Industrial surface inspection by wavelet analysis

Wavelet analysis is a processing method for the description of single- or multi-dimensional signals in multiple scales and therefore well suited for describing technical surfaces with variable resolution. Here optically measured height data of technical surfaces are wavelet-transformed along two dimensions with two different objectives: One is the representation with only a few coefficients in the sense of an efficient data compression, the other is the reliable detection of defects, which can be regarded as a pattern recognition task. A systematic comparison of various wavelet families results in the choice of the biorthogonal pseudo-coiflets for representing the surfaces, and differentiating wavelets like Burt-Adelson-wavelet or short-range Daubechies-wavelets for solving the defect detection problem. It is shown that the representation can be improved by not using the most significant wavelet-values - which can be interpreted as low-pass filtered coefficients, but to maintain those with the largest weights. Thus the variance between the original surface and that reconstructed from the representation data is minimized by a factor up to 4. Defect detection is best performed with separate transformation in two orthogonal directions with subsequent superposition. The procedures obtained here are applied to surfaces like a coin-surface, a copper-mirror surface, and a lacquered surface.