Phase Screen Method Research Articles

Three methods of visco‐acoustic migration based on the De Wolf approximation and comparison of their migration images

AbstractThe viscosity of a medium affects the amplitude attenuation and velocity dispersion of seismic waves. Therefore, it is necessary to consider these factors during migration. First, to eliminate the viscous effect of a medium, we combine the Futterman model with the integral equation of the De Wolf approximation to construct a compensation operator of the De Wolf approximation for a visco‐acoustic medium. Next, we use the visco‐acoustic screen approximation method to realize the continuation operator then establish a prestack depth migration algorithm. Finally, an error analysis, impulse response test and model test are performed. The results show that three different generalized visco‐acoustic screen methods (phase screen method, generalized screen method and extended local Born Fourier method) can satisfactorily compensate for the attenuation of deep interface amplitude. Among these methods, the visco‐acoustic extended local Born Fourier method has the highest accuracy and the best compensation effect.

Investigation of the transmission characters of Ince-Gaussian beams in oceanic turbulence

Abstract We focus on the transmission characteristics of InceGaussian (IG) beams in oceanic turbulence which is simulated by the random phase screen method. The transmission characteristics of IG beams with different distances
and turbulence intensities are also shown in the experiments. The impacts of
the temperature and salinity in oceanic turbulence are discussed in detail. The
experimental results show that the IG beam maintains the intensity distribution well
after transmission. In addition, compared with the others’ structured beams, the IG
beams show better robustness in oceanic turbulence with different salinity, turbulence
intensity and suspended solids. Our work paves the way for leveraging IG beams in
underwater optical communication.

Modified compressible turbulence phase distortion formula and compressible turbulence spectrum simulation

In order to better study the imaging characteristics of high-speed moving targets in atmospheric turbulence, it is necessary to solve the optical distortion caused by aerodynamic optical effects, and the optical distortion needs to be described by compressible turbulence spectrum. In order to better understand the spectral characteristics of aero-optical distortion, according to the Maxwell equation, the Boltzmann factor equation is introduced based on the existing compressible turbulence spectrum theory, and the analytical expression of the modified compressible turbulence spectrum is derived and verified. Then, based on the freezing theory, the compressible turbulence spectrum is simulated by the phase screen method of power spectrum inversion. The influence of the distance from the moving target wall and turbulence intensity on the compressible turbulence phase screen is simulated and analyzed. Compared with atmospheric turbulence, it is found that the intensity of turbulence is proportional to the compressible turbulence, but the compressible turbulence is also inversely proportional to the distance of the moving target wall. As the distance from the moving target wall decreases, the phase fluctuation of the compressible turbulence is larger, which also indicates that the aero-optical effect mainly occurs in the boundary layer annex of the moving target, and the nearer the target, the aero-optical effect becomes more serious.

Propagation properties of a partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beam through anisotropic atmospheric turbulence.

Using the extended Huygens-Fresnel principle and the Rytov approximation, the analytical formula for the propagation of a partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beam (PCEShVB) in anisotropic atmospheric turbulence has been theoretically derived. Detailed studies have been conducted on the evolution characteristics of the average intensity, the degree of coherence (DOC), and the degree of polarization (DOP) of the beam in turbulence. The results show that during propagation, the intensity distribution of the beam will exhibit a spiral structure, and the overall distribution of the light spots will rotate in a direction related to the sign of the topological charge. The DOC distribution of PCEShVB will display a pattern reminiscent of beam interference fringes with an increase in propagation distance, with the number of "interference fringes" greatly impacted by the hyperbolic sine parameter. Furthermore, PCEShVB with a large initial coherent length and hyperbolic sine parameter will increase the degree of separation of the spots and yield a large DOP. Finally, for the validation of the theoretical findings, the random phase screen method was employed to simulate the propagation of PCEShVB through anisotropic atmospheric turbulence. The studies revealed a consistent alignment between the simulation results and the theoretical predictions.

