A two-dimensional isotropic spline filter

• A 2D spline filter was developed for roughness, waviness and form separation.
• The filtered surface was approximated using combined B-splines.
• The distance between the B-spline nodes is much larger than the sampling step.
• The tests show the superiority of the third-order filter over the second-order one.

The work deals with the development of a two-dimensional isotropic spline filter with application to the separation of components of the surface topography, i.e. roughness, waviness and form. An appropriate variational problem was formulated to define the mapping of primary surface data into filtered surface data with a transfer function of a circularly symmetric low-pass Butterworth filter of a given order. The variational problem was solved by approximating the filtered surface data by means of two-dimensional B-spline functions. The Fourier transform of the filter impulse response was determined to estimate the quality of approximation of the Butterworth filter and to select the appropriate filter cutoff. The paper presents one application of the designed filter to determine 3D roughness of an inner ring race of a ball bearing.