Mathematical limitations of the CIE mesopic photometry system

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.