Wave Structure Function Research Articles

Wave structure function, spatial coherence radius, and Fried parameter of optical wave propagating through ocean turbulence with a slant path.

The analytical formula for characteristic parameters of optical wave (wave structure function, spatial coherence radius, and Fried parameter) in the slant path of ocean turbulence are derived and analyzed. Under the Rytov approximation, the wave structure function derived by the oceanic power spectrum of the refractive index of optical turbulent fluctuations in the slant path still complies with the five-thirds power law of the Kolmogorov spectrum in the inertial subregion, and the relationship between spatial coherence radius and Fried parameters satisfies 2.1 times. The correctness of analytical formulation of the wave structure function is demonstrated by comparing the numerical results of the original integral formula with the analytical formula of the derived in this paper.

Energy focusability of spatial incoherent beam combining for pulse laser propagation in marine atmosphere.

In this study, we have deduced the generalized scintillation index of the plane wave and plane wave structure function based on the modified non-Kolmogorov power spectrum of atmospheric refractive index with the spectrum power index α. In addition, we have analyzed the fluctuation of atmospheric density due to thermal blooming. Based on the interaction of six beams in thermal blooming, the thermal phase screening and intensity distribution are simulated. Under the influence of atmospheric turbulence and thermal blooming, the six-beam combination is then simulated numerically to obtain the equivalent radius with long exposure (RL), power in the bucket (PIB), Strehl ratio (SR), and peak value of intensity (Ip). Results show that PIB, Ip, and SR of the pulse beam combination decrease with an increase in α; however, RL operates in reverse mode and the short pulse durations reduce the thermal blooming. Moreover, laser of short duration cannot generate high ring energy on the target.

Spatial coherence length and wave structure function for plane waves transmitted in anisotropic turbulent oceans.

The spatial coherence length and wave phase structure function are two important factors in describing turbulence's effect on light propagation in seawater. This paper derives the wave phase structure function and spatial coherence length of plane waves in moderate to strong turbulent channels by deriving a "modification seawater turbulence power spectrum" and an oceanic-modified Rytov approximation. The evolutions in wave structure function, coherence length with the temperature dissipation rate, energy dissipation rate, anisotropy turbulence factor, signal wavelength, and propagation distance are analyzed by numerical calculation. In the moderate and strong turbulence regions, the phase structure function and spatial coherence length increase and decrease with increasing transmission distance and turbulence strength, respectively, and there is a saturation tendency for both. The fluctuation of seawater salinity has a greater effect on the phase structure function and coherence length than the temperature fluctuation. In addition, the wave structure function decreases with increasing signal wavelength and degree of turbulent anisotropy, but the trend of spatial coherence length is reversed.

Modulation transfer function variation through anisotropic turbulence in biological tissue

Analysis of the long-exposure modulation transfer function (MTF) is performed for optical imaging using plane and spherical waves through anisotropic turbulence in biological tissues. To obtain the MTF, the wave structure functions of plane and spherical waves are obtained in closed-form expressions. Results are presented depending on various parameters of the turbulent medium and optical beam. The positive effect of anisotropy on optical imaging is remarkable in turbulent biological tissues. Besides scattering and absorption, taking anisotropy into account as well as turbulence will lead to a more accurate description of the performance of the medical imaging systems that use optical spectrums in biological tissues.

Transmittance and energy transfer of Gaussian beam propagation in anisotropic compressible turbulence

Turbulence affects the transmittance of optical wave propagation. Reduced transmittance causes increased power loss in wireless communication systems. This phenomenon is even more pronounced in compressible turbulence, which generally occurs near supersonic or hypersonic aircraft. Compressible turbulence alters the level of power attenuation on optical wave propagation, reducing the performance of aircraft communication. In this paper, the wave structure function (WSF) and optical intensity of a Gaussian beam propagating in anisotropic compressible turbulence are deduced. The effect of anisotropic compressible turbulence on a Gaussian beam is investigated. The results show that the essential effect of turbulence on Gaussian beams is the dispersion of energy instead of attenuation. Anisotropic compressible turbulence improves the power efficiency of wireless communication systems. In addition, compressible turbulence effects on the transmittance of Gaussian beams are represented versus wavelengths and waist widths of the beams.

Structure functions for optical waves in a complex medium of turbulent biological tissues.

