Optimal transmitter energy normalization algorithm for vapor detection and estimation using frequency agile lasers

Frequency-agile lidar (FAL) with the capability of tuning to more than 60 wavelengths within 1 second, can provide better vapor detection and multimaterial discrimination ability than two-wavelength differential absorption lidar. This paper extends an earlier optimal approach for processing FAL data to include signals with a fluctuating component due to shot-to-shot variations in the transmitted pulse energy whenever a local measurement of that energy is available. Traditional methods for performing this so-called transmit energy normalization have typically ratioed the received lidar signal by the energy monitor data. It is shown that this is, in general, not only a suboptimal approach, but can degrade the performance of the lidar below that achieved by not normalizing the data at all. The optimal approach is shown to be a linear correction to the received signal proportional to the monitor data. The estimated correlation between the transmitted and received signals provides the optimal proportionality factor at each wavelength. Simple approximate expressions are derived for comparing the performance of the optimal versus ratio estimators. The approach is illustrated on both synthetic and actual FAL data.