Measuring colloidomer hydrodynamics with holographic video microscopy.

In-line holographic video microscopy records a wealth of information about the microscopic structure and dynamics of colloidal materials. Powerful analytical techniques are available to retrieve that information when the colloidal particles are well separated. Large assemblies of close-packed particles create holograms that are substantially more challenging to interpret. We demonstrate that Rayleigh-Sommerfeld back propagation is useful for analyzing holograms of colloidomer chains, close-packed linear assemblies of micrometer-scale emulsion droplets. Colloidomers are fully flexible chains and undergo three-dimensional configurational changes under the combined influence of random thermal forces and hydrodynamic forces. We demonstrate the ability of holographic reconstruction to track these changes as colloidomers sediment through water in a horizontal slit pore. Comparing holographically measured configurational trajectories with predictions of hydrodynamic models both validates the analytical technique for this valuable class of self-organizing materials and also provides insights into the influence of geometric confinement on colloidomer hydrodynamics.

Spectral holographic trapping: Creating dynamic force landscapes with polyphonic waves.

Acoustic trapping uses forces exerted by sound waves to transport small objects along specified trajectories in three dimensions. The structure of the time-averaged acoustic force landscape acting on an object is determined by the amplitude and phase profiles of the sound's pressure wave. These profiles typically are sculpted by deliberately selecting the amplitude and relative phase of the sound projected by each transducer in large arrays of transducers, all operating at the same carrier frequency. This approach leverages a powerful analogy with holographic optical trapping at the cost of considerable technical complexity. Acoustic force fields also can be shaped by the spectral content of the component sound waves in a manner that is not feasible with light. The same theoretical framework that predicts the time-averaged structure of monotone acoustic force landscapes can be applied to spectrally rich sound fields in the quasistatic approximation, creating opportunities for dexterous control using comparatively simple hardware. We demonstrate this approach to spectral holographic acoustic trapping by projecting acoustic conveyor beams that move millimeter-scale objects along prescribed paths. Spectral control of reflections provides yet another opportunity for controlling the structure and dynamics of an acoustic force landscape. We use this approach to realize two variations on the theme of a wave-driven oscillator, a deceptively simple dynamical system with surprisingly complex phenomenology.

Refractive-index and density-matched emulsions with programmable DNA interactions.

Emulsion droplets on the colloidal length scale are a model system of frictionless compliant spheres. Direct imaging studies of the microscopic structure and dynamics of emulsions offer valuable insights into fundamental processes, such as gelation, jamming, and self-assembly. A microscope, however, can only resolve the individual droplets in a densely packed emulsion if the droplets are closely index-matched to their fluid medium. Mitigating perturbations due to gravity additionally requires the droplets to be density-matched to the medium. Creating droplets that are simultaneously index-matched and density-matched has been a long-standing challenge for the soft-matter community. The present study introduces a method for synthesizing monodisperse micrometer-sized siloxane droplets whose density and refractive index can be precisely and independently tuned by adjusting the volume fraction of three silane precursors. A systematic optimization protocol yields fluorescently labeled ternary droplets whose densities and refractive indexes match, to the fourth decimal place, those of aqueous solutions of glycerol or dimethylsiloxane. Because all of the materials in this system are biocompatible, we functionalize the droplets with DNA strands to endow them with programmed inter-droplet interactions. Confocal microscopy then reveals both the three-dimensional structure and the network of droplet-droplet contacts in a class of self-assembled droplet gels, free from gravitational effects. This experimental toolbox creates opportunities for studying the microscopic mechanisms that govern viscoelastic properties and self-assembly in soft materials.

Aberration compensation for enhanced holographic particle characterization.

Holographic particle characterization treats holographic microscopy of colloidal particles as an inverse problem whose solution yields the diameter, refractive index and three-dimensional position of each particle in the field of view, all with exquisite precision. This rich source of information on the composition and dynamics of colloidal dispersions has created new opportunities for fundamental research in soft-matter physics, statistical physics and physical chemistry, and has been adopted for product development, quality assurance and process control in industrial applications. Aberrations introduced by real-world imaging conditions, however, can degrade performance by causing systematic and correlated errors in the estimated parameters. We identify a previously overlooked source of spherical aberration as a significant source of these errors. Modeling aberration-induced distortions with an operator-based formalism identifies a spatially varying phase factor that approximately compensates for spherical aberration in recorded holograms. Measurements on model colloidal dispersions demonstrate that phase-only aberration compensation greatly improves the accuracy of holographic particle characterization without significantly affecting measurement speed for high-throughput applications.

Anomalous tumbling of colloidal ellipsoids in Poiseuille flows.