Although optical wave propagation is investigated based on the absorption and scattering in biological tissues, the turbulence effect can also not be overlooked. Here, the closed-form expressions of the wave structure function (WSF) and phase structure function (PSF) of plane and spherical waves propagating in biological tissue are obtained to help with future research on imaging, intensity, and coherency in turbulent biological tissues. This paper presents the effect of turbulent biological tissue on optical wave propagation to give a perception of the performance of biomedical systems that use optical technologies. The behavior of optical waves in different types of turbulent biological tissues such as a liver parenchyma (mouse), an intestinal epithelium (mouse), a deep dermis (mouse), and an upper dermis (human) are investigated and compared. It is observed that turbulence becomes more effective with an increase in the characteristic length of heterogeneity, propagation distance, and the strength of the refractive index fluctuations. However, an increase in the fractal dimension, wavelength, and small length scale factor has a smaller turbulence effect on the propagating optical wave. We envision that our results may be used to interpret the performance of optical medical systems operating in turbulent biological tissues.

Analysis of MTF for Optical Waves Propagation in Hypersonic Plasma Turbulence

In this study, new expressions for wave structure functions (WSFs) for optical planes and spherical waves propagating in plasma turbulence are derived based on the refractive index undulation power spectrum of hypersonic plasma turbulence and Rytov approximation theory. On this basis, the mathematical expressions for plasma turbulence modulation transfer function (MTF) for optical planes and spherical waves are obtained using WSF expression. The mathematical expressions describe the attenuation effect of plasma turbulence on optical imaging systems. The effects of different wavelengths, turbulent outer scales, and refractive index undulation variance on plasma turbulence MTF were calculated and analyzed. Results show that increasing the incident wavelength reduces the effect of plasma turbulence on the imaging system. Moreover, increasing the turbulence outer scale and reducing the refractive index undulation variance can also improve the imaging results.

Wave structure functions of optical waves in weakly compressible turbulence

Accurate expressions for the wave structure functions of plane waves, spherical waves and Gaussian waves propagating in weakly compressible turbulence are derived by the recently proposed refractive index spectrum for the first time. To make the results easy to use, approximate forms of the spatial coherence radius of plane waves and spherical waves and the exact form of the spatial coherence radius of Gaussian waves are developed. A numerical evaluation shows that the spherical wave is less affected by turbulence than the other two waves. The waves propagation in weakly compressible flow is different from that in the atmosphere, it has the characteristics of short distance and large disturbance. There is also a large wavefront distortion in short-distance transmission. Our derived results provide important support for accurately predicting aero-optical effects.

Structure function, coherence length, and angle-of-arrival variance for Gaussian beam propagation in turbulent waters.

Wave structure function, coherence length, and angle-of-arrival variance are derived analytically for a Gaussian beam propagating in an underwater turbulent medium. The recently introduced oceanic turbulence optical power spectrum model [J. Opt. Soc. Am. A37, 1614 (2020)JOAOD60740-323210.1364/JOSAA.399150] is used, and results are obtained for the case of large separations. The effect of temperature, salinity, rates of dissipation of mean-squared temperature and energy, temperature-salinity gradient ratio, wavelength, and aperture diameter, is presented. Further, a Gaussian beam is compared with the plane and spherical waves in terms of their effect on wave structure function, coherence length, and angle-of-arrival fluctuations. The presented results can be beneficial to set the parameters of imaging and communication systems using a Gaussian beam in an underwater turbulent medium and can be used for the optimization of the design of these systems.

Wave and phase structure functions of plane and spherical waves in particle-free natural turbulent waters

The expressions for the wave and the phase structure functions of a plane wave and a spherical wave propagating in the natural water turbulence characterized by the recently developed spatial power spectrum (Yao et al., 2020) are evaluated in general and in the limits of large and small separations. The spatial coherence radius for both plane and spherical waves is then deduced. The angle-of-arrival variance of these wavefronts at the collecting lens of the receiving system is also evaluated. In-depth numerical illustrations of the dependence of these quantities on the average temperature/salinity, temperature/energy dissipation rates, and the temperature–salinity gradient ratio are included. Our results are of utmost importance for underwater imaging and sensing technologies.

