Intensity Scintillation Index Research Articles

Statistical Uncertainty in the Frequency Dependence of the Intensity Scintillation Index (S4)

AbstractThe intensity scintillation index (S4) exhibits a linear frequency dependence derived from a power law phase screen model, with the exponent determined by the phase spectral index (p). However, it is well known that a departure from linearity occurs as S4 increases and saturates under strong scatter conditions. Additionally, statistical errors over a finite time window can also cause the scintillation statistic to deviate from the power law dependence on frequency. This paper presents a parametric analysis on the deviation in the S4 frequency dependence from the power law form. This investigation focuses on the contribution of statistical uncertainty in S4 calculations to the deviation in the frequency dependence according to the selected parameters: S4 and Fresnel frequency (fF). The deviation is determined by comparing p estimates calculated from the power law relationship of S4 at different L‐band frequencies with those inferred from a model‐fitting method using a multi‐frequency global navigation satellite system scintillation data set. The results show the well‐known departure from linearity as S4 increases, and reveal increasing deviations with decreasing fF. The spectral analysis indicates that the variability at the lowest frequencies of intensity spectra contributes to the statistical errors in S4 calculations due to the finite time window, particularly when scintillations are dominated by low‐frequency contributions at low fF. Simulation results of scintillation realizations show much lower deviations with a 30‐min compared to 1‐min window. This suggests a 1‐min window can be too short for reliable S4 calculations due to statistical uncertainty, especially at low fF.

Simulation and Analysis of Mie-Scattering Lidar-Measuring Atmospheric Turbulence Profile.

Based on the residual turbulent scintillation theory, the Mie-scattering lidar can measure the intensity of atmospheric turbulence by detecting the light intensity scintillation index of the laser return signal. In order to evaluate and optimize the reliability of the Mie-scattering lidar system for detecting atmospheric turbulence, the appropriate parameters of the Mie-scattering lidar system are selected and optimized using the residual turbulent scintillation theory. Then, the Fourier transform method is employed to perform the numerical simulation of the phase screen of the laser light intensity transformation on the vertical transmission path of atmospheric turbulence. The phase screen simulation, low-frequency optimization, and scintillation index calculation methods are provided in detail, respectively. Based on the phase distribution of the laser beam, the scintillation index is obtained. Through the relationship between the scintillation index and the atmospheric turbulent refractive index structure constant, the atmospheric turbulence profile is inverted. The simulation results show that the atmospheric refractive index structure constant profile obtained by the iterative method is consistent with the input HV5/7 model below 6500 m, which has great guiding significance to carry out actual experiments to measure atmospheric turbulence using the Mie lidar.

Modeling solar eclipse shadow bands using wave optics simulation through distributed turbulence.

Thin, wavy ribbons of light known as "shadow bands" can be seen moving and undulating on the ground just preceding and following the occurrence of a total solar eclipse. Using the scattering scintillation theory, Codona [Astron. Astrophys.164, 415 (1986)AAEJAF0004-6361] presented theoretical investigations that explain recorded features of shadow bands and suggest the turbulence mainly responsible for the bands is within the bottom 2-3 km of the atmosphere. This paper proposes an approach to model the shadow band phenomena using a numerical wave optics simulation. The simulation approach employs numerical wave optics techniques to model a crescent-shape source, propagation of component plane waves through turbulence phase screens, and observation of the light at the ground. The simulation produces intensity patterns with structures and evolution that are consistent with actual shadow band observations and Codona's theory. The contribution of the turbulence phase screens as a function of height to the shadow band intensity scintillation index is simulated and excellent correspondence is found with the theory. Finally, the practical utility of the simulation is illustrated by creating intensity frames that show the temporal evolution of the patterns due to wind. The simulation approach is adaptable and can be applied to scintillation and imaging problems involving other incoherent objects or sources that subtend relatively large angles and are observed through atmospheric turbulence.

Echo characteristics of laser beams reflected from rough targets with a finite size in atmospheric turbulence

Based on the extended Huygens-Fresnel principle, echo characteristics of the plane and spherical waves reflected from a rough target with a finite size in atmospheric turbulence were studied. The expressions of the intensity variance, covariance functions and scintillation index of the plane and spherical waves reflected from a rough target in double-path propagation through atmospheric turbulence were proposed considering the turbulence perturbations. The expressions were numerically calculated, and the results show that the intensity fluctuation caused by turbulence decreases with increasing target size. It is also found that under weak turbulence, it is mainly the log-amplitude fluctuations that affect the second-order statistical properties of the received beam intensity. Results obtained can potentially provide theoretical and technical guidance for the future applications of laser target detection and target recognition in space.

