Precision Measurements of Colloidal Dynamics with Holographic Microscopy

Abstract

To build a holographic microscope, take a standard optical microscope and illuminate the sample with a coherent light source like a laser. Light scattered by the specimen interferes with the transmitted beam, producing an interference pattern called a hologram, a two-dimensional image that encodes three-dimensional information about the sample. While holograms are typically interpreted through reconstruction, recent advances in computational methods have enabled a new approach: extracting information directly from holograms using generative modeling. The combination of holographic microscopy and model-based analysis is well suited to applications where precise, quantitative results are needed with high acquisition speed, including characterizing colloidal dispersions, following the motion of microscopic objects in three dimensions, or measuring colloidal interactions.

I overview methods and applications of generative modeling to holographic microscopy. I then consider the application of those methods to understanding colloidal suspensions, micrometer-scale particles suspended in fluids. With holographic microscopy, we can characterize and track colloidal particles in three dimensions with high precision. However, the accuracy of particle tracking and characterization depends on how well we model hologram formation. I investigate the effects of spherical aberration on the structure of single-particle holograms and on the accuracy of particle characterization. I show that fitting a model that accounts for spherical aberration decreases aberration-dependent error, even when the spherical aberration in the optical train is unknown. With this new generative model, the inferred parameters are consistent across different levels of aberration, making particle characterization more robust.

Finally, I use holographic microscopy and generative modeling to characterize short-ranged colloid interactions. Understanding the interactions between colloidal particles is essential for predicting and controlling colloidal self-assembly, but methods to characterize these interactions can be limited to observing highly constrained particles. Moreover, these methods can face issues with precision due to multiple scattering between particles and out-of-plane fluctuations. I demonstrate an alternative method to infer particle potentials from holographic data. This method rigorously accounts for scattering effects, works in three dimensions, and does not require the particles to be trapped in an optical potential. With this method, I precisely track pairs of freely-diffusing spheres in three dimensions and at high frame rates. I show that by using Bayesian inference, we can measure separation distances as small as a few nanometers between micrometer scale particles to nanometer-scale precision. From these precise measurements of gap distances, I quantify the short-ranged forces acting on the colloidal particles with model-free and model-based methods. I characterize a range of depletion-driven particle interactions with varying particle size and depletant concentration, and precisely quantify the well curvature about the potential minimum.