitivity of the human red and green color mechanisms,” Vision Res. 15, 879–881 (1975).
[CrossRef] [PubMed]

Chumbly, J. I.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
[CrossRef] [PubMed]

Cicerone, C. M.

C. M. Cicerone, D. G. Green, “Relative modulation sensitivities of the red and green color mechanisms,” Vision Res. 18, 1593–1598 (1978).
[CrossRef] [PubMed]

Cobbs, W. H.

E. N. Pugh, W. H. Cobbs, “Visual transduction in vertebrate rods and cones: a tale of two transmitters, calcium and cyclic GMP,” Vision Res. 26, 1613–1643 (1986).
[CrossRef] [PubMed]

Colby, C. L.

P. H. Schiller, C. L. Colby, “The responses of single cells in the lateral geniculate nucleus of the rhesus monkey to color and luminance contrast,” Vision Res. 23, 1631–1641 (1983).
[CrossRef] [PubMed]

Cole, G. R.

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Chromatic suppression of cone inputs to the luminance flicker mechanism,” Vision Res. 27, 1113–1137 (1987).
[CrossRef] [PubMed]

Coletta, N. J.

N. J. Coletta, A. J. Adams, “Spatial extent of rod–cone and cone–cone interactions for flicker detection,” Vision Res. 26, 917–925 (1986).
[CrossRef]

Conner, J. D.

J. D. Conner, “The temporal properties of rod vision.” J. Physiol. (London) 332, 139–155, 1982.

Creutzfeldt, O. D.

O. D. Creutzfeldt, B. B. Lee, A. Elephandt, “A quantitative study of chromatic organisation and receptive fields of cells in the lateral geniculate body of the rhesus monkey,” Exp. Brain Res. 35, 527–545 (1979).
[CrossRef] [PubMed]

De Lange, H.

de Monasterio, F. M.

F. M. de Monasterio, “Properties of concentrically organized X and Y ganglion cells of macaque retina,”J. Neurophysiol. 41, 1394–1417 (1978).
[PubMed]

DeValois, R. L.

DeVries, H.

H. DeVries, “The luminosity curve of the eye as determined by measurement with the flicker photometer,” Physica 14, 319–348 (1948).
[CrossRef]

Drum, B. A.

Du Croz, J. J.

G. S. Brindley, J. J. Du Croz, W. A. H. Rushton, “The flicker fusion frequency of the blue-sensitive mechanism of colour vision,”J. Physiol. (London) 183, 497–500 (1966).

Eisner, A.

Elephandt, A.

O. D. Creutzfeldt, B. B. Lee, A. Elephandt, “A quantitative study of chromatic organisation and receptive fields of cells in the lateral geniculate body of the rhesus monkey,” Exp. Brain Res. 35, 527–545 (1979).
[CrossRef] [PubMed]

Emerick, J. O.

C. R. Ingling, B. H.-P. Tsou, T. J. Gast, S. A. Burns, J. O. Emerick, L. Riesenberg, “The achromatic channel—I. The non-linearity of minimum-border and flicker matches,” Vis. Res. 18, 379–390 (1978).
[CrossRef]

Estevez, O.

O. Estevez, C. R. Cavonius, “Flicker sensitivity of the human red and green color mechanisms,” Vision Res. 15, 879–881 (1975).
[CrossRef] [PubMed]

C. R. Cavonius, O. Estevez, “Sensitivity of human color mechanisms to gratings and flicker,”J. Opt. Soc. Am. 65, 966–968 (1975).
[CrossRef] [PubMed]

O. Estevez, H. Spekreijse, “A spectral compensation method for determining the flicker characteristics of the human colour mechanisms,” Vision Res. 14, 823–830 (1974).
[CrossRef] [PubMed]

Fitzke, F. W.

F. W. Fitzke, R. W. Massof, “Absolute cone thresholds derived from the Ferry–Porter law,” Invest. Ophthalmol. Vis. Sci. Suppl. 19, 212 (1980).

Franssila, R.

