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

Edwin Malkiel1, Jian Sheng1, Joseph Katz1,* and J. Rudi Strickler2

1 Johns Hopkins University, Department of Mechanical Engineering, N. Charles Street, Baltimore, MD 21218, USA
2 Great Lakes WATER Institute, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53204, USA

* Author for correspondence (e-mail: Katz{at}jhu.edu)

Accepted 7 July 2003


    Summary
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 Summary
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
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 copepod's 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 (7.2x10-9 N), its excess density (6.7 kg m-3) and the propulsive force generated by its feeding appendages (1.8x10-8 N).

Key words: digital in-line holography, particle image velocimetry, copepod, Diaptomus minutus, flow


    Introduction
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 Summary
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
The average concentration of marine copepods has been estimated at about one per liter, making them the most numerous multicelled animals on earth (Boxshall, 1998Go). These micro-crustaceans form major links between the plankton world and nektonic organisms. The rate and specificity of their feeding can control phytoplankton population growth, while copepods themselves are an important source of food for fish, euphausiids and coelenterates (Mann and Lazier, 1996Go). Along with food availability and predator pressure, the copepod population dynamics are affected by swimming behavior and the types of flow fields they generate to capture food, which is species dependent (Strickler, 1982Go). The quantity of food depends on the volume of water they can scan and their ability to locate prey (Koehl, 1984Go). Locomotion and the generation of feeding currents increase the encounter rates with food, and can enhance the copepod's detection ability by stimulating escapes in motile prey (Yen and Strickler, 1996Go). Alternately, motionless sinking can make the copepod less conspicuous to predators or prey. Within the species, advertisement is important for reproduction (Doall et al., 1998Go; Yen and Strickler, 1996Go). Because copepods sense their environment utilizing antennules studded with arrays of setae that respond to fluid deformation, the flow field that a swimming animal generates is a `lens' through which the copepod views its surroundings. Knowledge about this flow field is important for understanding the impact of swimming behavior on the success of a copepod in locating food, avoiding predators and finding mates.

Current knowledge is largely based on video observations, including a Schlieren system for visualizing wakes (Strickler, 1977Go), high-speed cinematography for understanding how food particles are captured and feeding currents are generated (Koehl and Strickler, 1981Go; Strickler, 1984Go), and three-dimensional (3-D) video tracking of free-swimming copepods in particle fields (Paffenhöfer et al., 1995Go; Strickler, 1985Go). The latter combines particle tracks at different times to observe two-dimensional (2-D) flow fields in lateral and dorsal views. More recently, Particle Image Velocimetry (PIV) has been used to map instantaneous 2-D flow fields around tethered specimens (van Duren et al., 1998Go). However, since flow fields around copepods are 3-D, unsteady and vary with swimming speeds and orientations (Bundy and Paffenhöfer, 1996Go; Strickler, 1982Go; van Duren et al., 1998Go), 3-D measurements are essential. Considering the importance of copepods in the aquatic and marine food webs, and 30 years of related hypotheses, it seems worthwhile to investigate whether digital cinematographic holography may break barriers and allow us to test these hypotheses.

Unlike video microscopy, holography maintains the same lateral resolution over a substantial depth (Vikram, 1992Go). This advantage has led to the development of several submersible holography systems for studying plankton, starting with a sample volume of a few ml (Carder et al., 1982Go), to samples of one liter and above (Katz et al., 1999Go; Malkiel et al., 1999Go; O'Hern et al., 1988Go; Watson et al., 2001Go). The latter utilize pulsed lasers and emulsions as recording media. Cinematographic holography was introduced for laboratory research decades ago (Heflinger et al., 1978Go; Knox and Brooks, 1969Go), but difficulties in acquiring and processing data resulted in limited applications. Recent development in digital imaging, which simplifies the acquisition, and computing power, which enables numerical reconstruction, has led to renewed interest in cinematic holography (Kebbel et al., 1999Go; Owen and Zozulya, 2000Go; Xu et al., 2001Go). The limited resolution of digital imaging, which is at least an order of magnitude lower than that of holographic emulsions, restricts us to in-line holography. This technique (details follow) maximizes the fringe spacing. Because the reference beam typically passes through the sample volume, it becomes increasingly degraded with increasing particle concentration. Consequently, the reconstructed images are noisier and the maximum particle concentration is lower compared to off-axis holograms (Zhang et al., 1997Go).