Shear flows cause aspherical colloidal particles to tumble so that their orientations trace out complex trajectories known as Jeffery orbits. The Jeffery orbit of a prolate ellipsoid is predicted to align the particle's principal axis preferentially in the plane transverse to the axis of shear. Holographic microscopy measurements reveal instead that colloidal ellipsoids' trajectories in Poiseuille flows strongly favor an orientation inclined by roughly π/8 relative to this plane. This anomalous observation is consistent with at least two previous reports of colloidal rods and dimers of colloidal spheres in Poiseuille flow and therefore appears to be a generic, yet unexplained feature of colloidal transport at low Reynolds numbers.

Machine learning enables precise holographic characterization of colloidal materials in real time.

Holographic particle characterization uses in-line holographic video microscopy to track and characterize individual colloidal particles dispersed in their native fluid media. Applications range from fundamental research in statistical physics to product development in biopharmaceuticals and medical diagnostic testing. The information encoded in a hologram can be extracted by fitting to a generative model based on the Lorenz-Mie theory of light scattering. Treating hologram analysis as a high-dimensional inverse problem has been exceptionally successful, with conventional optimization algorithms yielding nanometer precision for a typical particle's position and part-per-thousand precision for its size and index of refraction. Machine learning previously has been used to automate holographic particle characterization by detecting features of interest in multi-particle holograms and estimating the particles' positions and properties for subsequent refinement. This study presents an updated end-to-end neural-network solution called CATCH (Characterizing and Tracking Colloids Holographically) whose predictions are fast, precise, and accurate enough for many real-world high-throughput applications and can reliably bootstrap conventional optimization algorithms for the most demanding applications. The ability of CATCH to learn a representation of Lorenz-Mie theory that fits within a diminutive 200 kB hints at the possibility of developing a greatly simplified formulation of light scattering by small objects.

Acoustodynamic mass determination: Accounting for inertial effects in acoustic levitation of granular materials.

Acoustic traps use forces exerted by sound waves to confine and transport small objects. The dynamics of an object moving in the force landscape of an acoustic trap can be significantly influenced by the inertia of the surrounding fluid medium. These inertial effects can be observed by setting a trapped object in oscillation and tracking it as it relaxes back to mechanical equilibrium in its trap. Large deviations from Stokesian dynamics during this process can be explained quantitatively by accounting for boundary-layer effects in the fluid. The measured oscillations of a perturbed particle then can be used not only to calibrate the trap but also to characterize the particle.

Holographic analysis of colloidal spheres sedimenting in horizontal slit pores.

The mobility of a colloidal particle in a slit pore is modified by the particle's hydrodynamic coupling to the bounding surfaces and therefore depends on the particle's position within the pore and its direction of motion. We report holographic particle tracking measurements of colloidal particles' diffusion and sedimentation between parallel horizontal walls that yield the mobility for motions perpendicular to the walls, including its dependence on height within the channel. These measurements complement previous studies that probed colloidal mobility parallel to confining surfaces. When interpreted with effective-medium theory, holographic characterization measurements yield estimates for the sedimenting spheres' densities that can be compared with kinematic values to draw insights into the spheres' compositions. This comparison suggests, for example, that the silica spheres used in this study are slightly porous, but that their pores are too small for water to penetrate.

Dexterous holographic trapping of dark-seeking particles with Zernike holograms.

The intensity distribution of a holographically-projected optical trap can be tailored to the physical properties of the particles it is intended to trap. Dynamic optimization is especially desirable for manipulating dark-seeking particles that are repelled by conventional optical tweezers, and even more so when dark-seeking particles coexist in the same system as light-seeking particles. We address the need for dexterous manipulation of dark-seeking particles by introducing a class of "dark" traps created from the superposition of two out-of-phase Gaussian modes with different waist diameters. Interference in the difference-of-Gaussians (DoG) trap creates a dark central core that is completely surrounded by light and therefore can trap dark-seeking particles rigidly in three dimensions. DoG traps can be combined with conventional optical tweezers and other types of traps for use in heterogeneous samples. The ideal hologram for a DoG trap being purely real-valued, we introduce a general method based on the Zernike phase-contrast principle to project real-valued holograms with the phase-only diffractive optical elements used in standard holographic optical trapping systems. We demonstrate the capabilities of DoG traps (and Zernike holograms) through experimental studies on high-index, low-index and absorbing colloidal particles dispersed in fluid media.

Multi-angle holographic characterization of individual fractal aggregates.

