One embodiment relates to a method of model-based optical metrology. An area of a geometrical structure of dispersive materials on a substrate is illuminated with polarized incident electromagnetic radiation using an illuminator of a scatterometer apparatus. Spectral components of the incident electromagnetic radiation reflected from the area are measured using a detector of the scatterometer apparatus. Using a computer for the scatterometer apparatus, parameter values are determined that minimize an objective function which represents a difference between the measured spectral components and computed spectral components based on a parameterized model of the geometrical structure. Steps for determining the parameter values that minimize the objective function include: computing a solution to state equations driven by a function representing the incident electromagnetic radiation, and computing a solution to an adjoint to the state equations. Other embodiments and features are also disclosed.