Holographic deconvolution microscopy for high-resolution particle tracking

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.

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.

Advancing the science of dynamic airborne nanosized particles using Nano-DIHM

In situ and real-time characterization of aerosols is vital to several fundamental and applied research domains including atmospheric chemistry, air quality monitoring, or climate change studies. To date, digital holographic microscopy is commonly used to characterize dynamic nanosized particles, but optical traps are required. In this study, a novel integrated digital in-line holographic microscope coupled with a flow tube (Nano-DIHM) is demonstrated to characterize particle phase, shape, morphology, 4D dynamic trajectories, and 3D dimensions of airborne particles ranging from the nanoscale to the microscale. We demonstrate the application of Nano-DIHM for nanosized particles (≤200 nm) in dynamic systems without optical traps. The Nano-DIHM allows observation of moving particles in 3D space and simultaneous measurement of each particle's three dimensions. As a proof of concept, we report the real-time observation of 100 nm and 200 nm particles, i.e. polystyrene latex spheres and the mixture of metal oxide nanoparticles, in air and aqueous/solid/heterogeneous phases in stationary and dynamic modes. Our observations are validated by high-resolution scanning/transmission electron microscopy and aerosol sizers. The complete automation of software (Octopus/Stingray) with Nano-DIHM permits the reconstruction of thousands of holograms within an hour with 62.5 millisecond time resolution for each hologram, allowing to explore the complex physical and chemical processes of aerosols.

Improving axial localization of weak phase particles in digital in-line holography

One shortcoming of digital in-line holography (DIH) is the low axial position accuracy due to the elongated particle traces in the reconstruction field. Here, we propose a method that improves the axial localization of DIH when applying it to track the motion of weak phase particles in dense suspensions. The proposed method detects particle positions based on local intensities in the reconstruction field consisting of scattering and incident waves. We perform both numerical and experimental tests and demonstrate that the proposed method has a higher axial position accuracy than the previous method based on the local intensities in the reconstructed scattered field. We show that the proposed method has an axial position error below 1.5 particle diameters for holograms with a particle concentration of 4700particles/mm³. The proposed method is further validated by tracking the Brownian motion of 1µmparticles in dense suspensions.

3D monitoring of the surface slippage effect on micro-particle sedimentation by digital holographic microscopy

In several phenomena in biology and industry, it is required to understand the comprehensive behavior of sedimenting micro-particles in fluids. Here, we use the numerical refocusing feature of digital holographic microscopy (DHM) to investigate the slippage effect on micro-particle sedimentation near a flat wall. DHM provides quantitative phase contrast and three-dimensional (3D) imaging in arbitrary time scales, which suggests it as an elegant approach to investigate various phenomena, including dynamic behavior of colloids. 3D information is obtained by post-processing of the recorded digital holograms. Through analysis of 3D trajectories and velocities of multiple sedimenting micro-particles, we show that proximity to flat walls of higher slip lengths causes faster sedimentation. The effect depends on the ratio of the particle size to (1) the slip length and (2) its distance to the wall. We corroborate our experimental findings by a theoretical model which considers both the proximity and the particle interaction to a wall of different hydrophobicity in the hydrodynamic forces.

Three-dimensional volumetric deconvolution in coherent optics and holography

Methods of three-dimensional deconvolution (3DD) or volumetric deconvolution of optical complex-valued wavefronts diffracted by 3D samples with the 3D point spread function are presented. Particularly, the quantitative correctness of the recovered 3D sample distributions is addressed. Samples consisting of point-like objects can be retrieved from their 3D diffracted wavefronts with non-iterative (Wiener filter) 3DD. Continuous extended samples, including complex-valued (phase) samples, can be retrieved with iterative (Gold and Richardson-Lucy) 3DD algorithms. It is shown that quantitatively correct 3D sample distribution can be recovered only with iterative 3DD, and with the optimal protocols provided. It is demonstrated that 3DD can improve the lateral resolution to the resolution limit, and the axial resolution can be at least four times better than the resolution limit. The presented 3DD methods of complex-valued optical fields can be applied for 3D optical imaging and holography.

