Effect of speckle on lidar pulse-pair ratio statistics

The ratio of temporally adjacent lidar pulse returns is commonly used in differential absorption lidar (DIAL) to reduce correlated noise. These pulses typically are generated at different wavelengths with the assumption that the dominant noise is common to both. This is not the case when the mean number of laser speckle integrated per pulse by the lidar receiver is small (namely, less than 10 speckles at each wavelength). In this case a large increase in the standard deviation of the ratio data results. We demonstrate this effect both theoretically and experimentally. The theoretical value for the expected standard deviation of the pulse-pair ratio data compares well with the measured values that used a dual CO(2) laser-based lidar with a hard target. Pulse averaging statistics of the pulse-pair data obey the expected varsigma(1)/ radicalN reduction in the standard deviation, varsigma(N), for N-pulse averages. We consider the ratio before average, average before ratio, and log of the ratio before average methods for noise reduction in the lidar equation. The implications of our results are discussed in the context of dual-laser versus single-laser lidar configurations.