Holographic particle characterization uses quantitative analysis of holographic microscopy data to precisely and rapidly measure the diameter and refractive index of individual colloidal spheres in their native media. When this technique is applied to inhomogeneous or aspherical particles, the measured diameter and refractive index represent properties of an effective sphere enclosing each particle. Effective-sphere analysis has been applied successfully to populations of fractal aggregates, yielding an overall fractal dimension for the population as a whole. Here, we demonstrate that holographic characterization also can measure the fractal dimensions of an individual fractal cluster by probing how its effective diameter and refractive index change as it undergoes rotational diffusion. This procedure probes the structure of a cluster from multiple angles and thus constitutes a form of tomography. Here we demonstrate and validate this effective-sphere interpretation of aspherical particles' holograms through experimental studies on aggregates of silica nanoparticles grown under a range of conditions.

An Interlaboratory Comparison on the Characterization of a Sub-micrometer Polydisperse Particle Dispersion.

The measurement of polydisperse protein aggregates and particles in biotherapeutics remains a challenge, especially for particles with diameters of ≈ 1 µm and below (sub-micrometer). This paper describes an interlaboratory comparison with the goal of assessing the measurement variability for the characterization of a sub-micrometer polydisperse particle dispersion composed of five sub-populations of poly(methyl methacrylate) (PMMA) and silica beads. The study included 20 participating laboratories from industry, academia, and government, and a variety of state-of-the-art particle-counting instruments. The received datasets were organized by instrument class to enable comparison of intralaboratory and interlaboratory performance. The main findings included high variability between datasets from different laboratories, with coefficients of variation from 13 % to 189 %. Intralaboratory variability was, on average, 37 % of the interlaboratory variability for an instrument class and particle sub-population. Drop-offs at either end of the size range and poor agreement on maximum counts of particle sub-populations were noted. The mean distributions from an instrument class, however, showed the size-coverage range for that class. The study shows that a polydisperse sample can be used to assess performance capabilities of an instrument set-up (including hardware, software, and user settings) and provides guidance for the development of polydisperse reference materials.

Holographic characterization and tracking of colloidal dimers in the effective-sphere approximation.

An in-line hologram of a colloidal sphere can be analyzed with the Lorenz-Mie theory of light scattering to measure the sphere's three-dimensional position with nanometer-scale precision while also measuring its diameter and refractive index with part-per-thousand precision. Applying the same technique to aspherical or inhomogeneous particles yields measurements of the position, diameter and refractive index of an effective sphere that represents an average over the particle's geometry and composition. This effective-sphere interpretation has been applied successfully to porous, dimpled and coated spheres, as well as to fractal clusters of nanoparticles, all of whose inhomogeneities appear on length scales smaller than the wavelength of light. Here, we combine numerical and experimental studies to investigate effective-sphere characterization of symmetric dimers of micrometer-scale spheres, a class of aspherical objects that appear commonly in real-world dispersions. Our studies demonstrate that the effective-sphere interpretation usefully distinguishes small colloidal clusters in holographic characterization studies of monodisperse colloidal spheres. The effective-sphere estimate for a dimer's axial position closely follows the ground truth for its center of mass. Trends in the effective-sphere diameter and refractive index, furthermore, can be used to measure a dimer's three-dimensional orientation. When applied to colloidal dimers transported in a Poiseuille flow, the estimated orientation distribution is consistent with expectations for Brownian particles undergoing Jeffery orbits.

Holographic immunoassays: direct detection of antibodies binding to colloidal spheres.

The size of a probe bead reported by holographic particle characterization depends on the proportion of the surface area covered by bound target molecules and so can be used as an assay for molecular binding. We validate this technique by measuring the kinetics of irreversible binding for the antibodies immunoglobulin G (IgG) and immunoglobulin M (IgM) as they attach to micrometer-diameter colloidal beads coated with protein A. These measurements yield the antibodies' binding rates and can be inverted to obtain the concentration of antibodies in solution. Holographic molecular binding assays therefore can be used to perform fast quantitative immunoassays that are complementary to conventional serological tests.

Interpreting holographic molecular binding assays with effective medium theory.

Holographic molecular binding assays use holographic video microscopy to directly detect molecules binding to the surfaces of micrometer-scale colloidal beads by monitoring associated changes in the beads' light-scattering properties. Holograms of individual spheres are analyzed by fitting to a generative model based on the Lorenz-Mie theory of light scattering. Each fit yields an estimate of a probe bead's diameter and refractive index with sufficient precision to watch a population of beads grow as molecules bind. Rather than modeling the molecular-scale coating, however, these fits use effective medium theory, treating the coated sphere as if it were homogeneous. This effective-sphere analysis is rapid and numerically robust and so is useful for practical implementations of label-free immunoassays. Here, we assess how measured effective-sphere properties reflect the actual properties of molecular-scale coatings by modeling coated spheres with the discrete-dipole approximation and analyzing their holograms with the effective-sphere model.

Quantitative Differentiation of Protein Aggregates From Other Subvisible Particles in Viscous Mixtures Through Holographic Characterization.

