Characterizing and tracking single colloidal particles with video holographic microscopy

Cybloids - creation and control of cybernetic colloids

Colloids play an important role in fundamental science as well as in nature and technology. They have had a strong impact on the fundamental understanding of statistical physics. For example, colloids have helped to obtain a better understanding of collective phenomena, ranging from phase transitions and glass formation to the swarming of active Brownian particles. Yet the success of colloidal systems hinges crucially on the specific physical and chemical properties of the colloidal particles, i.e. particles with the appropriate characteristics must be available. Here we present an idea to create particles with freely selectable properties. The properties might depend, for example, on the presence of other particles (hence mimicking specific pair or many-body interactions), previous configurations (hence introducing some memory or feedback), or a directional bias (hence changing the dynamics). Without directly interfering with the sample, each particle is fully controlled and can receive external commands through a predefined algorithm that can take into account any input parameters. This is realized with computer-controlled colloids, which we term cybloids - short for cybernetic colloids. The potential of cybloids is illustrated by programming a time-delayed external potential acting on a single colloid and interaction potentials for many colloids. Both an attractive harmonic potential and an annular potential are implemented. For a single particle, this programming can cause subdiffusive behavior or lend activity. For many colloids, the programmed interaction potential allows to select a crystal structure at wish. Beyond these examples, we discuss further opportunities which cybloids offer.

Observation of Brownian elastohydrodynamic forces acting on confined soft colloids

Confined motions in complex environments are ubiquitous in microbiology. These situations invariably involve the intricate coupling between fluid flow, soft boundaries, surface forces, and fluctuations. In the present study, such a coupling is investigated using a method combining holographic microscopy and advanced statistical inference. Specifically, the Brownian motion of soft micrometric oil droplets near rigid walls is quantitatively analyzed. All the key statistical observables are reconstructed with high precision, allowing for nanoscale resolution of local mobilities and femtonewton inference of conservative or nonconservative forces. Strikingly, the analysis reveals the existence of a novel, transient, but large, soft Brownian force. The latter might be of crucial importance for microbiological and nanophysical transport, target finding, or chemical reactions in crowded environments, and hence the whole life machinery.

Mie scattering theory applied to light scattering of large nonhomogeneous colloidal spheres

Colloidal suspensions made of smart core-shell structures are of current interest in many fields. Their properties come from the possibility of varying the core and shell materials for modifying the composite particles' chemical, biological, and optical properties. These particles are formed with a material with a constant refractive index core and a shell with a refractive index decaying until it matches the solvent refractive index. Poly(N-IsoPropyl AcrylaMide) (PNIPAM) is a typical example of materials forming shells. In this report, we present how to apply Mie scattering theory to predict and understand the static light scattering of large nonhomogeneous colloidal particles with spherical symmetry whose size is comparable with or larger than the light wavelength used for developing scattering experiments, where the Rayleigh-Gans-Debye approximation is not valid. Here, the refractive index decay was approximated by a Gaussian RI profile numerically evaluated through a multilayer sphere. We calculated the form factor functions of suspensions of PNIPAM microgels previously reported and core-shell suspensions made of polystyrene/PNIPAM at 20 and 40 °C synthesized by us. In all the cases, our method succeeded in providing the scattering intensity as a function of the angle. The software for using the numerical method is fairly straightforward and is accessible as an open-source code. The results can not only help predict and understand the photonic properties of microgels with large core-shell structures but also for any particle with a refractive index distribution with spherical symmetry, as in the case of microgels with super chaotropic agents, hollow microgels, or microparticles.

Measuring Vesicle Loading with Holographic Microscopy and Bulk Light Scattering

We report efforts to quantify the loading of cell-sized lipid vesicles using in-line digital holographic microscopy. This method does not require fluorescent reporters, fluorescent tracers, or radioactive tracers. A single-color LED light source takes the place of conventional illumination to generate holograms rather than bright field images. By modeling the vesicle's scattering in a microscope with a Lorenz-Mie light scattering model and comparing the results to data holograms, we are able to measure the vesicle's refractive index and thus loading. Performing the same comparison for bulk light scattering measurements enables the retrieval of vesicle loading for nanoscale vesicles.

Cross-correlation image analysis for real-time single particle tracking

Accurately measuring the translations of objects between images is essential in many fields, including biology, medicine, chemistry, and physics. One important application is tracking one or more particles by measuring their apparent displacements in a series of images. Popular methods, such as the center of mass, often require idealized scenarios to reach the shot noise limit of particle tracking and, therefore, are not generally applicable to multiple image types. More general methods, such as maximum likelihood estimation, reliably approach the shot noise limit, but are too computationally intense for use in real-time applications. These limitations are significant, as real-time, shot-noise-limited particle tracking is of paramount importance for feedback control systems. To fill this gap, we introduce a new cross-correlation-based algorithm that approaches shot-noise-limited displacement detection and a graphics processing unit-based implementation for real-time image analysis of a single particle.

