CONSTRAINED FEM SELF-CALIBRATION

Polynomial models have been adopted as standard analytical tools in im aging metrology for attenuating image distortions for which correction s are applied to image point measurements. An alternative correction m odel, the finite element approach, stems from the fact that the displa cement of a point in the image plane is projectively equivalent to a p roportional change in the principal distance. By dividing the image pl ane into smaller entities, distortions can be modeled by piecewise pri ncipal distance correction using the finite element method (FEM) of se lf-calibration. Problems can arise, however, when a large number of fi nite elements is employed. The application of shape function constrain ts is proposed to overcome rank defects arising from sparse point dist ribution for those cases. The adequacy of this modified FEM approach i s tested relative to an accepted polynomial model for three different data sets. The evaluation criteria include the degree of compensation for distortions, object space precision and accuracy, and parameter co rrelation.