Simulation and high-precision wavelength determination of noisy 2D Fabry-Pérot interferometric rings for direct-detection Doppler lidar and laser spectroscopy

Doppler wind lidar (DWL) measurements by the fringe-imaging technique in front of aircrafts at flight speed require rapid processing of backscattered signals. We discuss the measurement principle to derive the 3D wind vector from three line-of-sight (LOS) measurements. Then we simulate realistic fringe patterns of a Fabryâ��P�©rot-interferometer (FPI) on a 2D charge-coupled device (CCD) localized at the focal plane behind it, taking atmospheric and instrument properties like scattering and noise into account. A laser at 355 nm with pulse energies of 70 mJ at 100 Hz repetition rate and a range bin of only 10 m were assumed. This yields count rates of 24 (13) million photons per pulse at 56 (76) m distance and 8.5 km altitude that are distributed on a CCD with up to 960��780 pixels without intensification and therefore generate noisy pixel signals. We present two methods for the precise determination of the radii, i.e., wavelengths of these simulated FPI rings and show that both are suitable for eliminating pixel noise from the output and coping with fringe broadening by Rayleigh scattering. One of them proves to reach the accuracy necessary for LOS velocity measurements. A standard deviation of 2.5 m/s including center determination can be achieved with only 20 images to average. The bias is 7 m/s. For exactly known ring centers, each can be even better than 2 m/s. The methods could also be useful for high-resolution laser spectroscopy