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.

Digital in-line holographic microscopy for label-free identification and tracking of biological cells

Digital in-line holographic microscopy (DIHM) is a non-invasive, real-time, label-free technique that captures three-dimensional (3D) positional, orientational, and morphological information from digital holographic images of living biological cells. Unlike conventional microscopies, the DIHM technique enables precise measurements of dynamic behaviors exhibited by living cells within a 3D volume. This review outlines the fundamental principles and comprehensive digital image processing procedures employed in DIHM-based cell tracking methods. In addition, recent applications of DIHM technique for label-free identification and digital tracking of various motile biological cells, including human blood cells, spermatozoa, diseased cells, and unicellular microorganisms, are thoroughly examined. Leveraging artificial intelligence has significantly enhanced both the speed and accuracy of digital image processing for cell tracking and identification. The quantitative data on cell morphology and dynamics captured by DIHM can effectively elucidate the underlying mechanisms governing various microbial behaviors and contribute to the accumulation of diagnostic databases and the development of clinical treatments.

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.

Real-time 3D tracking of swimming microbes using digital holographic microscopy and deep learning

The three-dimensional swimming tracks of motile microorganisms can be used to identify their species, which holds promise for the rapid identification of bacterial pathogens. The tracks also provide detailed information on the cells' responses to external stimuli such as chemical gradients and physical objects. Digital holographic microscopy (DHM) is a well-established, but computationally intensive method for obtaining three-dimensional cell tracks from video microscopy data. We demonstrate that a common neural network (NN) accelerates the analysis of holographic data by an order of magnitude, enabling its use on single-board computers and in real time. We establish a heuristic relationship between the distance of a cell from the focal plane and the size of the bounding box assigned to it by the NN, allowing us to rapidly localise cells in three dimensions as they swim. This technique opens the possibility of providing real-time feedback in experiments, for example by monitoring and adapting the supply of nutrients to a microbial bioreactor in response to changes in the swimming phenotype of microbes, or for rapid identification of bacterial pathogens in drinking water or clinical samples.

Label-Free Single Nanoparticle Identification and Characterization in Demanding Environment, Including Infectious Emergent Virus

Unknown particle screening-including virus and nanoparticles-are keys in medicine, industry, and also in water pollutant determination. Here, RYtov MIcroscopy for Nanoparticles Identification (RYMINI) is introduced, a staining-free, non-invasive, and non-destructive optical approach that is merging holographic label-free 3D tracking with high-sensitivity quantitative phase imaging into a compact optical setup. Dedicated to the identification and then characterization of single nano-object in solution, it is compatible with highly demanding environments, such as level 3 biological laboratories, with high resilience to external source of mechanical and optical noise. Metrological characterization is performed at the level of each single particle on both absorbing and transparent particles as well as on immature and infectious HIV, SARS-CoV-2 and extracellular vesicles in solution. The capability of RYMINI to determine the nature, concentration, size, complex refractive index and mass of each single particle without knowledge or model of the particles' response is demonstrated. The system surpasses 90% accuracy for automatic identification between dielectric/metallic/biological nanoparticles and ≈80% for intraclass chemical determination of metallic and dielectric. It falls down to 50-70% for type determination inside the biological nanoparticle's class.

Detectability of unresolved particles in off-axis digital holographic microscopy

Off-axis digital holographic microscopy (DHM) provides both amplitude and phase images, and so it may be used for label-free 3D tracking of micro- and nano-sized particles of different compositions, including biological cells, strongly absorbing particles, and strongly scattering particles. Contrast is provided by differences in either the real or imaginary parts of the refractive index (phase contrast and absorption) and/or by scattering. While numerous studies have focused on phase contrast and improving resolution in DHM, particularly axial resolution, absent have been studies quantifying the limits of detection for unresolved particles. This limit has important implications for microbial detection, including in life-detection missions for space flight. Here we examine the limits of detection of nanosized particles as a function of particle optical properties, microscope optics (including camera well depth and substrate), and data processing techniques and find that DHM provides contrast in both amplitude and phase for unresolved spheres, in rough agreement with Mie theory scattering cross-sections. Amplitude reconstructions are more useful than phase for low-index spheres and should not be neglected in DHM analysis.