Assessing LoRa for Satellite-to-Earth Communications Considering the Impact of Ionospheric Scintillation

Since the appearance of 5G, Internet of Things (IoT) has gained an increased interest, with multiple technologies emerging and converging to cover different user needs. One of the biggest challenges today is to have global IoT coverage, ensuring seamless communication with IoT devices placed in rural and even remote areas. Satellite constellations, and in particular CubeSats orbiting in Low Earth Orbit, can provide a solution to these challenges. Out of the technologies available, LoRa (Long Range) has a great potential for implementation in space-to-Earth satellite communications. As the space-to-Earth channel is different with respect to the conventional Earth-to-Earth one, it is important to asses the capabilities of LoRa in this new environment. This paper presents a study of different LoRa device configurations to identify the constrains for each one and determine which one is better for particular mission requirements. Also, the effect of ionospheric scintillation is assessed with a SDR-based (Software-Defined Radio) test set-up that evaluates the performance of this technology against with Humprey's ionospheric scintillation model. This phenomena produces deep signal intensity fadings and phase fluctuations in equatorial regions, and mainly phase fluctuations in high latitudes. The obtained metrics are the received power and the packet delivery ratio as a function of the intensity scintillation index, and show the robustness of the LoRa modulation in these new environments.

Scintillation properties of a partially coherent vector beam with vortex phase in turbulent atmosphere.

We undertake a computational and experimental study of an advanced class of structured beams, partially coherent radially polarized vortex (PCRPV) beams, on propagation through atmospheric turbulence. A computational propagation model is established to simulate this class of beams, and it is used to calculate the average intensity and on-axis scintillation index of PCRPV beams. On comparison with other classes of structured beams, such as partially coherent vortex beams and partially coherent radially polarized beams, it is found that the PCRPV beams, which structure phase, coherence and polarization simultaneously, show marked improvements in atmospheric propagation. The simulation results agree reasonably well with the experimental results. These beams will be useful in free-space optical communications and remote sensing.

On the Relationship Between the Rate of Change of Total Electron Content Index (ROTI), Irregularity Strength (CkL), and the Scintillation Index (S4)

AbstractWe present a new quantitative theory for the rate of change of total electron content index (ROTI) by noting its straightforward relationship to the phase structure function of ionospheric turbulence. The theory provides the dependence of ROTI on the sampling interval, satellite motion, propagation geometry, and the spectral shape, strength, anisotropy, and drift of the irregularities. We also present useful approximations to the full theory that elucidate the principal dependencies. We show, for example, that ROTI varies with the effective scan velocity (Veff) to the power ν − 1/2, where 2ν + 1 is the spectral index of the 3‐D irregularities. This dependence on Veff persists in the ratio of ROTI to the intensity scintillation index (S4), which thus depends on the particular viewing geometry for each satellite. While irregularity strength cancels when forming this ratio, the dependence on Fresnel scale remains. We validate the theory by comparing predictions of irregularity strength (CkL) and S4 from 1‐Hz ROTI measurements with calculations derived from 20‐Hz intensity samples collected at Ascension Island. The theory explains the observations well, except when the scan is directed nearly along the field‐aligned irregularities (within 20° of meridional). For cross‐field scans the standard deviations of the error in predicting S4 from 1‐Hz ROTI were 0.05, 0.11, and 0.14 for weak, moderate, and strong scintillation, respectively. These encouraging results suggest the possibility of using dense networks of inexpensive total electron content monitors to provide quantitative diagnostics of ionospheric scintillation and the irregularities that cause them.

The preliminary study on fluctuation of ocean sound field

The ocean environmental variation causes the amplitude and phase fluctuations of acoustic signals that travel in the ocean acoustic waveguide. Sound propagation fluctuation is studied based on the deep water fixed-point sound propagation experiment data acquired in the northern South China Sea in 2016. In this experiment, two sets of submerged buoy systems, which integrate the emission and receiving of sound wave, have continuously and steadily worked as long as three months. Considering the Doppler frequency shift, the amplitude and phase of acoustic signals are calculated after matched filtering. The sound intensity scintillation index computed for the entire record is 0.8, which is less than the saturation value of one. In contrast, the scintillation index computed for the 2001 ASIAEX South China Sea Experiment is 2.6 and 1.7. The ocean environmental variation and its relation with sound propagation fluctuation are analyzed.

A theory of scintillation for two‐component power law irregularity spectra: Overview and numerical results

AbstractWe extend the power law phase screen theory for ionospheric scintillation to account for the case where the refractive index irregularities follow a two‐component inverse power law spectrum. The two‐component model includes, as special cases, an unmodified power law and a modified power law with spectral break that may assume the role of an outer scale, intermediate break scale, or inner scale. As such, it provides a framework for investigating the effects of a spectral break on the scintillation statistics. Using this spectral model, we solve the fourth moment equation governing intensity variations following propagation through two‐dimensional field‐aligned irregularities in the ionosphere. A specific normalization is invoked that exploits self‐similar properties of the structure to achieve a universal scaling, such that different combinations of perturbation strength, propagation distance, and frequency produce the same results. The numerical algorithm is validated using new theoretical predictions for the behavior of the scintillation index and intensity correlation length under strong scatter conditions. A series of numerical experiments are conducted to investigate the morphologies of the intensity spectrum, scintillation index, and intensity correlation length as functions of the spectral indices and strength of scatter; retrieve phase screen parameters from intensity scintillation observations; explore the relative contributions to the scintillation due to large‐ and small‐scale ionospheric structures; and quantify the conditions under which a general spectral break will influence the scintillation statistics.

