Fast and robust volumetric refractive index measurement by unified background-oriented schlieren tomography

We propose a novel approach to background-oriented schlieren (BOS) tomography (BOST) that unifies the deflection sensing and reconstruction algorithms. BOS is a 2D flow visualization technique that renders light deflections due to refraction in the fluid. Simultaneous BOS measurements from unique vi...

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Bibliographic Details
Published in:Experiments in fluids Vol. 61; no. 3
Main Authors: Grauer, Samuel J., Steinberg, Adam M.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2020
Springer Nature B.V
Subjects:
Algorithms
Best practice
Cameras
Complexity
Deflection
Distortion
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Flow visualization
Fluid- and Aerodynamics
Heat and Mass Transfer
Image reconstruction
Inverse problems
Mathematical models
Optical flow (image analysis)
Refractivity
Research Article
Robustness (mathematics)
Schlieren tomography
Tomography
Two dimensional flow
ISSN:0723-4864, 1432-1114
Online Access:Get full text
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Summary:We propose a novel approach to background-oriented schlieren (BOS) tomography (BOST) that unifies the deflection sensing and reconstruction algorithms. BOS is a 2D flow visualization technique that renders light deflections due to refraction in the fluid. Simultaneous BOS measurements from unique views can be reconstructed by tomography to estimate the fluid’s 3D refractive index field. The cameras are focused through the fluid on textured background patterns. Deflections between an undistorted reference image and distorted image are typically determined by gradient-based optical flow (OF), which is a complex inverse problem and potential source of error in BOST. This paper presents an alternative approach to BOST that unifies the OF equations and deflection model. Our new operator simultaneously calculates the image distortions seen by each camera for a discrete refractive index distribution. Unified BOST (UBOST) thus reconstructs observed image distortions instead of inferred deflections, which are influenced by user-selected OF parameters. The UBOST operator has one third as many equations as the classical BOST operator. We show that our formulation reduces the effects of model error and the computational cost of reconstruction. These advantages are demonstrated with a numerical experiment using phantoms of varied complexity. Best practice UBOST reconstructions were more accurate than classical reconstructions of the exact deflections for each phantom. Moreover, UBOST estimates converged substantially faster, resulting in a ≥ 62.5% speedup with our solver. Graphic abstract
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ISSN:0723-4864
1432-1114
DOI:10.1007/s00348-020-2912-1