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In this paper, we present an elongated speckle images produced from diffusers using sharp elliptical apertures. The orientation of the elliptic aperture is recognized from the direction of the elongation in the speckle images. The aperture tilting out of the plane is investigated. Three models of elliptical apertures are considered and the corresponding speckle images are obtained. The 1st model is composed of two orthogonal ellipses or plus symbol pupil; the 2nd has four symmetric ellipses with an angle of 45° between each of them or in the form of a snow flake pupil and the 3rd model looks like an airplane. Also, the autocorrelation profiles of the speckle images corresponding to the diffused airplane are obtained from which the average speckle size is computed. Finally, the reconstructed images of the described elliptical models and its autocorrelation images, making use of Mat lab code, are obtained.
In this paper, homotopy analysis method (HAM) and Padé approximant will be considered for finding analytical solution of three-dimensional viscous flow near an infinite rotating disk which is a well-known classical problem in fluid mechanics. The solution is compared to the numerical (fourth-order Runge-Kutta) solution and the convergence of the obtained series solution is carefully analyzed. The results illustrate that HAM-Padé is an appropriate method in solving the systems of nonlinear equations.