The use of Bessel functions to extend the range of optical diffraction techniques for in-process surface finish measurements of high precision turned parts

To extend the useful range of optical diffraction techniques, algorithms are derived to extract the roughness parameter from the diffraction pattern when the ratio Rq/ lambda <0.03. It is shown that when Rq/ lambda <0.03 the optical Fourier transform of a surface is directly related to the mathematical Fourier transform of the surface profile. These algorithms, closely related to Bessel functions, will extend the range to Rq/ lambda =0.13. They are applied to experimental data and produce a good correlation with values obtained by conventional stylus techniques.