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The effects of random phase errors introduced by way of a composite material radome on the sidelobes of a low-sidelobe transmitting antenna are investigated. The nominal sidelobe level of interest is - 40 dB below maximum directive gain outside a minimum conical angle about boresight. The radome used was constructed using strips of fiberglass cloth pre-impregnated with epoxy resin with each strip overlapping adjacent strips. The overlapping is staggered so that the final thickness contains roughtly the same number of layers. The shape of the radome is cylindrical on the side, capped by a hemispherical sector. The radome curvature is large with respect to wavelength, and is several wavelengths thick at band (37 GHz). Measurements made on the radiation patterns of a large aperture low-sidelobe lens antenna enclosed by the radome indicate that the sidelobe degradation introduced by the radome can be directly related to the construction technique and materials used. Subsequent measurements on the insertion phase versus position on the radome support these conclusions. In particular, the correlation length of the random insertion phase introduced upon transmission through the radome was determined to be essentially that of the overlapping width used in the fiberglass layup. Furthermore, periodicities in insertion phase having the basic period of the overlap width cause grating lobes to occur in the radiation pattern, further degrading the sidelobes.