Mathematical limitations of the CIE mesopic photometry system

Abstract

The International Commission on Illumination (CIE) has published a recommended system for mesopic photometry based on visual performance. The system provides means for determining mesopic photometric values based on measuring the spectral composition and intensity of light. The system uses an iterative calculation method. We investigate the conditions under which this system is applicable and identify potential problems with the iterative method. We show that the system works well for the vast majority of lighting applications. However, it has non-convergence and discontinuity issues for sources with very high and very low values of scotopic-photopic ratio. A set of parameterised formulae is presented that approximates the mesopic model and provides a continuous, closed-form solution for the adaptation level in all lighting conditions.

Effectiveness of an alternative model for establishing mesopic luminance

“…The iterative approach is used as the reference against which the model is compared. While some studies have pointed out errors in the iteration approach, 8,9 these tend to concern very high S/P ratios or low luminances that are not of practical significance.…”

Theoretical consideration on convergence of the fixed-point iteration method in CIE mesopic photometry system MES2

“…F m = Recently, Gao et al [4] have shown that, with the values for a and b given by (6), the equation ( ) 0 F m = may have either no solution or more than one, and, in agreement with Shpak et al [5], they have recommended that the values for the parameters a and b should be better replaced by 10 5 1 1 , . 3 3…”

“…The CIE MES2 system [1] was proposed in 2010 as an intermediate between the USP-system developed by Rea et al [2] in 2004, and the Move-system developed by Goodman et al [3] in 2007. In the MES2 system, the spectral luminance efficiency function in the mesopic range from then the coefficient of adaptation m , defined by ( 4) and (5), should be also the solution of the equation ( ) 0.…”

“…Recently, Gao et al [4] and Shpak et al [5] have reported that the convergence of the fixed-point iteration method depends on the ratio / , S P and for large values of / S P the method does not converge. Shpak et al [5] suspected that, to achieve convergence, the ratio / S P cannot be larger than 17.…”

An optimal spectral model for phosphor‐converted white light‐emitting diodes used in the mesopic vision

“…In 2010, the International Commission on Illumination (CIE) published the technical report (No.191:2010) and recommended a system for mesopic photometry based on the visual performance . The system covers a photometry range between the scotopic and photopic photometry, placing a particular emphasis on the visual performance in road lighting applications . In terms of the mesopic vision, the ratio of the scotopic lumen to the photopic one (i.e., S/P ) is a key factor to determine the performance of the lighting source, which is related to both the eye vision and energy saving .…”