Tomographic reconstruction of light field PIV based on a backward ray-tracing technique

Abstract

The calculation of the weight matrix is one of the key steps of the tomographic reconstruction in the light field particle image velocimetry (light field PIV) system. At present, the existing calculation method of the weight matrix in light field PIV based on the forward ray-tracing technique (named as Fahringer's method) is very time-consuming. To improve the computational efficiency of the weight matrix, this paper presents a computational method for the weight matrix based on the backward ray-tracing technique in combination with Gaussian function (named as Gaussian function method). An Expectation-Maximization (EM) algorithm is employed for the reconstruction of the 3D particle field, and a summed line-ofsight (SLOS) estimation is further used to accelerate the reconstruction process. The computational accuracy and efficiency of the weight matrix, the reconstruction quality of the 3D particle field, and the velocity field accuracy by Gaussian function method are numerically investigated. Finally, experiments are carried out to verify the feasibility of the weight matrix by Gaussian function method. Numerical results illustrated that Gaussian function method can improve the computational efficiency of the weight matrix by more than 10 times. SLOS is capable of further accelerating the computational efficiency of the overall reconstruction process including the pre-determination, the calculation of the weight matrix and the reconstruction. The velocity field accuracy by Gaussian function method is almost the same as that by Fahringer's method. The experimental results of the 3D-3C velocity field of a laminar flow further verify the feasibility of the computational method for the weight matrix based on Gaussian function.

Approach to select optimal cross-correlation parameters for light field particle image velocimetry

“…To balance this trade-off, the previous study [48] suggested that the fog droplets or TiO 2 particles with a diameter of 1 to 5 μm can be used in the gas flow measurement, while the glass spheres with a diameter of 10 to 50 μm can be employed in liquid flow measurement. In the LF-PIV, the particle size also affects the elongation lengths of the reconstructed particles [35] and hence the accuracy of the displacement estimation. From this perspective, the particle size that can alleviate the reconstruction elongation effect is preferred in the LF-PIV.…”

“…In addition to the particle concentration, the reconstruction accuracy is also affected by the particle size. It has been demonstrated that severe elongation effects can be produced in particle reconstructions with the use of large tracer particles [34,35], which subsequently decreases the accuracy in locating the correlation peak. Therefore, the selection of the particle size should also consider its effects on particle reconstruction accuracy.…”

Perspective on the development and application of light-field cameras in flow diagnostics

“…For more details, early development of the plenoptic-PIV technique is described by Lynch et al [47], while subsequent improvements are covered in [24,48,49]. Like tomo-PIV, numerous alternatives to MART were proposed to improve accuracy or expedite convergence, including dense ray-tracing reconstruction [50], filtered refocusing [51], deconvolution [52] and expectation-maximization with summed line-of-sight estimation [53]. Expediting convergence is significant for plenoptic-PIV due to the computational cost of iterating through a large number of perspective-views compared to just four in tomo-PIV.…”

“…While w i, j is often used in the direction of mapping 3D voxel to 2D pixel, Cao et al [53] recently developed a new scheme that employs the reversed tracing direction for a plenoptic 2.0 camera. The main motivation being that reversed-tracing connects one pixel to multiple voxels at once, thereby reducing the total number of ray-tracing computations.…”

3D Measurements of a Two-Phase Flow Inside an Optical Cylinder Based on Full-Field Cross-Interface Computed Tomography

“…For con ned-space tomography problems, the optical signal eld is enclosed by the facility walls while the imaging system is set outside. Some portions of the facility walls are made of transparent materials to allow the access of optical signal, such as optical internal combustion engines (Meng Zhang et al, 2019) and wind/water tunnels (Cao et al, 2021;Yang Zhang and Vanierschot, 2021). Examples of 3D tomography approaches in these facilities include the burning velocity, topology and winked structure measurements of turbulent ames in a 1 MPa combustion chamber (Meng Zhang et al, 2019), and the ame ignition dynamics measurements in a Mach 2 combustor (Ma et al, 2015).…”