A generalized and comprehensive slant channel modeling method for underwater wireless optical communication and its system performance analysis

The underwater wireless slant optical link is a more generalized type of communication links compared with vertical and horizontal links. Since several oceanic factors including temperature and salinity variations with the seawater depth, the performance of the slant link for the underwater wireless optical communication (UWOC) will be overestimated under the assumptions of constant temperature and salinity. To this end, this paper proposes a model of slant link considering the depth-dependent and inclination-angle-dependent turbulence and scattering that are the main causes of multipath fading for UWOC. Specifically, to model the turbulence-induced fluctuations of light fields, the random phase screen method is exploited, where the power spectrum of refractive index is calculated using the oceanic turbulence optical power spectrum (OTOPS) model and the light fields at the receivers are derived by the angular spectrum method. To emulate the scattering-induced divergence, the scattering phase function is applied, where the motion directions and coordinates of light spots propagating among phase screens are deduced using Rodrigues’ Rotation Formula. Simulation results demonstrate the effects of the depths and inclination angles of transmitters on the performance of UWOC by analyzing the scintillation index, channel impulse response, and BER (bit error rate).

Thermal Blooming Effect of Power-Exponent-Phase Vortex Beams Propagating through the Atmosphere

The thermal blooming effect of power-exponent-phase vortex (PEPV) beam propagating in the atmosphere is investigated by employing the multiple phase screen method. The influences of propagation distance, topological charge, power exponent, wind speed, and absorption coefficient on thermal blooming effect are analyzed in detail. The results show that (1) the thermal blooming effect exhibits a significant perturbation on the intensity and phase distribution of PEPV beams, with its influence becoming more pronounced as the propagation distance increases; (2) when the power exponent is fixed at 4, comparing the thermal blooming effect of PEPV beams with different topological charges indicates that a PEPV beam with topological charges of 3 is the most sensitive to thermal blooming; (3) when the topological charge is fixed at 3, the thermal blooming effect decreases with the increase in power exponent; and (4) an increase in wind speed or a decrease in absorption coefficient can reduce the thermal blooming effect. The research results obtained in this article have guiding significance for the application of research into high-energy PEPV beams in the atmosphere.

Quality and spatial intensity distribution characteristics of short-exposure spot images of a supercontinuum laser in a turbulent atmosphere.

In this study, considering the combined effects of atmospheric attenuation and turbulence, we examine the spot quality and spatial intensity distribution characteristics of a supercontinuum (SC) laser propagating in a turbulent atmosphere using the multi-layer phase-screen method. An increase in turbulence strength or a decrease in the initial beam radius resulted in a greater impact of the atmospheric turbulence on the SC laser. A decrease in source coherence results in the deterioration of the image quality of the far-field spot. Under moderate to strong turbulence, the scintillation index decreased as the source coherence decreased; however, the opposite trend was observed under weak turbulence. These results are significant for the advancement and optimization of SC laser systems.

High-precision calculation and experiments on the thermal blooming of high-energy lasers.

Thermal blooming (TB) is one of the important factors affecting the quality of high-energy laser beams. Reasonable simulation of thermal blooming is important to the application of a high-energy laser. However, reported investigations on TB simulation are mainly based on one method, such as the perturbation method or the phase screen method, which often leads to obvious errors in some conditions. In the paper, the reasonable ranges of optical generalized distortion parameters for both methods are determined based on the reported experimental data, which solves the problem of accurate TB simulations for the first time. In addition, the dynamic effect of thermal blooming is also calculated. Finally, the formula method is presented to extract the phase of thermal blooming distortion. We then use LC-SLM (Liquid crystal spatial light modulator) to emulate thermal blooming effect in the lab. The experimental results are more consistent with the numerical simulation results than conventional phase extraction methods. Our work provides a quantitatively and programmable way to accurately simulate TB with LC-SLM in the lab.