Spatial Property of Optical Wave Propagation through Anisotropic Atmospheric Turbulence

For the free‐space optical (FSO) communication system, the spatial coherence of a laser beam is influenced obviously as it propagates through the atmosphere. This loss of spatial coherence limits the degree to which the laser beam is collimated or focused, resulting in a significant decrease in the power level of optical communication and radar systems. In this work, the analytic expressions of wave structure function for plane and spherical wave propagation through anisotropic non‐Kolmogorov turbulence in a horizontal path are derived. Moreover, the new expressions for spatial coherence radius are obtained considering different scales of atmospheric turbulence. Using the newly obtained expressions for the spatial coherent radius, the effects of the inner scales and the outer scales of the turbulence, the power law exponent, and the anisotropic factor are analyzed. The analytical simulation results show that the wave structure functions are greatly influenced by the power law exponent α, the anisotropic factor ζ, the turbulence strength , and the turbulence scales. Moreover, the spatial coherence radiuses are also significantly affected by the anisotropic factor ζ and the turbulence strength , while they are gently influenced by the power law exponent α and the inner scales of the optical waves.

Interferential seeing monitor, a seeing monitor for atmospheric turbulence studies: calibration with the differential image motion monitor

ABSTRACT In this work, we aim to calibrate an interferential seeing monitor (ISM), which is a testing instument used at astronomical sites. Its method is based on the study of the diffraction pattern produced by a Young’s double-slit at the focus plane of a telescope. This method allows us to obtain the wave structure function by taking into account both phase and amplitude fluctuations of the light wavefront. A phase seeing εϕ was assigned to phase fluctuations and an amplitude seeing εχ was assigned to amplitude fluctuations (scintillation phenomenon), which allows us to obtain both phase and amplitude fluctuations. The feasibility of the ISM method was demonstrated by numerical simulations presented in a previous work. In this work, we have conducted a cross-calibration campaign of the ISM with a differential image motion monitor (DIMM) over 16 nights at the Oukaimeden and Atlas Golf Marrakech Observatories. The goal of this campaign was to study the reliability of this new method. In this paper, we present the calibration measurements and a comparison between the seeing measured by the ISM (εϕ, εχ) and that obtained by the DIMM (εdimm). These results show good agreement between the phase- eeing εϕ and εdimm.

Influence of Oceanic Turbulence on the Performance of Underwater Quantum Satellite Communication

Oceanic turbulence is one of the important factors that affect the transmission of quantum optical signals in the seawater medium. However, up to now, none research on the influence of oceanic turbulence on the parameters of quantum communication channel is in progress. In order to fill such vacancies, we simulate in this paper the relationship of oceanic turbulence parameters to the optical wave structure function and the optical wave spatial coherence length to acquire the relationship between the oceanic turbulence intensity and oceanic turbulence parameters. Then, the relationships between the oceanic turbulence parameters and the channel entanglement, the bit-flip channel capacity, and the channel error rate are respectively established and simulated. The simulation results provide a reference for underwater quantum communication with the influence of oceanic turbulence.

Wave Structure Function and Long-Exposure MTF for Gaussian-Beam Waves Propagating in Anisotropic Maritime Atmospheric Turbulence

The expressions of wave structure function (WSF) and long-exposure modulation transfer function (MTF) for laser beam propagation through non-Kolmogorov turbulence were derived in our previous work. In this paper, based on anisotropic maritime atmospheric non-Kolmogorov spectrum, the new analytic expression of WSF for Gaussian-beam waves propagation through turbulent atmosphere in a horizontal path is derived. Moreover, using this newly derived expression, long-exposure MTF for Gaussian-beam waves is obtained for analyzing the degrading effects in an imaging system. Using the new expressions, WSF and MTF for Gaussian-beam waves propagating in terrestrial and maritime atmospheric turbulence are evaluated. The simulation results show that Gaussian-beam waves propagation through maritime turbulence obtain more degrading effects than terrestrial turbulence due to the humidity and temperature fluctuations. Additionally, the degrading effects under anisotropic turbulence get less loss than that of isotropic turbulence.

Effects of Turbulence on the Vortex Modes Carried by Quasi-Diffracting Free Finite Energy Beam in Ocean

By developing new wave structure function of a beam waves, we derive the transmitting probability of signal vortex modes in oceanic turbulence based on Rytov approximation theory. Applying this transmitting probability of signal vortex modes, we study the influence of oceanic turbulence on the transmittance of the vortex modes carried by Mathieu-Gaussian beam. This model shows the transmitting probability of Mathieu-Gaussian beam with narrow initial beam width, long wavelength, and small ellipticity parameter is higher than the transmitting probability of the signal vortex modes in case of the beam with wide initial beam width, short wavelength, and great ellipticity parameter. Furthermore, when Mathieu-Gaussian beam has a suitable semi-cone angle, the effect of weak-turbulence channel on the transmitting probability of signal vortex modes with different topological charge can be ignored. Mathieu-Gaussian beam is a more suitable carrier for high information channel of underwater wireless optical communication than Laguerre-Gaussian beam.

