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 edge technique is a new and powerful method for measuring small frequency shifts. With the edge technique a laser is located on the steep slope of a high-resolution spectral filter, which produces large changes in transmission for small frequency shifts. A differential technique renders the frequency shift measurement insensitive to both laser and filter frequency jitter and drift. The measurement is shown to be insensitive to the laser width and shape for widths that are less than the half-width of the edge filter. The theory of the measurement is given with application to the lidar measurement of wind. The edge technique can be used to measure wind with a lidar by using either the aerosol or molecular backscattered signal. Examples of both measurements are presented. Simulations for a ground-based lidar at 1.06 microm using reasonable instrumental parameters are used to show an accuracy for the vector components of the wind that is better than 0.5 m/s from the ground to an altitude of 20 km for a 100-m vertical resolution and a 100-shot average. For a 20-m vertical resolution and a 10-shot average, simulations show an accuracy of better than 0.2 m/s in the first 2 km and better than 0.5 m/s to 5 km.

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.