Estimation of the accuracy of a reflector surface from the measured rms error

The statistical estimation of the surface accuracy from measured data affected by random normal uncertainties due to the three-dimensional measuring equipment is determined to a given confidence level on the base of a normal approximation of the probability distribution of the measured mean-square error. The exact distribution is used to set a lower limit on the number of measured points for the above approximation to hold. The presented analysis has been developed for application to the panels of the Atacama Large Millimeter Array (ALMA) European prototype antenna.