Directional conjugate smoothing for analysis of axi-symmetric fluid vibrations

Numerical implementation of the Abel transform for the construction of digital fluid holographic images is analyzed in this paper. Volumetric strains are obtained from the numerical calculations using the displacement formulation by the method of finite elements. Then the field of volumetric strain is obtained by using the procedure of conjugate approximation with smoothing. Numerical procedure is developed for the calculation of the Abel transform on the basis of the right rectangle numerical integration rule and thus the digital holographic image is constructed. The obtained digital holographic images are used in the hybrid experimental – numerical procedure for the determination of the correlation with the experimental holographic images