Holographic PIV is the only technique to date that can measure a 3-D instantaneous velocity distribution over a finite volume (Barnhart et al., 1994Go; Pu and Meng, 2000Go; Sheng et al., 2003Go; Tao et al., 2002Go; Zhang et al., 1997Go) at a resolution of millions of vectors. The velocity is obtained by recording two exposures of a flow field seeded with microscopic particles, and measuring the displacement of these particles. However, the depth coordinate of a reconstructed particle is less accurate than the lateral coordinates, severely reducing the ability to estimate the corresponding velocity component. This problem has been solved by recording two inclined holograms, using each for determining a 3-D distribution of two velocity components, and matching the two sets to obtain the 3-D velocity. Utilizing emulsion and off-axis holography, Tao et al. (2002Go) measured 136x130x128 3-D velocity vectors in a cubic sample with sides of about 45 mm. By inserting an inclined mirror in the path of the illuminating beam inside the test facility, the incident and reflected beams create two views that can be recorded on the same emulsion (Sheng et al., 2003Go). Using off-axis holography, this method enables measurement of particle locations to within 7 µm, and resolves about 200 particles mm-3. We adopt this approach, but use digital in-line holography to record a time series of a free-swimming copepod and the flow field surrounding this animal. To our knowledge, this is the first time that digital holographic PIV has been implemented as a tool for simultaneous observation of the animal's behavior and measurement of the complex flow around it.


    Materials and methods
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 Summary
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
Digital in-line holography is a two-step process, consisting of first recording an in-line hologram on a digital recording medium, and then numerical reconstruction. The recording process entails back-illuminating a sample volume filled with objects by a coherent light source. A diffraction pattern is generated as a result of interference between the illuminating beam and light scattered from the objects. Coherence of the light source is important in order to enhance the visibility (or contrast) of the interference pattern, which conveys information on the shape and location of an object in space. As shown in Fig. 1 we use a standard, single mode, 3 mW Helium-Neon laser, which generates a CW (continuous wave) polarized beam of red light (632.8 nm) with a coherence length far beyond that required for digital in-line holography (which is on the order of 1 cm). The beam is spatially filtered and expanded to cover at least the entire test section. Collimating the expanded beam enables recording of the diffraction patterns at a constant magnification. This nonessential choice simplifies the numerical reconstruction by avoiding a calibration procedure to determine the origin of the illumination source.



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Fig. 1. Optical setup for digital in-line holography and test section.

 

The expanded beam illuminates an 80 ml sample volume constructed of antireflection-coated windows attached to two supporting prisms. First-surface mirrors are attached to the inclined side walls of the test chamber to direct the illumination beam through the test section. These mirrors provide two perpendicular views of objects located in regions where the incident and reflected beams overlap (cf. Fig. 2). One view is created by light that is first reflected from the mirror and then incident on the object, while the other (mirrored view) is generated by light incident on the object and then reflected off the mirror. The two views are recorded onto a single recording plane, but they are laterally separated. During reconstruction, the first view appears in focus at its original location, while the second perpendicular view is a mirror image (right side of Fig. 2). Use of two mirrors (Fig. 1) doubles the triangular overlapping volume without necessitating an increase in recording area.



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Fig. 2. Recording and reconstruction of an object near a mirror.

 

The interference patterns are recorded on a lensless Megaplus ES 4.0 digital camera, which has a 2048x2048 pixel CCD sensor with a 7.4 µm pitch, providing a 15 mmx15 mm field of view. The in-line system minimizes the angle between the light scattered from the objects and the remaining reference beam. Consequently, the fringe spacing is maximized (Vikram, 1992Go), overcoming the limited resolution of the CCD. The CCD's interline transfer capability eliminates the need for a shutter. Because the experiment involves recording moving objects (a copepod and seed particles), the exposure time is adjusted to be short enough to prevent the smallest resolvable fringe spacing from smearing. Here, the velocity does not exceed 4 mm s-1 (540 pixels s-1), and the electronic shuttering of the camera (0.1 ms exposure time) is sufficient to reduce the movement during exposure to much less than 1 pixel. Faster flows (~1 m s-1) would require higher power, even pulsed lasers, to generate the energy required for recording a hologram. Images have been recorded at the maximum frame rate of the present camera, 15 frames per second, buffering 10 s segments (150 frames) to the RAM of the computer hosting the image acquisition card.

