Statistical characteristics of the orbital angular momentum (OAM) of a Laguerre-Gaussian laser beam propagating through a turbulent atmosphere have been studied in the Monte Carlo numerical simulation. We have analyzed variations in the probability density of OAM versus its initial value, turbulent conditions along the propagation path, the diffraction parameter of the beam, and the receiving aperture size. This distribution is shown to be symmetrical near-Gaussian for an infinite receiving aperture and to be well approximated by an Edgeworth series. The probability density function significantly changes for finite-size apertures. The range of sizes of the receiving aperture has been found where fluctuations of the moment of energy flux density and fluctuations of light flux recorded can be considered uncorrelated.
We use a non-Kolmogorov power spectrum for theoretical investigation of laser beam propagation in the double-passage problem: transmitter–target–receiver. The major application of our work is the light detection and ranging (LIDAR) system operating in the zone of the atmosphere where non-Kolmogorov turbulence may be present. We show that the scintillation index is substantially affected by non-Kolmogorov turbulent channels at any turbulence strength. We consider the case of a small unresolved target and our analysis is valid for both the bistatic and monostatic configuration of the LIDAR system, in which the latter leads to the enhanced backscattering effects. Additionally, the paper contains a discussion of the simulation approach to light propagation through non-Kolmogorov turbulence. The simulation results and a discussion of their agreement with the theory are included. We found that the theory and the results of the simulations agree only to a certain extent. The “giant spikes” that occur when propagating through “deep turbulence” are responsible for the lack of better agreement. Their influence on the scintillation index and also on the probability density function of intensity probably requires a theoretical approach.
Computational efficiency and accuracy of wave-optics-based Monte–Carlo and brightness function numerical simulation techniques for incoherent imaging of extended objects through atmospheric turbulence are evaluated. Simulation results are compared with theoretical estimates based on known analytical solutions for the modulation transfer function of an imaging system and the long-exposure image of a Gaussian-shaped incoherent light source. It is shown that the accuracy of both techniques is comparable over the wide range of path lengths and atmospheric turbulence conditions, whereas the brightness function technique is advantageous in terms of the computational speed.
The dependences of the orbital angular momentum of a Laguerre–Gaussian beam propagating through a turbulent atmosphere on its azimuthal index and atmospheric turbulence strength are analyzed in the numerical simulation. The effect of errors in alignment of the beam and receiver axes on the average value and variance of orbital angular momentum fluctuations is studied. The statistics of the orbital angular momentum distribution at the end of the atmospheric propagation path is analyzed.
Numerical simulation and analytical calculations of the variance of fluctuations of the total orbital angular momentum (OAM) of Laguerre—Gaussian and Gaussian laser beams propagating in the randomly inhomogeneous atmosphere have been carried out. It is shown that as such beams propagate in the weakly turbulent atmosphere, the relative variance of OAM fluctuations remains much smaller than the relative variance of intensity fluctuations.
The phase noise that originates in the multi-channel master-oscillator power amplifier (MOPA) system of a coherent
tiled fiber-array beam director may drastically impact the efficiency of laser beam projection on a remotely located target
in the atmosphere. The recently proposed near-field phase locking (NFPL) technique mitigates the MOPA-induced phase
noise and gives an opportunity for programmable control of local (on-subaperture) piston and tip/tilt phases of the
outgoing fiber-array beams (beamlets). In the present paper, we evaluate the influence of both NFPL and programmable
phase control on the beam director performance for different laser beam propagation paths and atmospheric turbulence
conditions. Our analysis is based on wave-optics numerical simulation.
Modern laser tracking systems use digital video cameras for imaging the tracked objects in atmosphere. Using images
from camera for measurement lead to a measurement error of object coordinates and all other related parameters due to
atmospheric turbulence and thermal blooming of laser beam which track the object.
In our investigation the turbulent and thermal blooming features of object coordinates measurement error are considered.
The estimations in the conditions of mutual action of distorting atmospheric effects mentioned above are generated.
