The theory of the double-edge lidar technique for measuring the wind with molecular backscatter is described. Two high-spectral-resolution edge filters are located in the wings of the Rayleigh-Brillouin profile. This doubles the signal change per unit Doppler shift, the sensitivity, and improves measurement accuracy relative to the single-edge technique by nearly a factor of 2. The use of a crossover region where the sensitivity of a molecular- and an aerosol-based measurement is equal is described. Use of this region desensitizes the molecular measurement to the effects of aerosol scattering over a velocity range of +/-100 m/s. We give methods for correcting short-term, shot-to-shot, frequency jitter and drift with a laser reference frequency measurement and methods for long-term frequency correction with a servo control system. The effects of Rayleigh-Brillouin scattering on the measurement are shown to be significant and are included in the analysis. Simulations for a conical scanning satellite-based lidar at 355 nm show an accuracy of 2-3 m/s for altitudes of 2-15 km for a 1-km vertical resolution, a satellite altitude of 400 km, and a 200 km x 200 km spatial resolution.

The theory of the double-edge technique is described by a generalized formulation that substantially extends the capabilities of the edge technique. It uses two edges with opposite slopes located about the laser frequency. This doubles the signal change for a given Doppler shift and yields a factor of 1.6 improvement in the measurement accuracy compared with the single-edge technique. Use of two high-resolution edge filters reduces the effects of Rayleigh scattering on the measurement by as much as an order of magnitude and allows the signal-to-noise ratio to be substantially improved in areas of low aerosol backscatter. We describe a method that allows the Rayleigh and aerosol components of the signal to be independently determined. The effects of Rayleigh scattering are then subtracted from the measurement, and we show that the correction process does not significantly increase the measurement noise for Rayleigh-to-aerosol ratios as high as 10. We show that for small Doppler shifts a measurement accuracy of 0.4 m/s can be obtained for 5000 detected photons, 1.2 m/s for 1000 detected photons, and 3.7 m/s for 50 detected photons for a Rayleigh-to-aerosol ratio of 5. Methods for increasing the dynamic range to more than +/-100 m/s are given.

We study numerically the propagation of classical waves through a network of wave guides, with a randomly varying index of refraction in two and three dimensions. We find evidence for the localization of these waves by disorder, although the localization lengths appear to be typically larger than for quantum waves.