Unravelling DNA Organization with Single-Molecule Force Spectroscopy Using Magnetic Tweezers

Genomes carry the genetic blueprint of all living organisms. Their organization requires strong condensation as well as carefully regulated accessibility to specific genes for proper functioning of their hosts. The study of the structure and dynamics of the proteins that organize the genome has benefited tremendously from the development of single-molecule force spectroscopy techniques that allow for real-time, nanometer accuracy measurements of the compaction of DNA and manipulation with pico-Newton scale forces. Magnetic tweezers, in particular, have the unique ability to complement such force spectroscopy with the control over the linking number of the DNA molecule, which plays an important role when DNA-organizing proteins form or release wraps, loops, and bends in DNA. Here, we describe all the necessary steps to prepare DNA substrates for magnetic tweezers experiments, assemble flow cells, tether DNA to a magnetic bead inside a flow cell, and manipulate and record the extension of such DNA tethers. Furthermore, we explain how mechanical parameters of nucleoprotein filaments can be extracted from the data.

Photothermal heterodyne imaging of micron-sized objects

Micron-sized dye-doped polymer beads were imaged using transmitted/reflected light microscopy and photothermal heterodyne imaging (PHI) measurements. The transmitted/reflected light images show distinct ring patterns that are attributed to diffraction effects and/or internal reflections within the beads. In the PHI experiments pump laser induced heating changes the refractive index and size of the bead, which causes changes in the diffraction pattern and internal reflections. This creates an analogous ring pattern in the PHI images. The ring pattern disappears in both the reflected light and PHI experiments when an incoherent light source is used as a probe. When the beads are imaged in an organic medium heat transfer changes the refractive index of the environment, and gives rise to a ring pattern external to the beads in the PHI images. This causes the beads to appear larger than their physical dimensions in PHI experiments. This external signal does not appear when the beads are imaged in air because the refractive index changes in air are very small.

Holographic imaging platform for particle discrimination based on simultaneous mass density and refractive index measurements

Real-time detection, classification and identification of aerosol particles is crucial in various industries and public health areas. In order to circumvent the limitations of existing particle analysis methods for efficient discrimination, we demonstrate a compact digital in-line holographic microscopy platform with an inertial spectrometer for simultaneous measurement of two independent fingerprint parameters at single species level. In particular, by interrogating the particle location and size captured with the platform, particle mass density can be estimated. Furthermore, by employing Monte Carlo fitting to the Lorenz-Mie theory, the refractive index of each particle can also be extracted from the interference patterns. It is demonstrated that the combination of mass density and optical density characterization unambiguously enhances the discriminatory power of the system, especially when dealing with particles that exhibit similar mass densities but distinctive refractive indices or vice versa. This innovative approach represents a significant advancement in particle characterization and composition identification, with potential applications in various industrial, scientific, and research domains. An iOS-based app interface is then customized for wireless controlling of the CMOS imager, image acquisition, reconstruction, and data analysis. The imaging platform proposed in this work has prominent advantages including compactness, accuracy, efficiency, high throughput, and remote sensing capability, which is especially relevant for applications where on-site/remote metrology and identification of particles is required.

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.

Precise characterization of nanometer-scale systems using interferometric scattering microscopy and Bayesian analysis

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.

Multispectral in-line hologram reconstruction with aberration compensation applied to Gram-stained bacteria microscopy

In multispectral digital in-line holographic microscopy (DIHM), aberrations of the optical system affect the repeatability of the reconstruction of transmittance, phase and morphology of the objects of interest. Here we address this issue first by model fitting calibration using transparent beads inserted in the sample. This step estimates the aberrations of the optical system as a function of the lateral position in the field of view and at each wavelength. Second, we use a regularized inverse problem approach (IPA) to reconstruct the transmittance and phase of objects of interest. Our method accounts for shift-variant chromatic and geometrical aberrations in the forward model. The multi-wavelength holograms are jointly reconstructed by favouring the colocalization of the object edges. The method is applied to the case of bacteria imaging in Gram-stained blood smears. It shows our methodology evaluates aberrations with good repeatability. This improves the repeatability of the reconstructions and delivers more contrasted spectral signatures in transmittance and phase, which could benefit applications of microscopy, such as the analysis and classification of stained bacteria.

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.

