Holographic measurements of anisotropic three-dimensional diffusion of colloidal clusters

Time-Resolved Four-Channel Jones Matrix Measurement of Birefringent Materials Using an Ultrafast Laser

A method for ultrafast time-resolved four-channel Jones matrix measurement of birefringent materials using an ultrafast laser is investigated. This facilitated the acquisition of a four-channel angular multiplexing hologram in a single shot. The Jones matrix information of a birefringent sample was retrieved from the spatial spectrum of a hologram. The feasibility of this approach was established by measuring the Jones matrix of starch granules in microfluidic chips and the complex amplitude distribution and phase delay distribution of liquid crystal cell at different voltages. Moreover, when the picosecond laser was switched to a femtosecond laser, ultrafast measurements were possible provided that the time interval between two detection pulses was larger than the pulse width.

Improving holographic particle characterization by modeling spherical aberration

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 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.

Brownian dynamics simulations of sphere clusters in optical tweezers

Computationally modeling the behavior of wavelength-sized non-spherical particles in optical tweezers can give insight into the existence and stability of trapping equilibria as well as the optical manipulation of such particles more broadly. Here, we report Brownian dynamics simulations of non-spherical particles that account for detailed optical, hydrodynamic, and thermal interactions. We use a T-matrix formalism to calculate the optical forces and torques exerted by focused laser beams on clusters of wavelength-sized spheres, and we incorporate detailed diffusion tensors that capture the anisotropic Brownian motion of the clusters. For two-sphere clusters whose size is comparable to or larger than the wavelength, we observe photokinetic effects in elliptically-polarized beams. We also demonstrate that multiple trapping equilibria exist for a highly asymmetric chiral cluster of seven spheres. Our simulations may lead to practical suggestions for optical trapping and manipulation as well as a deeper understanding of the underlying physics.

Brownian fluctuations and hydrodynamics of a microhelix near a solid wall

We combine two-photon lithography and optical tweezers to investigate the Brownian fluctuations and propeller characteristics of a microfabricated helix. From the analysis of mean squared displacements and time correlation functions we recover the components of the full mobility tensor. We find that Brownian motion displays correlations between angular and translational fluctuations from which we can directly measure the hydrodynamic coupling coefficient that is responsible for thrust generation. By varying the distance of the microhelices from a no-slip boundary we can systematically measure the effects of a nearby wall on the resistance matrix. Our results indicate that a rotated helix moves faster when a nearby no-slip boundary is present, providing a quantitative insight on thrust enhancement in confined geometries for both synthetic and biological microswimmers.

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.

Large depth-of-field tracking of colloidal spheres in holographic microscopy by modeling the objective lens

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.

Axial electrokinetic trapping of anisotropic particles

Anti-Brownian electrokinetic trapping is a method for trapping single particles in liquid based on particle position measurements and the application of feedback voltages. To achieve trapping in the axial direction, information on the axial particle position is required. However, existing strategies for determining the axial position that are based on measuring the size of the first diffraction ring, theory fitting, advanced optical setups or pre-determined axial image stacks are impractical for anisotropic particles. In this work, axial electrokinetic trapping of anisotropic particles is realized in devices with planar, transparent electrodes. The trapping algorithm uses Fourier-Bessel decomposition of standard microscopy images and is learning from the correlation between applied voltages and changes in the particle appearance. No previous knowledge on the particle appearance, theory fitting or advanced optical setup is required. The particle motion in the trap and the influence of screening of the electric field on this motion are analyzed. The axial trapping method opens new possibilities for measuring properties of anisotropic or isotropic particles and forces acting on such particles.

