Weighted Least Squares (WLS) Density Integration for Background Oriented Schlieren (BOS)

Abstract

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.

arXiv commentsubmitted to Experiments in Fluids

References in corpus (5)

• Dot-Tracking Methodology for Background Oriented Schlieren (BOS)
• PIV/BOS Synthetic Image Generation in Variable Density Environments for Error Analysis and Experiment Design
• Uncertainty Quantification in density estimation from Background Oriented Schlieren (BOS) measurements
• Two Regime Cooling in Flow Induced by a Spark Discharge
• Uncertainty amplification due to density/refractive-index gradients in volumetric PTV and BOS experiments

Cited by in corpus (2)

• Vortex rings drive entrainment and cooling in flow induced by a spark discharge
• Meta-Uncertainty for Particle Image Velocimetry