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

Autofocusing in digital holography based on an adaptive genetic algorithm

In digital holography (DH), determining the reconstruction distance is critical to the quality of the reconstructed image. However, traditional focal plane detection methods require considerable time investment to reconstruct and evaluate holograms at multiple distances. To address this inefficiency, this paper proposes a fast and accurate autofocusing method based on an adaptive genetic algorithm. This method only needs to find several reconstruction distances in the search area as an initial population, and then adaptively optimize the reconstruction distance through iteration to determine the optimal focal plane in the search area. In addition, an off-axis digital holographic optical system was used to capture the holograms of the USAF resolution test target and the coin. The simulation and experimental results indicated that, compared with the traditional autofocusing, the proposed method can reduce the computation time by about 70% and improve the focal plane accuracy by up to 0.5 mm.

Ultraviolet digital holographic microscopy (DHM) of micron-scale particles from shocked Sn ejecta

A cloud of very fast, O(km/s), and very fine, O(µm), particles may be ejected when a strong shock impacts and possibly melts the free surface of a solid metal. To quantify these dynamics, this work develops an ultraviolet, long-working distance, two-pulse Digital Holographic Microscopy (DHM) configuration and is the first to replace film recording with digital sensors for this challenging application. A proposed multi-iteration DHM processing algorithm is demonstrated for automated measures of the sizes, velocities, and three-dimensional positions of non-spherical particles. Ejecta as small as 2 µm diameter are successfully tracked, while uncertainty simulations indicate that particle size distributions are accurately quantified for diameters ≥4 µm. These techniques are demonstrated on three explosively driven experiments. Measured ejecta size and velocity statistics are shown to be consistent with prior film-based recording, while also revealing spatial variations in velocities and 3D positions that have yet to be widely investigated. Having eliminated time-consuming analog film processing, the methodologies proposed here are expected to significantly accelerate future experimental investigation of ejecta physics.

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.

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.

Single-shot phase-shifting image-plane digital holography with tri-focal Fibonacci-Billet split lens

Phase-shifting holography has been widely applied in the field of non-destructive testing and interference imaging. Compared to the previous single-shot phase-shifting holography, here tri-focal Fibonacci-Billet split lens was introduced into Mach-Zehnder interferometer, in which the upper half of the Fibonacci-Billet split lens can realize three phase-locking copies of the planar reference wave and the lower half is used to generate three identical copies of object. The interference pattern is recorded by a detector in one single exposure. The test object can be reconstructed by three-step phase-shifting interferometry. The corresponding experiment is carried out to verify the effectiveness of this method. With advantages of real-time reconstruction and amplitude-only diffraction lens, it is very useful for fast imaging and optical element detection.

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.

Improving the spatial dynamic range of digital inline particle holography

Digital inline holography has been proven to provide three-dimensional droplet position, size, and velocity distributions with a single camera. These data are crucial for understanding multiphase flows. In this work, we examine the performance of this diagnostic in the limit of very small particles, on the order of a pixel in diameter and smaller, and propose a postprocessing method to improve them: Lanczos interpolation. The Lanczos interpolation kernel is the digital implementation of the Whittaker sinc filter and strikes a compromise between maintaining the spatial frequency ceiling of the original digital image and computational cost of the interpolation. Without Lanczos interpolation, or supersampling, the ultimate detectable particle size floor is on the order of four pixel widths. We show in this work that this limit can be reduced by 50% or more with supersampling, depending upon the desired diameter accuracy, and examine the effect of supersampling on the resulting accuracy of the extracted size and position of spherical particles. Extending this resolution limit increases the overall detection efficiency of the diagnostic. Since this increases the spatial dynamic range of the diagnostic, it can also allow a larger field of view to be captured with the same particle size floor.

