Engineering surface analysis with different wavelet bases

Traditional surface texture analysis involves filtering surface profiles into different wavelength bands commonly referred to as roughness, waviness and form. The primary motivation in filtering surface profiles is to map each band to the manufacturing process that generated the part and the intended functional performance of the component. Current trends in manufacturing are towards tighter tolerances and higher performance standards that require close monitoring of the process. Thus, there is a need for finer bandwidths for process mapping and functional correlation. Wavelets are becoming increasingly popular tools for filtering profiles in an efficient manner into multiple bands. While they have broadly been demonstrated as having superior performance and capabilities than traditional filtering, fundamental issues such as choice of wavelet bases have remained unaddressed. The major contribution of this paper is to present the differences between wavelets in terms of the transmission characteristics of the associated filter banks, which is essential for surface analysis. This paper also reviews fundamental mathematics of wavelet theory necessary for applying wavelets to surface texture analysis. Wavelets from two basic categories-orthogonal wavelet bases and biorthogonal wavelet bases are studied. The filter banks corresponding to the wavelets are compared and multiresolution analysis on surface profiles is performed to highlight the applicability of this technique.