The calculation of error using our estimations in most cases became two orders faster. Modeling is performed for the
case of strong turbulent fluctuations as well as for the case of weak turbulence.
The error caused by atmospheric turbulence, in determining the orientation angle of an object (a series of reflectors) has
been studied. The orientation angle was determined by studying the image of the object. Numerical modeling was
performed involving construction of the image of a series of reflectors as if they were observed through a turbulent
medium, calculation of the coordinates of reflector mass centers, finding of the line closest to the reflector mass centers,
and determination of its slope angle. Variance of the slope angle fluctuations is calculated.
The paper considers the error caused by atmospheric turbulence, in determining the motion speed of an object by using
its successive images recorded on a matrix of a digital camera. Numerical modeling of the image of a moving object in
successive time moments is performed. Fluctuation variance of the image mass centre affecting the measurement error
is calculated. Error dependences on the distance to the object and path slope angle are obtained for different turbulence
models. Considered are the situations, when the angular displacement of the object between two immediate shots of the digital camera is greater than the isoplanatism angle as well as the situations when the angular displacement is smaller
than this angle.
A new approach to formation of random turbulent screens is proposed. Simulation of temporal fluctuations of refractive index inhomogeneities helps in removing the spatial periodicity arising at the transversal displacement of the screen. This improvement allows the formation of random turbulent screens having an infinite extension. Some examples of the problems of atmospheric turbulent optics are presented along with their numerical solution obtained using the algorithm proposed. The problems under consideration involve simulating long (in time) observation series of characteristics of laser beams propagating through the atmosphere.
The energy and statistical characteristics of laser radiation reflected from an infinite surface in the form of an array of
single retroreflectors have been investigated. The study of the reflecting properties of such a surface involved the
calculation of the coherence function of the radiation in the reflection plane. Rigorous and high-accuracy approximate
expressions have been obtained for this characteristic.
The intensity in the far zone and the coherence function of the reflected radiation at an arbitrary distance from the
surface have been calculated. Approximate equations have been derived for these characteristics of the radiation. The
results of numerical simulation by the Monte Carlo technique have been compared with the rigorous and approximate
calculations. It has been shown that in the most significant cases the approximate equations proposed give a deviation
within 5% from the rigorous ones and from the results of averaging over numerical realizations.
The approximate equations obtained have been used to solve the problem of radiation propagation along sensing paths,
including the forward propagation through the turbulent atmosphere, reflection, and backward propagation.
Photon budget analysis for laser target tracking systems under atmospheric turbulence conditions is performed in the paper. This analysis includes evaluations of the effects of molecular and aerosol absorption/scattering at various propagation distances and tracking angles for the following laser tracking wavelengths: 0.53 micrometers, 1.06 micrometers and 1.55 micrometers and evaluations of tracking beam/target interaction (target light scattering, target-induced coherence degradation, influence of target shape) for targets with rough surfaces, retro-reflective tape, and a single retro-reflector.
Investigations of the dynamics of turbulent characteristics were carried out for different tracking paths based on theoretical equations. A multi-screen model and single-screen one for turbulent atmosphere have been constructed for numerical simulation of laser beam propagation along atmospheric paths within the framework of the paraxial approximation. These models are suitable for simulation of the propagation along both homogeneous and inhomogeneous paths. Within this model, the Fried radius, the scintillation index, the effective beam radius, and the coherence length of radiation were calculated. The values obtained in the numerical experiment were compared with those calculated analytically.
The diffraction of narrow sharply focused beam propagating through the free space and nonlinear medium was studied. The validity of two approximated approaches for analysis of narrow beam diffraction was studied on the base of comparison with the solution of Kirchgof-Helmholtz diffraction. Both of these approaches is based on the particular solution of Helmholtz equation, which is corresponded with propagation of unidirectional wave. In the first of them attenuating waves are taken into account for the case where the spatial spectrum width is greater than the wave number. The second one is based on the neglect of contribution from attenuating waves. Also, validity of a parabolic wave equation for these situations was researched.
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