Application of the discrete wavelet transform to SEM and AFM micrographs for quantitative analysis of complex surfaces

The discrete wavelet transform (DWT) has found significant utility in process monitoring, filtering, and feature isolation of SEM, AFM, and optical images. Current use of the DWT for surface analysis assumes initial knowledge of the sizes of the features of interest in order to effectively isolate and analyze surface components. Current methods do not adequately address complex, heterogeneous surfaces in which features across multiple size ranges are of interest. Further, in situations where structure-to-property relationships are desired, the identification of features relevant for the function of the material is necessary. In this work, the DWT is examined as a tool for quantitative, length-scale specific surface metrology without prior knowledge of relevant features or length-scales. A new method is explored for determination of the best wavelet basis to minimize variation in roughness and skewness measurements with respect to change in position and orientation of surface features. It is observed that the size of the wavelet does not directly correlate with the size of features on the surface, and a method to measure the true length-scale specific roughness of the surface is presented. This method is applied to SEM and AFM images of non-precious metal catalysts, yielding new length-scale specific structure-to-property relationships for chemical speciation and fuel cell performance. The relationship between SEM and AFM length-scale specific roughness is also explored. Evidence is presented that roughness distributions of SEM images, as measured by the DWT, is representative of the true surface roughness distribution obtained from AFM.