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A new pure rotational Raman lidar (PRRL) system at a wavelength of 532.25 nm has been designed for profiling the atmospheric temperature of the planetary boundary layer. A newly compact spectroscope structured with three fiber Bragg gratings (FBG) is designed to separate two pure rotational Raman signals for atmospheric temperature retrieval, and to simultaneously block the Mieand Rayleigh-scattering signals with a rejection rate of 107. A numerical simulation shows that the PRRL is capable of profiling the atmospheric temperature and a statistical temperature error less than 1 K is achieved up to a height of 2.0 km and 2.2 km for daytime and nighttime measurement, respectively.