MESOPIC (ROD-CONE) LUMINOUS EFFICIENCY FUNCTIONS

Introduction

Mesopic luminous efficiency is the most inherently complex and most difficult to standardize or model because it depends on the outputs of both the rod and the cone photoreceptors. Not only are there differences in the spectral sensitivities between the rods and cones themselves but also between the properties of the postreceptoral pathways through which the rod and cone signals are transmitted. The nature and balance of these pathways are constantly changing with mesopic luminance.

Stockman and Sharpe [50] provided a list of the complexities affecting mesopic luminous efficiency, including (1) mixed rod and cone spectral sensitivities; (2) rod saturation at high mesopic levels (see, e.g., [51, 52]); (3) rod-cone interactions (e.g., [53–65]); (4) different spatial (retinal) distributions of the rods and cones (e.g., [66, 67]); (5) different spatial properties of rod and cone vision (e.g. [68–71]); (6) large temporal differences between rodand cone-generated signals (e.g., [72–75]); (7) substantial changes in temporal properties that occur in the mesopic range in both the rod and cone systems (e.g., [76]); (8) rod-cone self-cancellation [75, 77]; and (9) rod-rod self-cancellation between signals transmitted through different postreceptoral pathways [78–81]. As a consequence of these complexities, any measure of mesopic luminous efficiency will depend not only on the illumination level, but also on the spectral content of the stimuli used to probe performance, their retinal location, their spatial frequency content, and their temporal frequency content. There is no straightforward or simple solution.

Models of Mesopic Luminous Efficiency

So far, the main approach has been to measure luminous efficiency as a function of mesopic luminance level and then try to model the results as a weighted linear combination of the scotopic and photopic functions. Not surprisingly, the modeling has proven to be difficult. Quite aside from the difficulties listed, it has to be considered which photopic luminous efficiency function is appropriate for comparison. Because the scotopic luminous efficiency function corresponds to a large or peripheral retinal region, if additivity is the concern, as in all practical photometry, then the most appropriate available photopic function is probably the 10° diameter (large viewing field) photopic V10*(λ) function. However, in some cases the 10° viewing function based on HBM may be more suitable than the V10*(λ) function, which is based on HFP.

Mesopic luminous efficiency functions have been measured several times (e.g., [82– 90]). Several attempts have been made to model empirically the scotopic-to-photopic transition. Implicit in most of these models is the assumption that rod and cone signals interact. For instance, Palmer [84] derived a nonlinear empirical formula relating V′(λ) and V10(λ), while Kokoschka and Bodmann [91] derived a model in which the contributions of the three different cone types as well as the rods were considered (see also [92]). More recently, Ikeda and Shimozono [93] and Sagawa and Takeich [87] modeled the logarithm of the mesopic luminous efficiency as the weighted sum of the logarithms of the scotopic and photopic functions (i.e., the geometric mean), but both groups used the CIE brightness rather than the CIE luminance function V(λ) (see also [86, 88]). In fact, as these authors argued, because mesopic luminous efficiency is typically measured by