Fundamental Bounds for Off-Axis Illumination in Interferometric and Rotating Coherent Scattering Microscopy

Abstract: Coherent localization microscopy enables three-dimensional localization with nanoscale precision. Previous studies have characterized the fundamental precision limits for on-axis illumination geometries. In this paper, we theoretically analyze 3D particle localization precision under oblique illumination in interferometric scattering microscopy (iSCAT). We show that (quantum) Cramer-Rao bounds reveal an information gain in the off-axis case, potentially enabling enhanced localization precision. We find that rotating coherent scattering microscopy (ROCS), which employs off-axis illumination, provides worse localization precision than \iscat, despite offering higher spatial resolution. This shows that key metrics, like spatial resolution, are often insufficient to fully characterize a microscopy technique.