Efficient and accurate intensity diffraction tomography of multiple-scattering samples

Optical Diffraction Tomography (ODT) is a label-free method to quantitatively estimate the 3D refractive index (RI) distributions of microscopic samples. Recently, significant efforts were directed towards methods to model multiple-scattering objects. The fidelity of reconstructions rely on accurately modelling light-matter interactions, but the efficient simulation of light propagation through high-RI structures over a large range of illumination angles is still challenging. Here we present a solution dealing with these problems, proposing a method that allows one to efficiently model the tomographic image formation for strongly scattering objects illuminated over a wide range of angles. Instead of propagating tilted plane waves we apply rotations on the illuminated object and optical field and formulate a new and robust multi-slice model suitable for high-RI contrast structures. We test reconstructions made by our approach against simulations and experiments, using rigorous solutions to Maxwell's equations as ground truth. We find the proposed method to produce reconstructions of higher fidelity compared to conventional multi-slice methods, especially for the challenging case of strongly scattering samples where conventional reconstruction methods fail.

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.

Spectroscopic atomic sample plane localization for precise digital holography

In digital holography, the coherent scattered light fields can be reconstructed volumetrically. By refocusing the fields to the sample planes, absorption and phase-shift profiles of sparsely distributed samples can be simultaneously inferred in 3D. This holographic advantage is highly useful for spectroscopic imaging of cold atomic samples. However, unlike e.g. biological samples or solid particles, the quasi-thermal atomic gases under laser-cooling are typically featureless without sharp boundaries, invalidating a class of standard numerical refocusing methods. Here, we extend the refocusing protocol based on the Gouy phase anomaly for small phase objects to free atomic samples. With a prior knowledge on a coherent spectral phase angle relation for cold atoms that is robust against probe condition variations, an "out-of-phase" response of the atomic sample can be reliably identified, which flips the sign during the numeric back-propagation across the sample plane to serve as the refocus criterion. Experimentally, we determine the sample plane of a laser-cooled ³⁹K gas released from a microscopic dipole trap, with a δz ≈ 1 µm ≪ 2λ_p/NA² axial resolution, with a NA=0.3 holographic microscope at λ_p = 770 nm probe wavelength.

Recent advances in experimental design and data analysis to characterize prokaryotic motility

Bacterial motility plays a key role in important cell processes such as chemotaxis and biofilm formation, but is challenging to quantify due to the small size of the individual microorganisms and the complex interplay of biological and physical factors that influence motility phenotypes. Swimming, the first type of motility described in bacteria, still remains largely unquantified. Light microscopy has enabled qualitative characterization of swimming patterns seen in different strains, such as run and tumble, run-reverse-flick, run and slow, stop and coil, and push and pull, which has allowed for elucidation of the underlying physics. However, quantifying these behaviors (e.g., identifying run distances and speeds, turn angles and behavior by surfaces or cell-cell interactions) remains a challenging task. A qualitative and quantitative understanding of bacterial motility is needed to bridge the gap between experimentation, omics analysis, and bacterial motility theory. In this review, we discuss the strengths and limitations of how phase contrast microscopy, fluorescence microscopy, and digital holographic microscopy have been used to quantify bacterial motility. Approaches to automated software analysis, including cell recognition, tracking, and track analysis, are also discussed with a view to providing a guide for experimenters to setting up the appropriate imaging and analysis system for their needs.

Spectroscopy of individual Brownian nanoparticles in real-time using holographic localization

Individual nanoparticle spectroscopic characterization is fundamental, but challenging in liquids. While confocal selectivity is necessary to isolate a particle in a crowd, Brownian motion constantly offsets the particle from the light collection volume. Here, we present a system able to acquire holograms and reconstruct them to precisely determine the 3D position of a particle in real time. These coordinates drive an adaptive system comprising two galvanometric mirrors (x,y, transverse directions) and a tunable lens (z, longitudinal) which redirect light scattered from the corresponding region of space towards the confocal entrance of a spectrometer, thus allowing long spectral investigations on individual, freely-moving particles. A study of the movements and spectra of individual 100 nm Au nanoparticles undergoing two types of aggregations illustrates the possibilities of the method.

Effect of hologram plane position on particle tracking using digital holographic microscopy

This paper discusses the effect of hologram plane position on the tracking of particle motions in a 3D suspension using digital holography microscopy. We compare two optical configurations where the hologram plane is located either just outside the particle suspension or in the middle of the suspension. In both cases, we record two axially separated holograms using two cameras and subsequently adopt an iterative phase retrieval approach to solve the virtual image problem. We measure the settling motions of 2 µm spheres in a 2 mm thick sample containing 300 to 1500p a r t i c l e s/m m ³. We show that the optical setup where the hologram plane is located in the middle of the sample provides superior tracking results compared to the other, including higher accuracy in the measurement of particle displacement and longer particle trajectories. The accuracy of particle displacement increases by a maximum of 18%, and the trajectory length increases by a maximum of 16%. This superior outcome is due to the less overlapping of the diffraction patterns on the holograms when the separation distance between particles and the hologram plane is minimized.