We demonstrate the use of holographic video microscopy to detect individual subvisible particles dispersed in biopharmaceutical formulations and to differentiate them based on material characteristics measured from their holograms. The result of holographic analysis is a precise and accurate measurement of the concentrations and size distributions of multiple classes of subvisible contaminants dispersed in the same product simultaneously. We demonstrate this analytical technique through measurements on model systems consisting of human IgG aggregates in the presence of common contaminants such as silicone oil emulsion droplets and fatty acids. Holographic video microscopy also clearly identifies metal particles and air bubbles. Being able to differentiate and characterize the individual components of such heterogeneous dispersions provides a basis for tracking other factors that influence the stability of protein formulations including handling and degradation of surfactant and other excipients.

Holographic molecular binding assays.

We demonstrate that holographic particle characterization can directly detect binding of proteins to functionalized colloidal probe particles by monitoring the associated change in the particles' size. This label-free molecular binding assay uses in-line holographic video microscopy to measure the diameter and refractive index of individual probe spheres as they flow down a microfluidic channel. Pooling measurements on 104 particles yields the population-average diameter with an uncertainty smaller than 0.5 nm, which is sufficient to detect sub-monolayer coverage by bound proteins. We demonstrate this method by monitoring binding of NeutrAvidin to biotinylated spheres and binding of immunoglobulin G to spheres functionalized with protein A.

CATCH: Characterizing and Tracking Colloids Holographically Using Deep Neural Networks.

In-line holographic microscopy provides an unparalleled wealth of information about the properties of colloidal dispersions. Analyzing one colloidal particle's hologram with the Lorenz-Mie theory of light scattering yields the particle's three-dimensional position with nanometer precision while simultaneously reporting its size and refractive index with part-per-thousand resolution. Analyzing a few thousand holograms in this way provides a comprehensive picture of the particles that make up a dispersion, even for complex multicomponent systems. All of this valuable information comes at the cost of three computationally expensive steps: (1) identifying and localizing features of interest within recorded holograms, (2) estimating each particle's properties based on characteristics of the associated features, and finally (3) optimizing those estimates through pixel-by-pixel fits to a generative model. Here, we demonstrate an end-to-end implementation that is based entirely on machine-learning techniques. Characterizing and Tracking Colloids Holographically (CATCH) with deep convolutional neural networks is fast enough for real-time applications and otherwise outperforms conventional analytical algorithms, particularly for heterogeneous and crowded samples. We demonstrate this system's capabilities with experiments on free-flowing and holographically trapped colloidal spheres.

The role of the medium in the effective-sphere interpretation of holographic particle characterization data.

The in-line hologram of a micrometer-scale colloidal sphere can be analyzed with the Lorenz-Mie theory of light scattering to obtain precise measurements of the sphere's diameter and refractive index. The same technique also can be used to characterize porous and irregularly shaped colloidal particles provided that the extracted parameters are interpreted with effective-medium theory to represent the properties of an equivalent effective sphere. Here, we demonstrate that the effective-sphere model consistently accounts for changes in the refractive index of the medium as it fills the pores of porous particles and therefore yields quantitative information about such particles' structure and composition. In addition to the sample-averaged porosity, holographic perfusion porosimetry gauges the polydispersity of the porosity. We demonstrate these capabilities through measurements on mesoporous spheres, fractal protein aggregates and irregular nanoparticle agglomerates, all of which are noteworthy for their industrial significance.

Above and beyond: holographic tracking of axial displacements in holographic optical tweezers.

How far a particle moves along the optical axis in a holographic optical trap is not simply dictated by the programmed motion of the trap, but rather depends on an interplay of the trap's changing shape and the particle's material properties. For the particular case of colloidal spheres in optical tweezers, holographic video microscopy reveals that trapped particles tend to move farther along the axial direction than the traps that are moving them and that different kinds of particles move by different amounts. These surprising and sizeable variations in axial placement can be explained by a dipole-order theory for optical forces. Their discovery highlights the need for real-time feedback to achieve precise control of colloidal assemblies in three dimensions and demonstrates that holographic microscopy can meet that need.

Optimizing the Synthesis of Monodisperse Colloidal Spheres Using Holographic Particle Characterization.

Holographic particle characterization measures the sizes and compositions of individual colloidal particles dispersed in fluid media and rapidly amasses statistics on the distributions of these properties, even for complex heterogeneous dispersions. This information is useful for analyzing and optimizing protocols for synthesizing colloidal particles. We illustrate how holographic characterization can guide process design through a case study on a particularly versatile model system composed of an aqueous dispersion of micrometer-scale spheres synthesized from the organosilane monomer 3-(trimethoxysilyl)propyl methacrylate.