An Effective Frequency Technique for Laser Measurements with Finite Spectral Bandwidth

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This paper describes a fundamentally new method of treating the effects of laser finite bandwidth for both integrated path and differential ranging lidar measurements of differential absorption. We show that, for laser bandwidths less than the atmospheric line width, the effects of finite bandwidth on a measurement near the center of an absorption line can be treated as due to an equivalent monochromatic measurement at an effective frequency. The method is applied to measurements in the atmosphere with various laser line shapes. The effective frequency is shown to have a simple form which is independent of the detailed atmospheric line shape. Complex laser line shapes including multi-mode spectral structure can be simply treated using this technique. The effective frequency method greatly simplifies the computation of forward problems in radiative transfer1. More importantly, it allows the inverse problem of species concentration to be solved using algebraic methods as opposed to complicated inversion techniques2.