Luminosity functions

    Luminous efficiency functions are the basis of present photometry. They were introduced by the CIE to provide a psychophysical analog of radiance called luminance. The functions give the ratio of the energy of a spectral light of the wavelength, λmax, to which the eye is most sensitive, to the energy of a spectral light of wavelength, λ, at which the two lights produce equivalent luminous sensations. Luminosity functions are typically tabulated in energy units, but  we provide both energy and quantal versions.

    In general, measurement methods that yield results consistent with linear additivity of spectral lights or Abney's Law (Abney & Festing, 1886, Abney, 1913) are to be preferred.  The measurement tasks most commonly used today are typically heterochromatic flicker photometry (HFP), in which continuously alternating lights of different wavelength are matched in intensity to minimize the perception of flicker,  or a version of side-by-side matching, in which the relative intensities of the two half fields is set so that the border between them appears "minimally distinct" (MDB). Both tasks minimize contributions from the S-cones (see above), and produce nearly additive results (e.g., Ives, 1912; Wagner & Boynton, 1972).

(i) Earlier luminosity functions. The original V(λ) function, which was adopted by the CIE in 1924 and is still used to define luminance today, was originally proposed by Gibson & Tyndall (1923). The function was based on data obtained using several methods at several laboratories (Ives, 1912; Coblentz & Emerson, 1918; Hyde, Forsythe & Cady, 1918; Gibson & Tyndall, 1923). Surprisingly, the 1924 V(λ) function at short-wavelengths follows the least plausible data of Hyde, Forsythe and Cady, even though those data are more than a log unit less sensitive than the other data in that region (see Fig 2.13a of Stockman & Sharpe, 1999).

    In 1951, Judd proposed a substantial revision to the V(λ) function in an attempt to improve the function at short wavelengths (Judd, 1951). He retained the older photopic sensitivities at 460 nm and longer wavelengths, but increased the sensitivity at shorter wavelengths, to produce the Judd modified V(λ). Unfortunately, this adjustment artificially created an average observer with an implausibly high macular pigment density for a 2° field. Vos (1978) subsequently made minor adjustments to the Judd modified CIE V(λ) function below 410 nm to produce the Judd-Vos modified CIE V(λ) [also known as the CIE VM(λ) function].

(ii) Cone spectral sensitivities and the luminosity function. The luminosity function, V(λ), falls into a completely different category from cone spectral sensitivities, yet it is typically treated as if it did not. Unlike cone spectral sensitivities, the shape of the luminosity function changes with chromatic adaptation (e.g., De Vries, 1948; Eisner & MacLeod, 1981), and is highly dependent on the observing conditions (e.g., size, retinal eccentricity, duration and intensity of the viewing field) and the measurement criterion. Thus, any luminosity function is only of limited applicability, since it is not generalizable to other conditions of chromatic adaptation, or necessarily to other measurement tasks. In contrast, cone spectral sensitivities (and CMFs, in general), which are determined by the cone photopigments, do not change with adaptation, until photopigment bleaching becomes significant (in which case, the changes reflect the reduction in photopigment optical density).

    Both the M- and L-cones contribute to the luminance efficiency, though their contribution is typically dominated by the L-cones (e.g., Cicerone & Nerger, 1989; Vimal et al., 1989). The contribution of the S-cones to luminance has been somewhat contentious (Eisner & MacLeod, 1980; Stockman & MacLeod, 1987; Verdon & Adams, 1987; Lee & Stromeyer, 1989; Stockman, MacLeod & DePriest, 1991), but it now seems clear that the S-cones do make a small contribution under certain conditions, in particular when the M- & L-cones are selectively adapted to an intense long-wavelength field (Lee & Stromeyer, 1989; Stockman, MacLeod & DePriest, 1991).

    Since any small S-cone contribution is not only small, but also strongly temporal-frequency- and adaptation-dependent-to the extent that it might add at some frequencies and subtract at others (Stockman, MacLeod & DePriest, 1991)-it is of practical convenience to treat it as negligible or null; which is the assumption that Sharpe, Stockman Jagla & Jägle (2005) make in deriving V2*(λ), the new luminosity function.

