We propose an improved density integration methodology for Background Oriented Schlieren (BOS) measurements that overcomes the noise sensitivity of the commonly used Poisson solver. The method employs a weighted least-squares (WLS) optimization of the 2D integration of the density gradient field by solving an over-determined system of equations. Weights are assigned to the grid points based on density gradient uncertainties to ensure that a less reliable measurement point has less effect on the integration procedure. Synthetic image analysis with a Gaussian density field shows that WLS constrains the propagation of random error and reduces it by 80% in comparison to Poisson for the highest noise level. Using WLS with experimental BOS measurements of flow induced by a spark plasma discharge show a 30% reduction in density uncertainty in comparison to Poisson, thereby increasing the overall precision of the BOS density measurements.
Forward and inverse modeling of depth-of-field effects in background-oriented schlieren
Pennsylvania State University（宾夕法尼亚州立大学）；University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）；Office National d’Études et de Recherches Aérospatiales（法国国家航空航天研究局）
Flow over an espresso cup: Inferring 3D velocity and pressure fields from tomographic background oriented schlieren videos via physics-informed neural networks
High-resolution pressure imaging via background-oriented schlieren tomography: a spatiotemporal measurement for MHz ultrasound fields and hydrophone calibration
Unified Deflection Estimation and Error Analysis for Background-Oriented Schlieren
Institute of Fluid Mechanics & Aircraft and Propulsion Laboratory, Ningbo Institute of Technology, Beihang University（北京航空航天大学宁波理工学院流体机械与航空推进实验室）；Tianmushan Laboratory（天目山实验室）
Estimating density, velocity, and pressure fields in supersonic flow using physics-informed BOS
Pennsylvania State University（宾夕法尼亚州立大学）；CSIR-National Aerospace Laboratories（印度国家航空航天实验室）；Case Western Reserve University（凯斯西储大学）；National Research Council Canada（加拿大国家研究委员会）
