Parameterless detection of liquid–liquid interfaces with sub-micron resolution in single-molecule localization microscopy

Hypothesis: Knowing the exact location of soft interfaces, such as between water and oil, is essential to the study of nanoscale wetting phenomena. Recently, iPAINT was used to visualize soft interfaces in situ with minimal invasiveness, but computing the exact location of the interface remains challenging. We propose a new method to determine the interface with high accuracy. By modelling the localizations as points generated by two homogeneous Poisson processes, the exact location of the interface can be determined using a maximum likelihood estimator (MLE). Experiments: An MLE was constructed to estimate the location of the interface based on the discontinuity in localization density at the interface. To test the MLE, we collected experimental data through iPAINT experiments of oil–water interfaces and generated simulated data using the Monte Carlo method. Findings: Simulations show that the interface given by the MLE rapidly converges to the true interface location. The error of the MLE drops below the experimental localization precision. Furthermore, we show that the MLE remains accurate even if the field-of-view is reduced or when one or more particles are on the interface within the field-of-view. This work provides a key step towards the in situ, sub-micron characterization of (nanoparticle-laden) interfaces with minimal invasiveness.