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Since the sun is an extremely strong radiation source at L-band, accounting for sun glint over the ocean, i.e., solar radiation reflected by the sea surface toward downward-looking radiometers, raises a significant challenge for the remote sensing of sea surface salinity. This paper describes a dedicated physical model for sun glint at L-band frequencies and provides quantitative and qualitative estimates of the sun glint contamination impinging the antenna of the Microwave Imaging Radiometer with Aperture Synthesis interferometer onboard the future European Space Agency's Soil Moisture and Ocean Salinity (SMOS) mission. The sun brightness temperature expected during the mission period is first estimated from past solar flux data with an expected range of to about . Numerical simulations of the predicted illumination of the SMOS antenna by solar radiation scattered by the rough sea surface are then performed at key dates of the seasonal cycle using different asymptotic scattering models and several representative surface conditions. Although the center of the sun's glitter pattern will never be located within the useful part of SMOS' synthesized field of view, the expected contamination due to roughness scattering will range between 0 K and about 500 K, depending on the target position, the season period, the roughness state at the target, and the level of solar activity at the time of measurements. In particular, we find the sun glint contamination to be more intense when SMOS will probe ocean surfaces in the Southern Hemisphere, reaching maxima in descending passes with highest values expected at dates around winter solstices.