Slant Atmospheric Turbulence Research Articles

Inverse synthetic aperture lidar imaging and compensation in slant atmospheric turbulence with phase gradient algorithm compensation

To systematically study the influence of slant atmospheric turbulence on the inverse synthetic aperture lidar (ISAL) imaging, the atmospheric random phase screen with the modified von Kármán spectrum was numerically simulated via the fast Fourier transform spectral inversion method. Intensity phase distribution and brightness images of the Gaussian beam slant transmission were simulated under different turbulence intensities. Using the Kirchhoff approximation and convolution back-projection algorithm, ISAL images of rough surface (rough square and rough circular plates), rough graphics and rough body with different roughnesses under various turbulence intensities were obtained. The analyses showed that these ISAL images of rough targets can be resolved under weak turbulence but not under moderately strong turbulence. Aiming at the reduction of the resolution of the rough target ISAL images caused by atmospheric turbulence, the phase gradient autofocus (PGA) algorithm was used to improve image focusing and distinguish the shapes of rough targets.

Effect of multi-beam propagation on free-space coherent optical communications in a slant atmospheric turbulence

Based on the multi-beam propagation theory, a mathematic model of log-intensity fluctuation variance under multi-beam propagation in slant path atmospheric turbulence near the ground for free-space optical communication is established. Taking single beam, double beam, three beam, and four beams as examples, the intensity fluctuation characteristics of single beam and multi-beam are obtained, and the relationship between the log-intensity fluctuation and the bit error rate (BER) of the heterodyne detection coherent optical communications based on binary phase shift keying modulation is deduced. The results show that, with the increase of beam number, the variance of signal log-intensity fluctuation is significantly mitigated, and the BER of the system is significantly reduced. It proves that the multi-beam propagation method can be effectively applied to the long-distance coherent optical communications, and improve the performance of the system.

Theoretical and experimental investigation on the performance of heterodyne detection system affected by the beam mode of partially coherent beams in atmospheric turbulence

The mathematical model of the effect of beam mode (It contains fundamental mode and other higher orders mode) on the heterodyne efficiency of heterodyne detection system was established, and the effect of beam mode on the performance of heterodyne detection system was theoretically investigated for partially coherent GSM beam in slant atmospheric turbulence conditions. The results show that the inner scale of turbulence has a greater effect on the heterodyne efficiency and normalized M2. (It is used to evaluate beam quality.) The larger the mode orders are, the lower the proportion of the fundamental mode and heterodyne efficiency are. Finally, the changes of beam mode caused by turbulence was obtained by a heterodyne detection system in an experiment investigating optical communication at a distance of 1.3 km. The results of this experiment verified that the mode orders are increased by turbulence effect and the beam mode increases with an increase in the turbulence intensity, resulting in a decrease in the corresponding the peak-to-peak value of the IF signal.

Influence of coma and spherical aberration on transmission characteristics of vortex beams in slant atmospheric turbulence

Vortex beam has potential applications in free space optical communication because of its capacity of data transmission. Therefore, it is necessary to study the propagation characteristics of vortex beams in atmospheric turbulence. When the vortex beam propagates in the atmospheric turbulence the beam drift will occur, which has a great influence on the free space optical communication. In this paper, the beam drift of vortex beams with coma and spherical aberration transmitted in atmospheric turbulence is studied by using multi-phase screen and Fourier transform method. The numerical results show that as the transmission distance increases, the effects of both coma and spherical aberration on the beam drift are enhanced. The larger the transmission zenith angle and the coma coefficients, the greater the beam drift of the vortex beam is. However, the beam drift decreases with spherical aberration coefficient increasing. When the zenith angle and the transmission distance are both unchanged, the beam drift of the both vortex beams decrease with topological charges increasing. The influence of coma aberration on beam drift is bigger than that of spherical aberration.

Analysis of a heterodyne detection system affected by irradiance and phase fluctuations in slant atmospheric turbulence.

A mathematical model considering the effects of amplitude and phase random fluctuations on the signal-to-noise ratio (SNR) of heterodyne detection was established, and the effects of irradiance and phase fluctuations on the performance of heterodyne detection were investigated. The results show that the inner scale of turbulence significantly affects the SNR. The first 20 Zernike modes have a greater effect on the SNR of the heterodyne detection system. The SNR is affected more significantly by phase fluctuations than by irradiance fluctuations. The SNR decreases by four orders of magnitude because of amplitude and phase fluctuations.

Effect of angle-of-arrival fluctuation on heterodyne detection in slant atmospheric turbulence.

A mathematical model of the effect of random pointing errors on the mixing efficiency of heterodyne detection is established, and the effect of angle-of-arrival fluctuation on the mixing efficiency of heterodyne detection is investigated. The results show that the average mixing efficiency is significantly affected by the angle-of-arrival fluctuation in the outer scale. The larger the obscuration ratio and receiving aperture of the optical system, the lower the average mixing efficiency is. The closer the value of D/r0 is to 0.79, the closer the bit error rate of heterodyne detection is to 1×10-9 under weak turbulence.

