OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 9, Iss. 11 — Nov. 1, 1992
  • pp: 1889–1904

Analysis of visual modulation sensitivity. V. Faster visual response for G- than for R-cone pathway?

Russell D. Hamer and Christopher W. Tyler  »View Author Affiliations

JOSA A, Vol. 9, Issue 11, pp. 1889-1904 (1992)

View Full Text Article

Enhanced HTML    Acrobat PDF (2522 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

Original Manuscript: June 26, 1990
Revised Manuscript: July 9, 1992
Manuscript Accepted: July 3, 1992
Published: November 1, 1992

Russell D. Hamer and Christopher W. Tyler, "Analysis of visual modulation sensitivity. V. Faster visual response for G- than for R-cone pathway?," J. Opt. Soc. Am. A 9, 1889-1904 (1992)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. C. Porter, “Contributions to the study of flicker,” Proc. R. Soc. London Ser. A 70, 313–329 (1902). [CrossRef]
  2. H. E. Ives, “A theory of intermittent vision,”J. Opt. Soc. Am. Rev. Sci. Instrum. 6, 343–361 (1922). [CrossRef]
  3. 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]
  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]
  5. 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]
  6. J. D. Conner, “The temporal properties of rod vision.” J. Physiol. (London) 332, 139–155, 1982.
  7. 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).
  8. D. G. Green, “Sinusoidal flicker characteristics of the color-sensitive mechanisms of the eye,” Vision Res. 9, 591–601 (1969). [CrossRef] [PubMed]
  9. R. M. Boynton, D. N. Whitten, “Selective chromatic adaptation in primate photoreceptors,” Vision Res. 12, 855–874 (1972). [CrossRef] [PubMed]
  10. D. H. Kelly, “Spatio-temporal frequency characteristics of color-vision mechanisms,”J. Opt. Soc. Am. 64, 983–990 (1974). [CrossRef]
  11. 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]
  12. 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]
  13. 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).
  14. A. Giorgi, “Effect of wavelength on the relationship between critical flicker frequency and intensity in foveal vision,”J. Opt. Soc. Am. 53, 480–486 (1963). [CrossRef] [PubMed]
  15. J. Pokorny, V. C. Smith, “Luminosity and CFF in deuteranopes and protanopes,”J. Opt. Soc. Am. 62, 111–117 (1972). [CrossRef] [PubMed]
  16. H. De Lange, “Research into the dynamic nature of the human fovea-cortex systems with intermittent and modulated light. I. Attenuation characteristics with white and colored light,”J. Opt. Soc. Am. 48, 777–784 (1958). [CrossRef]
  17. P. L. Walraven, H. J. Leebeek, “Phase shift of sinusoidally alternating colored stimuli,”J. Opt. Soc. Am. 54, 78–82 (1964). [CrossRef] [PubMed]
  18. A. Eisner, D. I. A. MacLeod, “Flicker photometric study of chromatic adaptation: selective suppression of cone inputs by colored backgrounds,”J. Opt. Soc. Am. 71, 705–718 (1981). [CrossRef] [PubMed]
  19. F. A. Abraham, M. Alpern, D. B. Kirk, “Electroretinograms evoked by sinusoidal excitation of human cones,”J. Physiol. (London) 363, 135–150 (1985).
  20. M. H. Bornstein, L. E. Marks, “Photopic luminosity measured by the method of critical frequency,” Vision Res. 12, 2023–2033 (1972). [CrossRef] [PubMed]
  21. 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]
  22. 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]
  23. C. W. Tyler, R. D. Hamer, “The jurisdiction of the Ferry–Porter law,” Invest. Ophthalmol. Vis. Sci. Suppl. 27, 72 (1986).
  24. 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]
  25. O. Estevez, C. R. Cavonius, “Flicker sensitivity of the human red and green color mechanisms,” Vision Res. 15, 879–881 (1975). [CrossRef] [PubMed]
  26. C. M. Cicerone, D. G. Green, “Relative modulation sensitivities of the red and green color mechanisms,” Vision Res. 18, 1593–1598 (1978). [CrossRef] [PubMed]
  27. C. R. Cavonius, O. Estevez, “Sensitivity of human color mechanisms to gratings and flicker,”J. Opt. Soc. Am. 65, 966–968 (1975). [CrossRef] [PubMed]
  28. P. Lennie, “Temporal modulation sensitivities of red- and green-cone-sensitive systems in dichromats,” Vision Res. 24, 1995–1999 (1984). [CrossRef]
  29. G. Oesterberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophthalmol. Suppl. 6, 1–102 (1935).
  30. S. Polyak, The Retina (U. Chicago Press, Chicago, Ill., 1941).
  31. 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]
  32. D. H. Kelly, “Visual responses to time-dependent stimuli. I. Amplitude sensitivity measurements,”J. Opt. Soc. Am. 51, 422–429 (1961). [CrossRef]
  33. J. Levinson, L. D. Harmon, “Studies with artificial neurons, III. Mechanisms of flicker fusion,” Kybernetik 1, 107–117 (1961). [CrossRef]
  34. 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]
  35. 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]
