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The basic radial-line slot-array antenna (RLSA) consists of a set of slot antennas arranged on the upper face of a radial line. The line is usually fed by a probe located at the center of the line. Any type of polarization may be obtained from an RLSA depending on the slot arrangement along the radial line. While the circular polarization version is commercially available, the linearly polarized RLSA (LPRLSA) presents some inherent drawbacks which impair its competence. This work describes a method whereby the influence of the whole slot array, as seen from the probe, can advantageously be viewed as an equivalent reflection coefficient Rc. Once Rc is computed, the sleeved probe can be efficiently optimized in reasonable time.