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The Filtered Abel Transform and Its Application in Combustion Diagnostics

The Filtered Abel Transform and Its Application in Combustion Diagnostics


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About the Book

Many non-intrusive combustion diagnosis methods generate line-of-sight projections of a flame field. To reconstruct the spatial field of the measured properties, these projections need to be deconvoluted. When the spatial field is axisymmetric, commonly used deconvolution method include the Abel transforms, the onion peeling method and the two-dimensional Fourier transform method and its derivatives such as the filtered back projection methods. This paper proposes a new approach for performing the Abel transform method is developed, which possesses the exactness of the Abel transform and the flexibility of incorporating various filters in the reconstruction process. The Abel transform is an exact method and the simplest among these commonly used methods. It is evinced in this paper that all the exact reconstruction methods for axisymmetric distributions must be equivalent to the Abel transform because of its uniqueness and exactness. Detailed proof is presented to show that the two dimensional Fourier methods when applied to axisymmetric cases is identical to the Abel transform. Discrepancies among various reconstruction method stem from the different approximations made to perform numerical calculations. An equation relating the spectrum of a set of projection date to that of the corresponding spatial distribution is obtained, which shows that the spectrum of the projection is equal to the Abel transform of the spectrum of the corresponding spatial distribution. From the equation, if either the projection or the distribution is bandwidth limited, the other is also bandwidth limited, and both have the same bandwidth. If the two are not bandwidth limited, the Abel transform has a bias against low wave number components in most practical cases. This explains why the Abel transform and all exact deconvolution methods are sensitive to high wave number noises. The filtered Abel transform is based on the fact that the Abel transform of filtered projection data is equal to


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Product Details
  • ISBN-13: 9781721569649
  • Publisher: Createspace Independent Publishing Platform
  • Publisher Imprint: Createspace Independent Publishing Platform
  • Height: 279 mm
  • No of Pages: 32
  • Spine Width: 2 mm
  • Width: 216 mm
  • ISBN-10: 1721569642
  • Publisher Date: 20 Jun 2018
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 100 gr


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