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.

2D vs 3D tracking in bacterial motility analysis

<abstract> <p>Digital holographic microscopy provides the ability to observe throughout a large volume without refocusing. This capability enables simultaneous observations of large numbers of microorganisms swimming in an essentially unconstrained fashion. However, computational tools for tracking large 4D datasets remain lacking. In this paper, we examine the errors introduced by tracking bacterial motion as 2D projections vs. 3D volumes under different circumstances: bacteria free in liquid media and bacteria near a glass surface. We find that while XYZ speeds are generally equal to or larger than XY speeds, they are still within empirical uncertainties. Additionally, when studying dynamic surface behavior, the Z coordinate cannot be neglected.</p> </abstract>

Height distribution and orientation of colloidal dumbbells near a wall

Geometric confinement strongly influences the behavior of microparticles in liquid environments. However, to date, nonspherical particle behaviors close to confining boundaries, even as simple as planar walls, remain largely unexplored. Here, we measure the height distribution and orientation of colloidal dumbbells above walls by means of digital in-line holographic microscopy. We find that while larger dumbbells are oriented almost parallel to the wall, smaller dumbbells of the same material are surprisingly oriented at preferred angles. We determine the total height-dependent force acting on the dumbbells by considering gravitational effects and electrostatic particle-wall interactions. Our modeling reveals that at specific heights both net forces and torques on the dumbbells are simultaneously below the thermal force and energy, respectively, which makes the observed orientations possible. Our results highlight the rich near-wall dynamics of nonspherical particles and can further contribute to the development of quantitative frameworks for arbitrarily shaped microparticle dynamics in confinement.

Regularized inverse holographic volume reconstruction for 3D particle tracking

The key limitations of digital inline holography (DIH) for particle tracking applications are poor longitudinal resolution, particle concentration limits, and case-specific processing. We utilize an inverse problem method with fused lasso regularization to perform full volumetric reconstructions of particle fields. By exploiting data sparsity in the solution and utilizing GPU processing, we dramatically reduce the computational cost usually associated with inverse reconstruction approaches. We demonstrate the accuracy of the proposed method using synthetic and experimental holograms. Finally, we present two practical applications (high concentration microorganism swimming and microfiber rotation) to extend the capabilities of DIH beyond what was possible using prior methods.

Real-time parallel 3D multiple particle tracking with single molecule centrifugal force microscopy

Real-time tracking of multiple particles is key for quantitative analysis of dynamic biophysical processes and materials science via time-lapse microscopy image data, especially for single molecule biophysical techniques, such as magnetic tweezers and centrifugal force microscopy. However, real-time multiple particle tracking with high resolution is limited by the current imaging processes or tracking algorithms. Here, we demonstrate 1 nm resolution in three dimensions in real-time with a graphics-processing unit (GPU) based on a compute unified device architecture (CUDA) parallel computing framework instead of only a central processing unit (CPU). We also explore the trade-offs between processing speed and size of the utilized regions of interest and a maximum speedup of 137 is achieved with the GPU compared with the CPU. Moreover, we utilize this method with our recently self-built centrifugal force microscope (CFM) in experiments that track multiple DNA-tethered particles. Our approach paves the way for high-throughput single molecule techniques with high resolution and efficiency. LAY DESCRIPTION: Particles are widely used as probes in life sciences through their motions. In single molecule techniques such as optical tweezers and magnetic tweezers, microbeads are used to study intermolecular or intramolecular interactions via beads tracking. Also tracking multiple beads' motions could study cell-cell or cell-ECM interactions in traction force microscopy. Therefore, particle tracking is of key important during these researches. However, parallel 3D multiple particle tracking in real-time with high resolution is a challenge either due to the algorithm or the program. Here, we combine the performance of CPU and CUDA-based GPU to make a hybrid implementation for particle tracking. In this way, a speedup of 137 is obtained compared the program before only with CPU without loss of accuracy. Moreover, we improve and build a new centrifugal force microscope for multiple single molecule force spectroscopy research in parallel. Then we employed our program into centrifugal force microscope for DNA stretching study. Our results not only demonstrate the application of this program in single molecule techniques, also indicate the capability of multiple single molecule study with centrifugal force microscopy.

