Edwin Malkiel

Digital holographic microscope for measuring three-dimensional particle distributions and motions

Better understanding of particle-particle and particle-fluid interactions requires accurate 3D measurements of particle distributions and motions. We introduce the application of in-line digital holographic microscopy as a viable tool for measuring distributions of dense micrometer (3.2 microm) and submicrometer (0.75 microm) particles in a liquid solution with large depths of 1-10 mm. By recording a magnified hologram, we obtain a depth of field of approximately 1000 times the object diameter and a reduced depth of focus of approximately 10 particle diameters, both representing substantial improvements compared to a conventional microscope and in-line holography. Quantitative information on depth of field, depth of focus, and axial resolution is provided. We demonstrate that digital holographic microscopy can resolve the locations of several thousand particles and can measure their motions and trajectories using cinematographic holography. A sample trajectory and detailed morphological information of a free-swimming copepod nauplius are presented.

Digital holographic microscopy reveals prey-induced changes in swimming behavior of predatory dinoflagellates

The shallow depth of field of conventional microscopy hampers analyses of 3D swimming behavior of fast dinoflagellates, whose motility influences macroassemblages of these cells into often-observed dense “blooms.” The present analysis of cinematic digital holographic microscopy data enables simultaneous tracking and characterization of swimming of thousands of cells within dense suspensions. We focus on Karlodinium veneficum and Pfiesteria piscicida, mixotrophic and heterotrophic dinoflagellates, respectively, and their preys. Nearest-neighbor distance analysis shows that predator and prey cells are randomly distributed relative to themselves, but, in mixed culture, each predator clusters around its respective prey. Both dinoflagellate species exhibit complex highly variable swimming behavior as characterized by radius and pitch of helical swimming trajectories and by translational and angular velocity. K. veneficum moves in both left- and right-hand helices, whereas P. piscicida swims only in right-hand helices. When presented with its prey (Storeatula major), the slower K. veneficum reduces its velocity, radius, and pitch but increases its angular velocity, changes that reduce its hydrodynamic signature while still scanning its environment as “a spinning antenna.” Conversely, the faster P. piscicida increases its speed, radius, and angular velocity but slightly reduces its pitch when exposed to prey (Rhodomonas sp.), suggesting the preferred predation tactics of an “active hunter.”

The three-dimensional flow field generated by a feeding calanoid copepod measured using digital holography.

SUMMARY Digital in-line holography is used for measuring the three-dimensional (3-D) trajectory of a free-swimming freshwater copepod Diaptomus minutus, and simultaneously the instantaneous 3-D velocity field around this copepod. The optical setup consists of a collimated He-Ne laser illuminating a sample volume seeded with particles and containing several feeding copepods. A time series of holograms is recorded at 15 Hz using a lensless 2Kx2K digital camera. Inclined mirrors on the walls of the sample volume enable simultaneous recording of two perpendicular views on the same frame. Numerical reconstruction and matching of views determine the 3-D trajectories of a copepod and the tracer particles to within pixel accuracy (7.4 μm). The velocity field and trajectories of particles entrained by the copepod have a recirculating pattern in the copepods frame of reference. This pattern is caused by the copepod sinking at a rate that is lower than its terminal sinking speed, due to the propulsive force generated by its feeding current. Consequently, the copepod sees the same fluid, requiring it to hop periodically to scan different fluid for food. Using Stokeslets to model the velocity field induced by a point force, the measured velocity distributions enable us to estimate the excess weight of the copepod (7.2×10-9 N), its excess density (6.7 kg m-3) and the propulsive force generated by its feeding appendages (1.8×10-8 N).

Single beam two-views holographic particle image velocimetry

Holographic particle image velocimetry (HPIV) is presently the only method that can measure at high resolution all three components of the velocity in a finite volume. In systems that are based on recording one hologram, velocity components parallel to the hologram can be measured throughout the sample volume, but elongation of the particle traces in the depth direction severely limits the accuracy of the velocity component that is perpendicular to the hologram. Previous studies overcame this limitation by simultaneously recording two orthogonal holograms, which inherently required four windows and two recording systems. This paper introduces a technique that maintains the advantages of recording two orthogonal views, but requires only one window and one recording system. Furthermore, it enables a quadruple increase in the spatial resolution. This method is based on placing a mirror in the test section that reflects the object beam at an angle of 45 degrees. Particles located in the volume in which the incident and reflected beams from the mirror overlap are illuminated twice in perpendicular directions. Both views are recorded on the same hologram. Off-axis holography with conjugate reconstruction and high-pass filtering is used for recording and analyzing the holograms. Calibration tests show that two views reduce the uncertainty in the three-dimensional (3-D) coordinates of the particle centroids to within a few microns. The velocity is still determined plane-by-plane by use of two-dimensional particle image velocimetry procedures, but the images are filtered to trim the elongated traces based on the 3-D location of the particle. Consequently, the spatial resolution is quadrupled. Sample data containing more than 200 particles/mm3 are used for calculating the 3-D velocity distributions with interrogation volumes of 220 x 154 x 250 microm, and vector spacing of 110 x 77 x 250 microm. Uncertainty in velocity is addressed by examining how well the data satisfies the continuity equation. The results show significant improvements compared with previous procedures. Limitations of the technique are also discussed.

