Researches into the application of multidimensional correlation techniques for the determination of edges using high-resolution optical measuring machines.

presented to the faculty of Mechanical Engineering at the Ilmenau University of Technology by Dipl.-Phys. Volker Tympel

This study explores the potential of microscopic image series from different focal positions for the exact localisation and characterisation of objects. The proposed technique of extrafocal correlation is described in detail in simulations and experiments on edge objects. Concludingly an outlook is given for applications on more complex objects. Introductorily the theoretically known edge-steepening effect of coherent illumination will be proven experimentally and the terms optical resolution and depth of focus on microscopical systems will be critically discussed. For the benefit of securing as much as possible numerical power effective data formats, Fast-Fourier-Transformation and parallelisation will be also elaborated. It was possible to show that correlation techniques can take advantage of the generally disruptive behaviour of oscillations on edge boarders, if the expected values of the correlation consider these oscillations. The integration of extrafocal image layers can likewise  increase the reproducibility of the detection of edge positions, meaning layers outside a defined depth of focus may be used to effectively determine the position of an edge, if the gain of information exceeds the deficit by increasing noise. In certain ranges of parameters the extrafocal correlation with expected values outclasses pure averaging with neighbouring image layers, particularly in the case of coherent illumination. Extra-focal correlation based on the Least Squares Method is indeed time-consuming but often more successful than the quicker Fourier-cross-correlation. The algorithm of the extrafocal correlation may also be used serial in order to analyse 2-dimensional trends of edges, as is the case with the determination of homogeneities of critical dimensions. The expansion of the technique to analyse more complex objects is mentioned using the example of the serial determination of circle diameters in this study because the essential 4-dimensional correlation with large  amounts of data is reserved for future computer generations. A special method of contrast enhancement called Negative-Contrast-Mixture-Method is appended.