A new concept of spectrum analyzer is proposed for short-range lidar measurements in airborne applications. It implements a combination of two fringe-imaging Michelson interferometers to analyze the Rayleigh-Mie spectrum backscattered by molecules and particles at 355 nm. The objective is to perform simultaneous measurements of four variables: the air speed, the air temperature and density, and the particle scattering ratio. The Cramer-Rao bounds are calculated to evaluate the best expectable measurement accuracies. The performance optimization shows that a Michelson interferometer with a path difference of 3 cm is optimal for air speed measurements in clear air. To optimize density, temperature, and scattering ratio measurements, the second interferometer should be set to a path difference of 10 cm at least; 20 cm would be better to be less sensitive to the actual Rayleigh-Brillouin line shape.