Measuring and Analyzing Cross-Sectional Profiles of Rotating Objects Using Light Sectioning

This paper presents the instrumentation and analysis methods for the measurement of cross-sectional profiles. The object is rotated in front of a light-sectioning system, which repeatedly measures the local geometry. A least-mean-square approximation of the local geometry by a circle is performed. The radius of the circle is used as an estimate for the radius of curvature, and the position of the upper horizontal tangent to the circle is used to estimate the position of the object. It is shown that the tangent position is a more accurate measure of position than the center of the circle. The period of revolution is determined from the aperiodic autocorrelation sequence of the eccentricity of the object. The curve corresponding to the profile of the object is a smooth Jordan curve: This fact is used to take advantage of harmonic filtering to suppress noise and perturbations and to reconstruct the curve from the measured radii of curvature. The implementation of the “curve from curvature” algorithm in Matlab is presented. Diameter deviations of the curve are analyzed by simulating a caliper measurement. The periodicity of the curvature is used as a measure to firmly detect curves of constant width. A least-square approximation of curves of constant width using elliptical Fourier descriptors is presented. All methods are demonstrated with real data from industrial measurements.