A dinoflagellate exploits toxins to immobilize prey prior to ingestion

Toxins produced by the harmful algal bloom (HAB) forming, mixotrophic dinoflagellate Karlodinium veneficum have long been associated with fish kills. To date, the perceived ecological role for toxins has been relief from grazing pressures. Here, we demonstrate that karlotoxins also serve as a predation instrument. Using high-speed holographic microscopy, we measure the swimming behavior of several toxic and nontoxic strains of K. veneficum and their prey, Storeatula major, within dense suspensions. The selected strains produce toxins with varying potency and dosages, including a nontoxic one. Results clearly show that mixing the prey with the predatory, toxic strains causes prey immobilization at rates that are consistent with the karlotoxins’ potency and dosage. Even prey cells that continue swimming slow down after exposure to toxic predators. The swimming characteristics of predators vary substantially in pure suspensions, as quantified by their velocity, radii of helical trajectories, and direction of helical rotation. When mixed with prey, all toxic strains that are involved in predation slow down. Furthermore, they substantially reduced their predominantly vertical migration, presumably to remain in the vicinity of their prey. Conversely, the nontoxic control strain does not alter its swimming and does not affect prey behavior. In separate experiments, we show that exposing prey to exogenous toxins also causes prey immobilization at rates consistent with potency. Clearly, the toxic predatory strains use karlotoxins as a means of stunning their prey, before ingesting it. These findings add a substantiated critical understanding for why some HAB species produce such complex toxin molecules.

Measurements of plankton distribution in the ocean using submersible holography

A submersible holography system for in situ recordings of the spatial distribution of plankton has been developed and deployed. The system utilizes a ruby laser with an in-line recording configuration and has a sample volume of 732 ml. The reconstructed images have a resolution ranging from 10-20 µm for spherical particles and 3 µm for linear particles that lie within 100 mm from the film. Reconstructed volumes from holograms recorded during two recent deployments in the Strait of Georgia are scanned to obtain focused images of the particles, their position, size and orientation. The particles are also classified to several groups based on their morphological characteristics. The holograms include a set recorded during a 15 min vertical transect of the top 30 m of the water column. Along with the holograms, the data include records of depth, temperature, salinity, dissolved oxygen and optical transmissivity. The results show substantial variations in population makeup between layers spaced a short distance apart, particle concentration maxima at and near a pycnocline and evidence of zooplankton migration. A predominant horizontal diatom orientation is indicated in the region of peak diatom concentration. Individual holograms show clustering within different classes of plankton.

Automated scanning and measurements of particle distributions within a holographic reconstructed volume

Scanning and analysis of reconstructed holograms of a one-litre sample volume containing particles with varying sizes and shapes at high resolution is a major challenge. A completely automated system for analysing in-line holograms recorded in the ocean, which resolves particles larger than 10 µm, has been developed. It measures the three-dimensional coordinates of all the particles within the reconstructed volume and records their in-focus images. Scanning and analysing a reconstructed volume of about 500 cm3 that contains several thousand particles takes about 5 h. The analysis consists of several steps. After compensating for exposure non-uniformities, the reconstructed images are scanned continuously with a digital camera. Then, superposition of thresholded images weighted by depth is introduced as a method compressing the 3D data to a plane to increase the efficiency of segmentation analysis. Subsequently, edge filtering is used for pinpointing the depth coordinate. To detect particles smaller than 50 µm, the reconstructed images are band-pass filtered optically. This approach is based on analysis that identifies interference of the reference beam with off-axis scattered light as the primary contributor to background noise. The scanning, thresholding and edge detection processes are repeated for the small particles. Additional procedures remove duplicate detections, and post-processing classifies the particles based on geometrical parameters. Sample data are presented.

Buffer layer structures associated with extreme wall stress events in a smooth wall turbulent boundary layer

