Existing electroanalytical techniques used to measure the state of charge of battery electrodes are a mere approximation. Conventional methods assume a one-to-one correspondence between electrons transferred and guest ions inserted into the host cathode material. Competing electrochemical processes which consume electrons — solid electrolyte interface formation, parasitic redox reactions, lithium plating, etc. — bypass the intended ion insertion. This systematic violation negates the one-to-one assumption leading to progressively inaccurate state of charge measurements. Through extraction of the complex polarizability of individual nano-particles and thin films Quantitative Scattering Microscopy (QSCAT), a differential phase contrast-based optical microscopy technique, enables quantification of guest ions within a cathode host independent of electron transfer. Relative guest-ion concentrations in a host lattice proportionally alter the refractive index which encodes an optical phase shift (∆𝜙) in the backscattered light. QSCAT provides a non-destructive, label-free, and electro-chemically independent readout, stemming from a direct proportionality relating ∆𝜙 to the spatial distribution of Re(𝛼) and Im(𝛼). Acts one and two introduce, apply, and validate the optical framework enabling quantitative extraction of ∆𝜙 through determination of the physical height of chromium features on a USAF 1951 resolution test target with 98.7% agreement against atomic force microscopy. Act three demonstrates the deployment of QSCAT, including current sensitivity limitations and the way forward, towards optical de-termination of gold nanoparticles solely from the extracted complex polarizabilities. Act four details the quantitative characterization of two host-guest model systems — Nile Red-loaded polystyrene beads and Er-doped NaYF4 nanocrystals) through gold-standard analytical techniques establishing ground truth to benchmark projected QSCAT performance. Together these results establish QSCAT as a quantitative optical platform for guest-host materials characterization, with a path towards operando single-particle imaging in electrochemical energy storage systems where the electroanalytical assumption breaks down.

