An iterative algorithm for calculating stylus radius unambiguously

The stylus radius is an important specification for stylus instruments and is commonly provided by instrument manufacturers. However, it is difficult to measure the stylus radius unambiguously. Accurate profiles of the stylus tip may be obtained by profiling over an object sharper than itself, such as a razor blade. However, the stylus profile thus obtained is a partial arc, and unless the shape of the stylus tip is a perfect sphere or circle, the effective value of the radius depends on the length of the tip profile over which the radius is determined. We have developed an iterative, least squares algorithm aimed to determine the effective least squares stylus radius unambiguously. So far, the algorithm converges to reasonable results for the least squares stylus radius. We suggest that the algorithm be considered for adoption in documentary standards describing the properties of stylus instruments.