Fig. 3. Grating locations for a single beam with phase control to the subarray level. phasing periodicities in the antenna array, replicas of the main beam are also formed at grating lobe locations. Grating lobe spacings for a lunar antenna with 104 m subarrays are shown in Fig. 3. Lobes occur on the Earth in a rectangular matrix projecting the periodicity of antenna subarrays; they are spaced at intervals of \R0/D^ where Ra = 380,000 km, X = 12.25 cm, and Dx is the distance between antenna phase centers. The 1 km SPS antenna incorporated 7,220 subarrays, each 10.4 m on a side, while an equivalent 10 km LPS antenna would have 7,220 subarrays, 104 m on a side. Mechanical alignment of the microwave array must be controlled very precisely (±1 arc minute in the baseline SPS) to keep grating lobes at low energy levels coincident with nulls in the subarray's electromagnetic gain pattern (4). The additional beam transmission distance for a lunar antenna (approximately 380,000 km) causes additional tilt deflection of the subarray pattern, and a steep increase in the magnitudes of retrodirectively steered grating lobes. Computer simulations of microwave transmission under tilt conditions were made for various LPS configurations as shown in Fig. 4. With 104 m subarrays and one arc minute antenna tilt, the 10 km lunar antenna produced grating lobe power density peaks of 3 mW/cm2, a factor of 300 higher than the SPS grating lobe requirement of .01 mW/cm2. To alleviate this grating lobe concern, the lunar microwave array must use smaller subarrays as shown in Fig. 4. Phased subarrays of 10.4 m by 10.4 m meet the .01 mW/cm2 environmental grating lobe requirement at an antenna tilt of 1 arc minute. In
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