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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 20 — Jul. 10, 2009
  • pp: 3894–3902

Abel inversion of deflectometric data: comparison of accuracy and noise propagation of existing techniques

Pankaj S. Kolhe and Ajay K. Agrawal  »View Author Affiliations


Applied Optics, Vol. 48, Issue 20, pp. 3894-3902 (2009)
http://dx.doi.org/10.1364/AO.48.003894


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Abstract

Abel inverse integral to obtain local field distributions from path-integrated measurements in an axisymmetric medium is an ill-posed problem with the integrant diverging at the lower integration limit. Existing methods to evaluate this integral can be broadly categorized as numerical integration techniques, semianalytical techniques, and least-squares whole-curve-fit techniques. In this study, Simpson’s 1 / 3 rd rule (a numerical integration technique), one-point and two-point formulas (semianalytical techniques), and the Guass–Hermite product polynomial method (a least-squares whole-curve-fit technique) are compared for accuracy and error propagation in Abel inversion of deflectometric data. For data acquired at equally spaced radial intervals, the deconvolved field can be expressed as a linear combination (weighted sum) of measured data. This approach permits use of the uncertainty analysis principle to compute error propagation by the integration algorithm. Least-squares curve-fit techniques should be avoided because of poor inversion accuracy with large propagation of measurement error. The two-point formula is recommended to achieve high inversion accuracy with minimum error propagation.

© 2009 Optical Society of America

OCIS Codes
(000.2190) General : Experimental physics
(100.6950) Image processing : Tomographic image processing
(120.5820) Instrumentation, measurement, and metrology : Scattering measurements
(280.1740) Remote sensing and sensors : Combustion diagnostics
(280.2490) Remote sensing and sensors : Flow diagnostics

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: April 6, 2009
Revised Manuscript: June 1, 2009
Manuscript Accepted: June 15, 2009
Published: July 1, 2009

Citation
Pankaj S. Kolhe and Ajay K. Agrawal, "Abel inversion of deflectometric data: comparison of accuracy and noise propagation of existing techniques," Appl. Opt. 48, 3894-3902 (2009)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-20-3894

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