An optical metrology system is disclosed that has a measuring system configured to irradiate a metrology mark and record a portion of a reflected, a transmitted, or both, electromagnetic field and a characterization device configured to determine from the recorded field a mark shape parameter indicative of the structure of the metrology mark, the characterization device comprising: a field calculation unit configured to calculate an expected field for reflection, transmission, or both, from a theoretical reference mark based on an algebraic eigenvalue-eigenvector representation of the expected field, a field derivative calculation unit configured to calculate a first order derivative, a higher order derivative, or both, of the expected field with respect to the mark shape parameter by first deriving analytical forms for corresponding derivatives of eigenvalues and eigenvectors of the eigenvalue-eigenvector representation, and an optimization unit configured to use the outputs from the field and field derivative calculation units to determine an optimized mark shape parameter for which the expected field substantially matches the recorded field.