Our subject animal, a female Diaptomus minutus Lilljeborg 1889, was freshly caught in Lake Michigan and transported to Baltimore in a Dewar's jar. The test section was filled with artesian well water from the Pryor Street well in Milwaukee. It was seeded with monodisperse, 20 µm diameter polystyrene spheres (specific gravity 1.05) at a concentration of 4 mm-3. Although denser seeding would improve the spatial resolution of the flow, it would also reduce the signal-to-noise ratio of reconstructed images. Image acquisition to RAM was started when the copepod appeared in the field of view. Successful image sequences, which captured the copepod in a region with two views, and were sufficiently far from the wall (>4 mm), were stored. Fig. 3 is a sample digital in-line hologram containing two interference patterns (`shadows') of the same copepod, along with the very faint diffraction patterns of the seed particles.



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Fig. 3. A sample digital hologram containing two views of the same swimming copepod in a seeded test section. Scale bar, 1 mm.

 

Digital reconstruction regenerates the original light intensity distribution at any desired distance from the recording plane. The amplitude of light U(x,y,z) at any point in the reconstruction volume is a superposition of light reaching this point from an array of source wavelets distributed over the entire recording plane (the hologram). Using the Fresnel-Huygens Principle (Hecht, 2002Go) with a paraxial approximation,

(1)
Here, ({xi},{eta}) are coordinates of the hologram, {Sigma} indicates the area of the entire hologram, {otimes} indicates convolution and k=(2{pi}/{lambda}), where {lambda} is the reconstruction wavelength. If {lambda} is set equal to the recording wavelength, the volume is reconstructed at its original depth. The intensity of the light, I(x,y,z), is calculated from I(x,y,z)=UU*, where U* is the complex conjugate of U. Use of the paraxial approximation is justified because we record predominantly forward scattered light. Furthermore, due to the limited resolution of the recording medium, the camera can resolve only near forward fringes. Equation 1 is actually a 2-D convolution integral parameterized by z, the distance between the hologram and the reconstruction plane. The kernel hz is the 3-D field generated by an infinitesimal point source located at (x,y,z). The discretized version of this convolution is performed over the entire hologram for each desired depth. Because of the large convolution kernel and image size, the integration is more efficiently performed in Fourier space. After calculating the 2-D Fourier transforms of both the recorded image and the convolution kernel, they are multiplied. Then, an inverse Fourier transform provides the intensity distribution in the desired plane. A similar approach is presented in Milgram and Li (2002Go), where further details on the mathematics can be found. We typically reconstruct 45 planes separated by 0.2 mm.

The purpose of the next phase of the analysis is to match the in-focus perpendicular views of particles in order to determine their exact locations in space. Recall that a single view can provide lateral positional accuracy to within a pixel (7.4 µm) in the lateral plane, but is substantially less accurate in the axial direction (0.5 mm). These views are laterally separated (as in Fig. 3). An automated procedure for matching the two views in densely seeded flows recorded using off-axis holography (on emulsion) is outlined in Sheng et al. (2003Go). There, the array of reconstructed images is thresholded, the particles are segmented into 3-D volumes, and then reduced to line segments that pass through the barycenters of these volumes and have lengths corresponding to their axial extent. The intersection of two perpendicular line segments determines the 3-D coordinates of the particle centroid. The analysis requires the calibration of the location and orientation of the mirror, achieved by manually matching corresponding views of several reference particles. The calibrated mirror orientation is used to transform (flip) the mirrored views onto their original locations in space. For two views of the same particle to be matched, we require that the perpendicular segments are less than a particle diameter away from each other. The 3-D coordinates of the particle centroid are approximated as the midpoint of the shortest line segment connecting the views.

