An efficient surface profile measurement with the scanning path based on Hilbert and Gosper fractal curves

Abstract

This paper proposes a non-contact efficient measurement method of surface morphology with the scanning path based on the Hilbert and Gosper fractal curves. By comparing the proposed two types of fractals scanning curves with the traditional reciprocating S-curves, it can be found that the plane distribution of measuring points of the fractal curves is much more uniform, and then the measurement performance is much improved. The two fractal curves with different iterative times are introduced as a measurement path of the surface morphology, and the local three-dimensional roughness and overall shape tolerances of the parts are determined. In the view of the measurement point uniformity, different total number of fractals of iterations are compared as the measurement path of the surface morphology. In order to verify the accuracy of the proposed method, a specialized measuring device is developed, and measurement verification is made with the optical profilometer.