Denoising differential column image motion lidar signal using singular value decomposition

Abstract

Differential column image motion lidar (DCIM lidar) is a recent turbulence monitor for acquiring atmospheric turbulence profile based on active beacon. By imaging the differential column onto a CCD, DCIM lidar can obtain the Fried’s transverse coherence length (r 0 ) of different altitudes with a high spatial and temporal resolution. Atmospheric turbulence profile can be recovered from r 0 profile based on the integral relationship between r 0 of spherical wave and the refractive structure constant (C 2 n ). In order to ensure the retrieved precision of atmospheric turbulence profile, singular value decomposition (SVD) is used to denoise r 0 profile before inversion. The theory of DCIM lidar and SVD denoising is described. The Hankel matrix is constructed from the noisy signal and then the SVD is used to obtain the singular values. The rank reduction parameter is determined from the sharp variation of singular value curve. The denoised signal can be reconstructed by choosing the bigger singular values according to the rank reduction parameter. The numeric simulations and experiments are both carried out to validate the denoised method of SVD. The results show that the SVD can increase signal-to-noise ratio of r0 profile, thus enhancing the accuracy of the recovered atmospheric turbulence profile.