Accurate unsupervised estimation of aberrations in digital holographic microscopy for improved quantitative reconstruction

In the context of digital in-line holographic microscopy, we describe an unsupervised methodology to estimate the aberrations of an optical microscopy system from a single hologram. The method is based on the Inverse Problems Approach reconstructions of holograms of spherical objects. The forward model is based on a Lorenz-Mie model distorted by optical aberrations described by Zernike polynomials. This methodology is thus able to characterize most varying aberrations in the field of view in order to take them into account to improve the reconstruction of any sample. We show that this approach increases the repeatability and quantitativity of the reconstructions in both simulations and experimental data. We use the Cramér-Rao lower bounds to study the accuracy of the reconstructions. Finally, we demonstrate the efficiency of this aberration calibration with image reconstructions using a phase retrieval algorithm as well as a regularized inverse problems algorithm.

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.

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.

Label-free viability assay using in-line holographic video microscopy

Total holographic characterization (THC) is presented here as an efficient, automated, label-free method of accurately identifying cell viability. THC is a single-particle characterization technology that determines the size and index of refraction of individual particles using the Lorenz-Mie theory of light scattering. Although assessment of cell viability is a challenge in many applications, including biologics manufacturing, traditional approaches often include unreliable labeling with dyes and/or time consuming methods of manually counting cells. In this work we measured the viability of Saccharomyces cerevisiae yeast in the presence of various concentrations of isopropanol as a function of time. All THC measurements were performed in the native environment of the sample with no dilution or addition of labels. Holographic measurements were made with an in-line holographic microscope using a 40[Formula: see text] objective lens with plane wave illumination. We compared our results with THC to manual counting of living and dead cells as distinguished with trypan blue dye. Our findings demonstrate that THC can effectively distinguish living and dead yeast cells by the index of refraction of individual cells.

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.

Optical Microscopy Systems for the Detection of Unlabeled Nanoparticles

Label-free detection of nanoparticles is essential for a thorough evaluation of their cellular effects. In particular, nanoparticles intended for medical applications must be carefully analyzed in terms of their interactions with cells, tissues, and organs. Since the labeling causes a strong change in the physicochemical properties and thus also alters the interactions of the particles with the surrounding tissue, the use of fluorescently labeled particles is inadequate to characterize the effects of unlabeled particles. Further, labeling may affect cellular uptake and biocompatibility of nanoparticles. Thus, label-free techniques have been recently developed and implemented to ensure a reliable characterization of nanoparticles.

This review provides an overview of frequently used label-free visualization techniques and highlights recent studies on the development and usage of microscopy systems based on reflectance, darkfield, differential interference contrast, optical coherence, photothermal, holographic, photoacoustic, total internal reflection, surface plasmon resonance, Rayleigh light scattering, hyperspectral and reflectance structured illumination imaging. Using these imaging modalities, there is a strong enhancement in the reliability of experiments concerning cellular uptake and biocompatibility of nanoparticles, which is crucial for preclinical evaluations and future medical applications.

Precision size and refractive index analysis of weakly scattering nanoparticles in polydispersions

Characterization of the size and material properties of particles in liquid suspensions is in very high demand, for example, in the analysis of colloidal samples or of bodily fluids such as urine or blood plasma. However, existing methods are limited in their ability to decipher the constituents of realistic samples. Here we introduce iNTA as a new method that combines interferometric detection of scattering with nanoparticle tracking analysis to reach unprecedented sensitivity and precision in determining the size and refractive index distributions of nanoparticles in suspensions. After benchmarking iNTA with samples of colloidal gold, we present its remarkable ability to resolve the constituents of various multicomponent and polydisperse samples of known origin. Furthermore, we showcase the method by elucidating the refractive index and size distributions of extracellular vesicles from Leishmania parasites and human urine. The current performance of iNTA already enables advances in several important applications, but we also discuss possible improvements.

Automatic numerical focus plane estimation in digital holographic microscopy using calibration beads

We present a new method to achieve autofocus in digital holographic microscopy. The method is based on inserting calibrated objects into a sample placed on a slide. Reconstructing a hologram using the inverse problems approach makes it possible to precisely locate and measure the inserted objects and thereby derive the slide plane location. Numerical focusing can then be performed in a plane at any chosen distance from the slide plane of the sample in a reproducible manner and independently of the diversity of the objects in the sample.

