Luminous efficiency function

Photopic (right) and scotopic (left) luminous efficiency functions. 

In Eqs. (7)—(10), 5(A) is the spectral power distribution of the illuminant, and R A) is the spectral reflectance factor of the object. Jc(A), y(A), and 5(A) are the color-matching functions of the observer. In the usual practice, k is defined so that the tristimulus value, Y, for a perfect reflecting diffusor (the reference for R A)) equals 100. Using the functions proposed by the CIE in 1931, y(A) was made identical to the spectral photopic luminous efficiency function, and consequently its tristimulus value, Y, is a measure of the brightness of objects. The X and Z values describe aspects of color that permit identification with various spectral regions. 

International Commission on Illumination 1990 CIE 1988 2° Spectral luminous Efficiency Function for Photopic Vision. Technical Report 86, International Commission on Illumination. 

Baylor et. al. have provided recent in-vitro isotropic absorption spectrum for Rhodonine based on Macaca fascicularis143. The data was collected over five and one-half orders of intensityusing transverse illumination at near 37 Celsius. Baylor, et. al. also provide a review of other available measurements and perform a circuitous calculation to compare the isotropic spectrum to the human scotopic luminous efficiency function attributed to Carpenter rather than the C.I.E. Based on ten photoreceptors, the peak sensitivity was estimated to be 491 nm. This is lower than most other investigators. However, data points were only collected at 20 nm intervals using filters of 10 nm nominal half-widths. This sampling plan does not support three digit accuracy in their peak value. 

The human eye responds to electromagnetic radiation in the wavelength range from about 360 nm (violet) to 820 nm (red), with a peak sensitivity near 555 nm (green). While the detailed shape of this response curve depends on the individual person, studies on representative samples of human subjects have led to adoption of a standard function relating the perceived brightness (luminous flux) to the actual power of the spectral radiation. This function is referred to as V(X), the photopic spectral luminous efficiency function, and it plays an important role in photometry. 

Reflectance, luminous n. Reflectance derived firom radiant flux by evaluating the radiant energy reflected according to its action upon a selective receptor (such as the eye), whose spectral sensitivity is defined by a standard relative luminous efficiency function. In popular usage, the term is used to describe the Y tristimulus value in the CIE system. 

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