Accurate bidirectional reflectance distribution function (BRDF) models are essential for computer graphics and remote sensing performance. The popular microfacet class of BRDF models is geometric-optics-based and computationally inexpensive. Fitting microfacet models to scatterometry measurements is a common yet challenging requirement that can result in a model being fit as one of several unique local minima. Final model fit accuracy is therefore largely based on the quality of the initial parameter estimate. This makes for widely varying material parameter estimates and causes inconsistent performance comparisons across microfacet models, as will be shown with synthetic data. We proposed a recursive optimization method for accurate parameter determination. This method establishes an array of local minima best fits by initializing a fixed number of parameter conditions that span the parameter space. The identified solution associated with the best fit quality is extracted from the local array and stored as the relative global best fit. This method is first applied successfully to synthetic data, then it is applied to several materials and several illumination wavelengths. This method proves to reduce manual parameter adjustments, is equally weighted across incident angles, helps define parameter stability within a model, and consistently improves fit quality over the high-error local minimum best fit from lsqcurvefit by an average of 71%.
Michael W. Bishop, Samuel D. Butler, and Michael A. Marciniak "Robust method of determining microfacet BRDF parameters in the presence of noise via recursive optimization," Optical Engineering 60(9), 094103 (6 September 2021). https://doi.org/10.1117/1.OE.60.9.094103