Enhancement of the 'tractor-beam' pulling force on an optically bound structure

Recently, increasing attention has been devoted to mastering a new technique of optical delivery of micro-objects tractor-beam'1, 2, 3, 4, 5, 6, 7, 8, 9. Such beams have uniform intensity profiles along their propagation direction and can exert a negative force that, in contrast to the familiar pushing force associated with radiation pressure, pulls the scatterer toward the light source. It was experimentally observed that under certain circumstances, the pulling force can be significantly enhanced6 if a non-spherical scatterer, for example, a linear chain of optically bound objects10, 11, 12, is optically transported. Here we demonstrate that motion of two optically bound objects in a tractor beam strongly depends on theirs mutual distance and spatial orientation. Such configuration-dependent optical forces add extra flexibility to our ability to control matter with light. Understanding these interactions opens the door to new applications involving the formation, sorting or delivery of colloidal self-organized structures.

Seeing the unseen: Imaging rotation in cells with designer anisotropic particles

Cellular functions are enabled by cascades of transient biological events. Imaging and tracking the dynamics of these events have proven to be a powerful means of understanding the principles of cellular processes. These studies have typically focused on translational dynamics. By contrast, investigations of rotational dynamics have been scarce, despite emerging evidence that rotational dynamics are an inherent feature of many cellular processes and may also provide valuable clues to understanding those cell functions. Such studies have been impeded by the limited availability of suitable rotational imaging probes. This has recently changed thanks to the advances in the development of anisotropic particles for rotational imaging. In this review, we will summarize current techniques for imaging rotation using particle probes that are anisotropic in shape or optical properties. We will highlight two studies that demonstrate how these techniques can be applied to explore important facets of cellular functions.

Compressive holographic video

Compressed sensing has been discussed separately in spatial and temporal domains. Compressive holography has been introduced as a method that allows 3D tomographic reconstruction at different depths from a single 2D image. Coded exposure is a temporal compressed sensing method for high speed video acquisition. In this work, we combine compressive holography and coded exposure techniques and extend the discussion to 4D reconstruction in space and time from one coded captured image. In our prototype, digital in-line holography was used for imaging macroscopic, fast moving objects. The pixel-wise temporal modulation was implemented by a digital micromirror device. In this paper we demonstrate 10× temporal super resolution with multiple depths recovery from a single image. Two examples are presented for the purpose of recording subtle vibrations and tracking small particles within 5 ms.

Spatially Resolved Two-Dimensional Infrared Spectroscopy via Wide-Field Microscopy

We report the first wide-field microscope for measuring two-dimensional infrared (2D IR) spectroscopic images. We concurrently collect more than 16 000 2D IR spectra, made possible by a new focal plane array detector and mid-IR pulse shaping, to generate hyperspectral images with multiple frequency dimensions and diffraction-limited spatial resolution. Both frequency axes of the spectra are collected in the time domain by scanning two pairs of femtosecond pulses using a dual acousto-optic modulator pulse shaper. The technique is demonstrated by imaging a mixture of metal carbonyl absorbed polystyrene beads. The differences in image formation between FTIR and 2D IR microscopy are also explored by imaging a patterned USAF test target. We find that our 2D IR microscope has diffraction-limited spatial resolution and enhanced contrast compared to FTIR microscopy because of the nonlinear scaling of the 2D IR signal to the absorptivity coefficient for the vibrational modes. Images generated using off-diagonal peaks, created from vibrational anharmonicities, improve the molecular discrimination and eliminate noise. Two-dimensional wide-field IR microscopy provides information on vibrational lifetimes, molecular couplings, transition dipole orientations, and many other quantities that can be used for creating image contrast to help disentangle and interpret complex and heterogeneous samples. Such experiments made possible could include the study of amyloid proteins in tissues, protein folding in heterogeneous environments, and structural dynamics in devices employing mid-IR materials.

