Improved computation of the adaptation coefficient in the CIE system of mesopic photometry

New values of parameters a and b are proposed for the CIE system of mesopic photometry MES2 [CIE Publication 191:2010], because from the original values this model may have no solution or multi-solutions. From the new values of parameters a and b it is shown that the CIE MES2 system has a unique solution. The difference however, between the original and the new values of parameters a and b is very small and the changes do not affect previous conclusions based on the MES2 model. To compute such a solution, we propose a Bisection-Newton method which exhibits fast convergence (8 iterations in the worst case), and improves the fixed-point method recommended by the CIE MES2 system, which has convergence problems for high values of the photopic luminance and very high values of the scotopic/photopic ratio. Comparative results for the fixed-point method, the Bisection method, the Newton method, and the Bisection-Newton method, in terms of the number of iterations necessary for convergence and the computation time used, are reported.