The case for denoising/smoothing X-ray photoelectron spectroscopy data by Fourier analysis

Traditionally, the smoothing of X-ray photoelectron spectroscopy (XPS) data has been avoided. Data smoothing should not be viewed as a means of “fixing” poorly collected or extremely noisy XPS data. However, it is not always possible or desirable to acquire high-quality data. Here, we suggest that, under appropriate circumstances, and with good algorithms, it may be appropriate to denoise XPS spectra. In particular, we propose the Fourier denoising of XPS data. Fourier analysis is commonly used in science and engineering. Fourier analysis of spectra is advantageous because it naturally divides the data into signal- and noise-dominated coefficients in reciprocal space. Accordingly, Fourier analysis has long been used to reduce or remove the high frequencies (noise) from data, leaving the lower frequencies (signal and baseline trends). We provide an overview of the Fourier transform. The Gauss-Hermite Fourier filter employed in this study shows improvements over the commonly used boxcar and Savitzky-Golay smooths, and also over other apodization approaches used in Fourier analysis, e.g., boxcar apodization. The Gauss-Hermite filter avoids sharp cutoffs that can introduce significant artifacts into data. The Fourier denoising/reconstruction of two XPS narrow scans, an Auger signal, and a valence band signal is demonstrated. Filtered spectra are compared to corresponding “true” spectra, that are obtained by signal averaging. Spectra denoised through the Gauss-Hermite filter can be more accurate approximations to the “true” spectra than the original noisy spectra.