Using the SHG amplitude and phase we estimate the total interfacial potential, Φ(0) !"! , and the second-order nonlinear susceptibility, c (2) . Using air as opposed to electrolyte, we first obtain the absolute zero phase from the uncoated portion of a glass microscope slide having one half coated with 10 nm nickel and then move the sample cell over by a few millimeters to determine the phase difference of the glass:air vs nickel:air interface to be = -76° ± 19° (standard deviation obtained from Gaussian histogram analysis of 15 electrodes, please see Supplementary Information Methods and Fig. ). We then add electrolyte, determine the phase difference of the nickel:air vs nickel:electrolyte interface to be 4° ± 18°, and obtain the point estimates (and associated uncertainties) for the SHG signal phase, jsig , at a given applied potential, F, from jsig = jfit,Fjfit,OCP -(76° ± 19°). We then normalize the SHG amplitude to the amplitude obtained at OCP. Fig. shows that jsig decreases with increasing applied potential in a sigmoidal fashion, with a total phase change relative to OCP of -90° at +0.9V applied. On the reverse scan, the phase advances back to 0°. The amplitude goes through minima at the applied potentials that coincide with the SHG intensity minima seen in Fig. . The experiment reproduces reasonably well over seven different electrodes (Supplementary Fig. ). We calibrate the SHG response from our Speelman and Geiger page 5 optical window against the second-order nonlinear susceptibility of another z-cut a-quartz piece put in place of the electrolyte solution , accounting for the normalization factor at OCP, the Fresnel coefficients, and the wave vector mismatch in our experimental geometry (please see Supplementary Information Fig. and Note S3). We then expand an optical model for quantifying Φ(0) !"! and c (2) from the SHG amplitude and phase measured at silica:water interfaces for high ionic strength to include the metal-specific contributions to the secondorder nonlinear susceptibility discussed earlier by Guyot-Sionnest et al. (for Ag) and Nagy and Roy (for Ni) . We obtain the following expression for the total potential drop across the electrode:electrolyte interface (see Supplementary Information Note S4):