Holographic Characterization of Protein Aggregates

We demonstrate how holographic video microscopy can be used to detect, count, and characterize individual micrometer-scale protein aggregates as they flow down a microfluidic channel in their native buffer. Holographic characterization directly measures the radius and refractive index of subvisible protein aggregates and offers insights into their morphologies. The measurement proceeds fast enough to build up population averages for time-resolved studies and lends itself to tracking trends in protein aggregation arising from changing environmental factors. Information on individual particle's refractive indexes can be used to differentiate protein aggregates from such contaminants as silicone droplets. These capabilities are demonstrated through measurements on samples of bovine pancreas insulin aggregated through centrifugation and of bovine serum albumin aggregated by complexation with a polyelectrolyte. Differentiation is demonstrated with samples that have been spiked with separately characterized silicone spheres. Holographic characterization measurements are compared with results obtained with microflow imaging and dynamic light scattering.

Rapid, high-throughput tracking of bacterial motility in 3D via phase-contrast holographic video microscopy

Tracking fast-swimming bacteria in three dimensions can be extremely challenging with current optical techniques and a microscopic approach that can rapidly acquire volumetric information is required. Here, we introduce phase-contrast holographic video microscopy as a solution for the simultaneous tracking of multiple fast moving cells in three dimensions. This technique uses interference patterns formed between the scattered and the incident field to infer the three-dimensional (3D) position and size of bacteria. Using this optical approach, motility dynamics of multiple bacteria in three dimensions, such as speed and turn angles, can be obtained within minutes. We demonstrated the feasibility of this method by effectively tracking multiple bacteria species, including Escherichia coli, Agrobacterium tumefaciens, and Pseudomonas aeruginosa. In addition, we combined our fast 3D imaging technique with a microfluidic device to present an example of a drug/chemical assay to study effects on bacterial motility.

High fidelity digital inline holographic method for 3D flow measurements

Among all the 3D optical flow diagnostic techniques, digital inline holographic particle tracking velocimetry (DIH-PTV) provides the highest spatial resolution with low cost, simple and compact optical setups. Despite these advantages, DIH-PTV suffers from major limitations including poor longitudinal resolution, human intervention (i.e. requirement for manually determined tuning parameters during tracer field reconstruction and extraction), limited tracer concentration, and expensive computations. These limitations prevent this technique from being widely used for high resolution 3D flow measurements. In this study, we present a novel holographic particle extraction method with the goal of overcoming all the major limitations of DIH-PTV. The proposed method consists of multiple steps involving 3D deconvolution, automatic signal-to-noise ratio enhancement and thresholding, and inverse iterative particle extraction. The entire method is implemented using GPU-based algorithm to increase the computational speed significantly. Validated with synthetic particle holograms, the proposed method can achieve particle extraction rate above 95% with fake particles less than 3% and maximum position error below 1.6 particle diameter for holograms with particle concentration above 3000 particles/mm³. The applicability of the proposed method for DIH-PTV has been further validated using the experiment of laminar flow in a microchannel and the synthetic tracer flow fields generated using a DNS turbulent channel flow database. Such improvements will substantially enhance the implementation of DIH-PTV for 3D flow measurements and enable the potential commercialization of this technique.

Robust and highly performant ring detection algorithm for 3d particle tracking using 2d microscope imaging

Three-dimensional particle tracking is an essential tool in studying dynamics under the microscope, namely, fluid dynamics in microfluidic devices, bacteria taxis, cellular trafficking. The 3d position can be determined using 2d imaging alone by measuring the diffraction rings generated by an out-of-focus fluorescent particle, imaged on a single camera. Here I present a ring detection algorithm exhibiting a high detection rate, which is robust to the challenges arising from ring occlusion, inclusions and overlaps, and allows resolving particles even when near to each other. It is capable of real time analysis thanks to its high performance and low memory footprint. The proposed algorithm, an offspring of the circle Hough transform, addresses the need to efficiently trace the trajectories of many particles concurrently, when their number in not necessarily fixed, by solving a classification problem, and overcomes the challenges of finding local maxima in the complex parameter space which results from ring clusters and noise. Several algorithmic concepts introduced here can be advantageous in other cases, particularly when dealing with noisy and sparse data. The implementation is based on open-source and cross-platform software packages only, making it easy to distribute and modify. It is implemented in a microfluidic experiment allowing real-time multi-particle tracking at 70 Hz, achieving a detection rate which exceeds 94% and only 1% false-detection.

