Axial scanning is inherent to optical profilometers, which sample a signal and infer the object height as the location of its maximum. Imaging confocal, interferometric or focus variation methods, are common example technologies for acquiring such signal. Of course, in these approaches, the precision and accuracy of any measurement is directly affected by those of the scanning system, usually based on piezo scanners or motorized linear stages. The latter provide an inexpensive solution but are subject to non-linearities between the commanded and executed positioning, yielding pseudo-random errors, which in practice limit the precision and accuracy of the measurement. We propose a computational method to correct such non-linearities on a measurement using data from the very same scan, therefore providing a zero-cost solution to increase the precision of profilometers employing motorized linear stages. The method is based on the reconstruction of two topographies that are axially shifted by a known amount. Assuming that the two topographies are identical, differences between these two topographies reflect only the errors of the positioning system. Our algorithm predicts and corrects the non-linearity errors by iteratively analyzing the differences in the topographies. Here, we explore two methods for obtaining the topography pair: by performing two scans, and by localizing two axially shifted features of the axial response from a single scan. To validate the technique, we measured a variety of samples including step heights and compared the results against the piezo-measured counterparts, obtaining equivalent performance.
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