be significantly improved with detailed quantitative analysis of the momentum transfer between the fish and the fluid during swimming behaviors. Fish swimming behavior is inherently three-dimensional (3D), with multifarious fin and body motions and fin-wake interactions. The complexity of these swimming behaviors suggests that 3D rendering, with sufficient spatial and temporal resolution, is necessary to simultaneously capture the relevant kinematics and hydrodynamics to facilitate the quantification of propulsive performance.Early work on fish swimming hydrodynamics employed qualitative shadowgraphy techniques, suggesting a series of linked 3D vortex rings in the wake of a steadily swimming fish, as well as during a "push and coast" swimming mode (McCutchen 1977). Looking to quantify wake hydrodynamics behind swimming fish, researchers turned to noninvasive techniques such as particle image velocimetry (PIV). PIV allows for non-intrusive measurements of the velocity field in a fluid by imaging, and then tracking, the motion of reflective flow tracers over time. Fundamental details on the implementation of algorithms used in PIV can be found in Raffel et al. (1998).PIV measurements taken behind steadily swimming fish along the horizontal mid-plane of the body reveal clear reverse Kármán street vortex configurations in the fish wake (e.g., Stamhuis and Videler 1995;Wolfgang et al. 1999;Müller et al. 2000). Using multiple planes of 2D PIV measurements behind the pectoral fin of a steadily swimming bluegill sunfish, Drucker and Lauder (1999) reconstruct the wake of this fin revealing a series of staggered and interconnected vortex rings. Along the horizontal center plane of these linked vortex rings, the telltale reverse Kármán street of a propulsive thrust wake is present.Abstract Synthetic aperture PIV (SAPIV) is used to quantitatively analyze the wake behind a giant danio (Danio aequipinnatus) swimming freely in a seeded quiescent tank. The experiment is designed with minimal constraints on animal behavior to ensure that natural swimming occurs. The fish exhibits forward swimming and turning behaviors at speeds between 0.9 and 1.5 body lengths/second. Results show clearly isolated and linked vortex rings in the wake structure, as well as the thrust jet coming off of a visual hull reconstruction of the fish body. As a benchmark for quantitative analysis of volumetric PIV data, the vortex circulation and impulse are computed using methods consistent with those applied to planar PIV data. Volumetric momentum analysis frameworks are discussed for linked and asymmetric vortex structures, laying a foundation for further volumetric studies of swimming hydrodynamics with SAPIV. Additionally, a novel weighted refocusing method is presented as an improvement to SAPIV reconstruction.