This approach did not work while analyzing the present in-line digital holograms. The primary reason was excessive background noise resulting from the reference (illuminating) beam passing through the sample volume. It should work with less heavily seeded flows and/or an optical setup with a separate reference beam that does not pass through the sample volume. The limited resolution of the digital camera prevented the implementation of off-axis holography, which is characterized by much finer fringe spacing. Consequently, we have used two semi-manual techniques to obtain the 3-D locations of particles and velocity fields.

The first task is to identify particles and distinguish them from background noise. Three successive exposures are superposed, and elongated traces, or three closely spaced spots resulting from the displacement of particles, are identified. This approach has turned out to be a very effective tool for distinguishing between real particles and speckle noise. Based on the location of these traces, we estimate (computationally) the most likely location of the mirrored view. The linear transformation used for this calculation is calibrated by matching corresponding views of the copepod's extremities, which can be easily identified. The mirrored view lies along an almost horizontal line that corresponds to the depth uncertainty of the first view. If we find three spots (or elongated traces) along this line, the two views of the same particle are matched. At the present particle concentration, having more than one match is very unlikely. If we do not find the second view of a particle along the expected line, for example, when it is located in the shadow of the copepod, the unmatched trace is disregarded.

When the second view is found, the program proceeds to measure the particle displacement in each of the two views, using cross-correlation of the intensity distribution, generated by the three exposures. Details on the cross-correlation procedures, including methods of achieving sub-pixel accuracy, are discussed by Roth and Katz (2001Go), Roth et al. (1999Go) and Sridhar and Katz (1995Go). The lateral displacement in each of the views and the average vertical displacements are combined into a 3-D velocity vector, positioned at the particle mean location. The uncertainty in velocity of individual particles is about 0.05 mm s-1.

Extended particle tracks in the vicinity of the copepod are more easily identified. Superposing sets of ten exposures near the plane of the copepod in each view, and placing them side-by-side, allows identification of corresponding tracks based on their elevation at a given time. This identification is verified by comparing subsequent sets of exposures. Combining the sets generates the 3-D trajectory of the particle. Even when one of the views is partially blocked by the copepod, it is usually possible to match the segments that are not blocked and then interpolate them to estimate the trajectory in the blocked section. The endpoints of segments are stored and used for measuring the velocity along the path of the particle. In regions with relatively high velocity, the tracks appear as a series of dots. In this case, individual traces are used for measuring the velocity as discussed before.


    Results
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 Summary
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
Fig. 4 shows reconstructed perpendicular views of the copepod and seed particles, computed from the hologram shown in Fig. 3. Note that the two views are reconstructed at different depths. Clearly, digital reconstruction of in-line holograms can resolve fine details of the copepod structure. Sample instantaneous distributions of 3-D velocity vectors in the vicinity of this copepod in the ambient and copepod reference frames are presented in Fig. 5A and B, respectively. The graphic representation of the copepod has the correct scales. Vectors that are located within the central two thirds span of the antennules are black; vectors outside of this span are gray. A recirculating flow pattern is evident in the copepod frame of reference, which sinks at an average speed of 0.29 mm s-1. Similar sets of 3-D velocity distributions are obtained from each pair of reconstructed holograms.



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Fig. 4. In-focus, numerically reconstructed, dorsal (A) and lateral (B) views of the same swimming copepod, from the hologram of Fig. 3. s, setae on antennule; f, feeding appendages; p, tracer particle (there are many). Inserts show the feeding appendages in up-stroke (top) and down-stroke (bottom) positions. Scale bar, 1 mm.

 


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Fig. 5. Measured instantaneous velocity near the copepod (A) in the ambient frame of reference, and (B) in the copepod frame of reference.

 

The reconstructed images from 15 sequences consistently show that the copepod sinks for several seconds. It then executes a short hop upwards and resumes sinking (see supporting movie). As it sinks, the copepod generates a feeding current by moving its feeding appendages. The present 15 Hz recording rate may not be sufficient for following the (high frequency) motion of the appendages, but different phases of their motion are discernible (Fig. 4). The `high'-speed flow generated by the appendages (Fig. 5A) is most evident in the ventral region of the copepod (z<79.5 mm), extending to its anterior and posterior regions. The feeding current generates a reaction force that propels the copepod. This vertically directed force acts against the copepod's excess weight (weight minus buoyancy) and drag, reducing its sinking rate compared to the terminal speed (speed with no feeding current).

