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.

中文翻译：

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面向背景纹影的基于不确定性的加权最小二乘密度积分

我们为背景定向纹影 (BOS) 测量提出了一种改进的密度积分方法，该方法克服了常用泊松求解器的噪声敏感性。该方法通过求解超定方程组对密度梯度场的二维积分进行加权最小二乘法 (WLS) 优化。根据密度梯度不确定性为网格点分配权重，以确保不太可靠的测量点对积分过程的影响较小。使用高斯密度场的合成图像分析表明，与最高噪声级别的泊松相比，WLS 限制了随机误差的传播并将其降低了 80%。