  Interferometric imaging is an emerging technique for particle tracking and
mass photometry. Mass or position are estimated from weak signals, coherently
scattered from nanoparticles or single molecules, and interfered with a
co-propagating reference. In this work, we perform a statistical analysis and
derive lower bounds on the measurement precision of the parameters of interest
from shot-noise limited images. This is done by computing the classical
Cram\'er-Rao bound for localization and mass estimation, using a precise
vectorial model of interferometric imaging techniques. We then derive
fundamental bounds valid for any imaging system, based on the quantum
Cram\'er-Rao formalism. This approach enables a rigorous and quantitative
comparison of common techniques such as interferometric scattering microscopy
(iSCAT), Coherent Brightfield microscopy (COBRI), and dark-field microscopy. In
particular, we demonstrate that the light collection geometry in iSCAT greatly
increases the axial position sensitivity, and that the Quantum Cram\'er-Rao
bound for mass estimation yields a minimum relative estimation error of
$\sigma_m/m=1/(2\sqrt{N})$, where $N$ is the number of collected scattered
photons.
