Direct background-oriented schlieren tomography using radial basis functions

Abstract

Background-oriented schlieren tomography (BOST) is effective for flow field measurement; however, different from general computed tomography (CT), the BOST utilizes the deflection of rays passing through an inhomogeneous field for measurement. It is sensitive to the refractive index gradient. Therefore, an additional integration step is typically employed to obtain the refractive index. In this article, a calculation method of projection matrix is proposed based on the radial basis function (RBF). The 3D distribution of the refractive index can be reconstructed directly. This method was first verified by numerical simulation. Then, the 3D instantaneous refractive index field above a candle flame was measured. The reprojection error was calculated by ray tracing. The results illustrate the accuracy and stability of the proposed method. This research provides a new and complete solution for the 3D instantaneous flow field (refractive index, density, or temperature) measurement.