The recirculating flow pattern generated by the copepod is clearly demonstrated in Fig. 6 by combining 130 reconstructed images, shifted in time, so that the image of the copepod is fixed. Since the copepod velocity is constant during this period, the shift applied to each image is a linear function of time. Blurring of the copepod occurs due to slight variations in sinking speed (<5%), and motion of the appendages. Streaks generated by the seed particles are clearly evident in both views. Above the copepod, several particles are drawn towards the center of the copepod. Below and to the sides of the copepod, particles are ejected downwards, subsequently looping around and migrating upward (relative to the copepod), some of them touching its antennules. Quantitative data on the trajectory and velocity along the path of selected particles are presented in Figs 7 and 8. The velocity peaks in a narrow domain near the tips of the appendages, reaching 3.6 mm s-1, i.e. 12.5 times the sinking velocity. We use these data to estimate the propulsive force generated by the feeding appendages.



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Fig. 6. Particle streaks in the copepod reference frame obtained by combining 130 appropriately shifted reconstructed images. In all cases the dorsal and lateral views are in focus.

 


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Fig. 7. Selected particle tracks (1-6) in 3 dimensions. A-A, see inset in Fig. 8.

 


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Fig. 8. Speeds of selected particles (1-6) approaching feeding appendages. Inset: Horizontal velocity component w near tail along line A-A of Fig. 7. z axis origin at center of mass.

 

Excess weight and propulsive force
The particles slightly beyond the reach of the antennules circumvent the copepod, creating a closed streamline pattern, without a separated wake. This pattern is characteristic of low Reynolds number flows (ReL=UL/{nu}, U and L being characteristic velocity and length scales, respectively, and {nu}, the kinematic viscosity of the liquid), such as Stokes flows with Re<<1, or Oseen flows with R~1 (Pozrikidis, 1992Go). The present Re, based on the sinking velocity and prosome length, is 0.29. Based on the diameter of the recirculation zone, Re increases to 1.2. Thus, the present flow lies in the transition region between Stokes and Oseen flows. Here we use the simpler Stokes flow in order to estimate the magnitude of the forces produced by the copepod.

The horizontal (u) and vertical (v) velocity components induced by a vertical point force (Stokeslet) in Stokes flow (Jiang et al., 2002cGo; Pozrikidis, 1992Go) are:

(2)
where f is the force, µ is the liquid viscosity, x and y are coordinates, and r is distance from the origin. The Stokeslet describes the far-field flow realistically, but neglects the fact that the object has a finite size. The far-field net effect of the copepod on the surrounding flow, its excess weight (wexcess), can be modeled as a Stokeslet.

The flow pattern generated by a Stokeslet in an absolute frame of reference is illustrated in Fig. 9A, with Uref=wexcess/8{pi}µL. A recirculating flow pattern appears in a frame of reference moving downward at a fraction of Uref (Fig. 9B). For the recirculation to form, there must be a residual downward velocity component (jet) below the object in its own reference frame. This flow can only be generated by a propulsive force. Thus, in reducing its sinking speed and generating a propulsive feeding current, the copepod creates a recirculating pattern that extends slightly beyond its antennae. This combination of sinking and feeding is not discussed in detailed conceptual and numerical analyses of the forces acting on a swimming copepod under various conditions (Jiang et al., 2002bGo,2002cGo). They include cases of stationary bodies producing feeding currents (hovering or conceivably tethered) and freely sinking bodies, both of which do not generate recirculating patterns.



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Fig. 9. Flow field generated by a Stokeslet (see Equation 3) at (A) the absolute reference frame and (B) the reference frame sinking at 0.33Uref.

