Luminous Efficiency Functions

Fig. 1. Illumination levels. Typical ambient light levels are compared with photopic luminance (log cd m−2), mean pupil diameter (mm), photopic and scotopic retinal illuminance (log photopic and scotopic trolands, respectively), and visual function. The scotopic, mesopic, and photopic regions are defined according to whether rods alone, rods and cones, or cones alone operate. The conversion from photopic to scotopic values assumes a white standard CIE (Commission Internationale de l’ Éclairage, International Lighting Commission) D65 illumination. (Based on the design of Hood and Finkelstein, [155].)

The goal of visually relevant light specification (photometry) is to provide a practical method of measuring and specifying the apparent perceived intensity of any monochromatic or spectrally broad-band light or mixtures thereof. This seemingly simple goal, however, is difficult to accomplish because the human visual system as a whole, unlike a typical radiometric detector, does not respond univariantly to light. First, rods and cones do not have the same spectral sensitivities: When measured in vivo, the sensitivities of the rods and the short-wavelength-sensitive (S), middle-wavelength-sensitive (M), and long-wavelength-sensitive (L) cones are displaced relative to one another and peak at about 507 and 440, 545, and 565 nm, respectively. Thus, different spectral luminous efficiency functions have to be defined for the different ranges of human vision: the scotopic luminous efficiency function mediated exclusively by the rods, the photopic luminous efficiency function mediated exclusively by the cones (predominantly

Wavelength (nm)

Fig. 2. Scotopic [CIE (Commission Internationale de l’ Éclairage, International Lighting Commission) 1951 V′(λ), black line] and photopic [V*(λ) function, gray line, [44] ] luminosity functions. The scotopic function is mediated exclusively by the rods; the photopic function is mediated by a linear combination of the L and M cones. The M-cone (long dashed line) and L- cone (short dashed line) spectral sensitivities [23] are also shown, plotted so that their weighted sum equals V *(λ).

the L and M cones), and the mesopic luminous efficiency function mediated by both the rods and cones. Figure 2 allows a comparison between representative scotopic (rod) and photopic (a weighted combination of the L- and M-cone sensitivities) spectral luminous efficiency functions. Second, the relative contributions of the different photoreceptor types to apparent intensity are strongly dependent on chromatic adaptation and other stimulus parameters, such as wavelength, temporal frequency, retinal location, and spatial frequency. These contributions are complicated by the existence of multiple postreceptoral channels that process the cone signals, which include the additive, luminance channel (L + M), and spectrally opponent chromatic channels (L − M) or (S − [L + M]) (e.g., [3–10]).

The essential element in converting radiometric measures (such as radiance) to photometric ones (such as luminance) is the derivation of a spectral luminous efficiency (luminosity) function, which defines the relative visual “effectiveness” of lights of different wavelength in specific matching or detection tasks. It is a dimensionless scalar or weighting function, normalized to a maximal value of unity. Dimensions are introduced by defining the luminous efficacy of the monochromatic radiant flux of the maximal value (see, e.g., [11, 12]). The choice of measurement task is crucial in defining luminous efficiency. For photometry to be as practicable as radiometry, the measured luminous efficiency of any mixture of lights must equal the sum of the luminous efficiencies of the component lights. Such additivity is known as obedience

to Abney’s law [13, 14]. The requirement for additivity typically means that the designated photometric or psychophysical task favors postreceptoral visual mechanisms that are themselves approximately additive, such as the luminance pathway.

Psychophysical Measures of Luminous Efficiency

The measurement of scotopic luminous efficiency is relatively straightforward because it depends on the activity of a single photoreceptor type, the rods. Since photoreceptors are univariant and additive (see the section on univariance), any technique that maintains rod isolation should yield additive measures of luminous efficiency. Obtaining additive measures of photopic and mesopic luminous efficiency is more challenging because, as noted, multiple photoreceptors and postreceptoral channels can be involved.

Many different psychophysical techniques have been used to estimate the photopic spectral luminous efficiency function, including heterochromatic flicker photometry (HFP), heterochromatic modulation photometry (HMP), minimally distinct border (MDB), minimum motion, direct heterochromatic brightness matching (HBM), step- by-step brightness matching, color matching, absolute threshold, increment threshold, critical flicker fusion (CFF), and visual acuity. Confusingly, many of these different procedures and criteria yield very different results (for reviews, see [12, 15–23]).

Broadly, the photopic techniques can be divided between those that produce an additive spectral luminous efficiency function and obey Abney’s law and those that do not. Those that do not obey Abney’s law are impractical for photometry and can be largely discarded, although they may have some limited application to specific viewing situations. Those that do include HFP, HMP, MDB, CFF, and minimum motion (e.g., [7, 16, 19, 20, 24, 25]). These additive techniques have in common the use of high temporal or spatial frequencies, which discriminate against the influence of signals from the short-wavelength-sensitive or S-cone pathways or signals in other chromatic pathways and favor signals from the additive, luminance pathway, which sums signals from the L and M cones. For example, in HFP, superimposed lights alternating at moderate-to-high temporal rates are adjusted to minimize the perception of flicker, while in MDB abutting side-by-side lights are adjusted to make the border between them appear minimally distinct.

Factors that Influence Luminous Efficiency

Even if we restrict our consideration to techniques that yield additive efficiency measurements, other factors need to be taken into account when specifying a standard spectral luminous efficiency function. One important factor is the sizable individual differences in spectral luminous efficiency that are found between observers due to individual variability in preretinal screening and photopigment optical density, both of which change with aging. These are discussed in more detail in a separate section. To define a standard, mean spectral luminous efficiency function for photometry, many subjects must be used in its derivation, so that the mean data are representative of the population as a whole (although distinct functions may have to be derived for different age groups). It is, however, important to recognize that the mean standard functions are unlikely to apply to most individual observers. Nonetheless, corrections, such as those outlined in the section on individual differences influencing luminous efficiency, can be made to the mean functions to make them more representative of the individual observer.