    For reviews, see Wyszecki & Stiles (1982), Wagner & Boynton (1972), Lennie et al., (1993), Stockman and Sharpe (1999).


Abney, W. (1913). Researches in colour vision. London: Longmans, Green.

Abney, W. & Festing, E.R. (1886). Colour photometry. Philosophical Transactions of the Royal Society, London, 177, 423-456.

Cicerone, C. M., & Nerger, J. L. (1989). The relative numbers of long-wavelength-sensitive to middle-wavelength-sensitive cones in the human fovea centralis. Vision Research, 29, 115-128.

Coblentz, W. W., & Emerson, W. B. (1918). Relative sensibility of the average eye to light of different color and some practical applications. U.S. Bureau of Standards Bulletin, 14, 167.

De Vries, H. L. (1948). The luminosity curve of the eye as determined by measurements with the flicker photometer. Physica, 14, 319-348.

Eisner, A., & MacLeod, D. I. A. (1980). Blue sensitive cones do not contribute to luminance. Journal of the Optical Society of America, 70, 121-123.

Eisner, A., & MacLeod, D. I. A. (1981). Flicker photometric study of chromatic adaptation: selective suppression of cone inputs by colored backgrounds. Journal of the Optical Society of America, 71, 705-718.

Gibson, K. S., & Tyndall, E. P. T. (1923). Visibility of radiant energy. Scientific Papers of the Bureau of Standards, 19, 131-191.

Hyde, E. P., Forsythe, W. E., & Cady, F. E. (1918). The visibility of radiation. Astrophysics Journal, 48, 65-83.

Ives, H. E. (1912). Studies in the photometry of lights of different colours. I. Spectral luminosity curves obtained by the equality of brightness photometer and flicker photometer under similar conditions. Philosophical Magazine Series 6, 24, 149-188.

Judd, D. B. (1951). Report of U.S. Secretariat Committee on Colorimetry and Artificial Daylight, Proceedings of the Twelfth Session of the CIE, Stockholm (pp. 11) Paris: Bureau Central de la CIE.

Lee, J., & Stromeyer, C. F. (1989). Contribution of human short-wave cones to luminance and motion detection. Journal of Physiology, 413, 563-593.

Lennie. P., Pokorny, J. & Smith, V.C. (1993). Luminance. Journal of the Optical Society of America A 10, 1283-1293.

Smith, V. C., & Pokorny, J. (1975). Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm. Vision Research, 15, 161-171.

Stockman, A., & MacLeod, D. I. A. (1987). An inverted S-cone input to the luminance channel: evidence for two processes in S-cone flicker detection. Investigative Ophthalmology and Visual Science (supplement), 28, 92.

Stockman, A., MacLeod, D. I. A., & DePriest, D. D. (1991). The temporal properties of the human short-wave photoreceptors and their associated pathways. Vision Research, 31, 189-208.

Stockman, A., & Sharpe, L. T. (1999). Cone spectral sensitivities and color matching. In K. Gegenfurtner & L. T. Sharpe (Eds.), Color vision: from genes to perception (pp. 51-85) Cambridge: Cambridge University Press.

Verdon, W., & Adams, A. J. (1987). Short-wavelength sensitive cones do not contribute to mesopic luminosity. Journal of the Optical Society of America A, 4, 91-95.

Vimal, R. L. P., Smith, V. C., Pokorny, J., & Shevell, S. K. (1989). Foveal cone thresholds. Vision Research, 29, 61-78.

Vos, J. J. (1978). Colorimetric and photometric properties of a 2-deg fundamental observer. Color Research and Application, 3, 125-128.

Wagner, G. & Boynton, R.M. (1972). Comparison of four methods of heterochromatic photometry. Journal of the Optical Society of America 62, 1508-1515.

Wyszecki, G. & Stiles, W.S. (1982). Color science: concepts and methods, quantitative data and formulae. New York: John Wiley.