History and metrology applications of a game-changing technology: digital holography [Invited]

In digital holography (DH), information in the hologram is recorded and stored in digital format in discrete bits. Like its parent, holography, DH evolved over many years with periods of dormancy and revival. Almost abandoned, multiple times, unanticipated events or developments in separate industries revived it with explosive, quantum jumps, making it useful and popular to a wide audience. Although its history has been treated in many papers and books, the field is dynamic and constantly providing new opportunities. Having been born long before low-cost, fast, powerful digital computers and digital detectors were available, DH was confined to the academic world, where practical applications and commercial opportunities were few if any. Consumer demand that led to low-cost personal computers, high-resolution digital cameras, supporting software, and related products changed the situation drastically by providing every potential researcher affordable, powerful hardware and software needed to apply image processing algorithms and move DH to new practical application levels. In this paper, as part of the sixtieth anniversary of off-axis holography, we include a brief introduction to the fundamentals of DH and examine the history and evolution of DH during its periods of rise and fall. We summarize many new emerging techniques, applications, and potential future applications along with additional details for metrological examples from the authors' research.

3D particle tracking using transport of intensity equation (TIE)

This article presents a simple and high-speed approach for tracking colloidal spheres in three dimensions. The method uses the curvature of the wavefront as determined by the transport of intensity equation (TIE) technique. Due to the fact that the TIE is applicable under partially coherent light, our technique is fully compatible with standard bright field microscopes, requiring no demanding environmental stability requirements or restrictions on the noise produced by related laser speckles. The method was validated experimentally to determine the sedimentation and diffusion coefficients of two different sizes of microspheres, 20 and 3 microns. The 3D position of the microspheres was calculated with an accuracy greater than 350 nm. Moreover, we examined the calculated 3D positions to determine the parameters of the microsphere interaction with its surrounding media, such as the sedimentation and diffusion coefficients. The results show that the measured sedimentation and diffusion of the microspheres have a good agreement with predicted values of about 2% and 10%, respectively, demonstrating the robustness of our proposed method.

Particles in Biopharmaceutical Formulations, Part 2: An Update on Analytical Techniques and Applications for Therapeutic Proteins, Viruses, Vaccines and Cells

Particles in biopharmaceutical formulations remain a hot topic in drug product development. With new product classes emerging it is crucial to discriminate particulate active pharmaceutical ingredients from particulate impurities. Technical improvements, new analytical developments and emerging tools (e.g., machine learning tools) increase the amount of information generated for particles. For a proper interpretation and judgment of the generated data a thorough understanding of the measurement principle, suitable application fields and potential limitations and pitfalls is required. Our review provides a comprehensive overview of novel particle analysis techniques emerging in the last decade for particulate impurities in therapeutic protein formulations (protein-related, excipient-related and primary packaging material-related), as well as particulate biopharmaceutical formulations (virus particles, virus-like particles, lipid nanoparticles and cell-based medicinal products). In addition, we review the literature on applications, describe specific analytical approaches and illustrate advantages and drawbacks of currently available techniques for particulate biopharmaceutical formulations.

Modification to axial tracking for mobile magnetic microspheres

Three-dimensional particle tracking is a routine experimental procedure for various biophysical applications including magnetic tweezers. A common method for tracking the axial position of particles involves the analysis of diffraction rings whose pattern depends sensitively on the axial position of the bead relative to the focal plane. To infer the axial position, the observed rings are compared with reference images of a bead at known axial positions. Often the precision or accuracy of these algorithms is measured on immobilized beads over a limited axial range, while many experiments are performed using freely mobile beads. This inconsistency raises the possibility of incorrect estimates of experimental uncertainty. By manipulating magnetic beads in a bidirectional magnetic tweezer setup, we evaluated the error associated with tracking mobile magnetic beads and found that the error of tracking a moving magnetic bead increases by almost an order of magnitude compared to the error of tracking a stationary bead. We found that this additional error can be ameliorated by excluding the center-most region of the diffraction ring pattern from tracking analysis. Evaluation of the limitations of a tracking algorithm is essential for understanding the error associated with a measurement. These findings promise to bring increased resolution to three-dimensional bead tracking of magnetic microspheres.

