Algorithm of surface relief retrieval at arbitrary phase shift between interferograms

Abstract

Improved algorithm for processing of interferograms obtained by a single arbitrary phase shift of the reference beam is proposed to reproduce the surface relief (SR). The advanced algorithm makes it possible to reproduce not only the relief of smooth or nanorough surfaces, but also its separate components, thus macrorelief (waviness) and nanorelief (roughness). Computer modulation of this algorithm was used to analyze the errors of complete SR and its components reproduction. The analysis allowed us to identify two factors that significantly affect the errors of the SR components determining by this algorithm. First, it turned out that the error of SR reproduction as the sum of macro- and nanoreliefs is much smaller than errors of these components reproduction, because the correlation coefficient between the errors fields of these components reproduction is close to 0,9. Therefore, it is better to extract the macrorelief phase map by filtering from the expanded (decyclized) SR phase map than from the collapsed (cyclic) one, which is possible by introducing the second iteration of SR recovery into the algorithm, which significantly reduces the errors. The second factor is related to boundary effects, which are observed during use of Fast Fourier transform (FFT) and spatial filtering to determine the macrorelief phase map and which increase its reproduction error. For this reason, it is proposed to eliminate the influence of boundary effects. The obtained dependences of the relief and its components reproduction errors from the test surfaces roughness for the advanced processing algorithm indicate a significant errors reduction comparing to the corresponding dependences for its previous version. These dependences are the theoretical limit for SR and its components reproduction errors in the case of using the advanced algorithm for interferograms processing.