Influence Analysis of Underwater Laser Pulse Arrival Delay

In order to explore the influence of pulse arrival delay in underwater laser timing technology, a fused channel model based on Monte Carlo method and phase screen method is adopted, and the influence of ocean turbulence environment on photon transmission is added in the simulation process. On this basis, the received waveform and pulse arrival delay distribution characteristics of laser pulses in two waters and different turbulent environments are analyzed. The results show that with the turbidity of waters, the enhancement of ocean turbulence and the increase of transmission distance, the received pulses waveform gradually show a positive skewed distribution, and the pulse broadening and arrival delay are continuously increasing.

Scintillation Characteristics of Gaussian Vortex Beam Propagation in Turbulent Flume

Aiming at the low sensitivity of weak turbulent wake detection of underwater vehicles, studied the laser propagation characteristics in underwater weak turbulence, and then proposed a method based on the statistical characteristics of the scintillation peak of Gaussian vortex beam for detecting the weak turbulence fluctuation. According to the refractive index power spectrum of turbulent flume, the intensity distribution images of Gaussian vortex beam propagating through turbulent flume are simulated by using the random phase screen method, and the scintillation characteristics of Gaussian vortex beam under different conditions are studied. For the simulation results, under the weak turbulence conditions with low refractive index structure coefficient, the average scintillation indexes near the peak value of spot scintillation indexes are obviously higher than those of the whole image. Under the condition that the temperature difference between hot plate and cold plate, between hot plate and water are about 6.4°C and 5.8°C, respectively, the scintillation indexes of the laser propagation intensity image under different temperature gradient (turbulence intensity) are calculated in the experiment. The results show that, the mean values of the scintillation indexes near the spot scintillation peak fluctuate around 1.02 and 1.07, and the mean values in whole image fluctuate around 0.58 and 0.68, respectively, when the temperature gradient is small, which verify the effectiveness of the statistical characteristics of the scintillation peak in detecting weak turbulence.

Effect of Self-Focusing on Propagation of a Laser Beam in the Atmosphere Along a Slant Path

The equivalent B-integral phase screen (EBPS) method of numerical simulation is proposed to study the propagation of a high-power laser beam in the atmosphere along a slant path, and the computational accuracy and efficiency of the EBPS method are confirmed. It is shown that a decrease of the self-focusing caused by the atmosphere refraction effect. However, the refraction correction for the elevation angle is hardly affected by the self-focusing effect. On the other hand, the analytical expressions of the B integral and the optimal initial beam power of a high-power laser beam propagating in the atmosphere along a slant path are derived. It is found that the optimal beam power and the target maximum intensity decrease as the apparent elevation angle decreases, while the optimal beam power decreases but the target maximum intensity increases as the wavelength decreases. A method to optimize the beam quality on the target is presented.

Methodology for Estimating Communication Reliability in Shortwave Radio-Frequency Transmission Channels with Rician Fading Given Ionospheric Diffusivity

Introduction. There exists a technique for estimating the dependence of communication reliability in a shortwave radio-frequency transmission channel (SWRC) with a single discrete beam and diffuse wave scattering across small-scale ionospheric inhomogeneities on the selected operating frequency taking into account the given signal-to-noise ratio and ionospheric diffusivity. In this technique, the Nakagami m-distribution is used to describe interference fading of the received signal. However, in a single-beam SWRC, fading signal amplitudes are described by the Rician or generalized Rayleigh, rather than by Nakagami, distribution in 90 % of all cases. At the same time, the results obtained using the Nakagami distribution to approximate fading and to assess its effect on communication quality agrees well with those obtained by the Rician distribution only in two cases: the presence of Rayleigh distribution or the complete absence of fading.Aim. To develop a methodology for estimating communication reliability in a single-beam SWRC with Rician fading and to compare its results with that under Nakagami fading.Materials and methods. The effect of operating frequency and ionospheric diffusivity on fading distribution parameters in a single-beam SWRC was estimated by simulating transionospheric communication channels based on a radio-physical phase screen method. The effect of Rician fading parameters on communication reliability was simulated in the MatLab environment. The initial data on ionospheric parameters were obtained using the IRI-2016 model.Results. A three-stage methodology for estimating communication reliability in a single-beam SWRC with Rician fading was developed; its results were compared with that under Nakagami fading. Dependencies were obtained to describe communication reliability in a single-beam SWRC during the day and at night on the selected operating frequency relative to the maximum applicable frequency and on the level of ionospheric diffusivity during Rician and Nakagami fading.Conclusion. The conducted analysis showed that, at different levels of ionospheric diffusivity, communication reliability in a single-beam SWRC with Nakagami fading can be significantly overestimated (up to 12 %), compared to that under Rician fading.