Three-dimensional tracking of nanoparticles by dual-color position retrieval in a double-core microstructured optical fiber

Elastic light scattering-based three-dimensional (3D) tracking of objects at the nanoscale level is essential for unlocking the dynamics of individual species or interactions in fields such as biology or surface chemistry. In this work, we introduce the concept of dual-color 3D tracking in a double-core microstructured optical fiber that for the first time allows for full 3D reconstruction of the trajectory of a diffusing nanoparticle in a water-filled fiber-integrated microchannel. The use of two single-mode cores provides two opposite decaying evanescent fields of different wavelengths within the microchannel, bypassing spatial domains of ambiguous correlation between the scattered intensity and position. The novelty of the fiber design is the use of two slightly different single-mode cores, preventing modal crosstalk and thus allowing for longitudinally invariant dual-color illumination across the entire field of view. To demonstrate the capabilities of the scheme, a single gold nanosphere (80 nm) diffusing in the water-filled microchannel was tracked for a large number of images (about 32 000) at a high frame rate (1.389 kHz) over a long time (23 s), with the determined hydrodynamic diameters matching expectations. The presented 3D tracking approach yields unique opportunities to unlock processes at the nanoscale level and is highly relevant for a multitude of fields, particularly within the context of understanding sophisticated interaction of diffusing species with functionalized surfaces within the context of bioanalytics, nanoscale materials science, surface chemistry or life science.

Multifocal imaging for precise, label-free tracking of fast biological processes in 3D

Many biological processes happen on a nano- to millimeter scale and within milliseconds. Established methods such as confocal microscopy are suitable for precise 3D recordings but lack the temporal or spatial resolution to resolve fast 3D processes and require labeled samples. Multifocal imaging (MFI) allows high-speed 3D imaging but is limited by the compromise between high spatial resolution and large field-of-view (FOV), and the requirement for bright fluorescent labels. Here, we provide an open-source 3D reconstruction algorithm for multi-focal images that allows using MFI for fast, precise, label-free tracking spherical and filamentous structures in a large FOV and across a high depth. We characterize fluid flow and flagellar beating of human and sea urchin sperm with a z-precision of 0.15 µm, in a volume of 240 × 260 × 21 µm, and at high speed (500 Hz). The sampling volume allowed to follow sperm trajectories while simultaneously recording their flagellar beat. Our MFI concept is cost-effective, can be easily implemented, and does not rely on object labeling, which renders it broadly applicable.

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.

Light scattering from colloidal aggregates on a hierarchy of length scales

Disordered dielectrics with structural correlations on length scales comparable to visible light wavelengths exhibit interesting optical properties. Such materials exist in nature, leading to beautiful structural non-iridescent color, and they are also increasingly used as building blocks for optical materials and coatings. In this article, we explore the angular resolved single-scattering properties of micron-sized, disordered colloidal assemblies. The aggregates act as structurally colored supraparticles or as building blocks for macroscopic photonic glasses. We obtain first experimental data for the differential scattering and transport cross-section. Based on existing macroscopic models, we develop a theoretical framework to describe the scattering from densely packed colloidal assemblies on a hierarchy of length scales.

A Novel Approach for a Chip-Sized Scanning Optical Microscope

The recent advances in chip-size microscopy based on optical scanning with spatially resolved nano-illumination light sources are presented. This new straightforward technique takes advantage of the currently achieved miniaturization of LEDs in fully addressable arrays. These nano-LEDs are used to scan the sample with a resolution comparable to the LED sizes, giving rise to chip-sized scanning optical microscopes without mechanical parts or optical accessories. The operation principle and the potential of this new kind of microscope are analyzed through three different implementations of decreasing LED dimensions from 20 µm down to 200 nm.

Characterising soft matter using machine learning

Machine learning is making a major impact in materials research. I review current progress across a selection of areas of ubiquitous soft matter. When applied to particle tracking, machine learning using convolution neural networks is providing impressive performance but there remain some significant problems to solve. Characterising ordered arrangements of particles is a huge challenge and machine learning has been deployed to create the description, perform the classification and tease out an interpretation using a wide array of techniques often with good success. In glass research, machine learning has proved decisive in quantifying very subtle correlations between the local structure around a site and the susceptibility towards a rearrangement event at that site. There are also beginning to be some impressive attempts to deploy machine learning in the design of composite soft materials. The discovery aspect of this new materials design meets the current interest in teaching algorithms to learn to extrapolate beyond the training data.

Astigmatic dual-beam interferometric particle imaging for metal droplet 3D position and size measurement

We propose astigmatic dual-beam interferometric particle imaging (ADIPI) to simultaneously measure the three-dimensional (3D) position and size of spherical metal droplets. A theoretical model reveals that the orientation and spacing of the ADIPI fringes generated from the two reflections propagating through an astigmatic imaging system relate to the depth position and size, respectively. Proof-of-concept experiments on micron-sized gallium droplets are performed, and the tilted fringes in elliptical patterns are observed in the ADIPI interferogram, confirming theoretical predictions. Droplet 3D position and size are determined with ADIPI, and the relative discrepancies are within 5% and 2% compared to those with a dual-view digital inline holography system, demonstrating the feasibility and high accuracy of ADIPI.

