Topography restoration in white-light interferometry using an instrument transfer function evaluated with binary pseudo-random arrays

Accurate knowledge of the instrument transfer function (ITF) is vital for topography measurements using white-light interferometry (WLI). To this end, we derive a complete set of analytical expressions for the power spectral density (PSD) of a discretely sampled binary pseudo-random array (BPRA) as a theoretical benchmark. We then determine the ITF by comparing this theoretical PSD with the measured PSD of the BPRA. For the Zygo ZeGage Pro HR with a 50× objective, the determined ITF closely matches the nominal modulation transfer function (MTF). Accordingly, we integrate the nominal MTF into Fourier-domain restoration filters and apply them to practical WLI topography data, yielding restored topographies that show improved agreement with atomic force microscopy measurements. Overall, our integrated BPRA-based ITF measurement and filtering methodology offers a robust yet practical means of characterizing WLI performance and enhancing the accuracy of surface measurements.