Sedimentation data acquired with the interference optical scanning system of the Optima XL-I analytical ultracentrifuge can exhibit time- invariant noise components, as well as small radial-invariant baseline offsets, both superimposed onto the radial fringe shift data resulting from the macromolecular solute distribution. A well-established method for the interpretation of such ultracentrifugation data is based on the analysis of time-differences of the measured fringe profiles, such as employed in the g(s*) method. We demonstrate how the technique of separation of linear and nonlinear parameters can be used in the modeling of interference data by unraveling the time-invariant and radial-invariant noise components. This allows the direct application of the recently developed approximate analytical and numerical solutions of the Lamm equation to the analysis of interference optical fringe profiles. The presented method is statistically advantageous since it does not require the differentiation of the data and the model functions. The method is demonstrated on experimental data and compared with the results of a g(s*) analysis. It is also demonstrated that the calculation of time-invariant noise components can be useful in the analysis of absorbance optical data. They can be extracted from data acquired during the approach to equilibrium, and can be used to increase the reliability of the results obtained from a sedimentation equilibrium analysis.