The effect of signal bandwidth on partially saturated broadband ocean acoustic transmission scintillation in a shallow water waveguide

The acoustic field in a shallow water waveguide at small source-receiver separations <3 km are partially saturated. Here, we examine the scintillation statistics of partially saturated broadband ocean acoustic transmissions in the low to mid frequency range collected using a high-resolution towed horizontal coherent hydrophone array system. The standard deviation of intensity fluctuations and scintillation index are quantified as a function of signal bandwidth and source-receiver separation. The amplitude and intensity distributions are compared with corresponding distribution models for the partially saturated field to determine the number of independent statistical fluctuations present in the broadband data.

Kriging method to perform scintillation maps based on measurement and GISM model

AbstractThis paper presents an ionosphere scintillation mapping algorithm. The technique used is a Kriging technique, well known in geostatistics. It is an interpolation method applied to a set of random data, namely, in this application, to the intensity scintillation (S4) index. The paper focuses on the importance of the regression model used in the algorithm. The one‐dimensional and then the two‐dimensional problems have been investigated. One example of results combining measurement data recorded by two different networks in Peru is presented. The accuracy of the results has been verified using a cross‐validation technique, which consists in removing part of the known data set and comparing the interpolated results to it.

Variation of the ionospheric scintillation index with elevation angle of the transmitter

We have analyzed GPS data from 2007–2011 to determine the nature of variation of scintillation index with elevation of the direction of propagation at an observing point Warsaw, Poland, and Hornsund, Svalbard. To compare with the theory, the intensity scintillation index is simulated as a function of elevation angle, azimuth, magnetic field inclination, and shape of irregularities, using the phase screen model of scintillation as formulated by Rino (1979). Data analysis has been done for the seasonal as well as geomagnetic activity dependence of ionospheric scintillation. Scintillation index is a power-law function of the cosecant of the elevation angle. Results show that the power law strongly depends on the form of irregularities, being larger than in isotropic case for irregularities with dimension along the magnetic field direction smaller than those across the magnetic field. The present work also shows the need to use experimentally derived dependence on elevation.

The Influence of Propagation Focusing on Clutter Statistics

Fluctuations in reverberation (clutter) from scatterers at long range in shallow water can be affected by many mechanisms. Their statistics, in particular the scintillation index (SI), depend not only on the statistics of the scatterers (their physical distribution, shape, orientation, etc.) but on the outward and return propagation paths. This paper investigates the focusing effects due to forward scattering from weak undulations in the seabed. Some existing Fresnel-Kirchhoff theory for monostatic, vertical incidence on a 2-D surface is adapted to demonstrate the behavior of the intensity's SI in bistatic geometry. In addition, using a simulation of bistatic geometry and a 1-D surface the intensity statistics are extended to include autocorrelation function and probability distribution. The behavior of these properties is investigated for various Gaussian-correlated roughnesses with or without an added component of uncorrelated roughness. Bistatic geometries include source and receiver moving with constant separation, and moving source with fixed receiver. Fairly modest vertical undulations can result in significant fluctuation due to reflection focusing with scintillation indices possibly greater than unity.

Experimental verification of optical backhaul links for high‐altitude platform networks: Atmospheric turbulence and downlink availability

AbstractOptical backhaul downlinks from high‐altitude platforms (HAPs) are investigated. An experiment demonstrated the advantages of optical links: a small and lightweight terminal with low power consumption was launched to the stratosphere and data transmitted down to a ground station at a rate of 1.25 Gbit/s. Owing to the chosen system parameters and the high budget margin, disturbing turbulence effects did not decrease the link performance.The scientific aspect of the experiment was to study turbulence effects in order to design future systems with higher transmission performance. On the day of the experiment, measured scintillation and wavefront distortions were minimal in the morning. The best atmospheric conditions were observed about 3 h after sunrise with a peak of the atmospheric coherence length r0 at 16 cm. An r0 of 4 cm was measured as the worst case before sunrise and later during the day. This trend could also be observed for power‐ ($ {\sigma _P^2} $) and intensity scintillation index ($ {\sigma _I^2} $). The latter $ {\sigma _I^2} $ changed from 0.28 (best case) to 1.12. For small $ {\sigma _I^2} $, a lognormal intensity probability density function was measured.Apart from the robust intensity modulation scheme with direct detection which was used for the trial, future improved systems could benefit from a coherent transmission scheme. According to the r0 measurements and further simulations on heterodyne efficiency it turned out that the aperture size can be decreased from 40 to 10 cm without any significant change in the link margin.Future stratospheric optical links between HAPs or links from platforms to satellites will not suffer from cloud blockage but it remains an issue for up/downlinks to a ground station. This can be mitigated by ground‐station diversity. Four optical ground stations in the southern part of Europe can lead to an availability of over 98%. The separation distance of the ground stations is about 900 km with a negligible correlation of cloud cover. A change of wavelength from the employed 1.55 to a wavelength around 11‐µm with minimum cloud attenuation would increase the link availability for thin clouds. Copyright © 2007 John Wiley &amp; Sons, Ltd.