Self-calibration for lensless color microscopy

Lensless color microscopy (also called in-line digital color holography) is a recent quantitative 3D imaging method used in several areas including biomedical imaging and microfluidics. By targeting cost-effective and compact designs, the wavelength of the low-end sources used is known only imprecisely, in particular because of their dependence on temperature and power supply voltage. This imprecision is the source of biases during the reconstruction step. An additional source of error is the crosstalk phenomenon, i.e., the mixture in color sensors of signals originating from different color channels. We propose to use a parametric inverse problem approach to achieve self-calibration of a digital color holographic setup. This process provides an estimation of the central wavelengths and crosstalk. We show that taking the crosstalk phenomenon into account in the reconstruction step improves its accuracy.

Comparison of three-dimensional particle tracking and sizing using plenoptic imaging and digital in-line holography

Digital in-line holography (DIH) and plenoptic photography are two techniques for single-shot, volumetric measurement of 3D particle fields. Here we present a comparison of the two methods by applying plenoptic imaging to experimental configurations that have been previously investigated with DIH. These experiments include the tracking of secondary droplets from the impact of a water drop on a thin film of water and tracking of pellets from a shotgun. Both plenoptic imaging and DIH successfully quantify the 3D nature of these particle fields. This includes measurement of the 3D particle position, individual particle sizes, and three-component velocity vectors. For the initial processing methods presented here, both techniques give out-of-plane positional accuracy of approximately 1-2 particle diameters. For a fixed image sensor, digital holography achieves higher effective in-plane spatial resolutions. However, collimated and coherent illumination makes holography susceptible to image distortion through index of refraction gradients, as demonstrated in the shotgun experiments. In contrast, plenoptic imaging allows for a simpler experimental configuration and, due to the use of diffuse, white-light illumination, plenoptic imaging is less susceptible to image distortion in the shotgun experiments.

High-throughput and label-free single nanoparticle sizing based on time-resolved on-chip microscopy

Sizing individual nanoparticles and dispersions of nanoparticles provides invaluable information in applications such as nanomaterial synthesis, air and water quality monitoring, virology, and medical diagnostics. Several conventional nanoparticle sizing approaches exist; however, there remains a lack of high-throughput approaches that are suitable for low-resource and field settings, i.e., methods that are cost-effective, portable, and can measure widely varying particle sizes and concentrations. Here we fill this gap using an unconventional approach that combines holographic on-chip microscopy with vapor-condensed nanolens self-assembly inside a cost-effective hand-held device. By using this approach and capturing time-resolved in situ images of the particles, we optimize the nanolens formation process, resulting in significant signal enhancement for the label-free detection and sizing of individual deeply subwavelength particles (smaller than λ/10) over a 30 mm(2) sample field-of-view, with an accuracy of ±11 nm. These time-resolved measurements are significantly more reliable than a single measurement at a given time, which was previously used only for nanoparticle detection without sizing. We experimentally demonstrate the sizing of individual nanoparticles as well as viruses, monodisperse samples, and complex polydisperse mixtures, where the sample concentrations can span ∼5 orders-of-magnitude and particle sizes can range from 40 nm to millimeter-scale. We believe that this high-throughput and label-free nanoparticle sizing platform, together with its cost-effective and hand-held interface, will make highly advanced nanoscopic measurements readily accessible to researchers in developing countries and even to citizen-scientists, and might especially be valuable for environmental and biomedical applications as well as for higher education and training programs.

Characterization of atomization and breakup of acoustically levitated drops with digital holography

A digital holographic particle tracking velocimetry system is applied to quantitatively study the drop atomization induced by capillary waves, and the breakup caused by increased sound pressure levels. A wavelet-based algorithm is used for particle detection and autofocusing with a wide size range of 20 μm-2 mm. To eliminate the influence of large particles on small particles, a two-step detection method is adopted. Large drops are first characterized and simulated by a diffraction-based model. Then the contributions of the drops are subtracted from the original hologram followed by the detection of small droplets. Finally, the velocity and size distribution of the secondary droplets are obtained from the experimental holograms. The results demonstrate the validity of the digital in-line holographic technique for the atomization and breakup study of acoustically levitated drops.

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.