Despite significant recent progress, dense, time-resolved imaging of complex, non-stationary 3D flow velocities remains an elusive goal. In this work we tackle this problem by extending an established 2D method, Particle Imaging Velocimetry, to three dimensions by encoding depth into color. The encoding is achieved by illuminating the flow volume with a continuum of light planes (a "rainbow"), such that each depth corresponds to a specific wavelength of light. A diffractive component in the camera optics ensures that all planes are in focus simultaneously. With this setup, a single color camera is sufficient for tracking 3D trajectories of particles by combining 2D spatial and 1D color information.
For reconstruction, we derive an image formation model for recovering stationary 3D particle positions. 3D velocity estimation is achieved with a variant of 3D optical flow that accounts for both physical constraints as well as the rainbow image formation model. We evaluate our method with both simulations and an experimental prototype setup.
We use structured monochromatic volume illumination with spatially varying intensity profiles, to achieve 3D intensity particle tracking velocimetry using a single video camera. The video camera records the 2D motion of a 3D particle field within a fluid, which is perpendicularly illuminated with depth gradients of the illumination intensity. This allows us to encode the depth position perpendicular to the camera, in the intensity of each particle image. The light intensity field is calibrated using a 3D laser-engraved glass cube containing a known spatial distribution of 1100 defects. This is used to correct for the distortions and divergence of the projected light. We use a sequence of changing light patterns, with numerous sub-gradients in the intensity, to achieve a resolution of 200 depth levels.
China launched the pilot construction of the carbon emission trading scheme (ETS) in 2011. The pilots have been running for many years. Does ETS significantly restrain the increase of carbon emission intensity? Based on China’s panel data for provinces and industries, this paper uses the policy assessment method to evaluate the inhibition by ETS of carbon emission intensity. The assessment scope includes six provincial pilots and pilot industries covered by ETS. The results show that ETS has significant suppression of carbon emission intensity only in Beijing and Guangdong. There is no significant impact on the carbon emission intensity of Tianjin, Shanghai, Chongqing, and Hubei. Through the carbon emission intensity inhibition analysis of the industries covered by ETS from Beijing and Chongqing, the results of the production and supply of electric power, steam and hot water, petroleum processing and coking in Beijing have a significant impact on the ETS. Only the smelting and pressing of ferrous metals in Chongqing has a significant impact on the ETS.
RainbowPIV is a recent imaging technology proposed for timeresolved 3D-3C fluid velocity measurement using a single RGB camera. It dramatically simplifies the hardware setup and calibration procedures compared to alternative 3D-3C measurement approaches. RainbowPIV combines optical design and tailored reconstruction algorithms, and earlier preliminary studies have demonstrated its ability to extract physically constrained fluid vector fields. This article addresses the issue of limited axial resolution, the major drawback of the original RainbowPIV system. We validate the new system with a direct, quantitative comparison to four-camera Tomo-PIV on experimental data. The reconstructed flow vectors of the two approaches exhibit a high degree of consistency, with the RainbowPIV results explicitly guaranteeing physical properties such as divergence free velocity fields for incompressible fluid flows.
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