Propagation and imaging analysis of vortex acoustic waves in ocean turbulence

AbstractVortex acoustic waves (VAW) with helical phase wavefronts could provide a new dimension for the detection and imaging of targets in the ocean. To explore the propagation characteristics of VAW under the effect of ocean turbulence (OT) and the impact on imaging, the phase screen method is used to simulate the propagation of VAW generated by a phase‐modulated uniform circular array under the effect of OT and the imaging of the target. The phase change and detection probability under the influence of the acoustic wave parameters and OT parameters during the propagation process are studied. Second, the azimuth resolution performance and focussing performance of the target imaging are studied. Under the effect of OT, the VAW of different frequencies and topological modes become scattered, and the degree of scattering is different when the parameters are different; and the resolution performance and focussing performance have also deteriorated. However, the VAW still has a reliable resolution under the effect of medium and low‐intensity OT, which provides theoretical support for the practice of the VAW in underwater target imaging.

Bit Error Rate Analysis in Atmospheric Turbulence Channel of Synthetic Double Vortex Beam

Random phase screen method was used to simulate the light intensity and phase distribution of the synthesized double vortex beams transmitted in atmospheric turbulence given the light intensity characteristics and phase characteristics of double Laguerre–Gaussian beams (DLGB) generated by coaxial superposition. Results show that the scintillation coefficient decreases initially, and then increases with the topological charge difference of the double vortex beam, and the topological charge difference is related to the number of split spots. When the number of split spots is small, the intensity distribution is concentrated, exhibiting a good penetrating effect on atmospheric turbulence.

Modelling the intensity distribution of underwater optical wave propagation in the presence of turbulence and air bubbles

Objectives:The objective of this paper is to derive a model for the irradiance distribution of underwater optical waves propagation in the combined presence of turbulence and air bubbles. The proposed distribution is based on modelling the medium index of refraction as a shot noise process and using the Rytov solution to the stochastic wave equation. Since the oceanic turbulence spectrum is different than the atmospheric spectrum, recent studies show that the well-known probability density functions poorly describe optical wave propagation underwater in the combined presence of air bubbles and turbulence, and that a mixture of distributions is generally needed. This conclusion, however, does not follow from theoretical investigations. Moreover, the physical aspects of the phenomena, such as the bubble size distribution, are not included in these models, and as such may limit their applicability. The approach introduced in this paper allows for including the environment physical properties directly in to the medium index of refraction. Method:In this paper, intensity distribution model is derived based on Rytov theory of propagation through weak turbulence. The physical processes in effect are directly included by assuming a shot noise index of refraction model. Results:Using the beam propagation method combined with the random phase screen method, the derived distribution is validated by simulation over a large range of turbulence levels and shows excellent agreement with the simulation data. In particular, the qualitative aspect of two peak distribution is modelled by the proposed distribution.