A. Raninen, R. Franssila, J. Rovamo, “Critical flicker frequency to red targets as a function of luminance and flux across the human visual field,” Vision Res. 31, 1875–1881 (1991).
[CrossRef] [PubMed]

Frumkes, T. E.

R. W. Nygaard, T. E. Frumkes, “Frequency dependence in scotopic flicker sensitivity,” Vision Res.115–127 (1985).
[CrossRef] [PubMed]

Gast, T. J.

C. R. Ingling, B. H.-P. Tsou, T. J. Gast, S. A. Burns, J. O. Emerick, L. Riesenberg, “The achromatic channel—I. The non-linearity of minimum-border and flicker matches,” Vis. Res. 18, 379–390 (1978).
[CrossRef]

Gilman, C. B.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
[CrossRef] [PubMed]

Giorgi, A.

Gorea, A.

Gouras, P.

S. Yamamoto, P. Gouras, C. J. MacKay, R. Lopez, “The cone ERG to focal and fullfield stimuli,” Invest. Ophthalmol. Vis. Sci. Suppl. 33, 836 (1992).

P. Gouras, R. Lopez, S. Yamamoto, H. Rosskothen, “Laser focal electroretinography reveals unique macular responses,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), 132–135.

Green, D. G.

C. M. Cicerone, D. G. Green, “Relative modulation sensitivities of the red and green color mechanisms,” Vision Res. 18, 1593–1598 (1978).
[CrossRef] [PubMed]

D. G. Green, “Sinusoidal flicker characteristics of the color-sensitive mechanisms of the eye,” Vision Res. 9, 591–601 (1969).
[CrossRef] [PubMed]

Grigsby, S. S.

S. S. Grigsby, C. R. Ingling, “An explanation of the phase shift between R- and G-mechanisms,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 322 (1989).

Guth, S. L.

S. L. Guth, H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity, and a new color model,”J. Opt. Soc. Am. 63, 450–462 (1973).
[CrossRef] [PubMed]

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
[CrossRef] [PubMed]

Hamer, R. D.

C. W. Tyler, R. D. Hamer, “Analysis of visual modulation sensitivity. IV Validity of the Ferry–Porter law,” J. Opt. Soc. Am. A 7, 743–758 (1990).
[CrossRef] [PubMed]

R. D. Hamer, C. W. Tyler, “The linear impulse response of cone pathways: variations with retinal locus,” Invest. Ophthalmol. Vis. Sci. Suppl. 28, 232 (1987).

C. W. Tyler, R. D. Hamer, “The jurisdiction of the Ferry–Porter law,” Invest. Ophthalmol. Vis. Sci. Suppl. 27, 72 (1986).

Harmon, L. D.

J. Levinson, L. D. Harmon, “Studies with artificial neurons, III. Mechanisms of flicker fusion,” Kybernetik 1, 107–117 (1961).
[CrossRef]

Hecht, S.

S. Hecht, S. Schlaer, “Intermittent stimulation by light. V. The relation between intensity and critical frequency for different parts of the spectrum,”J. Gen. Physiol. 19, 965–979 (1936).
[CrossRef] [PubMed]

S. Hecht, C. D. Verrijp, “Intermittent stimulation by light. III. The relation between intensity and critical fusion frequency for different retinal locations,”J. Gen. Physiol. 17, 251–268 (1933).
[CrossRef] [PubMed]

Hodgkin, A.

A. Hodgkin, H. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,”J. Physiol. (London) 117, 500–544 (1952).

Hodgkin, A. L.

D. A. Baylor, A. L. Hodgkin, T. D. Lamb, “The electrical response of turtle cones to flashes and steps of light,”J. Physiol. (London) 242, 685–727 (1974).

Huxley, H.

A. Hodgkin, H. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,”J. Physiol. (London) 117, 500–544 (1952).

Ingling, C. R.

S. S. Grigsby, C. R. Ingling, “An explanation of the phase shift between R- and G-mechanisms,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 322 (1989).

C. R. Ingling, B. H.-P. Tsou, T. J. Gast, S. A. Burns, J. O. Emerick, L. Riesenberg, “The achromatic channel—I. The non-linearity of minimum-border and flicker matches,” Vis. Res. 18, 379–390 (1978).
[CrossRef]

Ives, H. E.

