Regularization in ellipsometry

The continuous variation of the refractive index with the depth in the vicinity of surfaces can be determined by ellipsometry without destroying the object of measurements. The presented method does not impress any given structure to the profile and is applicable to just the range of layer thicknesses interesting to optics (about /4 to /2). The theoretical approach to interpret the measured data leads to an integral equation that is numerically inverted by regularization to filter out the destabilizing effects of measurement errors. The regularizing operator and regularization parameter responsible for this filtering are founded on physical arguments and experiment, respectively. These results can be transferred to other regularization problems based on quantities related to volume (e.g. density, temperature).