Applied Mathematics & Information Sciences

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The finite oscillator based on the Lie group of spin U(2) provides a model for finite one-dimensional (1D) arrays of N = 2 j +1 pixels, for j integer or half-integer which, as j → ¥, deforms to the continuous 1D model of geometric optics. Translations, linear transformations and aberrations in the latter are canonical and have their N×N unitary counterparts in the former. Since in U(N) there are only N2 independent transformations, we identify the finite counterparts of translations, linear transformations and aberrations within the finite model, applicable to the correction of aberrated images or signals on N-pixel linear arrays.

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