Error analysis in digital processing of the results of interferometric control of nano-scale local deviations of optical surfaces

A dynamic interferometry method for controlling nano-scale local deviations of optical surfaces from a prescribed profile is developed, theoretically substantiated, and experimentally verified on the basis of an algorithm for calculating an objective function, defined as the spectral density of a one-dimensional correlation function. Theoretical and experimental approaches to determining the root-mean-square error when finding local deviations of the optical surfaces for the element diameters ranging from 100 mm to 1,000 mm are presented, while taking into account the non-excluded systematic and random error components in determining the objective function.