Fitting of reference surfaces for engineering surfaces by nonlinear least-squares technique

Engineering surfaces cornprise form and waviness errors, which are separated from the measured surface by establishing a reference surface that represents these errors. An attempt is made for the first time to fit a reference surface for simultaneous separation of form and waviness errors. A second-degree polynomial and a set of sinusoidal functions are taken as basis functions to represent form and waviness, respectively, and fitting is done using a nonlinear least-squares method. Different examples of surfaces are considered and a comparison is also made with 3D Gaussian filter to bring out the nature of reference surfaces obtained by the present fitting approach.