International Standard

In 1951, the CIE (Commission Internationale de l’ Éclairage, International Lighting Commission) [32] formally adopted a standard scotopic luminous efficiency function known as V′(λ) (see Fig. 2; the values can be downloaded from the Web site http://www. cvrl.org). It is derived from (1) absolute thresholds for monochromatic targets (1° diameter target located 8° above the fovea) made by 22 fully dark-adapted young observers, with a mean age of 20 years [30], and (2) direct monochromatic brightness matches to a very dim white reference target 20° in diameter, made by 50 observers under 30 years of age [31]. Thus, strictly, V′(λ) applies to completely dark-adapted observers under the age of 30. The aging effect, mainly owing to the progressive yellowing of the eye’s lens (see the section on attenuation of spectral light by the lens and other ocular media ), which affects values below 500 nm, can be approximately compensated for by applying the following formula [31]:

where A is the observer’s age.

PHOTOPIC (CONE) LUMINOUS EFFICIENCY FUNCTION

Introduction

Defining luminous efficiency for photopic vision is much more complicated than for scotopic vision. Difficulties arise for two related reasons. First, unlike for the exclusively rod-dominated scotopic vision, univariance fails for photopic vision because at least two different types of cone photoreceptor, depending on the psychophysical measuring technique, are jointly contributing their responses to the luminous efficiency function. Thus, although the scotopic luminous efficiency function is determined primarily by receptoral events, the photopic (and the mesopic) functions are also determined by postreceptoral ones when the different cone signals are combined. If these postreceptoral mechanisms are color opponent, their influence will be wavelength dependent and consequently incompatible with additivity. Therefore, for practical photometry, the psychophysical measuring techniques have to be limited to those that tap into the additive postreceptoral mechanisms, which obey Abney’s law (see the section on psychophysical measures of luminous efficiency).

Second, even for those very restricted conditions for which additivity holds, photopic luminous efficiency functions are not fixed in spectral sensitivity but change with chromatic adaptation (e.g., [24, 33–41]). Thus, any particular photopic luminous efficiency function can only be of limited applicability because it defines luminance strictly only under the conditions for which it was measured. Different functions must be derived for different conditions, and any given function is not straightforwardly generalizable to other conditions of adaptation—particularly to other conditions of chromatic adaptation. Nevertheless, a luminous efficiency function is of practical use in many applications, especially for conditions that are similar to those under which the function was originally defined (e.g., neutral adaptation).