Reconstructing Gas Flows Using Light-Path Approximation

Yu Ji       Jinwei Ye       Jingyi Yu
University of Delaware


    Transparent gas flows are difficult to reconstruct: the refractive index field (RIF) within the gas volume is uneven and rapidly evolving, and correspondence matching under distortions is challenging. We present a novel computational imaging solution by exploiting the light field probe (LFProbe). A LF-probe resembles a view-dependent pattern where each pixel on the pattern maps to a unique ray. By observing the LF-probe through the gas flow, we acquire a dense set of ray-ray correspondences and then reconstruct their light paths. To recover the RIF, we use Fermat’s Principle to correlate each light path with the RIF via a Partial Differential Equation (PDE). We then develop an iterative optimization scheme to solve for all light-path PDEs in conjunction. Specifically, we initialize the light paths by fitting Hermite splines to ray-ray correspondences, discretize their PDEs onto voxels, and solve a large, over-determined PDE system for the RIF. The RIF can then be used to refine the light paths. Finally, we alternate the RIF and light-path estimations to improve the reconstruction. Experiments on synthetic and real data show that our approach can reliably reconstruct small to medium scale gas flows. In particular, when the flow is acquired by a small number of cameras, the use of ray-ray correspondences can greatly improve the reconstruction.

LF Probe-based Acquisition System

Left: a LF-probe maps each pattern pixel to a unique ray.  A combination of horizontal red gradient and vertical blue gradient behind each microlens to discriminate rays of different directions. To determine 2D positions, we use the variation of green channel.
Right: our experimental setup. We construct a LF-probe using a Ultra bright illumination, a diffuser, a high-resolution pattern and hexagonal lenslet array.
A simple Gaussian gas flow. (a) A rendered LF-probe image through the flow; (b) Optical flow results on the green channel; (c) Directional variations of rays; (d) The ground truth RIF; (e) Our estimated RIF after 1 iteration; (f) Our final result.
The fuel injection dataset. (a) A volume rendering of the ground truth data; (b) Optical flow results on the green channel; (c) Directional variations of rays; (d) Slices of our reconstructed RIF vs. the ground truth.
Reconstruction results on a real gas flow. Each row shows the reconstructed flow at a different time instance. (a) The captured LF-probe images; (b) Measured ray direction variations through the flow; (c)-(e) Three vertical slices of the reconstructed RIFs where (d) is the central slice.
Video: Real Gas Flow Results
This project was partially supported by the National Science Foundation under grants IIS-CAREER-0845268 and IIS-RI-1016395, and by the Air Force Office of Science Research under the YIP Award.