Combining ART and FBP for improved fidelity of tomographic BOS

Abstract

Engine component defects along the hot-gas path (HGP) of jet engines influence the density distribution of the flow, and thus result in characteristic patterns in the exhaust jet. These characteristic patterns can be reconstructed with the optical background-oriented schlieren (BOS) method in a tomographic set-up, which in turn allows the identification of defects inside the engine through an exhaust jet analysis.The quality of the tomographic reconstruction strongly influences how easily defects can be detected inside the jet engine. In particular, the presence of high gradients in the reconstruction area has a strong impact on the reconstruction quality. An algebraic reconstruction algorithm (ART) is implemented and compared to a filtered-back projection (FBP) algorithm in terms of the capability of performing high-gradient tomographic BOS reconstructions. A combination of both algorithms is presented which significantly improves the reconstruction quality of high-gradient tomographic BOS in terms of artifact reduction. The combination of both algorithms is applied to both synthetic and real measurement data in this paper, in order to show possible applications and the achievable improvement of high-gradient tomographic BOS reconstructions.

Monte Carlo-based a posteriori uncertainty quantification for background-oriented schlieren measurements

“…This turns on a tedious task owing to the wide diversity of methods to implement each one from the aforementioned procedures such as ring method, Henkel Fourier or Fourier expansion techniques for Abel inversion implementation (Kolhe and Agrawal (2009); Pretzier (1991); Fomin (1998)). Besides, in certain applications, multiple mathematical procedures are used in combination to reconstruct the refractive index field (Hartmann and Seume (2016)). Hence, the need for a modular and generic framework that can, in one hand, easily integrate and switch between the different reconstruction functions and, on the other hand, accounts for all possible errors regardless of their possible correlation.…”

“…For such an approach to be effective, it should be readily expandable into other mathematical procedures. The problem is more acute as the latter noticeably is increasing in number according to specific configurations, such as the use of ART combined with FBP (Hartmann and Seume (2016)) or the use of inverse gradient instead of the Poisson equation when derivation is not possible (presence of an object in the field). Another concern is that this kind of formulas requires the determination of correlation coefficients between errors.…”

Assessment of three-dimensional density measurements from tomographic background-oriented schlieren (BOS)

“…This study will test both the null gradient case and using FBP as an initial guess. The latter has been shown [9,11] to improve the rate of convergence of ART, and reduce its tendency for underprediction, when FBP is an accurate guess of the gradient field. The FBP solution needs to be filtered first to remove artefacts around the object.…”

“…The peak errors of FBP-ART vary slightly more from ART, with a tendency to have a marginally higher error than ART (average 0.1% higher) at 10 iterations and slightly lower peak error (average 0.5% higher) at 100 iterations. The idea of using FBP as the initial solution to reduce ART underprediction by preserving regions of high (or overpredicted) [9,11] is not realised in practice due to the strong artefacts throughout the domain (figure 11), possibly slightly exacerbated by the Gaussian mask which is necessary to reduce the growth of the FBP artefacts. This contrasting result to the previous studies on FBP-ART can be explained in terms of the flow under study.…”

“…Small-scale resolution is limited by high-spatialfrequency noise, or spatial averaging (which is also inherent in a BOS setup). Using an FBP solution as the first guess to ART iterations [9] is a promising development. Ideally, ART is directed towards a solution with an analytical basis where small scales have been captured.…”