Effects of noise on lidar data inversion with the backward algorithm

The lidar data-inversion algorithm widely known as the Klett method (and its more elaborate variants) has long been used to invert elastic-lidar data obtained from atmospheric sounding systems. The Klett backward algorithm has also been shown to be robust in the face of uncertainties concerning the boundary condition. Nevertheless electrical noise at the photoreceiver output unavoidably has an impact on the data-inversion process, and describing in an explicit way how it affects retrieval of the atmospheric optical coefficients can contribute to improvement in inversion quality. We examine formally the way noise disturbs backscatter-coefficient retrievals done with the Klett backward algorithm, derive a mathematical expression for the retrieved backscatter coefficient in the presence of noise affecting the signal, and assess the noise impact and suggest ways to limit it.