Study on self-repairing and non-diffraction of Airy beams in slant atmospheric turbulence

Study on self-repairing and non-diffraction of Airy beams in slant atmospheric turbulence

Spiral spectrum of Laguerre-Gaussian beams in slant non-Kolmogorov atmospheric turbulence

The beam carrying information will be affected by atmospheric turbulence as it propagates through the atmosphere. Under the modified Rytov method, using the non-Kolmogorov power spectrum, applying the atmospheric turbulent inner scale and the outer scale which changes with altitude, this paper obtained the expression of the spiral spectrum of the beam in slant atmospheric turbulence. The influences of wavelength, topological charge, zenith, waist radius, receiver aperture, radial index and inner scale on spiral spectrum are investigated. Numerical results reveal that spiral spectrum spread becomes more serious with longer distance, larger topological charge, larger zenith, smaller wavelength, larger receiver aperture and smaller inner scale. Radial index and waist radius have little effect on the spiral spectrum. In addition, the influence of the outer scale on the spiral spectrum under different fluctuation conditions is analyzed, the results show that if the outer scale is set as constant during the calculation of the spiral spectrum of the beam in the slant path, it will have little effect in the weak fluctuation area, but will bring large errors in the medium and strong fluctuation area.

Irradiance scintillation index on slant atmospheric turbulence: simple approach

Turbulence plays an important role in investigating the irradiance scintillation index (SI) for a free-space optical wave propagating through atmospheric turbulence. The Hufnagel–Valley model is used in most studies, where the SI of the slant path is obtained using numerical analysis. A polynomial is proposed for the refractive index structure parameter, on which a closed form is derived for the irradiance SI of a spherical optical wave propagating through a slant atmospheric turbulence. This is used to study signal-to-noise ratio and bit error rate for system performance evaluation. The obtained results demonstrate the simplicity of using the derived closed form of SI compared to statistical methods. The derived expression takes less computational time for SI, which reflects positively on the system performance, which is an essential issue in vehicular mobile applications, in particular.

Comparison of polarization property of partially coherent beam between propagating along an uplink path and a downlink path in atmospheric turbulence

In this article, we take partially coherent electromagnetic Gaussian-Schell model (EGSM) beam as a research object. Based on the unified theory of coherence and polarization and the generalized Stokes parameters of random electromagnetic beams, the expressions of degree of polarization (DoP) and orientation angle of EGSM beam that propagates in the slant atmospheric turbulence, are derived. And the expressions are used to investigate the difference in polarization property of EGSM beam between propagating along an uplink path and a downlink path in the atmospheric turbulence. The results show that under the same conditions, the DoP distribution of EGSM beam propagating along a downlink path is more concentrated than that along an uplink path. When EGSM beam propagates along a downlink path, the maximum DoP corresponding to the propagation distance is larger than along an uplink. Therefore, when EGSM beam propagates along a downlink path, the detector can receive beam information at the longer distances.

Echo-wave scattering characteristics of the diffuse target in the slant atmospheric turbulence

The extended Huygens–Fresnel principle is utilized to make analysis of the received intensity for laser beam propagation through the atmospheric turbulence in the slant path. For a diffuse target, the effects of the turbulence on the statistical parameters such as the mutual coherence function and the mean intensity are studied in detail. The influence of the incident wave radius and the distance of the incident beam on these parameters are discussed.

Depolarization characteristics of incompletely polarized and partially coherent laser beams in slant atmospheric turbulence

Based on the cross-spectral density function of transmission theory and the unified theory of coherence and polarization, the depolarization characteristics of incompletely polarized and partially coherent laser propagation in slant atmospheric turbulence are investigated. According to extended Huygens–Fresnel principle, the analytical expressions for intensity and degree of polarization in the slant path are derived. The effects of the wavelength, the initial spot size and the transmission distance on the intensity and degree of polarization are described. The results show that a more stable distribution of the degree of polarization at the receiver is obtained with increasing wavelength for a certain receiver height. The conclusions play an important role in optical communications and target recognition.

Scintillation of partially coherent Gaussian—Schell model beam propagation in slant atmospheric turbulence considering inner- and outer-scale effects

Based on the modified Rytov theory and the international telecommunication union-radio (ITU-R) slant atmospheric structure constant model, the uniform scintillation index of partially coherent Gaussian—Schell model (GSM) beam propagation in the slant path is derived from weak- to strong-turbulence regions considering inner- and outer-scale effects. The effects of wavelength of beams and inner- and outer-scale of turbulence on scintillation are analyzed numerically. Comparison between the scintillation of GSM beams under the von Karman spectrum and that of beams under the modified Hill spectrum is made. The results obtained show that the scintillation index obtained under the von Karman spectrum is smaller than that under the modified Hill spectrum. This study can find theory bases for the experiments of the partially coherent GSM beam propagation through atmospheric turbulence.