 

The data can be used for estimating wexcess. In a reference frame sinking at vsink, the vertical velocity component vanishes at y0wexcess/4{pi}µvsink. Estimating y0 as half the distance between the points with zero velocity in Fig. 6 (y0=2 mm), and since vsink= 0.29 mm s-1, one obtains wexcess=7.2x10-9 N. With a volume of 1.1x10-10 m3 (determined following Chojnacki, 1983Go), the estimated excess density of the copepod is 6.7 kg m-3 (1006.7 kg m-3). This value falls in the range measured by Svetlichny (1980Go) and Knutsen et al. (2001Go). The same analysis can be performed in any frame, including one without recirculation, by measuring the velocity and distance between points above and below the copepod with the same velocity.

One can also estimate the propulsive force, P, generated by the feeding appendages. Averaging {nu} of a Stokeslet at y=0 over a certain radius, R, one obtains . Based on Figs 7, 8, there are two regions with a radius of 200 µm and characteristic peak velocity of mm s-1 in the vicinity of the feeding appendages. Combining the two regions, , i.e. P=1.8x10-8 N, 2.5 times higher than wexcess. At a constant sinking velocity, P must balance the sum of wexcess and the drag force (Jiang et al., 2002cGo). Since the relative velocity around the copepod is downward (Figs 5, 6, 7, 8), so is the drag, requiring P to be larger than wexcess. Thus, the estimated drag is about 1.5 times the excess weight. The propulsive force also generates a moment (negative x direction), since it is applied at about 30 µm in front of the centerline of the prosome, based on the location of maximum . The magnitude of this moment is about 5.4x10-13 Nm. To overcome this moment and avoid tumbling, the copepod turns its tail, creating a velocity bias in the positive z direction (see insert in Fig. 8). Turning the flow creates a reaction force and a moment in the positive x direction. Based on the average velocity bias (~0.1 mm s-1, Fig. 8), over a radius of 250 µm (half the tail length), the force is 0.6x10-9 N. Multiplying it by the distance to the center of mass of the copepod (1 mm), the estimated moment is 6x10-13 Nm. Thus, the moment generated by the tail's redirection of fluid is of sufficient magnitude to compensate against the moment of the propulsive force, allowing the copepod to maintain a relatively vertical orientation.


    Discussion
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 Summary
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
The discussion is in two parts. The first compares holography to other 3-D imaging techniques, and the second focuses on the behavior of a copepod.

Comparison with other techniques
It is useful to compare the capabilities and difficulties of digital in-line holography with other 3-D particle tracking techniques, such as Stereo PIV and 3-D particle tracking with multiple cameras. 2-D PIV (Bartol et al., 2003Go; Drucker and Lauder, 2001Go; van Duren et al., 1998Go; Wilga and Lauder, 2002Go) provides high density data, but only in a plane. Typical stereo PIV (Nauen and Lauder, 2002Go; Prasad, 2000Go) provides all three velocity components, but still only in a plane. It also requires elaborate calibration procedures. Existing scanning PIV (Brucker, 1997Go) and potentially future stereo-scanning PIV, provide data in multiple planes at different times at the cost of added complexity. All are unsuitable for following the 3-D trajectories of swimming organisms.

Alternatively, multiple pinhole photography (Kieft et al., 2002Go; Maas et al., 1993Go; Moroni et al., 2003Go; Ott and Mann, 2000Go; Stuer et al., 1999Go; Virant and Dracos, 1997Go) and its variants (Pereira and Gharib, 2002Go) can be used for 3-D tracking of particles. The increased depth of focus required by this method is inherently coupled to reduced resolution and the need for bright illumination. Conversely, in holography the image resolution does not have to be compromised. Fine details, e.g. setae and swimming appendages can be imaged at any depth. Furthermore, in pinhole images, the elongated traces of particles extend in depth through the entire volume of interest. Consequently, matching of perpendicular views can only be performed at low particle concentrations. Multiple camera systems partially overcome this effect and can provide as many as 1600 vectors per time step, and may track as many as several hundred particles over extended periods (Virant and Dracos, 1997Go). Such systems require extensive calibration and relatively complex processing algorithms. In in-line holography, the elongated traces extend in depth less than 1 mm, enabling matching of views at concentrations as high as several particles per mm3 (i.e. 13 500 in the present overlapping volumes). The associated calibration process is also straightforward. On the other hand, one of the shortcomings of in-line holography, as shown in this paper, is the noise generated in a great part by deterioration of the reference beam. This problem can be partially resolved by using a separate reference beam that does not pass through the sample volume. A separate reference beam should also allow a much higher seeding concentration, but at the cost of added complexity to the optical setup. When using high-resolution emulsions, instead of a digital camera, we have successfully reconstructed 200 particles per mm3. Another shortcoming of holography is inherent to the use of coherent light, which makes the system more sensitive to the quality of windows and variations of density within the sample volume.

