Analytical resolution of least-squares applications for the circle in interferometry and radiometry

摘要

A new least-squares method for the circle using a set of coordinate data (x↓(i),Y↓(i)) is presented. This method provides analytical expressions for the coordinates (#(0), #(0)) of the central point of a circle and its radius R0. Expressions for the variances V(#↓(0)), V(#↓(0)) and V(#↓(0)), and the covariances cov(#↓(0), #↓(0)), cov(#(0), #↓(0)) and cov(#↓(0), #↓(0)) are also presented. The method is applied to two problems, one in interferometry and the other in radiometry.