Nano-level position resolution for particle tracking in digital in-line holographic microscopy

Three-dimensional particle tracking in biological systems is a quickly growing field, many techniques have been developed providing tracking characters. Digital in-line holographic microscopy is a valuable technique for particle tracking. However, the speckle noise, out-of-focus signals and twin image influenced the particle tracking. Here an adaptive noise reduction method based on bidimensional ensemble empirical mode decomposition is introduced into digital in-line holographic microscopy. It can eliminate the speckle noise and background of the hologram adaptively. Combined with the three-dimensional deconvolution approach in the reconstruction, the particle feature would be identified effectively. Tracking the fixed beads on the cover-glass with piezoelectric stage through multiple holographic images demonstrate the tracking resolution, which approaches 2 nm in axial direction and 1 nm in transverse direction. This would facilitate the development and use in the biological area such as living cells and single-molecule approaches.

Three-dimensional motion detection of a 20-nm gold nanoparticle using twilight-field digital holography with coherence regulation

In the twilight-field method for obtaining interference fringes with high contrast in in-line digital holography, only the intensity of the reference light is regulated to be close to the intensity of the object light, which is the ultra-weak scattered light from a nanoparticle, by using a low-frequency attenuation filter. Coherence of the light also strongly affects the contrast of the interference fringes. High coherence causes a lot of undesired coherent noise, which masks the fringes derived from the nanoparticles. Too-low coherence results in fringes with low contrast and a correspondingly low signal-to-noise ratio. Consequently, proper regulation of the coherence of the light source, in this study the spectral width, improves the minimum detectable size in holographic three-dimensional position measurement of nanoparticles. By using these methods, we were able to measure the position of a gold nanoparticle with a minimum diameter of 20 nm.

Wide-field FTIR microscopy using mid-IR pulse shaping

We have developed a new table-top technique for collecting wide-field Fourier transform infrared (FTIR) microscopic images by combining a femtosecond pulse shaper with a mid-IR focal plane array. The pulse shaper scans the delay between a pulse pair extremely rapidly for high signal-to-noise, while also enabling phase control of the individual pulses to under-sample the interferograms and subtract background. Infrared absorption images were collected for a mixture of W(CO)₆ or Mn₂(CO)₁₀ absorbed polystyrene beads, demonstrating that this technique can spatially resolve chemically distinct species. The images are sub-diffraction limited, as measured with a USAF test target patterned on CaF₂ and verified with scalar wave simulations. We also find that refractive, rather than reflective, objectives are preferable for imaging with coherent radiation. We discuss this method with respect to conventional FTIR microscopes.

3D tracking the Brownian motion of colloidal particles using digital holographic microscopy and joint reconstruction

In-line digital holography is a valuable tool for sizing, locating, and tracking micro- or nano-objects in a volume. When a parametric imaging model is available, inverse problem approaches provide a straightforward estimate of the object parameters by fitting data with the model, thereby allowing accurate reconstruction. As recently proposed and demonstrated, combining pixel super-resolution techniques with inverse problem approaches improves the estimation of particle size and 3D position. Here, we demonstrate the accurate tracking of colloidal particles in Brownian motion. Particle size and 3D position are jointly optimized from video holograms acquired with a digital holographic microscopy setup based on a low-end microscope objective (×20, NA 0.5). Exploiting information redundancy makes it possible to characterize particles with a standard deviation of 15 nm in size and a theoretical resolution of 2×2×5  nm³ for position under additive white Gaussian noise assumption.

Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders

Quantitative phase microscopy (QPM) has recently emerged as a new powerful quantitative imaging technique well suited to noninvasively explore a transparent specimen with a nanometric axial sensitivity. In this review, we expose the recent developments of quantitative phase-digital holographic microscopy (QP-DHM). Quantitative phase-digital holographic microscopy (QP-DHM) represents an important and efficient quantitative phase method to explore cell structure and dynamics. In a second part, the most relevant QPM applications in the field of cell biology are summarized. A particular emphasis is placed on the original biological information, which can be derived from the quantitative phase signal. In a third part, recent applications obtained, with QP-DHM in the field of cellular neuroscience, namely the possibility to optically resolve neuronal network activity and spine dynamics, are presented. Furthermore, potential applications of QPM related to psychiatry through the identification of new and original cell biomarkers that, when combined with a range of other biomarkers, could significantly contribute to the determination of high risk developmental trajectories for psychiatric disorders, are discussed.

Random-subset fitting of digital holograms for fast three-dimensional particle tracking [invited]

Fitting scattering solutions to time series of digital holograms is a precise way to measure three-dimensional dynamics of microscale objects such as colloidal particles. However, this inverse-problem approach is computationally expensive. We show that the computational time can be reduced by an order of magnitude or more by fitting to a random subset of the pixels in a hologram. We demonstrate our algorithm on experimentally measured holograms of micrometer-scale colloidal particles, and we show that 20-fold increases in speed, relative to fitting full frames, can be attained while introducing errors in the particle positions of 10 nm or less. The method is straightforward to implement and works for any scattering model. It also enables a parallelization strategy wherein random-subset fitting is used to quickly determine initial guesses that are subsequently used to fit full frames in parallel. This approach may prove particularly useful for studying rare events, such as nucleation, that can only be captured with high frame rates over long times.

Holographic time-resolved particle tracking by means of three-dimensional volumetric deconvolution

Holographic particle image velocimetry allows tracking particle trajectories in time and space by means of holography. However, the drawback of the technique is that in the three-dimensional particle distribution reconstructed from a hologram, the individual particles can hardly be resolved due to the superimposed out-of-focus signal from neighboring particles. We demonstrate here a three-dimensional volumetric deconvolution applied to the reconstructed wavefront which results in resolving all particles simultaneously in three-dimensions. Moreover, we apply the three-dimensional volumetric deconvolution to reconstructions of a time-dependent sequence of holograms of an ensemble of polystyrene spheres moving in water. From each hologram we simultaneously resolve all particles in the ensemble in three dimensions and from the sequence of holograms we obtain the time-resolved trajectories of individual polystyrene spheres.

Partially coherent digital in-line holographic microscopy in characterization of a microscopic target

Digital holographic microscopy enables the capture of large three-dimensional volumes. Instead of using a laser as an illumination source, partially coherent alternatives can be used, such as light-emitting diodes, which produce parasitic reflection and speckle-free holograms. Captured high-contrast holograms are suitable for the characterization of micrometer-sized particles. As the reconstructed phase is not usable in the case of multiple overlapping objects, depth extraction can be conducted on a reconstructed intensity. This work introduces a novel depth extraction algorithm that takes into consideration the possible locations of multiple objects at various depths in the imaged volume. The focus metric, the Tamura coefficient, is applied for each pixel in the reconstructed amplitude throughout the volume. This work also introduces an optimized version of the algorithm, which is run in two stages. During the first stage, coarse positions of the objects are extracted by applying the Tamura coefficient to nonoverlapping window blocks of intensity reconstructions. The second stage produces high-precision characterizations of the objects by calculating the Tamura coefficient with overlapping window blocks around axial positions extracted in the first stage. Experimental results with real-world microscopic objects show the effectiveness of the proposed method.

5D-Tracking of a nanorod in a focused laser beam--a theoretical concept

Back-focal plane (BFP) interferometry is a very fast and precise method to track the 3D position of a sphere within a focused laser beam using a simple quadrant photo diode (QPD). Here we present a concept of how to track and recover the 5D state of a cylindrical nanorod (3D position and 2 tilt angles) in a laser focus by analyzing the interference of unscattered light and light scattered at the cylinder. The analytical theoretical approach is based on Rayleigh-Gans scattering together with a local field approximation for an infinitely thin cylinder. The approximated BFP intensities compare well with those from a more rigorous numerical approach. It turns out that a displacement of the cylinder results in a modulation of the BFP intensity pattern, whereas a tilt of the cylinder results in a shift of this pattern. We therefore propose the concept of a local QPD in the BFP of a detection lens, where the QPD center is shifted by the angular coordinates of the cylinder tilt.