Three-dimensional velocity distributions and corresponding wall stresses are measured concurrently in the inner part of a turbulent boundary layer over a smooth wall using digital holographic microscopy. The measurements are performed in a square duct channel flow at Re δ = 50 000 and Re τ = 1470. A spatial resolution of 3-8 wall units (δ υ = 17 μm)in streamwise and spanwise directions and 1 wall unit in the wall-normal direction are sufficient for resolving buffer layer structures and for measuring the instantaneous wall shear stresses from velocity gradients in the viscous sublayer. Mean velocity and Reynolds stress profiles agree well with previous publications. Rudimentary observations classify the buffer layer three-dimensional flow into (i) a pair of counter-rotating inclined vortices, (ii) multiple streamwise vortices, some of them powerful, and (iii) no apparent buffer layer structures. Each appears in about one third of the realizations. Conditional sampling based on local wall shear stress maxima and minima reveals two types of three-dimensional buffer layer structures that generate extreme stress events. The first structure develops as spanwise vorticity lifts from the wall abruptly and within a short distance of about 10 wall units, creating initially a vertical arch. Its only precursors are a slight velocity deficit that does not involve an inflection point and low levels of vertical vorticity. This arch is subsequently stretched vertically and in the streamwise direction, culminating in formation of a pair of inclined, counter-rotating vortices with similar strength and inclination angle exceeding 45°. A wall stress minimum exists under the point of initial lifting. A pair of stress maxima develops 35δ υ downstream, on the outer (downflow) sides of the vortex pair and is displaced laterally by 35-40δ υ from the minimum. This flow structure exists not only in the conditionally averaged field but in the instantaneous measurement as well and appears in 16.4 % of the realizations. Most of the streamwise velocity deficit generated by this phenomenon develops during this initial lifting, but it persists between the pair of vortices. Distribution of velocity fluctuations shows that spanwise transport of streamwise momentum plays a dominant role and that vertical transport is small under the vortices. In other regions, e.g. during initial lifting, and between the vortices, vertical transport dominates. The characteristics of this structure are compared to early experimental findings, highlighting similarities and differences. Abundance of pairs of streamwise vortices with similar strength is inconsistent with conclusions of several studies based on analysis of direct numerical simulation (DNS) data. The second buffer layer structure generating high wall stresses is a single, predominantly streamwise vortex, with characteristic diameter of 20-40δ υ and inclination angle of 12°. It generates an elongated, strong stress maximum on one side and a weak minimum on the other and has been observed in 20.4 % of the realizations. Except for a limited region of sweep above the high-stress region, this low-lying vortex mostly induces spanwise momentum transport. This structure appears to be similar to those observed in several numerical studies.

Development of a free-drifting submersible digital holographic imaging system

Submersible film-based holographic systems have demonstrated the unique ability of holography to provide high resolution, three-dimensional, in-situ images of marine organisms. Inherently, use of film limits the frame rate and total number of holograms. This paper describes a submersible, free-drifting, digital holographic cinematography system that has a real-time fiber optic communication link. This system collects dual-view digital holograms at a rate of 15 frames per second, enabling the user to observe the behavior of marine plankton and distinguish motile organisms from abiotic particles. In order to follow the particles in time, the sample should have as little motion relative to the cameras as possible. To achieve this goal, the submersible is neutrally buoyant, and has high drag generating elements at the height of the sample volume. In addition, the components surrounding the sample are streamlined and designed to minimize the local flow disturbance. The data from the two digital cameras and other sensors are transmitted at 120 MB/s through a 1 km long, 250 /spl mu/m diameter, fiber optic cable to an acquisition system located on a research vessel. The optical fiber is spooled out from the submersible by a powered mechanism, as the submersible drifts away from the vessel Releasing the fiber out at a rate greater than that of the drifting speed minimizes the transmission of forces through the cable, effectively decoupling the submersible from the cable and vessel dynamics. A variable buoyancy system provides vertical position control while still allowing the system to drift vertically with the surrounding fluid, i.e., follow internal waves. The dual-view holo-camera records two in-line holograms from orthogonal directions, each with a volume of 40.5 cm/sup 3/. Without lenses, the resolution in the 3.4 cm/sup 3/ volume where the beams cross each other, is about 7.4 /spl mu/m in all three directions. Outside of the overlapping region, the resolution in the beam axial direction is lower, but the lateral resolution remains 7.4 /sup 3/. An optional 2/spl times/ lens doubles the resolution, but reduces the sample volume. The first field deployment for this system took place in June 2005, in the Ria de Pontevedra, Spain. It was used for examining thin layers of harmful algal blooms.

Experimental investigation of turbulent diffusion of slightly buoyant droplets in locally isotropic turbulence

High-speed inline digital holographic cinematography is used for studying turbulent diffusion of slightly buoyant 0.5–1.2 mm diameter diesel droplets and 50 μm diameter neutral density particles. Experiments are performed in a 50×50×70 mm3 sample volume in a controlled, nearly isotropic turbulence facility, which is characterized by two dimensional particle image velocimetry. An automated tracking program has been used for measuring velocity time history of more than 17 000 droplets and 15 000 particles. For most of the present conditions, rms values of horizontal droplet velocity exceed those of the fluid. The rms values of droplet vertical velocity are higher than those of the fluid only for the highest turbulence level. The turbulent diffusion coefficient is calculated by integration of the ensemble-averaged Lagrangian velocity autocovariance. Trends of the asymptotic droplet diffusion coefficient are examined by noting that it can be viewed as a product of a mean square velocity and a diffusion time s...