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Line 15: − The Fourier Analysis method of interferograms was created in 1982 by M. Takeda, H. Ina and S. Kobayashi and originally intended as an alternative to Moire Topography and the phase-shifting technique [1,2]. However, this method was ineffective at analyzing closed fringe patterns. A revision to the method, solved this problem by utilizing a Cartesian to polar coordinate transform [3]. The result of which could then be analyzed using the original method proposed. − + − + − − − [2] cuevas et al 2002 − − [3] ge et al 2001
Numerical Analysis of Interference Patterns (view source)
Revision as of 18:47, 17 October 2007
, 18:47, 17 October 2007→Fourier Analysis Method
== Fourier Analysis Method ==
== Fourier Analysis Method ==
[[Image:mexicanhat.jpg|thumb|A "Mexican Hat" function. (courtesy of [http://www.vector.org.uk/archive/v194/finn194.htm])]]
[[Image:mexicanhat.jpg|thumb|A "Mexican Hat" function. (courtesy of [http://www.vector.org.uk/archive/v194/finn194.htm])]]
The revised Fourier Analysis method does have several limitations. The first requirement is that the "measurement wave front be a monotonic function in the direction of the carrier frequency" [3]. For instance, if the surface to be analyzed resemble the image to the right were analyzed by the above method, it would look no different than a surface that decreased or increased from top to bottom. In order to analyze such a fringe pattern generated by such a surface, an additional fringe pattern giving the carrier frequency must be used.
The Fourier Analysis method of interferograms was created in 1982 by M. Takeda, H. Ina and S. Kobayashi and originally intended as an alternative to Moire Topography and the phase-shifting technique [[#References|[2]]],[[#References|[3]]] . However, this method was ineffective at analyzing closed fringe patterns. A revision to the method, solved this problem by utilizing a Cartesian to polar coordinate transform [[#References|[4]]]. The result of which could then be analyzed using the original method proposed.
The revised Fourier Analysis method does have several limitations. The first requirement is that the "measurement wave front be a monotonic function in the direction of the carrier frequency" [[#References|[4]]]. For instance, if the surface to be analyzed resemble the image to the right were analyzed by the above method, it would look no different than a surface that decreased or increased from top to bottom. In order to analyze such a fringe pattern generated by such a surface, an additional fringe pattern giving the carrier frequency must be used.
[1] takeda et al 1982
== Regularization Algorithms==
== Regularization Algorithms==