The Binary Residual Map and Gradient Binary Residual Map as Convenient, Qualitative, Information‐Dense, Graphical Tools for Understanding Spectral Analysis, Including in X‐Ray Photoelectron Spectroscopy

ABSTRACT We present the binary residual map (BRM) as a convenient, qualitative, information‐rich representation of multiple fits or analyses in data analysis. The BRM focuses on and retains the signs of the residuals, not necessarily their magnitudes, where these residuals are color coded with one color selected for positive residuals and another for negative residuals. To form a BRM, color‐coded residuals from multiple fits obtained with multiple fit parameter values are stacked/displayed as a function of the fit parameter value. Importantly, when a series of residual values in a fit are either all positive or all negative, the color‐coded residuals appear as a colored block or run. In general, longer runs indicate poorer fitting. The BRM contains an enormous amount of information in a small space. Accordingly, it can be used to quickly identify where the values of a fit produce better or worse fits. In a qualitative way, it guides the selection of fit parameters. Gradient BRMs that take into account the magnitude of the residuals can also be created. We demonstrate the creation of BRMs and/or gradient BRMs from the Fourier denoising of X‐ray photoelectron spectroscopy (XPS) spectra using a Gauss–Hermite (GH) filter function positioned at a series of different cutoff frequencies in reciprocal space, fits to carbon Auger XPS spectra with polynomials of different orders, and XPS peak fitting. BRMs should also be useful for evaluating the fits of other types of data (not just XPS data).