New Chromaticity Diagram

The Luminous Efficiency Function
compared to Daylight

Prepared by James T. Fulton


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Comparisons are frequently made in the literature to how closely the solar radiation matches the luminous efficiency function of the human eye.  This page will address this question in more detail using the following figure.

A comparison of solar radiation and the absorption characteristic of human vision

Background concerning the Luminous Efficiency Function

The dark adapted absorption characteristic of the eye has been described using a variety of names. An early name was the visibility function from which the designation V(sub-lambda) is derived.  More recently (1931)it has been described and standardized as the luminous efficiency function by the CIE based on data assembled in 1924.  The method of obtaining the empirical luminous efficiency function makes fun reading. The following quotation is from remarks by Professor Wright, an actual participant in the development of V(sub-lambda), in 1969.

"The CIE Colorimetry Committee recently in their wisdom have been looking at the old 1931 observer and have been smoothing the data to obtain more consistent calculations with computers.  This has also involved some extrapolation and, in smoothing, they have added some additional decimal places.  When I look at the revised table of the x (bar), y(bar), z(bar) functions, I am rather surprised to say the least.  You see, I know how inaccurate the actual measurements really were.  (Laughter from audience)  Guild did not take any observations below 400 nm and neither did I, and neither did Gibson and Tyndall on the V(sub-lambda) curve, and yet at a wavelength of 362 nm, for example, we find a value y(bar) of 0.000004929604!  This, in spite of the fact that at 400 nm the value of y(bar) may be in error by a factor of 10 (Laughter)."

The light sources used in the 1920's were grossly deficient in the short wavelength spectrum.  Judd, the chairman of the committee generating the original 1931 standard disowned it in 1951 and produced his own graph showing higher sensitivity in the short wavelength region of the spectrum.  This shortcoming was the fundamental reason underlying the proposal, of Judd and others coalescing up into the 1950's, to update the C.I.E. 1924 Standard.  The CIE chose not to act on these recommendations.  To alleviate such suggested changes, the C. I. E. defined a Standard Observer whose visual system actually performed according to their Standard Luminous Efficiency Function of 1931.

These remarks show the precision that applies to the current standard. The CIE Standard Observer is clearly not a normal human, or the average of a group of normal humans.

Origin of the CIE (1931) Standard Observer

Although not addressed significantly in the early literature, there has also been a problem related to the spectrum of the light used in vision experiments.  The Planck Radiation Formula was only promulgated within the theoretical physics community in 1900.  It appears that most of the experimenters working in vision up through at least the 1930's lacked an adequate understanding of the importance of the spectral distribution of light in their experiments.  They were primarily concerned with the total integrated energy, which might be called the photopic energy, entering the visual system and typically used lamps with a color temperature in the 2400-2800 K range.  The specific problem relates to the relationship between the amount of energy radiated by a source per unit spectral bandwidth versus the number of photons, the photon flux, radiated by that same source per unit bandwidth.  As late as 1963, the Committee on Colorimetry of the Optical Society of America (erroneously) defined an equal energy spectral distribution as one characterized by equal flux per unit wavelength interval.  Wyszecki & Stiles gave a correct interpretation of this relationship on page 4 of their 1982 work. The term "equal-energy" source began appearing in the vision literature in the 1950's.  The term was frequently shown as above in quotation marks and was seldom if ever defined rigorously. In reading the articles of that period, the typical experimenter was using a nearly fixed spectral bandwidth spectrometer to filter the luminance of a commercial tungsten lamp.  The goal was to control the total integrated energy entering the eye in accordance with Stefan's Law, rather than concern themselves with the uniformity of the flux entering the eye in accordance with the more detailed Planck Distribution Law.  This lack of definition leads to considerable difficulty in correlating the early data to the real world and any theory.

As a result, the current C.I.E. Standards represent the average values obtained from smoothed data collected with inadequate light sources and interpolated to a precision exceeding that of the original data by ten to one.

The problem is actually worse if Wyszecki & Stiles are correct on page 395.  Quoting, "The values adopted in 1924 were those suggested by Gibson and Tyndall (1923) who composed a smooth and symmetrical V(sub-lambda)-curve from the data cited above.  The final result was not an average of the experimental data, but a weighted assembly of the different sets of data.  From 400 to 490 nm, the V(sub-lambda)-curve represents roughly the results of Hartman (1918); from 490 to 540 nm, those of Coblentz and Emerson (1918); from 540 to 650 nm, those of Gibson and Tyndall; and above 650 nm, those of Coblentz and Emerson (1918)."

It is also noteworthy that there have been fundamental revisions (greater than 7%) in the relationship between the Candela and the Watt during the period 1920-1970.[17.2.2]

Explanation of the Figure

The absorption characteristics

The absorption characteristics of the individual chromophores of vision are shown along the bottom of the figure.  The shapes of the absorption characteristics are not similar because they are plotted versus wavelength instead of frequency.  However, these functions are not Gaussian, they are described by Fermi-Dirac statistics and are described as Helmhotz-Boltzman funcitons.

The UV-channel characteristic is not shown in this figure because it does not play a significant role in the achromatic response of the visual system unless an illuminant us used with a color temperature above 7000 Kelvin (as will become clear below).

The theoretical luminous efficiency function calculated from the logarithmic sum of the three spectra is shown by the red line.  If this luminous efficiency function is smoothed by a Gaussian filter with a spectral bandwidth of thirty nanometers, a function closely matching the CIE 1931 V(sub-lambda) is obtained (shown by the blue line).  This smoothing appears to represent the degree of averaging between investigators and subjects used in defining the original CIE (1931) Standard Observer.

The Solar Spectrum

The solar spectrum shows a great many fine perturbations due to various bright spectral lines present in the solar corona and various dark spectral lines due to absorption by the atmosphere.  However, when applied to the eye, these fine variations are lost through averaging due to the wide absorption spectra of each chromophore.  As a result, the solar spectrum can be considered smoothed to that of a blackbody of about 6500 Kelvin.  The relative energy flux generated as a function of wavelength is shown by the brown line for this color temperature.  However, it is important to note the chromophores of vision are not energy sensitive, they are quantum detectors responding to individual photons.  The dashed brown line shows the relative photon flux as a function of wavelength from a 6500 Kelvin source.

The match between the Solar Spectrum and the Luminous Efficiency Function

Looking at the upper and lower halves of the figure, it can be seen that the photon flux associated with a 6500 Kelvin source is relatively uniform across the visual spectrum.  However, it is deficient in photons at wavelengths shorter than 500 nanometers (0.5 microns).  The deficiency in on the order of 20% and explains why many investigators find the "blue channel" is not as important in the visual response as it should be.  Using a lower color temperature source in the laboratory exacerbates this problem.  A more optimuum color tempterature for careful measurements would be 7000 Kelvin.  This source provides a uniform photon flux across the spectral band of interest within +/-5.7%.



1Wright, W. (1969) The Origins of the 1931 CIE System Color Group Journal (G. Britain) As reproduced in Boynton, R. (1979) Color Vision NY: Holt, Rinehart Appendix, Part II

Copyright © 2005 James T. Fulton