Provided is a method for measuring multi-point interferometric angle changes beginning with an interferometric device capable of measuring at least one main point and at least one reference point. The method includes recording interferometric intensity changes on two or more spots using the main point and the reference point, and determining a sequence having a plurality of peak, local maximas and a plurality of valley, local minimas. The method includes sampling a first, partial sequence and comparing it to a neighboring, partial sequence using a perturbation analysis and additional calculation(s) to compile all phase angle changes for all measured points. Also provided is a computer implemented method to enable nanometer resolution sensitivity in a noisy signal and for characterization of a material in an interferometric device.