ANALYTICAL RESOLUTION OF LEAST-SQUARES APPLICATIONS FOR THE CIRCLE ININTERFEROMETRY AND RADIOMETRY

A new least-squares method for the circle using a set of coordinate da ta (x(i), y(i)) is presented. This method provides analytical expressi ons for the coordinates ((X) over cap(0), (Y) over cap(0)) of the cent ral point of a circle and its radius (R) over cap(0). Expressions for the variances V((X) over cap)(0), V((Y) over cap)(0) and V((R) over ca p(0)), and the covariances cov((X) over cap(0), (Y) over cap(0)), cov( (X) over cap(0), (R) over cap(0)) and cov((Y) over cap(0)(R) over cap( 0)) are also presented. The method is applied to two problems, one in interferometry and the other in radiometry.