Background-oriented Schlieren tomography using gated recurrent unit

Current Background-oriented schlieren tomography (BOST) methods rely primarily on iterative algorithms for reconstruction. Before reconstruction, a weight projection matrix was generated by performing 3D ray tracing using the projection relationship between the cameras, depending on the camera calibration parameters and large weight projection matrix which introduce artifacts and greatly reduce computational efficiency in the reconstruction. Considering that CT reconstruction uses spatial projection sequences from multiple directions, this study draws inspiration from the Recurrent Neural network(RNN) and utilizes spatial correlation between adjacent projection data to propose a background-oriented schlieren reconstruction method based on a gated recurrent unit (GRU) neural network. First, the model architecture is designed and implemented. Subsequently, numerical simulations were conducted using a methane combustion model to evaluate the proposed method, which achieved an average mean relative error (MRE) of 0.23%. Finally, reconstruction experiments were performed on the actual flow-field data above a candle flame, with a reprojection correlation coefficient of 89% and an average reconstruction time of only 1.04 s per frame. The results demonstrate that the proposed method outperforms traditional iterative reconstruction methods in terms of reconstruction speed and accuracy. This provides a feasible solution for the real-time reconstruction of three-dimensional instantaneous flow fields.