Binary pseudo-random gratings and arrays for calibration of modulation transfer functions of surface profilometers

Abstract

A technique for precise measurement of the modulation transfer function (MTF), suitable for characterization of a broad class of surface profilometers, is investigated in detail. The technique suggested in papers Yashchuk et al. (2007) [26], Yashchuk et al. (2008) [25] is based on use of binary pseudo-random (BPR) gratings and arrays as standard MTF test surfaces. Unlike most conventional test surfaces, BPR gratings and arrays possess white-noise-like inherent power spectral densities (PSD), allowing the direct determination of the one- and two-dimensional MTF, respectively, with a sensitivity uniform over the entire spatial frequency range of a profiler. In the cited work, a one-dimensional realization of the suggested method based on use of BPR gratings has been demonstrated. Here, a high performance of the MTF calibration technique is demonstrated via cross comparison measurements of a number of two-dimensional BPR arrays using two different interferometric microscopes and a scatterometer. We also present the results of application of the experimentally determined MTF correction to the measurement taken with the Micromap™-570 interferometric microscope of the surface roughness of a super-polished test mirror. In this particular case, without accounting for the instrumental MTF, the surface rms roughness over half of the instrumental spatial frequency bandwidth would be underestimated by a factor of approximately 1.4.