Analytical differentiation of the differential-absorption-lidar data distorted by noise

A method of analytical differentiation is developed for processing differential absorption lidar (DIAL) data. The method is based on simple analytical transformation of the DIAL on and off signal ratio. The derivatives consequently are found for either individual data points or local zones of the measurement range. The method makes possible the separation of local zones of interest and the separate investigation of these. The smoothing level is established by the selected value of the exponent in a transformation formula rather than by the selection of the resolution range. The method does not require the calculation of local signal increments. This reduces significantly the high-frequency noise in the measured concentration. The method is general and can be used for different experimental data, including inelastic (Raman) lidar data. The processing technique is practical and does not require a determination of the solution for a large set of algebraic equations. It is based on the simple repetition of the same type of calculations with different constants. The method can easily be implemented for practical computations.