Autocorrected preconditioning regularization inversion algorithm for an atmospheric turbulence profile

Abstract

Atmospheric turbulence profiles have great significance for adaptive optics, astronomical observations, laser propagation in atmospheres, and free space optical communications. The two-aperture differential scintillation method is a recent approach for analyzing remote-sensing atmospheric turbulence profiles that utilizes active beacons to make it suitable for different measurement situations. The relationship between differential scintillation and atmospheric turbulence profiles can be modeled using the Fredholm integral equation. To address this ill-posed integration problem, the discrete forward observation equation is first analyzed to obtain better integration intervals and measurement intervals needed for inversion. Then an autocorrected preconditioning conjugate gradient normal residual (PCGNR) algorithm is proposed to acquire atmospheric turbulence profiles. The algorithm contains a developed autocorrection strategy that incorporates incremental differences, adaptive thresholds, and weighted averages to correct for artefacts and marginal errors that arise from the PCGNR method. Compared with other regularized methods, the proposed autocorrected PCGNR method is more accurate and robust in the presence of noise.

A vertical DIM lidar for refractive index structure parameter profiles estimation in low‐layer atmosphere

“…A similar argument can be applied to Equation () allowing it to be written as: $$$\frac{{D}_{I}(S)}{\langle {I}_{1}\rangle \langle {I}_{2}\rangle }\cdot {A}_{D}={{\bf{C}}}_{{\bf{n}}}^{{\bf{2}}}\cdot {{\bf{W}}}_{{\bf{D}}},$$$in which A D represents its constant term, and W D represents the vector of the weighting function for D I ( S )/( < I 1 > < I 2 > ). Its relationship to the turbulence along the path and the detailed derivation of A D and W D can be found in Refs 16,17 …”

“…Its relationship to the turbulence along the path and the detailed derivation of A D and W D can be found in Refs. 16,17 Take L as 1000 m, and the normalized weighting functions W r and W D are calculated and compared in Figure 1. It can be seen that there is a significant difference between the two weighting functions, which provides a theoretical possibility for us to estimate turbulence with this difference.…”

Simulation Analysis of an Atmospheric Turbulence Wavefront Measurement System

“…Turbulence has long been considered one of the most important factors limiting the performance of optical systems in the atmospheric environment [1]. Monitoring the level of optical turbulence in the atmosphere is of great significance for estimating its impact on the functions of optoelectronic devices and systems operating through the atmosphere [2][3][4]. In order to overcome the interference of atmospheric turbulence, large ground-based astronomical telescopes have been equipped with adaptive optical systems in astronomical imaging observations [5,6].…”