Partially coherent Gaussian—Schell model pulse beam propagation in slant atmospheric turbulence

Based on the extended Huygens—Fresnel principle, a two-frequency, two-point cross-spectral density function of partially coherent Gaussian—Schell model pulse (GSMP) beam propagation in slant atmospheric turbulence is derived. Using the Markov approximation method and on the assumption that (ω1 − ω2)/(ω1 + ω2) ≤ 1, the theory obtained is valid for turbulence of any strength and can be applied to narrow-band signals. The expressions for average beam intensity, the beam size, and the two-frequency complex degree of coherence of a GSMP beam are obtained. The numerical results are presented, and the effects of the frequency, initial pulse width, initial beam radius, zenith angle, and outer scales on the complex degree of coherence are discussed. This study provides a better understanding of the second-order statistics of a GSMP beam propagating through atmospheric turbulence in the space-frequency domain.

Influence of different propagation paths on the propagation of laser in atmospheric turbulence

The analytical expressions for the average intensity, root mean square (RMS) beam width and angular spread of Gaussian Schell-model (GSM) beams propagating under slant atmospheric turbulence are derived, and they are used to study the influence of different propagation paths on the propagation of laser beams in atmospheric turbulence. It is shown that under the same condition, the influence of atmospheric turbulence along a downlink path on the GSM beam propagation is the smallest among the three paths. Therefore, the downlink propagation is more beneficial to the beam propagation through atmospheric turbulence compared with the uplink propagation and horizontal propagation.

部分相干厄米高斯光束在斜程大气湍流中的扩展

部分相干厄米高斯光束在斜程大气湍流中的扩展

SCINTILLATION INDEX OF A GAUSSIAN SCHELL-MODEL BEAM ON SLANT ATMOSPHERIC TURBULENCE

Based on the altitude-dependent model of the ITU-R slant atmospheric turbulence structure constant model, we present scintillation index calculations for a Gaussian Schell-model (GSM) beam under all irradiance fluctuation conditions. The longitudinal and radial components of the scintillation index are treated separately. Our results correctly reduce to the result of the horizontal path with atmospheric structure constant fixed, and simplify to a fully coherent beam with source coherence parameter ζs representing unit. The numerical conclusions indicate that within specific source and parameter ranges, the GSM beam is capable of offering less scintillation than the full coherent Gaussian beam. Before the maximum value of the scintillation, the scintillation index of the GSM beam will decrease with increased altitude. However, the off axis radial scintillation index will vanish when the Rytov variance is infinity.

Evolution of Intensity Distribution of Partially Coherent Sinusoidal-Gaussian Beams through Slant Atmospheric Turbulence

Based on the extended Huygens-Fresnel principle, the analytical expressions for the intensity of partially coherent sinusoidal-Gaussian beams with Schell-model correlator in atmospheric turbulence along a slant path are derived, and used to study the evolution of intensity distribution of partially coherent sinusoidal-Gaussian beams, including partially coherent sin-Gaussian (SiG), cos-Gaussian (CoG), sinh-Gaussian (ShG), cosh-Gaussian (ChG) beams. It is shown that the different intensity distribution at the source plane of the four beams evolve to the same Gaussian distribution in atmospheric turbulence along a slant path. The spreading of the partially coherent sinusoidal-Gaussian beams along a horizontal path is larger than that along a slant path in the long atmospheric propagation, and the slant path is more beneficial to the beam propagation through atmospheric turbulence in comparison with the horizontal propagation. The validity of our results is interpreted physically. Results in this paper may provide potential applications in free-space optical communications.

Study of Aperture-Averaged Scintillation for a Partially Coherent Gaussian Schell-Model Beam Propagation in Slant Atmospheric Turbulence

Based on the extended Huygens-Fresnel principle, scintillation of a partially coherent Gaussian Schell-model (GSM) beam propagation in weakly slant atmospheric turbulence is studied. The expression of aperture-averaging factor of the system receiver is derived. We analyzed the aperture-averaged scintillation index numerically. A comparison of the aperture-averaged scintillation of the beam propagation in slant path with that of the beam propagation in horizontal path is made. Results obtained show using partially coherent beams and considering aperture-averaging effect can decrease the scintillation and improve the optical communication system performance.

Scattering of a partially coherent Gaussian–Schell beam from a diffuse target in slant atmospheric turbulence

On the basis of the extended Huygens-Fresnel principle, the scattering of partially coherent Gaussian-Schell-model (GSM) beams from a diffuse target in slant double-passage atmospheric turbulence is studied and compared with that of fully coherent Gaussian beams. Using the cross-spectral density function of the GSM beams, we derive the expressions of the mutual coherence function, angle-of-arrival fluctuation, and covariance and variance of the intensity of the scattered field, taking into account the fluctuations of both the log-amplitude and phase. The numerical results are presented, and the influences of the wavelength, propagation distance, and waist radius on scattering properties are discussed. The perturbation region of the normalized intensity variance of the partially coherent GSM beam is smaller than that of the fully coherent Gaussian beam at the middle turbulence level. The normalized intensity variance of long-distance beam propagation is smaller than that of beam propagation along a short distance.