H. E. Ives, “A theory of intermittent vision,”J. Opt. Soc. Am. Rev. Sci. Instrum. 6, 343–361 (1922).
[CrossRef]

H. E. Ives, “Studies in the photometry of lights of different colours. II. Spectral luminosity curves by the method of critical frequency,” Philos. Mag. 24, 352–370 (1912).

Jacobs, G. H.

Kaiser, P. K.

B. B. Lee, P. R. Martin, P. K. Kaiser, A. Vallberg, “The physiological basis of the minimum distinct border (MDB),” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 323 (1989).

P. K. Kaiser, “Sensation luminance: a new name to distinguish CIE luminance from luminance dependent on an individual’s spectral sensitivity,” Vision Res. 28, 455–456 (1988).
[CrossRef]

Kelly, D. H.

King–Smith, P. E.

Kirk, D. B.

F. A. Abraham, M. Alpern, D. B. Kirk, “Electroretinograms evoked by sinusoidal excitation of human cones,”J. Physiol. (London) 363, 135–150 (1985).

Kraft, T. W.

J. L. Schnapf, T. W. Kraft, D. A. Baylor, “Spectral sensitivity of human cone photoreceptors,” Nature (London) 325, 439–441 (1987).
[CrossRef]

Kronauer, R. E.

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Chromatic suppression of cone inputs to the luminance flicker mechanism,” Vision Res. 27, 1113–1137 (1987).
[CrossRef] [PubMed]

Lamb, T. D.

D. A. Baylor, A. L. Hodgkin, T. D. Lamb, “The electrical response of turtle cones to flashes and steps of light,”J. Physiol. (London) 242, 685–727 (1974).

Landis, C.

C. Landis, “Determinants of the critical flicker-fusion threshold,” Physiol. Rev. 34, 259–286 (1954).
[PubMed]

Lane, C. E.

R. L. Wegel, C. E. Lane, “The auditory masking of one pure tone by another and its probable relation to the dynamics of the inner ear,” Phys. Rev. 23, 266–285 (1924).
[CrossRef]

Lee, B. B.

B. B. Lee, J. Pokorny, V. C. Smith, P. R. Martin, A. Vallberg, “Luminance and chromatic modulation sensitivity of macaque ganglion cells and human observers,” J. Opt. Soc. Am. A 7, 2223–2236 (1990).
[CrossRef] [PubMed]

B. B. Lee, P. R. Martin, P. K. Kaiser, A. Vallberg, “The physiological basis of the minimum distinct border (MDB),” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 323 (1989).

B. B. Lee, P. R. Martin, A. Vallberg, “A non-linear summation of M- and L-cone inputs to phasic retinal ganglion cells of the macaque,”J. Neurosci. 9, 1433–1442 (1989).
[PubMed]

B. B. Lee, P. R. Martin, A. Vallberg, “Sensitivity of macaque retinal ganglion cells to chromatic and luminance flicker,”J. Physiol. (London) 414, 223–243 (1989).

V. C. Smith, B. B. Lee, J. Pokorny, P. R. Martin, A. Vallberg, “Response of macaque ganglion cells to change in the phase of two flickering lights,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 323 (1989).

P. R. Martin, J. Pokorny, V. C. Smith, B. B. Lee, A. Vallberg, “Sensitivity of macaque ganglion cells to luminance and chromatic flicker,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 323 (1989).

B. B. Lee, P. R. Martin, A. Vallberg, “The physiological basis of heterochromatic flicker photometry demonstrated in the ganglion cells of the macaque retina,”J. Physiol. (London) 404, 323–347 (1988).

O. D. Creutzfeldt, B. B. Lee, A. Elephandt, “A quantitative study of chromatic organisation and receptive fields of cells in the lateral geniculate body of the rhesus monkey,” Exp. Brain Res. 35, 527–545 (1979).
[CrossRef] [PubMed]

Leebeek, H. J.

Lennie, P.

