A non-axisymmetric temperature field reconstruction method based on the compressive sensing background oriented Schlieren method

Measurement of the combustion temperature field is an extremely important issue in industrial production. Temperature is one of the key parameters in combustion studies. With the temperature field distribution of the combustion field obtained, heat transfer, heat convection, and heat radiation can be calculated directly and efficiently. Traditional background oriented Schlieren (BOS) is an effective method for non-axisymmetric temperature field measurements, but it requires simultaneous Schlieren imaging at multiple angles for tomographic reconstruction, which will greatly limit its application. In this paper, the compressive sensing algorithm is introduced into the temperature field reconstruction, which establishes the system of equations between the deflection angle and the refractive index gradient. Then, the reconstruction of the non-axisymmetric temperature field is realized by solving the underdetermined system of equations by the method of solving the sparse solution through the compressive sensing. First, light offsets across the non-axisymmetric temperature field are measured by the under-angled BOS system and image processing method. Second, the spatial refractive index field is reconstructed by the compressive sensing BOS method proposed in this paper. Finally, the spatial temperature field is obtained. The experimental results show that by comparing the iRadon reconstruction algorithm and the compressive sensing reconstruction algorithm, the temperature field reconstructed by the compressive sensing under the condition of the under-angled sampling of projection data had a higher accuracy than that reconstructed by the tomographic reconstruction algorithm under the same condition. The average error of the temperature field was reduced from 34.6 to 29.7 K under the same measurement conditions; however, the accuracy is better maintained by using the compressive sensing algorithm under the condition of undersampling projection.