The MES2 Model Of CIE Is Discussed Again

In photometry,there are three different type of visions.They are the photopic,Mesopic and scotopic visions.CIE(International Commission on Illumination)has long before defined the photometric measurements for the photopic and scotopic vision,while CIE has no guideline for photometric measurements for the mesopic vision till 2010.In CIE 191:2010 publication,MES2 system is recommended for computing the mesopic luminance.The MES2 system was developed based on visual experiments such as object identification and reaction time in the road lighting environments.In the MES2 system,the mesopic luminance depends on the ratio(a shorthand of the ratio of soctopic luminance and the photopic luminance),and adaptation coefficient.The coefficient satisfies a non-linear function and can be solved iteratively using the Fixed-Point iteration as recommended by the CIE 191:2010 publication.However,in the CIE document,some important problems such as if the nonlinear equation has a solution or not,if it has a unique solution,and if the Fixed-Point iteration converges or not,were not discussed yet.In this thesis,these problems were investigated.Firstly,it is found that the non-linear system of equation in the MES2 system may has no solution,and may have more than one solution as well,which is certainly a big problem since a unique solution is necessary for practical applications.Further investigation found that the problem is caused by the two parameters and in the MES2 system.It was found that the two parameters should satisfy two equations and by solving the two equations,new values for the parameters and were found.Under this two new parameters,it was shown that the non-linear system of equation always has a unique solution.At the same time it was also shown numerically,the two mesopic luminance predictions by the MES2 system using the original(when the original non-linear equation has a unique solution)and new parameters are almost identical,hence the new parameters and should be used in the CIE MES2 system.Secondly,the convergence property of the Fixed-Point iteration is investigated numerically for solving the non-linear system in CIE MES2 system.It was found that the method may not converge for large ratio.Next,we investigated how large the ratio can be in a theoretical sense for the LED light sources.It is found that the ratio can be up to 48.92 for four basic LEDs combination and can be up to 71.98 without any constraint.After that,the well-known Bisection and the Newton methods were applied for solving the non-linear system of equation.It was found that the Bisection method always converges and it roughly took about 17 iterations for the convergence,which is slower than the fixed-point iteration when it converges.While for the Newton method,it may not converge for small ratio and it converges for larger ratio.When the Newton method converges,it converges faster than the Fixed-Point iteration and the Bisection method.Finally,a new iteration method was developed.It is a hybrid method and is the combination of the Bisection and the Newton methods,named as Bisection-Newton method.It always converges like the Bisection method and it converges faster like the Newton method.Numerical comparisons show the new method is better than the Fixed-Point iteration,Bisection method and the Newton method.