A Generalized Model for Resolution-Dependent Roughness Measured by an Optical Profiler for Optical Surfaces

Abstract

In a recent paper, we proposed a model for the dependence of roughness on the resolution that was determined by an objective of an optical profiler, when surface grain diameter was smaller than the resolution. However, the model does not take into account the effect of waviness beneath surface grains whose wavelengths are larger than the resolution. The model is generalized by introducing terms that include the waviness. The area of a large cell with resolution determined by a low-magnification (SX) objective is adjusted to R2-times the area of a small cell with resolution determined by the high-magnification (LX) objective, where R is the ratio of the large cell area defined by the resolution of the SX objective to the small cell area defined by the resolution of the LX objective. If the wavelengths of the waviness and the diameters were random, the optical height in the large cell and R2-times the small cell would be divided into an invariable portion that is common to both large and small cells, and into the variable portions that are inherent to large and small cells. Finally, a new model is obtained as a result of multiplying the old model by a root term that takes the effect of waviness into account. The new model agrees well with the experimental results.