and extent of flow structures which pervade most turbulent flows. Moreover, turbulence is inherently 3D in nature, and a full description requires a measurement of the 3D velocity field and derivative quantities such as the stress tensor and vorticity vector. Current 3D PIV techniquesThese limitations have led to a number of efforts to develop 3D, 3C PIV-based measurement techniques. Advances such as

Plenoptic particle image velocimetry was recently introduced as a viable three-dimensional, three-component velocimetry technique based on light field cameras. One of the main benefits of this technique is its single camera configuration allowing the technique to be applied in facilities with limited optical access. The main drawback of this configuration is decreased accuracy in the out-of-plane dimension. This work presents a solution with the addition of a second plenoptic camera in a stereo-like configuration. A framework for reconstructing volumes with multiple plenoptic cameras including the volumetric calibration and reconstruction algorithms, including: integral refocusing, filtered refocusing, multiplicative refocusing, and MART are presented. It is shown that the addition of a second camera improves the reconstruction quality and removes the ‘cigar’-like elongation associated with the single camera system. In addition, it is found that adding a third camera provides minimal improvement. Further metrics of the reconstruction quality are quantified in terms of a reconstruction algorithm, particle density, number of cameras, camera separation angle, voxel size, and the effect of common image noise sources. In addition, a synthetic Gaussian ring vortex is used to compare the accuracy of the single and two camera configurations. It was determined that the addition of a second camera reduces the RMSE velocity error from 1.0 to 0.1 voxels in depth and 0.2 to 0.1 voxels in the lateral spatial directions. Finally, the technique is applied experimentally on a ring vortex and comparisons are drawn from the four presented reconstruction algorithms, where it was found that MART and multiplicative refocusing produced the cleanest vortex structure and had the least shot-to-shot variability. Filtered refocusing is able to produce the desired structure, albeit with more noise and variability, while integral refocusing struggled to produce a coherent vortex ring.

A novel 3-D, 3-C PIV technique is described, based on volume illumination and a plenoptic camera to measure a velocity field. The technique is based on plenoptic photography, which uses a dense microlens array mounted near a camera sensor to sample the spatial and angular distribution of light entering the camera. Various algorithms are then used to reconstruct a volumetric intensity field after the image is taken, and cross-correlation algorithms extract the velocity field from the reconstructed volume. This paper provides an introduction to the concepts of light fields and plenoptic photography, and describes the algorithms used to reconstruct the measurement volume. A comparison is made between the use of a combined computational refocusing and thresholding approach versus a direct tomographic reconstruction approach. This discussion lays the groundwork for a more detailed study of reconstruction accuracy, achieveable particle number density, reconstruction ambiguities (e.g., ghost particles), and other factors in a following study. Additionally, the construction of a prototype camera based on a 16-megapixel interline CCD sensor is described and preliminary experimental renderings are given.

A novel 3-D, 3-C PIV technique is described, based on volume illumination and a plenoptic camera to measure a velocity field. This technique is based on light-field photography, which uses a dense microlens array mounted near a camera sensor to sample the spatial and angular distribution of light entering the camera. Tomographic algorithms (MART) are then used to reconstruct a volumetric intensity field after the image is taken, and cross-correlation algorithms extract the velocity field from the reconstructed volume. This paper provides and introduction to the concepts of light fields and plenoptic photography, and describes the tomographic algorithms used to reconstruct the measurement volume. The first preliminary experimental results on a turbulent boundary layer are presented.

This paper describes current calibration methods for plenoptic cameras and introduces a new method of calibration that seeks to estimate the position and orientation of the microlens array based on the camera geometry and on a calibration image. A geometrical model was formulated to relate the position of a microlens to the location on the image sensor where the lens was focused. The location of the focal points were determined by stopping down the aperture of the main camera lens such that only a small beam of light was incident on each microlens. The position and orientation of the microlens array was assumed, and the predicted focal points were compared with the known points determined from the calibration data. This process was repeated until the root-mean-square difference between the expected and predicted results was minimal. The geometrical method was shown to provide a reasonable estimate for the orientation of the microlens array, as each translational parameter converged to less than one pixel and each rotational parameter converged to within 0.00034 radians. Preliminary results show that the best estimate for the image distance is obtained from a measurement of the magnification by imaging a ruler.

Plenoptic PIV offers a simple, single camera solution for volumetric velocity measurements of fluid flow. However, due to the novel manner in which the particle images are acquired and processed, few references exist to aid in determining the resolution limits of the measurements. This manuscript provides a framework for determining the spatial resolution of plenoptic PIV based on camera design and experimental parameters. This information can then be used to determine the smallest length scales of flows that are observable by plenoptic PIV, the dynamic range of plenoptic PIV, and the corresponding uncertainty in plenoptic PIV measurements. A simplified plenoptic camera is illustrated to provide the reader with a working knowledge of the method in which the light field is recorded. Then, operational considerations are addressed. This includes a derivation of the depth resolution in terms of the design parameters of the camera. Simulated volume reconstructions are presented to validate the derived limits. It is found that, while determining the lateral resolution is relatively straightforward, many factors affect the resolution along the optical axis. These factors are addressed and suggestions are proposed for improving performance.

The combination of the background oriented schlieren (BOS) technique with the unique imaging capabilities of a plenoptic camera, termed plenoptic BOS, is introduced as a new addition to the family of schlieren techniques. Compared to conventional single camera BOS, plenoptic BOS is capable of sampling multiple lines-of-sight simultaneously. Displacements from each line-of-sight are collectively used to build a four-dimensional displacement field, which is a vector function structured similarly to the original light field captured in a raw plenoptic image. The displacement field is used to render focused BOS images, which qualitatively are narrow depth of field slices of the density gradient field. Unlike focused schlieren methods that require manually changing the focal plane during data collection, plenoptic BOS synthetically changes the focal plane position during post-processing, such that all focal planes are captured in a single snapshot. Through two different experiments, this work demonstrates that plenoptic BOS is capable of isolating narrow depth of field features, qualitatively inferring depth, and quantitatively estimating the location of disturbances in 3D space. Such results motivate future work to transition this single-camera technique towards quantitative reconstructions of 3D density fields.

The volumetric calibration of a plenoptic camera is explored to correct for inaccuracies due to real-world lens distortions and thin-lens assumptions in current processing methods. Two methods of volumetric calibration based on a polynomial mapping function that does not require knowledge of specific lens parameters are presented and compared to a calibration based on thin-lens assumptions. The first method, volumetric dewarping, is executed by creation of a volumetric representation of a scene using the thin-lens assumptions, which is then corrected in post-processing using a polynomial mapping function. The second method, direct light-field calibration, uses the polynomial mapping in creation of the initial volumetric representation to relate locations in object space directly to image sensor locations. The accuracy and feasibility of these methods is examined experimentally by capturing images of a known dot card at a variety of depths. Results suggest that use of a 3D polynomial mapping function provides a significant increase in reconstruction accuracy and that the achievable accuracy is similar using either polynomial-mapping-based method. Additionally, direct light-field calibration provides significant computational benefits by eliminating some intermediate processing steps found in other methods. Finally, the flexibility of this method is shown for a nonplanar calibration.