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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Vydáno v:	Experiments in fluids Ročník 61; číslo 3
Hlavní autoři:	Grauer, Samuel J., Steinberg, Adam M.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2020 Springer Nature B.V
Témata:	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
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Abstract	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
AbstractList	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 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
ArticleNumber	80
Author	Steinberg, Adam M. Grauer, Samuel J.
Author_xml	– sequence: 1 givenname: Samuel J. orcidid: 0000-0003-2033-2371 surname: Grauer fullname: Grauer, Samuel J. email: sgrauer3@gatech.edu organization: Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology – sequence: 2 givenname: Adam M. surname: Steinberg fullname: Steinberg, Adam M. organization: Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology
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Snippet	We propose a novel approach to background-oriented schlieren (BOS) tomography (BOST) that unifies the deflection sensing and reconstruction algorithms. BOS is...
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SubjectTerms	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
Title	Fast and robust volumetric refractive index measurement by unified background-oriented schlieren tomography
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