Optical diffraction has been demonstrated to be a useful method with which to noninvasively examine materials and structures that result from lithographic processes used in the semiconductor industry to create integrated circuits. The process of inferring the geometry of the lithographically created structures from measurements of diffracted power is rather difficult, due to the highly nonlinear relationship between the properties of the diffracting structure and the diffraction measurements. To simplify this process, we describe a method that is based on determining the departures from a set of expected design values. We show that this method linearizes the otherwise highly nonlinear relationship between structure parameter values and diffraction measurements, and hence permits analyses using classical linear methods. We develop a linearized inversion technique to determine key parameters of a periodic structure from an analysis of diffraction data, and illustrate the proposed method for the retrieval of three geometrical parameters (groove depth, linewidth, and sidewall slope angle), both individually and together. We tested our method using simulated measurements of power diffracted by the grating, which were generated using rigorous coupled- wave theory. We show that our inversion algorithm predicts the correct value of these three parameters for a variety of geometrical configurations.