Optical diffractometry by rough phase steps

Optical diffractometry (OD) using a phase step is an alternative for interferometry, further, has least sensitivity to environmental vibrations. Therefore, OD has found numerous interesting metrological and technological applications. OD utilizes a phase step to detect the influence of objects under measurement by the changes in the Fresnel diffraction pattern. Recently, we showed that such measurements do not require infinitively sharp phase steps, although fabrication of such sharp elements is also impossible. Here, we address the issue of smoothness of the phase step surfaces. So far, in all of the OD applications the surfaces of the incorporated phase steps are considered to be optically smooth and flat. However, practically, some amount of roughness and unflatness is unavoidable even in precise and careful fabrication process. We show that preserving the OD-diffraction-pattern characteristics of a phase step depends on the level of roughness in the surfaces of the phase step. We define number of detectable fringes and autocorrelation functions of the diffraction patterns as the measures for evaluating the similarity of the rough phase step diffractions to the ideal case. We derive the theoretical description and confirm the results with simulations and experiments.