  36. W. S. Stiles, “Increment thresholds and the mechanisms of colour vision,” Doc. Ophthalmol. 3, 138–163 (1949). [CrossRef] [PubMed]
  37. G. Wald, “The receptors of human color vision,” Science 145, 1007–1017 (1964). [CrossRef] [PubMed]
  38. 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).
  39. 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.
  40. 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.
  41. R. W. Nygaard, T. E. Frumkes, “Frequency dependence in scotopic flicker sensitivity,” Vision Res.115–127 (1985). [CrossRef] [PubMed]
  42. 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.
  43. J. Rovamo, V. Virsu, “An estimation and application of the human cortical magnification factor,” Exp. Brain Res. 37, 495–510 (1979). [CrossRef] [PubMed]
  44. 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).
  45. F. W. Fitzke, R. W. Massof, “Absolute cone thresholds derived from the Ferry–Porter law,” Invest. Ophthalmol. Vis. Sci. Suppl. 19, 212 (1980).
  46. 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]
  47. 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.
  48. C. Landis, “Determinants of the critical flicker-fusion threshold,” Physiol. Rev. 34, 259–286 (1954). [PubMed]
  49. D. H. Kelly, “Visual responses to time-dependent stimuli. IV Effects of chromatic adaptation,”J. Opt. Soc. Am. 52, 940–947 (1962). [CrossRef]
  50. 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).
  51. 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]
  52. J. L. Schnapf, T. W. Kraft, D. A. Baylor, “Spectral sensitivity of human cone photoreceptors,” Nature (London) 325, 439–441 (1987). [CrossRef]
  53. 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.
  54. 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).
  55. G. Wyszecki, W. S. Stiles, Color Science: Concepts, Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).
  56. 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]
  57. 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]
  58. B. A. Drum, “Cone interactions at high flicker frequencies: evidence for cone latency differences,”J. Opt. Soc. Am. 67, 1601–1603 (1977). [CrossRef]
  59. H. DeVries, “The luminosity curve of the eye as determined by measurement with the flicker photometer,” Physica 14, 319–348 (1948). [CrossRef]
  60. J. J. Vos, P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971). [CrossRef] [PubMed]
  61. 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).
  62. R. M. Boynton, Human Color Vision (Holt, Rinehart and Winston, New York, 1979).
  63. 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).
  64. 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).
  65. 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).
  66. 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]
  67. 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).
  68. 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).
  69. 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).
  70. 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]
  71. 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]
  72. 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]
  73. R. L. DeValois, I. Abramov, G. H. Jacobs, “Analysis of response patterns of LGN cells,”J. Opt. Soc. Am. 56, 966–977 (1966). [CrossRef]
  74. 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]
  75. J. J. Vos, P. L. Walraven, “On the derivation of foveal receptor primaries,” Vision Res. 11, 795–818 (1971). [CrossRef]
  76. 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]
  77. F. M. de Monasterio, “Properties of concentrically organized X and Y ganglion cells of macaque retina,”J. Neurophysiol. 41, 1394–1417 (1978). [PubMed]
  78. D. H. Kelly, “Diffusion model of linear flicker responses,”J. Opt. Soc. Am. 59, 1665–1670 (1969). [CrossRef] [PubMed]
  79. A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979). [CrossRef] [PubMed]
  80. A. Gorea, C. W. Tyler, “New look at Bloch’s law for contrast,” J. Opt. Soc. Am. A 3, 52–611986. [CrossRef] [PubMed]
  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.
  82. 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).
  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). [CrossRef]
  86. 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]
  87. G. Wagner, R. M. Boynton, “Comparison of four methods of heterochromatic photometry,”J. Opt. Soc. Am. 62, 1508–1515 (1972). [CrossRef] [PubMed]
  88. 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]
  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.
  90. P. E. King–Smith, D. Carden, “Luminance and opponent-color contributions to visual detection and adaptation and to temporal and spatial integration,”J. Opt. Soc. Am. 66, 709–717 (1976). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited