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Chapter 4:
Surface Waviness
Most surfaces when viewed from sufficiently far away will appear to have a uniform texture. On close and detailed examination using modern techniques, however, all surfaces will reveal some patterning, even if only at the atomic level. Surface waviness is the periodic component of surface texture. It arises most frequently from induced vibrations of a single-point surface generator, and when surface profiles are Fourier analyzed it usually occupies a spatial frequency band between those of surface form and roughness. Optical surfaces, such as metal mirrors or infrared (IR) optics, generated by single-point diamond turning, are often influenced to some degree by waviness. The periodic nature of such a surface results in diffraction of a reflected or transmitted beam, giving rise to multiple images rather than a single image when the beam is brought into a focus. A surface generated by the more common process involving area contact between the lap and the work surface is unlikely to suffer in this way. Polishing by the use of a flexible lap at speed can give rise to an orange-peel effect that can exhibit dominant spatial frequencies when Fourier analyzed. Similar patterns are sometimes seen on painted surfaces. Very small periodic surface height variations of less than a nanometer can be measured by a microscope interferometer even in the presence of residual roughness. In practical terms, where waviness gives rise to spurious images varying in intensity, measurement of these images can be carried out radiometrically and thresholds set depending on the application. For machine diagnostic purposes, however, as well as for setting acceptance thresholds, ISO 10110-8:1997 recommends measurement of the PSD function as an alternative approach to setting thresholds for surface texture including roughness and waviness. This metric is the square of the Fourier transform of the measured surface profile along a line. The software employed by a computer-aided microinterferometer will often compute this algorithm. A typical surface has a maximum PSD at low spatial frequencies and an exponential decrease as the spatial frequency increases. Waviness will give rise to peaks at one or more spatial frequencies.
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