plane of the wafer see fig3 the robot 10 selects an arbitrary radial position with cartesian coordinates u v which is to be considered as a possible candidate for the best center for the n detected radial positions of the wafer the distance rn from u v to the nth given point xn yn is determined by the pythagorean equation the square sn of the distance rn is then determined by the following equation equation 3 is then expanded to put it into the form equation 4 is summed over n from n 1 to n n and the result is divided by n to effectively average each term in the equation over n this yields the result equ1 each of the five indicated averages that involve summations in the above equation are determined by the given coordinate data xn and yn so the above averages are given convenient abbreviations to clean up the appearance of the equation the abbreviations to be used are as follows equ2 this gives the means square distance s of the n detected radial positions of the wafer from the arbitrarily chosen point u v additional similar abbreviations to be used below are equ3 equation 11 is subtracted from equation 4 to evaluate the deviation of sn from the mean square distance s for all of the sn values equation 17 is then squared to compute the square of the deviation sn.