Experimental Assessment and Model Validation on How Shape Determines Sedimentation and Diffusion of Colloidal Particles

Understanding the hydrodynamics of colloids with complex shapes is of equal importance to widespread practical applications and fundamental scientific problems, such as gelation, crystallization, and phase behavior. Building on previous work, we present a comprehensive study of sedimentation, diffusion, intrinsic viscosities, and other shape-dependent quantities of clusters built from spherical nanoparticles. Cluster preparation is accomplished by assembling surface-modified polystyrene particles on evaporating emulsion droplets. This results in supracolloids that exhibit well-defined configurations, which are governed by the number of constituent particles. Sorting into uniform cluster fractions is achieved through centrifugation of the cluster mixture in a density gradient. Sedimentation coefficients are elucidated by differential centrifugal sedimentation. Rotational and translational diffusion of the clusters are investigated by polarized and depolarized dynamic light scattering. The experimental results are compared to data obtained via a bead-shell model suitable for predicting hydrodynamic quantities of particles with arbitrary shapes. The experimental data are in excellent agreement with the predictions from hydrodynamic modeling. The variety of investigated shapes shows the robustness of our approach and provides a complete picture of the hydrodynamic behavior of complex particles.

Flexible wide-field high-resolution scanning camera for continuous-wave acoustic holography

We present a system for measuring the amplitude and phase profiles of the pressure field of a harmonic acoustic wave with the goal of reconstructing the volumetric sound field. Unlike optical holograms that cannot be reconstructed exactly because of the inverse problem, acoustic holograms are completely specified in the recording plane. We demonstrate volumetric reconstructions of simple arrangements of objects using the Rayleigh-Sommerfeld diffraction integral and introduce a technique to analyze the dynamic properties of insonated objects.

Brownian Dynamics of Particles "Dressed" by Chiral Director Configurations in Lyotropic Chromonic Liquid Crystals

We study Brownian dynamics of colloidal spheres, with planar anchoring conditions, suspended in the nematic phase of the lyotropic chromonic liquid crystal disodium chromoglycate (DSCG). Unlike typical liquid crystals, the unusually small twist elastic modulus of DSCG permits two energetically distinct helical distortions (twisted tails) of the nematic director to "dress" the suspended spheres. Video microscopy is used to characterize the helical distortions versus particle size and to measure particle mean-square displacements. Diffusion coefficients parallel and perpendicular to the far-field director, and their anisotropy ratio, are different for the two twisted tail configurations. Moreover, the crossover from subdiffusive to diffusive behavior is anomalously slow for motion perpendicular to the director (>100  s). Simple arguments using Miesowicz viscosities and ideas about twist relaxation are suggested to understand the mean-square displacement observations.

Machine-learning techniques for fast and accurate feature localization in holograms of colloidal particles

Holograms of colloidal particles can be analyzed with the Lorenz-Mie theory of light scattering to measure individual particles' three-dimensional positions with nanometer precision while simultaneously estimating their sizes and refractive indexes. Extracting this wealth of information begins by detecting and localizing features of interest within individual holograms. Conventionally approached with heuristic algorithms, this image analysis problem can be solved faster and more generally with machine-learning techniques. We demonstrate that two popular machine-learning algorithms, cascade classifiers and deep convolutional neural networks (CNN), can solve the feature-localization problem orders of magnitude faster than current state-of-the-art techniques. Our CNN implementation localizes holographic features precisely enough to bootstrap more detailed analyses based on the Lorenz-Mie theory of light scattering. The wavelet-based Haar cascade proves to be less precise, but is so computationally efficient that it creates new opportunities for applications that emphasize speed and low cost. We demonstrate its use as a real-time targeting system for holographic optical trapping.

Measurements of polarization-dependent angle-resolved light scattering from individual microscopic samples using Fourier transform light scattering

We present a method to measure the vector-field light scattering of individual microscopic objects. The polarization-dependent optical field images are measured with quantitative phase imaging at the sample plane, and then numerically propagated to the far-field plane. This approach allows the two-dimensional polarization-dependent angle-resolved light scattered patterns from individual object to be obtained with high precision and sensitivity. Using this method, we present the measurements of the polarization-dependent light scattering of a liquid crystal droplet and individual silver nanowires over scattering angles of 50°. In addition, the spectroscopic extension of the polarization-dependent angle-resolved light scattering is demonstrated using wavelength-scanning illumination.