Local characterization of hindered Brownian motion by using digital video microscopy and 3D particle tracking

In this article we present methods for measuring hindered Brownian motion in the confinement of complex 3D geometries using digital video microscopy. Here we discuss essential features of automated 3D particle tracking as well as diffusion data analysis. By introducing local mean squared displacement-vs-time curves, we are able to simultaneously measure the spatial dependence of diffusion coefficients, tracking accuracies and drift velocities. Such local measurements allow a more detailed and appropriate description of strongly heterogeneous systems as opposed to global measurements. Finite size effects of the tracking region on measuring mean squared displacements are also discussed. The use of these methods was crucial for the measurement of the diffusive behavior of spherical polystyrene particles (505 nm diameter) in a microfluidic chip. The particles explored an array of parallel channels with different cross sections as well as the bulk reservoirs. For this experiment we present the measurement of local tracking accuracies in all three axial directions as well as the diffusivity parallel to the channel axis while we observed no significant flow but purely Brownian motion. Finally, the presented algorithm is suitable also for tracking of fluorescently labeled particles and particles driven by an external force, e.g., electrokinetic or dielectrophoretic forces.

Accurate 3D tracking and size measurement of evaporating droplets using in-line digital holography and "inverse problems" reconstruction approach

Digital in-line holography was used to study a fast dynamic 3D phenomenon: the evaporation of free-falling diethyl ether droplets. We describe an unsupervised reconstruction algorithm based on an "inverse problems" approach previously developed by our team to accurately reconstruct 3D trajectories and to estimate the droplets' size in a field of view of 7 × 11 × 20 mm 3. A first experiment with non-evaporating droplets established that the radius estimates were accurate to better than 0.1 μm . With evaporating droplets, the vapor around the droplet distorts the diffraction patterns in the holograms. We showed that areas with the strongest distortions can be discarded using an exclusion mask. We achieved radius estimates better than 0.5 μm accuracy for evaporating droplets. Our estimates of the evaporation rate fell within the range predicted by theoretical models.

Digital holography simulations and experiments to quantify the accuracy of 3D particle location and 2D sizing using a proposed hybrid method

The accuracy of digital in-line holography to detect particle position and size within a 3D domain is evaluated with particular focus placed on detection of nonspherical particles. Dimensionless models are proposed for simulation of holograms from single particles, and these models are used to evaluate the uncertainty of existing particle detection methods. From the lessons learned, a new hybrid method is proposed. This method features automatic determination of optimum thresholds, and simulations indicate improved accuracy compared to alternative methods. To validate this, experiments are performed using quasi-stationary, 3D particle fields with imposed translations. For the spherical particles considered in experiments, the proposed hybrid method resolves mean particle concentration and size to within 4% of the actual value, while the standard deviation of particle depth is less than two particle diameters. Initial experimental results for nonspherical particles reveal similar performance.

Accurate holographic imaging of colloidal particle pairs by Rayleigh-Sommerfeld reconstruction

In-line holographic optical imaging has the unique capability of high speed imaging in three dimensions at rates limited only by the imaging rate of the camera used. In this technique the 3D data is recorded on the detector in a form of a hologram generated by diffraction between the scattered and unscattered light passing through the sample. For dilute samples of single particles or a small cluster of particles, this technique was shown to result in particle tracking with spatial positioning accuracy of a few nanometers. For dense suspension only approximate reconstruction were achieved with systematic axial positioning errors. We propose a scheme to extend accurate holographic microscopy to dense suspensions, by calibrating the Rayleigh-Sommerfeld reconstruction algorithm against Lorentz-Mie scattering theory. We perform this calibration both numerically and experimentally and define the parameter space in which accurate imaging is achieved, and in which numerical calibration holds. We demonstrate the validity of our approach by imaging two attached particles and measuring the distance between their centers with 36 nm accuracy. A difference of 50 nm in particle diameter is easily measured.

