Abstract: For applications in Doppler radar processing, it is necessary to convolve a one-dimensional signal with spatially scaled versions of a single reference. To achieve this one can expand the reference in one dimension, image it though a system that has variable-magnification in this dimension, and perform a one- dimensional convolution with the input signal in the orthogonal direction. To realize the variable magnification imaging system, we consider the construction of a telescope that uses two hybrid diffractive-refractive elements. The refractive component for the elements is a cylindrical lens that provides bias focussing power. The diffractive component for the first element provides the modulation of the optical power necessary to achieve variable- magnification. The second diffractive component is used to correct the phase of the output image and produce a collimated output. Closed form and iterative designs are presented. !4
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