Vadim V. Dudorov

Speckle-field propagation in 'frozen' turbulence: brightness function approach.

Speckle-field long- and short-exposure spatial correlation characteristics for target-in-the-loop (TIL) laser beam propagation and scattering in atmospheric turbulence are analyzed through the use of two different approaches: the conventional Monte Carlo (MC) technique and the recently developed brightness function (BF) method. Both the MC and the BF methods are applied to analysis of speckle-field characteristics averaged over target surface roughness realizations under conditions of frozen turbulence. This corresponds to TIL applications where speckle-field fluctuations associated with target surface roughness realization updates occur within a time scale that can be significantly shorter than the characteristic atmospheric turbulence time. Computational efficiency and accuracy of both methods are compared on the basis of a known analytical solution for the long-exposure mutual correlation function. It is shown that in the TIL propagation scenarios considered the BF method provides improved accuracy and requires significantly less computational time than the conventional MC technique. For TIL geometry with a Gaussian outgoing beam and Lambertian target surface, both analytical and numerical estimations for the speckle-field long-exposure correlation length are obtained. Short-exposure speckle-field correlation characteristics corresponding to propagation in frozen turbulence are estimated using the BF method. It is shown that atmospheric turbulence-induced static refractive index inhomogeneities do not significantly affect the characteristic correlation length of the speckle field, whereas long-exposure spatial correlation characteristics are strongly dependent on turbulence strength.

Anisoplanatic turbulence correction in incoherent imaging by using reference sources with different wavelengths

The possibility of the phase compensation of turbulent distortions of incoherent images of an object illuminated by radiation with different wavelengths is investigated. The research is carried out based on the method that is a further improvement of the algorithm for the numerical simulation of incoherent imaging through the atmosphere in conditions of anisoplanatic turbulence developed by the authors [Lachinova S.L., Vorontsov M.A., Dudorov V.V., Kolosov V.V., Valley M.T. // Proc. SPIE. 2007. V. 6708. 67080E]. The dependence of the degree and region of the enhancement of the image on the ratio of the reference wavelength to the image-forming radiation one is shown.

Properties of vortex beams formed by an array of fibre lasers and their propagation in a turbulent atmosphere

Using a numerical simulation, we investigate the possibility of synthesising vortex laser beams with a variable orbital angular momentum by a hexagonal array of fibre lasers under a phase control of individual subapertures of the array. We report the requirements to the parameters of the device generating a vortex beam (number and size of subapertures, as well as their mutual arrangement). The propagation dynamics of synthesised vortex beams is compared with that of conventional Laguerre–Gaussian beams in free space and in a turbulent atmosphere. The spectral properties of the synthesised beam, represented as a superposition of different azimuthal modes, are determined during its propagation in free space. The energy and statistical parameters of the synthesised and Laguerre–Gaussian vortex beams are shown to coincide with increasing propagation distance in a turbulent medium.

Retrieval of crosswind velocity based on the analysis of remote object images: Part 1 — drift of a thin layer of turbulent inhomogeneities

Numerical simulation is carried out in order to estimate possibilities of crosswind velocity determination along an observation path between a distant object and observer. The estimation is based on the analysis of atmospheric distortions in the object images. The disturbing effect of limited atmospheric regions on the object image and possibilities of the drift velocity retrieval in these regions are analyzed. A new method for filtration of turbulent distortions by their characteristic sizes is suggested with the aim of estimating the wind velocity at different segments of the observation path. It is shown that the technique suggested allows one to determine crosswind velocity with high accuracy when it is applied to a thin layer of atmospheric inhomogeneities.

Accounting for the effect of large-scale atmospheric inhomogeneities in problems of laser radiation propagation along long high-altitude paths

We show that large-scale atmospheric inhomogeneities observed experimentally can significantly affect optical radiation propagation along long paths, and it is impossible to take into account this effect within the classical turbulence model. We suggest a new algorithm for numerical simulation of laser beam propagation along long low-inclined atmospheric paths with large-scale atmospheric inhomogeneities, which allows one to consider beam refraction and focusing at large-scale inhomogeneities along with beam distortions due to small-scale inhomogeneities and regular refraction in a vertical plane.

Retrieval of crosswind velocity based on the analysis of remote object images: Part 2—Drift of turbulent volume

Possibilities for the crosswind profiling along a path of observation of a distant object from the analysis of the video sequence of its images are studied in this work by numerical simulation. The method suggested for wind velocity estimation is based on the analysis of two adjacent incoherent images and exhibits better performance in comparison with counterparts, which is explained by there being no need to accumulate statistics of the parameters analyzed. A new method for the filtration of turbulent distortions of an image by their characteristic sizes is suggested with the aim of estimating the wind velocity in different segments of an observation path. The work shows a possibility of determining the drift velocity of several (no less than three) layers of turbulent atmosphere, located at different positions between the object observed and receiving optical system, under certain turbulent conditions.

Optimization of laser propagation for extensive atmospheric paths in conditions of thermal blooming

Numerical results of a propagation of the CW laser radiation for extensive slightly elevated atmospheric paths are presented in the paper. The calculations are carried out in the limits of the small-angle equation for the coherence function of the second order describing the partially coherent beam self-action. To solve the equation a new ray-tracing technique creating an effective numerical algorithm was used. The gas absorption was taken into account in frameworks of the average seasonal summer model of an atmosphere. The average cyclic and the volcanic models of an atmosphere were used for aerosol attenuation. High-altitude vertical profiles of turbulent fluctuations of a refractive index were determined for the best, average and worst turbulent conditions. Calculations were obtained for the radiation sources located at altitudes from 10 Km up to 25 Km. Paths up to 500 Km were considered. Lets note, that it is necessary to take into account the influence of the Earth surface curvature for these paths. To studying the problem of a minimization of an atmosphere influence on an energy transfer as a numerical criterion was selected the effective power density: Ieff = P/Seff, where P is a power of radiation at the reception plane, Seff is an effective square of a beam at the reception plane. The initial power, the initial beam focusing and the wavelength of radiation were optimized.

Fiber-array-based vortex beams propagation through a turbulent atmosphere

We suggest a technique for generation of optical vortex beams with a variable orbital angular momentum based on a fiber laser array. Requirements for the number of subbeams and the spatial arrangement for the vortex beam generation are determined. The propagation dynamics of a vortex beam synthesized is compared with that of a continuous Laguerre-Gaussian beam in free space and in a turbulent atmosphere. Spectral properties of a beam synthesized, which is represented as a superposition of different azimuth modes, are determined.

An algorithm for the calculation of the phase shift of electromagnetic waves in an inhomogeneous refractive medium

A new algorithm for calculating the phase shift of coherent electromagnetic waves propagating through an inhomogeneous refractive medium is suggested. The method is based on construction of energy-flux trajectories, tangents to which coincide with the direction of the Umov-Poynting vector. The applicability of this method is shown for the case of propagation through the turbulent atmosphere.

Incoherent phase-compensated imaging based on a field scattered by rough surface

Compensation of turbulence in atmospheric imaging is usually hampered by the lack of a reference point source. We consider the possibility of phase compensation based on the reference wave scattered by the rough surface of an object under review. Analysis has been made on the basis of numerical simulation. The recently developed method for incoherent imaging through the atmosphere in anisoplanatic turbulent conditions allows simulating both long-exposure and short-exposure images. We analyze the influence of the size of object reflecting reference wave on the efficiency of phase compensation. Image quality enhancement is observed for the object size significantly exceeding the diffractivelimited size with respect to the receiving aperture. Also we consider the features of phase compensation with the reference wavelength different from visible light ones.