As shown in this paper, digital holographic PIV is a relatively simple, but powerful tool for analysis of 3-D copepod (or other organism) dynamics and its interaction with its local environment, be it with other organisms or the local 3-D flow field.

Copepod behavior
While generating the feeding current (Strickler, 1982Go, 1984Go) the mouthparts, studded with chemoreceptors (Friedman and Strickler, 1975Go), scan the water flowing by them. When the presence of a food particle is perceived, additional movements of the mouthparts capture the particle and bring it to the mouth (Koehl and Strickler, 1981Go; Strickler, 1984Go, 1985Go). Sensory setae on the stretched out antennules (Fig. 4; Huys and Boxshall, 1991Go) are mechanoreceptors (Strickler and Bal, 1973Go), as well as chemoreceptors (Bundy and Paffenhöfer, 1993Go). These receptors enlarge the volume of water scanned for food (Jiang et al., 2002aGo; Strickler, 1985Go). Particles that do not smell `good enough' are either actively rejected after capture by the mouthparts, or passively rejected (allowed to pass without being captured). For a stationary hovering copepod, these rejected particles remain in the water below the copepod, and are not entrained into the feeding current again (Strickler, 1982Go).

The recirculating pattern in Figs 5, 6, 7, 8 is, to our knowledge, the first report of a multi-encounter feeding pattern in calanoid copepods. The combination of feeding and sinking results in particles being drawn toward the copepod with its feeding current, passively rejected and then recirculated. The recirculation is interrupted aperiodically, after 8.7 s in the present example, when the copepod hops. During a hop, the copepod jumps about 0.5 mm upward to a position where its mouthparts are just below the stagnation point of the previous recirculation zone. If it were not for the hop, the copepod would never encounter new particles, due to the closed recirculation pattern. The recirculation allows the copepod to taste some of the particles that have passed near the mouthparts once more, this time with different, perhaps even more sensitive chemoreceptors on its antennules. Considering that the 20 µm polystyrene, spherical particles are mechanically desirable but chemically undesirable, this additional sensing by the sensors on the antennules ensures that the animal does not forfeit potentially good food. The available sequences of holograms suggest that the timing between hops is sufficient for a rejected particle to reach the antennule (about half the recirculation cycle). We speculate that once the copepod senses, using its antennules, a particle that has already been tasted and rejected (and is still not acceptable), it hops to another volume to look for different food. These assertions require testing by altering the properties of the particles, e.g. replacing them with desirable food, and observing the behavior of the copepod.


    Acknowledgments
 
This work was supported by the National Science Foundation. J.R.S. dedicates this work to Owen Phillips for his support at a crucial moment years ago.


    Footnotes
 
Movies available on-line


    References
 TOP
 Summary
 Introduction
 Materials and methods
 Results
 Discussion
 References
 

Barnhart, D. H., Adrian, R. J. and Papen, G. C. (1994). Phase-conjugate holographic system for high-resolution particle image velocimetry. Appl. Opt. 30,7159 -7170.

Bartol, I. K., Gharib, M., Weihs, D., Webb, P. W., Hove, J. R. and Gordon, M. S. (2003). Hydrodynamic stability of swimming in ostraciid fishes: role of the carapace in the smooth trunkfish Lactophrys triqueter (Teleostei: Ostraciidae). J. Exp. Biol. 206,725 -744.[Abstract/Free Full Text]

Boxshall, G. A. (1998). Mating biology of copepod crustaceans - Preface. Philos. Trans. R. Soc. Lond. B 353,669 -670.[CrossRef]

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