Approaches for circle characterization in photolithography

The problem of determining the center and radius of a substrate in the shape of a circular disc is considered. We propose an original functional having a clear geometric interpretation. Determination of the extremum of this functional reduces to a linear problem. The matrix of the linear system corresponding to the functional is positively defined and well-posed for rather long arcs. Experimental studies show that the proposed method enables the determination of the center of the substrate with an accuracy of 10 μm, based on a small number of measurements of the coordinates of the substrate edge. This accuracy is sufficient for solving a number of applied problems.