Exploring neural cell dynamics with digital holographic microscopy

In this review, we summarize how the new concept of digital optics applied to the field of holographic microscopy has allowed the development of a reliable and flexible digital holographic quantitative phase microscopy (DH-QPM) technique at the nanoscale particularly suitable for cell imaging. Particular emphasis is placed on the original biological information provided by the quantitative phase signal. We present the most relevant DH-QPM applications in the field of cell biology, including automated cell counts, recognition, classification, three-dimensional tracking, discrimination between physiological and pathophysiological states, and the study of cell membrane fluctuations at the nanoscale. In the last part, original results show how DH-QPM can address two important issues in the field of neurobiology, namely, multiple-site optical recording of neuronal activity and noninvasive visualization of dendritic spine dynamics resulting from a full digital holographic microscopy tomographic approach.

Separation of overlapped particles in digital holographic microscopy

In this paper, we present a procedure to separate aggregates of overlapped particles in digital holograms, based on a focus plane analysis applied to each particle. The method can be applied either on phase or on amplitude objects, according that each object has a border in one focus plane. Numerical simulations are performed to quantify the robustness of the process by increasing the overlapping areas between the particles. The separation algorithm is successfully demonstrated experimentally on different types of aggregates.

Three-dimensional subpixel estimation in holographic position measurement of an optically trapped nanoparticle

We propose three-dimensional (3D) subpixel estimation in the position measurement of a nanoparticle held in optical tweezers in water by using an in-line, low-coherence digital holographic microscope. The 3D subpixel estimation was performed with the addition of axial subpixel estimation to the lateral subpixel estimation introduced in our previous work [Appl. Opt.50, H183 (2011)]. The axial subpixel estimation allowed the step length in the diffraction calculation of a hologram to be increased to ~20 nm while keeping the axial resolution of ~3 nm. This drastically decreased the computation time of the diffraction calculation to less than 10% of the two-dimensional subpixel estimation.

Digital holographic microscope with low-frequency attenuation filter for position measurement of a nanoparticle

We propose a new method for three-dimensional (3D) position measurement of nanoparticles using an in-line digital holographic microscope. The method improves the signal-to-noise ratio of the amplitude of the interference fringes to achieve higher accuracy in the position measurement by increasing weak scattered light from a nanoparticle relative to the reference light by using a low spatial frequency attenuation filter. We demonstrated the improvements of signal-to-noise ratio of the optical system and contrast of the interference fringes, allowing the 3D positions of nanoparticles to be determined more precisely.

Improved particle size estimation in digital holography via sign matched filtering

A matched filter method is provided for obtaining improved particle size estimates from digital in-line holograms. This improvement is relative to conventional reconstruction and pixel counting methods for particle size estimation, which is greatly limited by the CCD camera pixel size. The proposed method is based on iterative application of a sign matched filter in the Fourier domain, with sign meaning the matched filter takes values of ±1 depending on the sign of the angular spectrum of the particle aperture function. Using simulated data the method is demonstrated to work for particle diameters several times the pixel size. Holograms of piezoelectrically generated water droplets taken in the laboratory show greatly improved particle size measurements. The method is robust to additive noise and can be applied to real holograms over a wide range of matched-filter particle sizes.

Three-dimensional positioning of optically trapped nanoparticles

We firstly demonstrate the three-dimensional (3D) measurement of a nanometer-sized sphere held in optical tweezers in water using an in-line digital holographic microscope with a green light emitting diode. Suppressing the movement with optical tweezers enabled us to detect the three-dimensional position of a polystyrene sphere with a diameter of 200 nm. The positioning resolutions of the microscope were 3.2 nm in the transverse direction and 3.4 nm in the axial direction, from the standard deviation of measurements of the 200 nm sphere fixed on glass. Changes in the Brownian motion in response to a change in the trapping laser power were measured. We also demonstrated that this holographic measurement is an effective method for determining the threshold power of the optical trapping.