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Conference publicationsAbstractsXXII conferenceOn the solution of the inverse problem of a beam diagnostics of a thin-film Luneburg lensesPeoples’ Friendship University of Russia, 117198, Moscow, Miklukho-Maklaya str. 6. Tel. (095) 955-08-98, e-mail: andrey_r@front.ru 1 pp. (accepted)Сharacteristics of many integrated optical devices are determined by the parameters of the waveguide lenses that could shape the required amplitude and phase distribution of the field, make the Fourier transform, etc. The resolution of the planar lenses is limited by one-dimensional analogues of spherical aberration and coma aberration. The waveguide lens that in theory can cancel the geometrical aberrations is the thin film Lüneberg lens, which is a radially symmetric smooth thickening of the waveguide layer. In the manufacture of such lenses need to be able to measure the distribution of effective refractive index (ERI) of the waveguide. With this purpose in [1] it was proposed to use the beam diagnostics of the smooth inhomogeneities. It consists of the following: a waveguide structure is skipped by assemblage of parallel rays, in the lens area they are bent and on digitized trajectories, we compute the distribution of ERI of the lens. This problem was solved earlier by the method of treatment of the equations of the trajectories of the rays. And it was necessary to calculate the derivatives of an experimentally obtained trajectories that led to instability of the solution, its complexity and the loss of precision. In this paper, we propose an integral method for solving the inverse problem of beam diagnostics. It's idea is to build a ERI distribution that binds the input assemblage of rays with output assemblage of rays. It is known that passing through the area with radially symmetric inhomogeneity, the beam deflects at a certain angle. Due to symmetry, the impact parameters of the falling and deflected rays remain the same. In this case the ERI distribution of the lens is related to the dependence of the deflection angle from the impact parameter with the Abel integral transformation . Thus disappears necessity of derrivation of the experimental data. The deflection angle for each beam can be measured with high accuracy. All this improves the overall accuracy and speed of calculations.
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