Light field camera study of near-ground turbulence anisotropy and observation of small outer-scales.

Understanding turbulence effects on laser beam propagation is critical to the emerging design, study, and test of many long-range free space optical (FSO) communication and directed energy systems. Conventional studies make the prevalent assumption of isotropic turbulence, while more recent results suggest anisotropic turbulence for atmospheric channels within a few meters elevation above the ground. As countless FSO systems have been and continue to be deployed in such channels, analysis of anisotropic modelings has become one of the fastest growing areas in FSO research. This in turn motivates new tools that can distinguish anisotropic characteristics to improve both modeling accuracy and physical interpretations. Wavefront sensors such as Shack-Hartmann sensors, interferometers, and plenoptic sensors have been devised and used in experiments; however, they all require rigid alignments that lack resilience against temperature gradient buildup and beam wander. We find that by using a light field camera (LFC) that extracts perturbation of individual light rays, the wave structure function of turbulence can be retrieved with high reliability. Furthermore, we find through experiments that the outer scales of near-ground turbulence tend to be a magnitude smaller than conventional theoretical assumptions, agreeing with new findings by others but being absent in current theoretical modelings. As a result, we believe that the LFC is an ideal candidate in the frontier of turbulence research; it is both commercially available and easy to adapt to turbulence experiments.

Performance analysis of quantum key distribution in underwater turbulence channels

The current literature on quantum key distribution is limited mainly to transmissions over fiber optic, atmospheric, or satellite links and is not directly applicable to underwater environments with different channel characteristics. In this paper, we analyze the quantum bit error rate (QBER) and secret key rate (SKR) performance of the well-known BB84 protocol in underwater channels. As a path loss model, we consider a modified version of the Beer–Lambert formula, which takes into account the effect of scattering. We derive a closed-form expression for the wave structure function to determine the average power transfer over a turbulent underwater path and use this to obtain an upper bound on QBER as well as a lower bound on SKR. Based on the derived bounds, we present the performance of the BB84 protocol in different water types including clear, coastal, and turbid and under different atmospheric conditions such as clear, hazy, and overcast. We further investigate the effect of system parameters such as aperture size and detector field of view on QBER and SKR performance metrics.

Study on the wave structure function and spatial coherence radius with a power-law spectrum of oceanic turbulence

Based on the recently proposed power-law spectrum for oceanic turbulence [Opt. Express 26, 10188 (2018)] and the Rytov approximation, the new and exact theoretical forms for the wave structure function (WSF) of plane and spherical waves propagating in turbulent ocean are derived. To make the results easy to use, the simple formulas for the WSF and the associated spatial coherence radius in certain asymptotic regimes are also developed. Through numerical analysis, it is found that the existing results based on the Nikishov's spectrum predict a higher values for the WSF and thus a lower values for the spatial coherence radius than our results.

Capacity of underwater wireless optical links with pointing errors

Considering the effects of the oceanic turbulence and pointing error on the communication link, we derive the analytical expressions of the wave structure functions and the spatial coherence radius for Gaussian waves propagating through oceanic turbulence in the unstable stratification. Based on the new spatial coherence radius, we develop the analytical model of the pointing error variance in oceanic turbulence. By this pointing error variance, the channel capacity model is established. By investigating the effects of oceanic turbulence and light source parameters on the pointing errors and the channel capacity, we find that the outer scale and the inner scale of oceanic turbulence have a significant influence on the pointing error and the channel capacity.

Fiber coupling efficiency of Gaussian-Schell model beams in an ocean to fiber link with a Zernike tilt correction.

The fiber coupling efficiency of Gaussian-Schell model beams propagating through the oceanic turbulence of the Zernike tilt correction is studied. We derive the expression of the Zernike tilt corrected wave structure function. The numerical analysis reveals that a higher correction factor and spatial coherence of the laser beam increase the fiber coupling efficiency of the link. Our work shows that the increment of the fiber coupling efficiency caused by Zernike tilt correction under strong turbulence conditions is stronger than in the weak turbulence conditions, and the salinity fluctuation has a greater impact on it than temperature fluctuation does.