Using Image Attributes to Assure Accurate Particle Size and Count Using Nanoparticle Tracking Analysis

Nanoparticle tracking analysis (NTA) obtains particle size by analysis of particle diffusion through a time series of micrographs and particle count by a count of imaged particles. The number of observed particles imaged is controlled by the scattering cross-section of the particles and by camera settings such as sensitivity and shutter speed. Appropriate camera settings are defined as those that image, track, and analyze a sufficient number of particles for statistical repeatability. Here, we test if image attributes, features captured within the image itself, can provide measurable guidelines to assess the accuracy for particle size and count measurements using NTA. The results show that particle sizing is a robust process independent of image attributes for model systems. However, particle count is sensitive to camera settings. Using open-source software analysis, it was found that a median pixel area, 4 pixels², results in a particle concentration within 20% of the expected value. The distribution of these illuminated pixel areas can also provide clues about the polydispersity of particle solutions prior to using a particle tracking analysis. Using the median pixel area serves as an operator-independent means to assess the quality of the NTA measurement for count.

Differential dynamic microscopy of bidisperse colloidal suspensions

Research tasks in microgravity include monitoring the dynamics of constituents of varying size and mobility in processes such as aggregation, phase separation, or self-assembly. We use differential dynamic microscopy, a method readily implemented with equipment available on the International Space Station, to simultaneously resolve the dynamics of particles of radius 50 nm and 1 μm in bidisperse aqueous suspensions. Whereas traditional dynamic light scattering fails to detect a signal from the larger particles at low concentrations, differential dynamic microscopy exhibits enhanced sensitivity in these conditions by accessing smaller wavevectors where scattering from the large particles is stronger. Interference patterns due to scattering from the large particles induce non-monotonic decay of the amplitude of the dynamic correlation function with the wavevector. We show that the position of the resulting minimum contains information on the vertical position of the particles. Together with the simple instrumental requirements, the enhanced sensitivity of differential dynamic microscopy makes it an appealing alternative to dynamic light scattering to characterize samples with complex dynamics.

Automated tracking of colloidal clusters with sub-pixel accuracy and precision

Quantitative tracking of features from video images is a basic technique employed in many areas of science. Here, we present a method for the tracking of features that partially overlap, in order to be able to track so-called colloidal molecules. Our approach implements two improvements into existing particle tracking algorithms. Firstly, we use the history of previously identified feature locations to successfully find their positions in consecutive frames. Secondly, we present a framework for non-linear least-squares fitting to summed radial model functions and analyze the accuracy (bias) and precision (random error) of the method on artificial data. We find that our tracking algorithm correctly identifies overlapping features with an accuracy below 0.2% of the feature radius and a precision of 0.1 to 0.01 pixels for a typical image of a colloidal cluster. Finally, we use our method to extract the three-dimensional diffusion tensor from the Brownian motion of colloidal dimers.

Reversible Adsorption Kinetics of Near Surface Dimer Colloids

We investigate the effect of shape on reversible adsorption kinetics using colloidal polystyrene dimers near a solid glass surface as a model system. The interaction between colloid and wall is tuned using electrostatic, depletion, and gravity forces to produce a double-well potential. The dwell time in each of the potential wells is measured from long duration particle trajectories. The height of each monomer relative to the glass surface is measured to a resolution of <20 nm by in-line holographic microscopy. The measured transition probability distributions are used in kinetic equations to describe the flux of particles to and from the surface. The dimers are compared to independent isolated monomers to determine the effects of shape on adsorption equilibria and kinetics. To elucidate these differences, we consider both mass and surface coverage and two definitions of surface coverage. The results show that dimers with single coverage produce slower adsorption, lower surface coverage, and higher mass coverage in comparison to those of monomers, while dimers with double coverage adsorb faster and result in higher surface coverage.

Structure and dynamics of model colloidal clusters with short-range attractions

We examine the structure and dynamics of small isolated N-particle clusters interacting via short-ranged Morse potentials. "Ideally prepared ensembles" obtained via exact enumeration studies of sticky hard-sphere packings serve as reference states allowing us to identify key statistical-geometrical properties and to quantitatively characterize how nonequilibrium ensembles prepared by thermal quenches at different rates T[over ̇] differ from their equilibrium counterparts. Studies of equilibrium dynamics show nontrivial temperature dependence: nonexponential relaxation indicates both glassy dynamics and differing stabilities of degenerate clusters with different structures. Our results should be useful for extending recent experimental studies of small colloidal clusters to examine both equilibrium relaxation dynamics at fixed T and a variety of nonequilibrium phenomena.

