1. An apparatus for analyzing the characteristics of a periodic structure formed on a sample, comprising: a spectroscopic measurement system including a broad band probe beam directed to reflect off the periodic structure and a detection module for measuring one of a change in magnitude and a phase of the probe beam at a plurality of wavelengths and generating output signals corresponding thereto; and a processor system using the output signals generated by the measurement system to determine a rectangular model with a theoretical height and width for an element of the periodic structure which provides the best fit with the optically measured data, the processor system capable of deriving a second model using the determined rectangular model, the second model having a top width different from a bottom width and including at least two layers, the processor system capable of iteratively modifying a height and width of each of the at least two layers to determine the best fit with the optically measured data and adding additional theoretical intermediate widths and layers to the second model in an iterative best fit process until the level of fitness reaches a predetermined level.