Using the power spectral density method to characterise the surface topography of optical surfaces

Power Spectral Density (PSD) is an alternative method for specifying optical surfaces, and quantifies the contribution of each spatial regime to the total surface error. This approach naturally includes mid-range spatial frequency errors, which are often overlooked. The PSD method has recently been adopted by the Space and Astronomy industries, but has not yet received general acceptance within the synchrotron community. To assess the suitability for specifying synchrotron optics using PSD, Fast Fourier Transforms were performed on topography data from a range of optical surfaces of varying quality and manufacturing techniques. For each grade of optic, the entire regime (~100nm to ~50mm) of surface errors was measured, with overlapping bandwidths, using a micro-interferometer and a Fizeau interferometer. From this heuristic information, root-mean square "roughness" can be predicted over any desired spatial range, thus allowing direct comparison of metrology data obtained by instruments with different spatial bandwidths. We present an efficient approach for calculating 1-D and 2-D PSDs using MATLAB algorithms, and discuss analysis considerations, including "field of view" effects and instrument calibration.

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