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Interferometric scattering microscopy can image the dynamics of nanometer-scale systems. The typical approach to analyzing interferometric images involves intensive processing, which discards data and limits the precision of measurements. We demonstrate an alternative approach: modeling the interferometric point spread function and fitting this model to data within a Bayesian framework. This approach yields best-fit parameters, including the particle’s three-dimensional position and polarizability, as well as uncertainties and correlations between these parameters. Building on recent work, we develop a model that is parameterized for rapid fitting. The model is designed to work with Hamiltonian Monte Carlo techniques that leverage automatic differentiation. We validate this approach by fitting the model to interferometric images of colloidal nanoparticles. We apply the method to track a diffusing particle in three dimensions, to directly infer the diffusion coefficient of a nanoparticle without calculating a mean-square displacement, and to quantify the ejection of DNA from an individual lambda phage virus, demonstrating that the approach can be used to infer both static and dynamic properties of nanoscale systems.

Holographic microscopy combined with forward modeling and inference allows colloidal particles to be characterized and tracked in three dimensions with high precision. However, current models ignore the effects of optical aberrations on hologram formation. We investigate the effects of spherical aberration on the structure of single-particle holograms and on the accuracy of particle characterization. We find that in a typical experimental setup, spherical aberration can result in systematic shifts of about 2% in the inferred refractive index and radius. We show that fitting with a model that accounts for spherical aberration decreases this aberration-dependent error by a factor of two or more, even when the level of spherical aberration in the optical train is unknown. With the new generative model, the inferred parameters are consistent across different levels of aberration, making particle characterization more robust.

Holographic microscopy has developed into a powerful tool for 3D particle tracking, yielding nanometer-scale precision at high frame rates. However, current particle tracking algorithms ignore the effect of the microscope objective on the formation of the recorded hologram. As a result, particle tracking in holographic microscopy is currently limited to particles well above the microscope focus. Here, we show that modeling the effect of an aberration-free lens allows tracking of particles above, near, and below the focal plane in holographic microscopy, doubling the depth of field. Finally, we use our model to determine the conditions under which ignoring the effect of the lens is justified and in what conditions it leads to systematic errors.

The discipline of hydrology has long focused on quantifying the water balance, which is frequently used to estimate unknown water fluxes or stores. While technologies for measuring water balance components continue to improve, all components of the balance have substantial uncertainty at the watershed scale. Watershed‐scale evapotranspiration, storage, and groundwater import or export are particularly difficult to measure. Given these uncertainties, analyses based on assumed water balance closure are highly sensitive to uncertainty propagation and errors of omission, where unknown components are assumed negligible. This commentary examines how greater insight may be gained in some cases by keeping the water balance open rather than applying methods that impose water balance closure. An open water balance can facilitate identifying where unknowns such as groundwater import/export are affecting watershed‐scale streamflow. Strategic improvements in monitoring networks can help reduce uncertainties in observable variables and improve our ability to quantify unknown parts of the water balance. Improvements may include greater spatial overlap between measurements of water balance components through coordination between entities responsible for monitoring precipitation, snow, evapotranspiration, groundwater, and streamflow. Measuring quasi‐replicate watersheds can help characterize the range of variability in the water balance, and nested measurements within watersheds can reveal areas of net groundwater import or export. Well‐planned monitoring networks can facilitate progress on critical hydrologic questions about how much water becomes evapotranspiration, how groundwater interacts with surface watersheds at varying spatial and temporal scales, how much humans have altered the water cycle, and how streamflow will respond to future climate change.