A high-speed tomographic PIV system for measuring zooplanktonic flow

Quantification of the hydrodynamic disturbance of free-swimming zooplankton provides insight into propulsion as well as organism sensory interactions. Current flow measurement techniques, such as planar particle image velocimetry (PIV), are limited by their two-dimensional nature. These techniques also are challenged by the small spatial scale of zooplankton, by the high speeds achieved by many zooplankton species, and by zooplankton photosensitivity to a broad range of wavelengths. We present a high-speed tomographic PIV system using near-infrared laser illumination that is capable of measuring three-dimensional velocity vectors in a volume surrounding a plankter. This technique is assessed by recording and analyzing the time-resolved flow field created by a high-speed escape of a copepod (Calanus finmarchicus). Persistent body and wake vortices are created by the impulsive momentum transfer to the fluid surrounding the animal. It is shown that some aspects of this flow can be analytically modeled as an impulsive stresslet. Azimuthal asymmetry of the strength and position of the wake vortex is analyzed and attributed to the strong ventral flows created by the metachronally beating swimming legs. In addition, the energy required by a copepod escape jump is estimated by calculating the viscous energy dissipation rate using the spatial gradients of the measured three-dimensional velocity field. Finally, the challenges and benefits of the tomographic PIV technique are discussed. *Corresponding author: E-mail: [email protected]; Current Address: Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218-2681 USA; 205-746-9135 (phone); 404-894-2278 (fax) Acknowledgments The authors gratefully acknowledge financial support of the National Science Foundation (OCE-0928491). Thanks also to Steve Anderson, Callum Gray, Doug Neal, and Dirk Michaelis at LaVision for technical support. DOI 10.4319/lom.2012.10.1096 Limnol. Oceanogr.: Methods 10, 2012, 1096–1112 © 2012, by the American Society of Limnology and Oceanography, Inc. LIMNOLOGY and OCEANOGRAPHY: METHODS been used to quantify flow fields associated with free-swimming zooplankton behavior (e.g., Stamhuis et al. 2002). Planar PIV has been used to measure the flow fields associated with copepod swimming and jumping (Catton et al. 2007, 2012; Kiørboe et al. 2010a). Digital holographic PIV has been used to measure feeding flow in a three-dimensional volume (Malkiel et al. 2003). Whereas these previous studies were successful to some extent, quantifying the flow surrounding zooplankton presents the following four unique challenges: 1) Zooplankton behavior and flow disturbances are intrinsically three-dimensional, and capturing certain behaviors (such as a high-speed escape) within a laser light sheet is rare. 2D and stereo PIV are, therefore, highly restrictive for this purpose because they are inherently confined to quantifying the velocity field in a single illumination plane. 2) Zooplankton are small (0.1 to 5 mm) and respond to small strain rates (0.025 s–1). Hence, resolution of corresponding velocity gradients requires medium to high particle seeding and dense fields of velocity vectors. 3) Zooplankton swim quickly and generate highly unsteady flows, with copepod escape speeds reaching 1 m s–1 (500 body lengths per second) (Yen 2000). High temporal resolution is therefore required to resolve these events. 4) Zooplankton are phototactic to a broad range of wavelengths in the visual band. Use of intense laser illumination in this range induces a response that interferes with behavioral assays. Taken together, these four challenges necessitate a new approach to quantifying the flow fields surrounding zooplankton. Extensions to planar PIV Several approaches to extending the planar PIV technique to 3D have been developed during the past few years (Arroyo and Hinsch 2008). These include holographic PIV, scanning illumination approaches, defocusing PIV, and tomographic PIV. The advantages, disadvantages, and limitations of these approaches are briefly discussed. Holographic PIV has been developed by several researchers and offers the greatest spatial resolution (e.g., Hinsch 2002; Pu and Meng 2005; Katz and Sheng 2010; Orlov et al. 2010). The technique consists of recording a hologram of the light scattered off suspended particles in the flow to determine the 3D position of particles during post-processing (i.e., reconstruction) of the hologram. Subsequent cross-correlation or particle tracking analysis yields the 3D velocity vector field in the holographic volume. The disadvantages of the holographic PIV approach include processing of the emulsion plate in the dark room, tedious extraction of the particle positions during hologram interrogation, and lack of temporal repetition. Commercial holographic PIV systems are not available, largely because of these disadvantages, along with the advanced technical intricacy of the optical systems (Meng et al. 2004). In the past few years, the use of digital recording medium, such as CCD cameras, has been suggested as a method to overcome these disadvantages (Meng et al. 2004; Orlov et al. 2010). For instance, Malkiel et al. (2003) employed a 2K × 2K digital camera, which effectively records orders of magnitude less information than silver halide holographic film. The camera resolution necessitated low particle density, which resulted in modest velocity vector density and fairly high uncertainty for the velocity measurements. Holographic PIV has great promise and continues to be developed, but it currently lacks the robust operation with high spatial and temporal resolution that the application of flow around zooplankton requires. One technique to overcome the particle density limitation is to illuminate and image individual planes. Brücker (1997), Liberzon et al. (2004), Hoyer et al. (2005), and Cheng et al. (2011) each used a variation of the basic approach of illuminating parallel planes with a light sheet and recording the particle locations in each plane. The seeding density often can be similar to that for traditional 2D and stereo PIV. One disadvantage of this approach is that the planes often are illuminated sequentially; hence the image acquisition is not simultaneous for parallel planes. Alternatively, Liberzon et al. (2004) illuminated three planes simultaneously, which limits the seeding density and requires sophisticated post-processing to separate the imaged planes. Another disadvantage of the parallel plane illumination technique is that it results in discrete separation of the measurement planes. Another approach is to record the particle positions with three or more cameras during volume illumination of the flow. Willert and Gharib (1992), Pereira et al. (2000), and Kajitani and Dabiri (2005) describe a defocusing approach that employs offset apertures for 3-digital sensors to yield defocused images of the particles. The aperture geometry combined with the information from the three sensors yields the particle position relative to the focus plane. A potential advantage is that once the aperture arrangement is set, the system is effectively calibrated. However, commercially available systems that follow this approach are relatively inflexible in terms of size and resolution of the measurement volume. In tomographic PIV, the three-dimensional light intensity field of illuminated tracer particles in the flow is reconstructed from multiple cameras viewing the interrogation volume from different angles. The 3D volume of light scattered from the particle distribution is typically reconstructed via a multiplicative algebraic reconstruction technique (MART) algorithm. Velocity vectors are computed via an iterative threedimensional cross-correlation technique between consecutive reconstructed light intensity volumes using deformed interrogation volumes (Elsinga et al. 2006, 2008). The method has been advanced in recent years with the development of robust and efficient reconstruction procedures (Atkinson and Soria 2009; Novara et al. 2010), volumetric self-calibration techniques (Wieneke 2008), and identification techniques for ghost particles (Elsinga et al. 2011). Tomographic PIV has the advantage of a simple optical arrangement while allowing medium-seeding density. Tomographic PIV also allows for flexible selection of camera specifications and illumination type. The method is also attractive because it builds on the success of stereo PIV techniques with a simple modification to Murphy et al. A high-speed tomographic PIV system