Timothy W. Fahringer

Volumetric particle image velocimetry with a single plenoptic camera

A novel three-dimensional (3D), three-component (3C) particle image velocimetry (PIV) technique based on volume illumination and light field imaging with a single plenoptic camera is described. A plenoptic camera uses a densely packed microlens array mounted near a high resolution image sensor to sample the spatial and angular distribution of light collected by the camera. The multiplicative algebraic reconstruction technique (MART) computed tomography algorithm is used to reconstruct a volumetric intensity field from individual snapshots and a cross-correlation algorithm is used to estimate the velocity field from a pair of reconstructed particle volumes. This work provides an introduction to the basic concepts of light field imaging with a plenoptic camera and describes the unique implementation of MART in the context of plenoptic image data for 3D/3C PIV measurements. Simulations of a plenoptic camera using geometric optics are used to generate synthetic plenoptic particle images, which are subsequently used to estimate the quality of particle volume reconstructions at various particle number densities. 3D reconstructions using this method produce reconstructed particles that are elongated by a factor of approximately 4 along the optical axis of the camera. A simulated 3D Gaussian vortex is used to test the capability of single camera plenoptic PIV to produce a 3D/3C vector field, where it was found that lateral displacements could be measured to approximately 0.2 voxel accuracy in the lateral direction and 1 voxel in the depth direction over a voxel volume. The feasibility of the technique is demonstrated experimentally using a home-built plenoptic camera based on a 16-megapixel interline CCD camera and a array of microlenses and a pulsed Nd:YAG laser. 3D/3C measurements were performed in the wake of a low Reynolds number circular cylinder and compared with measurements made using a conventional 2D/2C PIV system. Overall, single camera plenoptic PIV is shown to be a viable 3D/3C velocimetry technique.

Tomographic Reconstruction of a 3-D Flow Field Using a Plenoptic Camera

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.

Calibration of a Microlens Array for a Plenoptic Camera

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.

On the resolution of plenoptic PIV

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.

Comparing Volumetric Reconstruction Algorithms for Plenoptic-PIV

A new algorithm for reconstruction of 3D particle fields from plenoptic image data is presented. The algorithm is based on the well-known technique of computational refocusing with the addition of a post reconstruction filter to remove the out of focus particles. This new algorithm is compared to the MART algorithm in terms of reconstruction quality on synthetic particle fields as well as velocity data. Preliminary results indicate that the new algorithm performs the same or better than the MART algorithm while requiring orders of magnitude less computational time.

Filtered refocusing: a volumetric reconstruction algorithm for plenoptic-PIV

A new algorithm for reconstruction of 3D particle fields from plenoptic image data is presented. The algorithm is based on the technique of computational refocusing with the addition of a post reconstruction filter to remove the out of focus particles. This new algorithm is tested in terms of reconstruction quality on synthetic particle fields as well as a synthetically generated 3D Gaussian ring vortex. Preliminary results indicate that the new algorithm performs as well as the MART algorithm (used in previous work) in terms of the reconstructed particle position accuracy, but produces more elongated particles. The major advantage to the new algorithm is the dramatic reduction in the computational cost required to reconstruct a volume. It is shown that the new algorithm takes 1/9th the time to reconstruct the same volume as MART while using minimal resources. Experimental results are presented in the form of the wake behind a cylinder at a Reynolds number of 185.

A Plenoptic Multi-Color Imaging Pyrometer

A three-color pyrometer has been developed based on plenoptic imaging technology. Three bandpass filters placed in front of a camera lens allow separate 2D images to be obtained on a single image sensor at three different and adjustable wavelengths selected by the user. Images were obtained of different blackor grey-bodies including a calibration furnace, a radiation heater, and a luminous sulfur match flame. The images obtained of the calibration furnace and radiation heater were processed to determine 2D temperature distributions. Calibration results in the furnace showed that the instrument can measure temperature with an accuracy and precision of 10 Kelvins between 1100 and 1350 K. Timeresolved 2D temperature measurements of the radiation heater are shown.

3D Particle Position Reconstruction Accuracy in Plenoptic PIV

The particle reconstruction capabilities of a novel 3-D, 3-C PIV technique, based on volume illumination and a plenoptic camera to measure a velocity field, are tested. 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 an introduction to the concepts of light fields and describes the tomographic algorithms used to reconstruct the measurement volume. A preliminary test on the accuracy of single particle reconstructions is presented, showing that laterally we can expect errors to be less than a voxel for most cases. A test on the reconstruction quality is presented for a volume of particles as a function of particle density and is shown to vary little as the particle density is increased. Finally a simulated Gaussian ring vortex is presented showing a full simulation as well as the velocity accuracy.

Comparison of Stereo-PIV and Plenoptic-PIV Measurements on the Wake of a Cylinder in NASA Ground Test Facilities.

A series of comparison experiments have been performed using a single-camera plenoptic PIV measurement system to ascertain the systems performance capabilities in terms of suitability for use in NASA ground test facilities. A proof-of-concept demonstration was performed in the Langley Advanced Measurements and Data Systems Branch 13-inch (33- cm) Subsonic Tunnel to examine the wake of a series of cylinders at a Reynolds number of 2500. Accompanying the plenoptic-PIV measurements were an ensemble of complementary stereo-PIV measurements. The stereo-PIV measurements were used as a truth measurement to assess the ability of the plenoptic-PIV system to capture relevant 3D/3C flow field features in the cylinder wake. Six individual tests were conducted as part of the test campaign using three different cylinder diameters mounted in two orientations in the tunnel test section. This work presents a comparison of measurements with the cylinders mounted horizontally (generating a 2D flow field in the x-y plane). Results show that in general the plenoptic-PIV measurements match those produced by the stereo-PIV system. However, discrepancies were observed in extracted pro les of the fuctuating velocity components. It is speculated that spatial smoothing of the vector fields in the stereo-PIV system could account for the observed differences. Nevertheless, the plenoptic-PIV system performed extremely well at capturing the flow field features of interest and can be considered a viable alternative to traditional PIV systems in smaller NASA ground test facilities with limited optical access.

Modeling the Effect of Refraction at a Flat Interface on Plenoptic Particle Reconstruction

As with any flow diagnostic imaging system, plenoptic PIV must be able to capture images under a wide variety of imaging conditions. One common problem is the change in magnification caused by a change in the index of refraction between a flow volume and the camera, often seen in water tunnel imaging. This work seeks to analytically derive the effect of refraction on the imaging equations and to find a correction factor for the depth of particles in a tomographic reconstruction of the volume. This solution was tested by a series of simulated images that were generated under three different conditions: no refractive interfaces, a flat refractive interface between the volume and the camera, and a flat refractive interface between the main lens and the microlens array. Results demonstrated that the depth of a particle is shifted with regard to the focal point of the system by a factor of the index of refraction. For an internal interface, this scaling remains true for all particles focused behind the interface, but there is significant deviation in particle depth for particles focused in front of this plane.