can all be present on one side of a substrate sub as shown in fig4 a or can be distributed to both sides as exemplified in fig4 b it is emphasized that the shown systems are demonstrative and not limiting and that any functional type of ellipsometer such as rotating analyzer rotating polarizer rotating compensator etc or discrete rotatable versions thereof and polarization modulation null etc can be utilized in practice of the present invention methodology it is to be understood that the terminology u201c step size u201d refers to the number of wavelengths between wavelengths at which data is acquired over a range of wavelengths it is specifically noted that the present invention methodology is characterized in that the obtained data is insufficient to directly one for one evaluate all parameters of the mathematical model over the wavelength range finally fig5 demonstrates a mean square error mse plot note the presence of a major minimum and a number of local minima as mentioned earlier an approach to obtaining good initial u201c educated guess u201d values for characterizing parameters in a mathematical model of a sample comprising a plurality of layers is a technique termed u201c global fitting u201d the u201c global fit u201d approach provides that a multiplicity of reasonable combinations of parameters that are to be fit to empirical data by a regression procedure be tested and the combination which provides the lowest square error value be identifed that combination of values is then entered to the regression procedure which serves to provide best fit values the global fit procedure helps insure that the regression procedure does not return parameter values that.