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.

Fast and Accurate Nanoparticle Characterization Using Deep-Learning-Enhanced Off-Axis Holography

Characterization of suspended nanoparticles in their native environment plays a central role in a wide range of fields, from medical diagnostics and nanoparticle-enhanced drug delivery to nanosafety and environmental nanopollution assessment. Standard optical approaches for nanoparticle sizing assess the size via the diffusion constant and, as a consequence, require long trajectories and that the medium has a known and uniform viscosity. However, in most biological applications, only short trajectories are available, while simultaneously, the medium viscosity is unknown and tends to display spatiotemporal variations. In this work, we demonstrate a label-free method to quantify not only size but also refractive index of individual subwavelength particles using 2 orders of magnitude shorter trajectories than required by standard methods and without prior knowledge about the physicochemical properties of the medium. We achieved this by developing a weighted average convolutional neural network to analyze holographic images of single particles, which was successfully applied to distinguish and quantify both size and refractive index of subwavelength silica and polystyrene particles without prior knowledge of solute viscosity or refractive index. We further demonstrate how these features make it possible to temporally resolve aggregation dynamics of 31 nm polystyrene nanoparticles, revealing previously unobserved time-resolved dynamics of the monomer number and fractal dimension of individual subwavelength aggregates.

Using the Gouy phase anomaly to localize and track bacteria in digital holographic microscopy 4D images

Described over 100 years ago, the Gouy phase anomaly refers to the additional π phase shift that is accumulated as a wave passes through focus. It is potentially useful in analyzing any type of phase-sensitive imaging; in light microscopy, digital holographic microscopy (DHM) provides phase information in the encoded hologram. One limitation of DHM is the weak contrast generated by many biological cells, especially unpigmented bacteria. We demonstrate here that the Gouy phase anomaly may be detected directly in the phase image using the z-derivative of the phase, allowing for precise localization of unlabeled, micrometer-sized bacteria. The use of dyes that increase phase contrast does not improve detectability. This approach is less computationally intensive than other procedures such as deconvolution and is relatively insensitive to reconstruction parameters. The software is implemented in an open-source FIJI plug-in.

Separating twin images in digital holographic microscopy using weak scatterers

When using inline digital holographic microscopy (DHM) and placing the hologram plane within a particle suspension, both real and virtual images come into focus during reconstruction, limiting our ability to resolve three-dimensional (3D) particle distribution. Here, we propose a new method to distinguish between real and virtual images in the 3D reconstruction field. This new method is based on the use of weak scatterers, and the fact that the real and virtual images of weak scatterers display distinct intensity distributions along the optical axis. We experimentally demonstrate this method by localizing and tracking 1 µm particles in a 3D volume with a particle concentration ranging from 200 to 6000particles/mm³. Unlike previous approaches to address the virtual image problem, this method does not require the recording of multiple holograms or the insertion of additional optical components. The proposed method allows the hologram plane to be placed within the sample volume, and extends the capability of DHM to measure the 3D movements of particles in deep samples far away from the optical window.

Diffusion-Based Height Analysis Reveals Robust Microswimmer-Wall Separation

Microswimmers typically move near walls, which can strongly influence their motion. However, direct experimental measurements of swimmer-wall separation remain elusive to date. Here, we determine this separation for model catalytic microswimmers from the height dependence of the passive component of their mean-squared displacement. We find that swimmers exhibit "ypsotaxis," a tendency to assume a fixed height above the wall for a range of salt concentrations, swimmer surface charges, and swimmer sizes. Our findings indicate that ypsotaxis is activity induced, posing restrictions on future modeling of their still-debated propulsion mechanism.

Microrheology for biomaterial design

Microrheology analyzes the microscopic behavior of complex materials by measuring the diffusion and transport of embedded particle probes. This experimental method can provide valuable insight into the design of biomaterials with the ability to connect material properties and biological responses to polymer-scale dynamics and interactions. In this review, we discuss how microrheology can be harnessed as a characterization method complementary to standard techniques in biomaterial design. We begin by introducing the core principles and instruments used to perform microrheology. We then review previous studies that incorporate microrheology in their design process and highlight biomedical applications that have been supported by this approach. Overall, this review provides rationale and practical guidance for the utilization of microrheological analysis to engineer novel biomaterials.