Surface description and defect detection by wavelet analysis

Wavelet analysis is a method to describe single- or multi-dimensional signals in multiple scales. Optically measured two-dimensional height data describing engineering surfaces are effectively represented by wavelet transforms enabling a reliable description of even complicated formed surfaces by a drastically reduced number of coefficients as well as the detection of component defects of different types. Reconstruction with only 0.1% of all wavelet coefficients of 4-4-pseudo-coiflets leads to a variance of the difference image between original and reconstructed surface of less than 0.07 of the variance of the original surface. Keeping the coefficients with highest values gives an up to four times better result than keeping the coefficients belonging to the lowest frequencies. Defects are effectively detected with the help of Burt–Adelson and Daubechies wavelets. Local defects in the range of 8 nm can be made visible. Lacquer pits are localized in the higher resolution stages of 4-4-pseudo-coiflet-transforms.