Newton method for computing the adaptation coefficient in the CIE system of mesopic photometry

A study by Gao et al found that the Newton method may not converge for certain combinations of the photopic luminance and the ratio of scotopic and photopic luminance for computing the adaptation coefficient m, for the CIE MES2 system for mesopic photometry. Hence, they proposed to use the Bisection-Newton method. In this short note, we propose the Newton method with a new initial guess for computing m. Numerical simulation has shown the proposed method not only converges, but also converges faster than the Bisection-Newton method.