page_title: Electrical capacitance volume tomography
section_title: ECVT Velocimetry
hierarchical_section_title: Electrical capacitance volume tomography / Principles / ECVT Velocimetry
caption_attribution_description: English: Velocimetry from ECVT data calculated from a method of gradients
context_page_description: Electrical capacitance volume tomography is a non-invasive 3D imaging technology applied primarily to multiphase flows. It was first introduced by W. Warsito, Q. Marashdeh, and L.-S. Fan as an extension of the conventional electrical capacitance tomography. In conventional ECT, sensor plates are distributed around a surface of interest. Measured capacitance between plate combinations is used to reconstruct 2D images of material distribution. In ECT, the fringing field from the edges of the plates is viewed as a source of distortion to the final reconstructed image and is thus mitigated by guard electrodes. ECVT exploits this fringing field and expands it through 3D sensor designs that deliberately establish an electric field variation in all three dimensions. The image reconstruction algorithms are similar in nature to ECT; nevertheless, the reconstruction problem in ECVT is more complicated. The sensitivity matrix of an ECVT sensor is more ill-conditioned and the overall reconstruction problem is more ill-posed compared to ECT. The ECVT approach to sensor design allows direct 3D imaging of the outrounded geometry.
context_section_description: Velocimetry refers to techniques used to measure velocity of fluids. The use of the sensitivity gradient enables the reconstruction of 3D velocity profiles using an ECVT sensor, which can readily provide information of fluid dynamics. The sensitivity gradient is defined as
  where  is the sensitivity distribution of an ECVT sensor as shown to the right. Upon application of the sensitivity gradient as described in, a 3D and 2D velocity profile corresponding to the figure above are shown in the figure to the right.
  The application of the sensitivity gradient provides significant improvement over more traditional (cross-correlation based) velocimetry, exhibiting better image quality and requiring less computational time. Another advantage of the sensitivity gradient based velocimetry is its compatibility with conventional image reconstruction algorithms used in ECVT.
caption: Normalized sensitivity distribution, sensitivity gradient between a pair of electrodes, reconstructed velocity profile when the spheres are moved in a 3D profile, and in a 2D profile in  plane.[11]
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