The moments analysis of the pulse propagation through plasma medium and its applications

Based on the theory of wave propagation and scattering in random medium, the analysis method of the pulse propagating in the plasma medium is presented. Under the condition of strong fluctuations, we have deduced the two-frequency second moment and fourth moment equations, and calculated the two-frequency intensity correlation function and scintillation index in terms of the different electron density spectra. The statistical parameters of the self-correlation function, the correlation bandwidth and time are obtained, in order to provide a basis for studing the characteristic of the pulse propagation in plasma medium.

On the kinematics of broadband multipath scintillation and the approach to saturation

Utilizing a simple model in which the acoustic wave function is a sum of independent Gaussian wave packets, the relative intensity variance or scintillation index (SI) is analytically calculated. The model has an unspecified probability density function (PDF) for wave packet amplitudes and Gaussian PDFs for travel-time-induced and non-travel-time-induced phase shifts; amplitudes and both phase shifts are assumed to be mutually uncorrelated. It is shown that a proper treatment of the mean field is required to obtain the saturation value, SI = 1, in the limit of a large number of interfering wave packets. The analytic formulas for SI allow identification of important wave packet parameters in the approach to saturation. Criteria are identified for both broadband and narrow-band cases for which the approach to saturation is from above and below 1. It is demonstrated that the broadband approach to saturation is much slower than the narrow-band cases, since wave packets separated in time by more than an inverse bandwidth do not strongly contribute to interference. This effect is quantified by the time-bandwidth product. The model is also used to obtain an analytic expression for pulse time spread; it is shown that multipath conditions which favor a rapid approach to saturation do not favor large pulse spread.

Fourth-moment calculation of optical propagation in a turbulent atmosphere with use of the split-step method I Plane wave

The split-step method was used to derive the full spatial dependence of the fourth moment of a plane-wave propagating in a two-dimensional turbulent atmosphere with a power-law spectrum for two values of the scattering parameter γk = 0 and 1 [ J. Opt. Soc. Am. A2, 2133 ( 1985)]. The changes in γk were obtained by the use of two different values of the inner scale of turbulence l0 while the operating wavelength and turbulent strength were kept constant. In this way the influence of l0 on the field statistics can be obtained. The results of intensity scintillation index σI2 and covariance function bI are also presented. The agreement of σI2 with the results of the reference cited above especially for γk = 0 is good. We also used the results of bI to study the asymptotic dependence of the characteristic correlation length on ζ, where ζ is the propagation-range scale.

Intensity scintillation index of finite beam opticalpropagation in a turbulent atmosphere

The split step method is used to model collimated beam optical propagation in a two-dimensional turbulent atmosphere with power law spectrum of the refractive index fluctuations. The authors present the intensity scintillation index in the weak and moderate scattering conditions for Gaussian beam radii 5 and 20 mm.

Double‐passage radar cross section enhancements

Transionospheric radar measurements reported by Knepp and Houpis (1991) verify the backscatter enhancement known to be associated with the double‐passage problem. Knepp and Reinking (1989) showed, moreover, that the enhancement is proportional to the intensity scintillation index on the one‐way path. While this result is easily derived, it is more difficult to characterize the complete angular distribution of backscattered waves of which the radar measurement represents one component. In this paper we develop a simple product expression for the backscattered spectrum from an incident plane wave. The spectrum of backscattered waves from a point source is then derived by transformation of the plane‐wave result. Motivated by a discussion in a recent paper by Fremouw and Ishimaru (1992), we show that both reciprocity and energy conservation are preserved in our wave‐space formulation, which is essentially exact. We also discuss the method of computing the scattering functions and the fourth‐order moments that appear in our results; however, the general expressions are the principal results of this paper.

Two-dimensional modelling of optical propagation in turbulent atmosphere

The split step method was used to model plane wave optical propagation in a turbulent atmosphere for inner scales of turbulence of 0 and 5.1 mm. The intensity scintillation index was derived from the random field along the propagation path. The propagation parameters cover weak scattering and strong scattering conditions. >