3.5 Space frequency functions

Conventional random process analysis cannot detect small changes in the statistics - for nano applications small changes can cause serious damage e.g. in wafer polishing. Extra machine tool monitoring can also be helpful. The following gives the formulae for the conventional random process function and the newer ones. These are listed here to show the similarities and differences. Compare:

(3.24)

Both space frequency functions have the 'core' of the random process analysis but have one extra variable, which enables statistical change in the surface to be detected (Figure 3.46).

Figure 3.46: Wavelet - mathematical zoom lens