P. Lennie, “Temporal modulation sensitivities of red- and green-cone-sensitive systems in dichromats,” Vision Res. 24, 1995–1999 (1984).
[CrossRef]

Levinson, J.

J. Levinson, L. D. Harmon, “Studies with artificial neurons, III. Mechanisms of flicker fusion,” Kybernetik 1, 107–117 (1961).
[CrossRef]

Lodge, H. R.

Lopez, R.

S. Yamamoto, P. Gouras, C. J. MacKay, R. Lopez, “The cone ERG to focal and fullfield stimuli,” Invest. Ophthalmol. Vis. Sci. Suppl. 33, 836 (1992).

P. Gouras, R. Lopez, S. Yamamoto, H. Rosskothen, “Laser focal electroretinography reveals unique macular responses,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), 132–135.

Lutze, M.

M. Lutze, V. C. Smith, J. Pokorny, “Critical flicker frequency in x-chromosome linked dichromats,” in Colour Vision Deficiencies IX, B. Drum, G. Verriest, eds. (Kluwer, Dordrecht, The Netherlands, 1989).
[CrossRef]

MacKay, C. J.

S. Yamamoto, P. Gouras, C. J. MacKay, R. Lopez, “The cone ERG to focal and fullfield stimuli,” Invest. Ophthalmol. Vis. Sci. Suppl. 33, 836 (1992).

MacLeod, D. I. A.

Marks, L. E.

M. H. Bornstein, L. E. Marks, “Photopic luminosity measured by the method of critical frequency,” Vision Res. 12, 2023–2033 (1972).
[CrossRef] [PubMed]

Martin, P. R.

B. B. Lee, J. Pokorny, V. C. Smith, P. R. Martin, A. Vallberg, “Luminance and chromatic modulation sensitivity of macaque ganglion cells and human observers,” J. Opt. Soc. Am. A 7, 2223–2236 (1990).
[CrossRef] [PubMed]

P. R. Martin, J. Pokorny, V. C. Smith, B. B. Lee, A. Vallberg, “Sensitivity of macaque ganglion cells to luminance and chromatic flicker,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 323 (1989).

V. C. Smith, B. B. Lee, J. Pokorny, P. R. Martin, A. Vallberg, “Response of macaque ganglion cells to change in the phase of two flickering lights,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 323 (1989).

B. B. Lee, P. R. Martin, A. Vallberg, “Sensitivity of macaque retinal ganglion cells to chromatic and luminance flicker,”J. Physiol. (London) 414, 223–243 (1989).

B. B. Lee, P. R. Martin, A. Vallberg, “A non-linear summation of M- and L-cone inputs to phasic retinal ganglion cells of the macaque,”J. Neurosci. 9, 1433–1442 (1989).
[PubMed]

B. B. Lee, P. R. Martin, P. K. Kaiser, A. Vallberg, “The physiological basis of the minimum distinct border (MDB),” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 323 (1989).

B. B. Lee, P. R. Martin, A. Vallberg, “The physiological basis of heterochromatic flicker photometry demonstrated in the ganglion cells of the macaque retina,”J. Physiol. (London) 404, 323–347 (1988).

Massof, R. W.

F. W. Fitzke, R. W. Massof, “Absolute cone thresholds derived from the Ferry–Porter law,” Invest. Ophthalmol. Vis. Sci. Suppl. 19, 212 (1980).

Meister, M.

J. L. Schnapf, B. J. Nunn, M. Meister, D. A. Baylor, “Visual transduction in cones of the monkey Macaca fascicularis,” J. Physiol. (London) 427, 681–713 (1990).

Nunn, B. J.

J. L. Schnapf, B. J. Nunn, M. Meister, D. A. Baylor, “Visual transduction in cones of the monkey Macaca fascicularis,” J. Physiol. (London) 427, 681–713 (1990).

Nygaard, R. W.

R. W. Nygaard, T. E. Frumkes, “Frequency dependence in scotopic flicker sensitivity,” Vision Res.115–127 (1985).
[CrossRef] [PubMed]

Oesterberg, G.

G. Oesterberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophthalmol. Suppl. 6, 1–102 (1935).

Patterson, M. M.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
[CrossRef] [PubMed]

Pokorny, J.

B. B. Lee, J. Pokorny, V. C. Smith, P. R. Martin, A. Vallberg, “Luminance and chromatic modulation sensitivity of macaque ganglion cells and human observers,” J. Opt. Soc. Am. A 7, 2223–2236 (1990).
[CrossRef] [PubMed]

T. Yeh, V. C. Smith, J. Pokorny, “The effect of background luminance on cone sensitivity functions,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 2077–2086 (1989).

V. C. Smith, B. B. Lee, J. Pokorny, P. R. Martin, A. Vallberg, “Response of macaque ganglion cells to change in the phase of two flickering lights,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 323 (1989).

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Other (13)

There are many methodological and empirical issues (e.g., retinal locus, temporal and spatial extent of the stimuli, isolation of scotopic versus photopic measures, threshold-measurement techniques, definition of standard observer) that require careful discussion when one is formulating a standardized protocol for absolute threshold measurements. However, such a discussion is beyond the scope of this paper.

This empirical treatment of the data is not arbitrary. It is similar to a solution of the linear component of the Hodgkin–Huxley equation82 applied to photoreceptor dynamics, an n-pole filter of the form F(s)=A(n-1)!/(T+s)n, where sis complex frequency, nis the number of poles, and Aand Tare constants. The time constant Tis inversely proportional to the Ferry–Porter slope. This filter equation was fitted to the 555- and 642-nm data of Figs. 2 and 3, with n= 9 and with Tvalues derived from the average Ferry–Porter slopes in each case. Taking the inverse Laplace transform of the resulting frequency responses yields the nine-pole linear impulse responses shown in the left-hand portion of Fig. 8.

The use of the terms “direct” and “indirect” here seem to be somewhat anachronistic and misleading. Direct methods refer to brightness matches between spatially segregated fields that are, for practical purposes, not changing in time. Flicker photometry is termed an indirect method because the fields being equated are spatially contiguous but alternate in time. This distinction seems artificial. It is traditional to think of stimuli unchanging in time as probes of a single point on a temporal continuum. Wyszecki and Stiles55 suggest the use of the term “flicker brightness” to refer to that which is matched in indirect (flicker) methods of photometry. We might propose that stimuli matched by this method be called “equimodulant.” The concept of equimodulance explicitly includes a dependence on the temporal parameters of the stimuli but may be extended to zero frequency (i.e., the temporal domain of so-called direct measures).

Kaiser85 has recently proposed the term “sensation luminance” or “s luminance” when an individual subject’s spectral sensitivity (as determined by HFP, for example) is the basis of a light measurement. The term “luminance” would be reserved strictly for the photometric units based on the CIE photopic luminous efficiency function. A well-calibrated photometer can measure luminance; however, s luminance, which is inherently subject dependent, must be measured by a suitable (i.e., one in which additivity holds) psychophysical technique. Thus, for example, a 570-nm reference stimulus at 10 cd/m2can be matched by HFP (or minimum distinct border) to a series of test spectral stimuli. These will then all be at the same s luminance for that subject, in this case 10 Ives/m2 (the unit Kaiser proposed for s luminances).Although the concept of s luminance is a sensible one, it does not solve the problem that we are addressing here, namely, that for an individual subject the shape of the spectral-sensitivity curve itself varies with the temporal frequency (and the mean retinal illuminance) used to measure it, because of the underlying differences between R- and G-cone temporal properties. Thus two stimuli that have been matched at 10 Ives/m2at a low temporal frequency will not match at a high frequency.

G. Wyszecki, W. S. Stiles, Color Science: Concepts, Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).

P. Gouras, R. Lopez, S. Yamamoto, H. Rosskothen, “Laser focal electroretinography reveals unique macular responses,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), 132–135.

