Modeling of direct detection Doppler wind lidar. I. The edge technique

Analytic models, based on a convolution of a Fabry-Perot etalon transfer function with a Gaussian spectral source, are developed for the shot-noise-limited measurement precision of Doppler wind lidars based on the edge filter technique by use of either molecular or aerosol atmospheric backscatter. The Rayleigh backscatter formulation yields a map of theoretical sensitivity versus etalon parameters, permitting design optimization and showing that the optimal system will have a Doppler measurement uncertainty no better than approximately 2.4 times that of a perfect, lossless receiver. An extension of the models to include the effect of limited etalon aperture leads to a condition for the minimum aperture required to match light collection optics. It is shown that, depending on the choice of operating point, the etalon aperture finesse must be 4-15 to avoid degradation of measurement precision. A convenient, closed-form expression for the measurement precision is obtained for spectrally narrow backscatter and is shown to be useful for backscatter that is spectrally broad as well. The models are extended to include extrinsic noise, such as solar background or the Rayleigh background on an aerosol Doppler lidar. A comparison of the model predictions with experiment has not yet been possible, but a comparison with detailed instrument modeling by McGill and Spinhirne shows satisfactory agreement. The models derived here will be more conveniently implemented than McGill and Spinhirne's and more readily permit physical insights to the optimization and limitations of the double-edge technique.