Brownian motion of arbitrarily shaped particles in two dimensions

We implement microfabricated boomerang particles with unequal arm lengths as a model for nonsymmetric particles and study their Brownian motion in a quasi-two-dimensional geometry by using high-precision single-particle motion tracking. We show that because of the coupling between translation and rotation, the mean squared displacements of a single asymmetric boomerang particle exhibit a nonlinear crossover from short-time faster to long-time slower diffusion, and the mean displacements for fixed initial orientation are nonzero and saturate out at long times. The measured anisotropic diffusion coefficients versus the tracking point position indicate that there exists one unique point, i.e., the center of hydrodynamic stress (CoH), at which all coupled diffusion coefficients vanish. This implies that in contrast to motion in three dimensions where the CoH exists only for high-symmetry particles, the CoH always exists for Brownian motion in two dimensions. We develop an analytical model based on Langevin theory to explain the experimental results and show that among the six anisotropic diffusion coefficients only five are independent because the translation-translation coupling originates from the translation-rotation coupling. Finally, we classify the behavior of two-dimensional Brownian motion of arbitrarily shaped particles into four groups based on the particle shape symmetry group and discussed potential applications of the CoH in simplifying understanding of the circular motions of microswimmers.

Machine-learning approach to holographic particle characterization

Holograms of colloidal dispersions encode comprehensive information about individual particles' three-dimensional positions, sizes and optical properties. Extracting that information typically is computationally intensive, and thus slow. Here, we demonstrate that machine-learning techniques based on support vector machines (SVMs) can analyze holographic video microscopy data in real time on low-power computers. The resulting stream of precise particle-resolved tracking and characterization data provides unparalleled insights into the composition and dynamics of colloidal dispersions and enables applications ranging from basic research to process control and quality assurance.

Fast feature identification for holographic tracking: the orientation alignment transform

The concentric fringe patterns created by features in holograms may be associated with a complex-valued orientational order field. Convolution with an orientational alignment operator then identifies centers of symmetry that correspond to the two-dimensional positions of the features. Feature identification through orientational alignment is reminiscent of voting algorithms such as Hough transforms, but may be implemented with fast convolution methods, and so can be orders of magnitude faster.

Real-time visualization of 3-D dynamic microscopic objects using optical diffraction tomography

3-D refractive index (RI) distribution is an intrinsic bio-marker for the chemical and structural information about biological cells. Here we develop an optical diffraction tomography technique for the real-time reconstruction of 3-D RI distribution, employing sparse angle illumination and a graphic processing unit (GPU) implementation. The execution time for the tomographic reconstruction is 0.21 s for 96(3) voxels, which is 17 times faster than that of a conventional approach. We demonstrated the real-time visualization capability with imaging the dynamics of Brownian motion of an anisotropic colloidal dimer and the dynamic shape change in a red blood cell upon shear flow.

High-precision tracking of brownian boomerang colloidal particles confined in quasi two dimensions

In this article, we present a high-precision image-processing algorithm for tracking the translational and rotational Brownian motion of boomerang-shaped colloidal particles confined in quasi-two-dimensional geometry. By measuring mean square displacements of an immobilized particle, we demonstrate that the positional and angular precision of our imaging and image-processing system can achieve 13 nm and 0.004 rad, respectively. By analyzing computer-simulated images, we demonstrate that the positional and angular accuracies of our image-processing algorithm can achieve 32 nm and 0.006 rad. Because of zero correlations between the displacements in neighboring time intervals, trajectories of different videos of the same particle can be merged into a very long time trajectory, allowing for long-time averaging of different physical variables. We apply this image-processing algorithm to measure the diffusion coefficients of boomerang particles of three different apex angles and discuss the angle dependence of these diffusion coefficients.

Brownian motion of boomerang colloidal particles

We investigate the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.