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

S. Polyak, The Retina (U. Chicago Press, Chicago, Ill., 1941).

M. Lutze, V. C. Smith, J. Pokorny, “Critical flicker frequency in x-chromosome linked dichromats,” in Colour Vision Deficiencies IX, B. Drum, G. Verriest, eds. (Kluwer, Dordrecht, The Netherlands, 1989).
[CrossRef]

It is possible to generate more complex models to explain our data. For example, we cannot entirely exclude an inhibitory interaction between R and G cones. However, such an interaction between the two cone types would have to be temporal-frequency dependent in order to mimic our data. This class of models seems to be unparsimonious, especially in the absence of any evidence for such interactions near CFF, beyond the range of chromatic modulation detection.

J. M. Van Buren, “A physiological–anatomical correlation in man and primates of the normal topographical anatomy of the retinal ganglion cell layer and its alterations with lesions of the visual pathways,” in The Retinal Ganglion Cell Layer, (Thomas, Springfield, Ill., 1963), pp. 62, 63.

Although it is indeed more difficult to isolate G cones, for reasons that will be elaborated in the discussion, we believe that G cones were detecting modulation of the green LED’s under the conditions of these experiments.

The frequency bandwidth of this envelope is 1 Hz at half-height, with the first sidelobe at −32 dB (−18 dB/octave attenuation). Thus, with a maximum sensitivity of ~1% (−40 dB) for these stimuli, sidelobes should not be detectable beyond ~5 Hz on either side of the stimulus frequency.

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Figures (8)

Fig. 1
Fig. 1

Schematic representation of linear, unadapted behavior of the visual system. Two sinusoidal inputs are depicted, one at a mean luminance of 20 Td and 100% modulation and the other at a mean luminance of 100 Td and 20% modulation. In both cases the absolute amplitude of modulation is the same. Near CFF, when the visual system is responding linearly,5,32,33 the fivefold increase in mean luminance will not decrease the detectability of the modulation, i.e., the two inputs will result in the same internal response (ΔR).

Fig. 2
Fig. 2

CFF/illuminance functions for four subjects tested at 35° in the temporal visual field (5.7°-diameter test field). Data obtained by using green (555-nm) and red (642-nm) lights are indicated by filled and open circles, respectively. The slopes of the individual function, in hertz/decade, are denoted by the numbers above each best-fitting Ferry–Porter line. To illustrate the slope differences, we have plotted all the data on a relative illuminance abscissa. Note that no simple shift on the illuminance axis can equate the 642- and 555-nm data.

Fig. 3
Fig. 3

(a) CFF/illuminance functions for one subject (RDH) tested in the foveola (0.5°-diameter test field) for red (642-nm, open circles) and green (555-nm, filled circles) flicker. The green-light function is steeper by 17%. (b) CFF data from Ives.44 Green- (510-nm) and red-light (650-nm) flicker stimuli, which were presented in a 5.2° × 8.6° rectangular field, were produced by a spectroscope and were viewed centrally through a 1 mm × 1 mm artificial pupil. The green-light function is steeper by 12.4%. (c) CFF/illuminance functions for narrow-band green (540-nm) and red (660-nm) light for a normal observer (RS) tested by Pokorny and Smith.15 The stimulus was a 1° field, viewed foveally through a 3-mm-diameter artificial pupil. Only the slopes of this observer’s functions were reported. The green-light function is steeper by 16.8%. (d) CFF/illuminance functions for green-light (mean of narrow-band 480- and 540-nm data) flicker and red-light (630-nm) flicker obtained by Giorgi.14 The average slopes for three observers are shown for each of the wavelength conditions. Stimuli were presented as 1° 40′ foveal fields viewed through an artificial pupil. The average green-light function is steeper than the average red-light function by 7.8%.