Analysis on the characteristics of vortex beam in field turbulence

In this study, we have investigated the propagation characteristics of single-mode Laguerre–Gaussian (LG) beams under field atmospheric turbulence conditions. We constructed a 1200 meter experimental platform for representing vortex beams in the field. Accordingly, we analyzed the spot changes in an LG beam after transmitted through atmospheric turbulence. Based on the principle of Fresnel diffraction and the random phase screen method, we studied the evolution and spiral spectrum distribution of low-order LG beams transmitted by atmospheric turbulence by numerical simulation. Moreover, we carried out an experimental study regarding the LG beam propagation characteristics mainly based on field experiments. The experimental results indicate that after near-surface turbulent propagation, the LG beam gradually spreads, degree of phase singularity drift becomes larger, and spot size of the Gaussian beam grows faster than that of the LG beam with greater propagation distances. Finally, we concluded that LG beams are not significantly affected by turbulence. It also lays a foundation for the experimental study of vortex beam detection and wavefront correction at the receiving end in multiplexing communication.

Analysis of the influence of atmospheric turbulence on modulating retro-reflector optical communication

The paper discusses the atmospheric turbulence effect on modulating retro-reflector (MRR) optical communication systems with theoretical analysis and experimental verification. The transmission model is proposed by the phase screen method. Based on this model, the scintillation indices (SI) are calculated, and the aperture averaging effect of the MRR terminal is analyzed. Furthermore, a test bed with 506 m transmission link is established. In the experiment, the SI values of the MRR link and the direct link are obtained and compared. Experimental data agree well with the numerical simulation results and verify the theoretical model. The theoretical results are useful for analyzing the influence of turbulence on MRR systems.

Waveform Distortion of Gaussian Beam in Atmospheric Turbulence Simulated by Phase Screen Method

The atmospheric turbulence phase screen is generated based on the power spectrum inversion method, and the multiple transmission processes are statistically averaged. The waveform distortion of the Gaussian beam in the atmospheric turbulence is analyzed; the simulation results show that the property of Gaussian beam has been destroyed after its passing through the atmospheric turbulence. When the beam waist radius is close to a certain radius, the degree of change becomes larger. When it approaches the critical value, the wave surface no longer changes sharply, and as the turbulence intensity increases, the phase fluctuation becomes more and more severe, the coherence of the beam is destroyed, and the spot may be split into several pieces. Finally, the relationship of intensity fluctuation, amplitude fluctuation, and bit error rate with distance is analyzed.

Probability property of orbital angular momentum distortion in turbulence

The probability property of the orbital angular momentum (OAM) distortion of the Bessel Gaussian beam propagating through the turbulence is investigated in this study. The mean and variance of the beam harmonic intensity are derived from the Rytov theory with a bias of less than 6% when compared with the data calculated by the phase-screen method. Based on these statistics, the probability density function (PDF) of the harmonic intensity fluctuation is proposed to characterize the randomness property of the beam OAM distortion, which agrees well with the result obtained from the phase-screen method. The PDF of the intensity difference between the fundamental and its adjacent crosstalk modes is derived. Furthermore, the probability of the OAM decoding error is also provided. This study not only facilitates beam OAM crosstalk characterization, but also provides the applicable condition of beam multiplexing for the beam parameter selection and the communication link design.

Average Intensity of SLVGB for Slant Path Propagation in Atmospheric Turbulent

The physical meaning of propagation characteristics of an (SLVGB) Super Lorentz vortex Gauss beam in a turbulent atmosphere is studied and analyzed. To use the method of Huygens-Fresnel integral. Likewise, to apply the ITU-R turbulence structure constant model and calculate the mean intensity of SLVGB in slant path beam propagation with different speared distances, and then used a random phase screen method to analyzing the scintillation index and investigated the turbulent in receiver plane, furthermore, the impact of the source size, and beam order factors of an SLVGB beam are checked into atmospheric blustery. The distribution belongings of an SLVGB beam via atmospheric turbulence are arithmetically computed and investigated. Additionally, the Kolmogorov atmospheric turbulence power spectrum model is used to find the propagation distance of an SLVGB beam in the turbulent atmosphere. To sum up, to set a value of normalized intensity is increased gradually in the turbulent atmosphere and finally, this work is creating a new beam propagation and its epitomized original article.