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A novel technique for the efficient synthesis of one-dimensional (1-D) Fabry-Perot leaky-wave antennas with low sidelobe levels is described. It is based on the study of the reflection characteristics presented by the two periodic surfaces that form the cavity. The synthesis technique avoids the search for modal solutions in the complex plane, which is typically needed to characterize the dispersion of the leaky modes associated with the antenna geometry. Instead, it involves the solution of two simple equations, so that the desired aperture distribution (amplitude and phase) can be directly synthesized. Numerical and experimental results show that the method can be used to efficiently synthesize 1-D Fabry-Perot low sidelobe leaky-wave antennas for any desired scanning angle.