Fig. 4
Fig. 4

642-nm (open circles) and 555-nm (filled circles) TMTF’s obtained at 35° (left) and in the foveola (right) for one observer (RDH). Also shown are the corresponding CFF/illuminance data obtained in the same session (open and filled triangles represent the 642- and 555-nm data, respectively) along with their best-fitting Ferry–Porter lines, all transformed appropriately for a frequency-response plot. The TMTF’s were obtained in each case by setting the stimulus illuminance 4 log units above the respective 642- and 555-nm absolute thresholds, as determined by extrapolation of the corresponding Ferry–Porter lines to zero frequency.45 This procedure resulted in the 642- and 555-nm TMTF’s having equal sensitivities at low temporal frequencies. At frequencies beyond the peak sensitivity (around 10–15 Hz in the periphery and around 7 Hz in the foveola), the 642- and 5665-nm TMTF’s are increasingly divergent. This indicates that systems with different temporal properties underlie the responses to the 555- and 642-nm stimuli. The response to 555-nm light clearly has the higher temporal cutoff at both locations.

Fig. 5
Fig. 5

Demonstration of linearity of CFF responses in the presence of homochromatic (660-nm) backgrounds. Here we have plotted the amplitude of the modulating component as a function of the base (background) upon which these were measured. This plot was derived from data presented in a previous paper (Ref. 5, Fig. 9) in which CFF/illuminance functions were measured at four modulation depths: 20%, 50%, 100%, and 127% (square-wave modulation). Data shown here were derived from horizontal cuts through the CFF/illuminance functions at five temporal frequencies: 5, 14.5, 28.4, 50.3, and 65.4 Hz. When there was no actual data point at that frequency, a value was determined by interpolation between the two nearest neighboring points. Within experimental error, the modulation sensitivities are independent of background level. The horizontal lines placed at the mean modulation threshold for each frequency have been extrapolated leftward to the approximate absolute, dark-adapted threshold for these conditions (~ −0.5 log Td, vertical dashed line). The oblique dashed lines through the 20%- and 127%-modulation data represent the slope of the Ferry–Porter function for these data sets.

Fig. 6
Fig. 6

Detection of red-light flicker in the presence of a green background light for two observers (RDH and CWT). The ordinate is the difference between CFF’s obtained without and with the background light. (See text for details regarding the stimuli.) The abscissa is the mean retinal illuminance from the red LED’s for each observer. Pupil sizes for RDH and CWT were 7 and 10 mm, respectively. The horizontal dashed lines indicate the 99% confidence limits for the difference between two CFF measures. The vertical arrows mark the illuminance of the red LED’s at which the overall (red light plus green background) mean retinal illuminance caused significant bleaching of rods and each of the two cone types. (Half-bleaching levels were assumed to be 4.3 log Td for each cone type.) Rod responses are severely saturated at 3 log scotopic Td (i.e., ~2 log photopic Td for 540-nm light,55 well below levels at which the green background begins to affect red-light CFF’s. For both observers a steady green background light that reduced the modulation of the R cones to ~20% and the modulation of the G cones to <3% did not affect the detection of red flicker until overall mean retinal illuminance approached R-cone bleaching levels.

Fig. 7
Fig. 7

Schematic depiction of the additive (top panels) and independence (bottom panels) models of flicker detection for 555- and 642-nm light. The solid curves represent underlying R- and G-cone-mediated Ferry–Porter lines shown here as frequency responses. In each panel the steeper curve is for R cones with a slope −1/mr and the shallower curve is for G cones with a slope −1/mg (corresponding to a faster G-cone response). The dashed curves indicate the outcome of the model predictions for the two wavelength conditions. The relative sensitivities of the R and G cones at 0 Hz were set according to the Smith–Pokorny76 cone-sensitivity functions.

Fig. 8
Fig. 8

(a) Best-fitting Ferry–Porter function to RDH’s 642-nm, 35° data replotted as a frequency response (as in Fig. 4), with a logarithmic frequency axis (solid curve). The dashed curve depicts the frequency response of the corresponding nine-pole filter.81 (b) This procedure was applied to the data in Figs. 2 and 3, with the time constants of the resulting nine-pole fits determined in each case by the average Ferry–Porter slope.81 Inverse Laplace transform of these frequency responses yielded the four linear, dark-adapted impulse responses shown here. Solid curves, 35°; dotted curves, foveola. The 555-nm data and the 642-nm data are labeled G and R, respectively.

Equations (2)

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L * = κ * m λ R λ T λ d λ ,
F(s)=A(n-1)!/(T+s)n,

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