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Journal Articles Optics and Lasers in Engineering Year : 2013

Using deconvolution to improve the metrological performance of the grid method

Michel Grediac
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Claudiu Badulescu


The use of various deconvolution techniques to enhance strain maps obtained with the grid method is addressed in this study. Since phase derivative maps obtained with the grid method can be approximated by their actual counterparts convolved by the envelope of the kernel used to extract phases and phase derivatives, non-blind restoration techniques can be used to perform deconvolution. Six deconvolution techniques are presented and employed to restore a synthetic phase derivative map, namely direct deconvolution, regularized deconvolution, Richardson-Lucy algorithm and Wiener filtering, the last two with two variants concerning their practical implementations. Obtained results show that the noise that corrupts the grid images must be thoroughly taken into account to limit its effect on the deconvolved strain maps. The difficulty here is that the noise on the grid image yields a spatially correlated noise on the strain maps. In particular, numerical experiments on synthetic data show that direct and regularized deconvolutions are unstable when noisy data are processed. The same remark holds when Wiener filtering is employed without taking into account noise autocorrelation. On the other hand, the Richardson-Lucy algorithm and Wiener filtering with noise autocorrelation provide deconvolved maps where the impact of noise remains controlled within a certain limit. It is also observed that the last technique outperforms the Richardson-Lucy algorithm. Two short examples of actual strain fields restoration are finally shown. They deal with asphalt and shape memory alloy specimens. The benefits and limitations of deconvolution are presented and discussed in these two cases. The main conclusion is that strain maps are correctly deconvolved when the signal-to-noise ratio is high and that actual noise in the actual strain maps must be more specifically characterized than in the current study to address higher noise levels with Wiener filtering.
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Dates and versions

hal-00801133 , version 1 (15-03-2013)



Michel Grediac, Frédéric Sur, Claudiu Badulescu, Jean-Denis Mathias. Using deconvolution to improve the metrological performance of the grid method. Optics and Lasers in Engineering, 2013, 51 (6), pp.716-734. ⟨10.1016/j.optlaseng.2013.01.009⟩. ⟨hal-00801133⟩
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