Systems and methods for phase-shift interferometry utilizing logarithmized probability density fit of phase shift interference data

A computer-implemented method for analyzing a sample, the computer-implemented method implemented by a computing device including at least one processor in communication with at least one memory device, the method comprising:

• receiving scan data of a sample to be analyzed for phase shift interferometry (PSI), wherein the scan data includes a plurality of images of the sample, wherein each image includes a plurality of pixels;
• for each pixel of the plurality of pixels, generating a sequence of interferences for a corresponding pixel of the plurality of pixels;
• for each pixel of the plurality of pixels, generating a wave form from the sequence of interferences for the corresponding pixel;
• for each pixel of the plurality of pixels, generating an approximated waveform based on the wave form and a non-normal distributed statistical distribution;
• for each pixel of the plurality of pixels, extracting a phase from the approximated waveform;
• and
• generating a phase image from the plurality of phases from each pixel of the plurality of pixels.