Zeng-Guang Yuan

National Center for Microgravity Research, Cleveland, Ohio

The Filtered Abel Transform and Its

Application in Combustion Diagnostics

NASA/CR—2003-212121

March 2003

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Zeng-Guang Yuan

National Center for Microgravity Research, Cleveland, Ohio

The Filtered Abel Transform and Its

Application in Combustion Diagnostics

NASA/CR—2003-212121

March 2003

National Aeronautics and

Space Administration

Glenn Research Center

Prepared under Cooperative Agreement NCC3–975

Prepared for the

1995 Fall Meeting, Western States Section

sponsored by The Combustion Institute

Stanford, California, October 30–31, 1995
Acknowledgments

The author gratefully acknowledges the help from Dr. David Urban (NASA Glenn), in the entire course of this

study, and the help from Paul Greenberg (NASA Glenn), and Paul Ferkul (Analex Corp. ), for their valuable

suggestions when the manuscript was reviewed. The author would like to thank Dr. Uday Hegde (NYMA, Inc.), for

his encouragement in the preparation of this paper, Dr. Fletcher Miller (Case Western Reserve University), for

informative discussions on the subject, and Robert Klimec for implementing the described method in an in-house

software. This study was supported by the Physical Sciences Research Division of the NASA Office of Biological

and Physical Research.

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Available electronically at http://gltrs.grc.nasa.gov
The Filtered Abel Transform and Its Application in Combustion Diagnostics

Zeng-Guang Yuan

National Center for Microgravity Research

Cleveland, Ohio 44135

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17

The Filtered Abel Transform and Its Application in Combustion Diagnostics

Zeng-Guang Yuan

Abel transform; Deconvolution; Laser; Diagnostics

Unclassified -Unlimited

Subject Categories: 64 and 74 Distribution: Nonstandard

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Prepared for the 1995 Fall Meeting, Western States Section sponsored by the Combustion Institute, Stanford, California,

October 30–31, 1995. Project Manager, Stephen N. Simons, Microgravity Science Division, NASA Glenn Research

Center, organization code 6700, 216–433–5277.

Abel transform is widely used for deconvoluting data acquired from an axisymmetric domain with noninstrusive

diagnostic methods. This paper shows the Abel transform is more efficient than other deconvolution methods for

axisymmetric case. An algorithm is presented to perform Abel transform that differs from conventional algorithm

which needs to calculate the derivatives of the raw data. By eliminating derivative calculation, the proposed algorithm not only runs faster, but also avoids errors from derivative calculations. It is also demonstrated that data

filtering procedures can be incorporated in the Abel transform, making it particularly efficient when multiple data

sets obtained with the same instrumentation needs to be processed, as often encountered in a three-dimensional

tomography. An example of using the filtered Abel transform to obtain the soot volume fraction is given at the end

of the paper.