Refractive Index Fluctuations Research Articles

IDSSI: Image Deturbulence with Semantic and Spatial–Temporal Information

The propagation of light through turbulent media results in refractive index fluctuations, causing distortion and blurring of images captured by imaging equipment. Consequently, it is of paramount importance to mitigate turbulence effects. Deep convolutional neural networks incorporating attention mechanisms have demonstrated remarkable success in dynamic video restoration. However, in most networks, the attention mechanism is limited to capturing simple contextual features, failing to adequately exploit multi-level image features. This paper introduces IDSSI, an effective model that utilizes semantic and spatio–temporal information for turbulence mitigation. A novel two-branch feature extraction structure is proposed, capable of extracting multi-scale enhanced features with semantic information under limited supervision. These perceived semantic features are subsequently fused into global features, enhancing multi-scale perception for turbulence repair. Furthermore, a new Spatial–Temporal feature learning strategy is proposed. This approach facilitates the extraction and modulation of temporal information by obtaining edge cues, effectively concatenating and merging with spatial features. This strategy serves as an efficient alternative to 3D convolution. Experimental results on relevant datasets demonstrate the superiority of the proposed model over current state-of-the-art turbulence repair methods.

X-band scintillations in Venus radio occultations observed by Akatsuki

Power fluctuations are observed on radio signals propagating through the Venus atmosphere. These scintillations, due to fluctuations in refractive index, are particularly strong between 56 and 72 km altitude where the strong convective stability favors gravity wave propagation. We examine low-latitude X-band radio occultation experiments performed by the Akatsuki spacecraft to assess the statistical variability of these scintillations. The observed root-mean-square scintillation amplitudes at a given altitude vary by a factor of about 3. Part of this range is due to the different geometry of the occultations: the corresponding variations in refractive structure constant at 60-70 km altitude span a factor of ∼2. These propagation characteristics may influence the optimization of the two-way radio link for the DAVINCI mission currently in development.

Polarization and coherence properties of a partially coherent elegant Laguerre–Gaussian vortex beam in turbulent plasma

The analytical expressions for the cross-spectral density matrix elements of the partially coherent elegant Laguerre–Gaussian (eLG) vortex beam propagating through anisotropic turbulent plasma were derived based on the extended Huygens-Fresnel principle and used to study the changes in the polarization degree and the coherence degree of the partially coherent eLG vortex beam in the turbulent plasma. The numerical results show that the polarization degree of a partially coherent eLG vortex beam reaches a specific value (which is equal to the degree of polarization in the source plane) after a long propagation distance in the turbulent plasma. Moreover, this value is independent of the beam order, topological charge, correlation coefficient, wavelength of the source plane, anisotropy parameter, refractive index fluctuation variance, and outer and inner scales of the turbulent plasma. The results also show that with increasing distance, the coherence degree first decreases from unity and then oscillates around zero. However, this oscillation gradually disappears after traveling a long distance. Our results intuitively present the beam polarization and coherence properties through anisotropic hypersonic turbulence, which can be useful for optical communication in hypersonic turbulent environments.

Comparison of Gaussian and vortex probe beams for deep-learning-based turbulence correction

Optical transmission through atmospheric turbulence is a critical issue for establishing optical communication based on photonic spatial degrees of freedom. Refractive index fluctuations by a turbulent atmosphere cause structural distortion on the transmitted laser beams, resulting in crosstalk between adjacent spatial modes. We study a deep-learning technique to compensate for the turbulence effect. In particular, we mainly focus on improving the correction performance according to the selection of a probe beam. Different modes of Laguerre-Gaussian beams, including the lowest order (Gaussian), are employed as optical probes, and their abilities to compensate for turbulence effects are compared. Our results show that the Gaussian probe beam achieves a higher average correlation coefficient and a lower error rate, i.e., better correction performance, despite the spot size smaller than higher-order modes. Finally, to demonstrate the origin of the performance difference, we examine residual phases by spatial position and discuss the correction coverages.

Investigations on OFDM UAV-based free-space optical transmission system with scintillation mitigation for optical wireless communication-to-ground links in atmospheric turbulence

The potential integration of unmanned aerial vehicles (UAVs) with free space optical (FSO) communication systems stands as a promising innovation in the realm of wireless network infrastructures. This study presents a comprehensive investigation into the application of orthogonal frequency division multiplexing (OFDM) in conjunction with UAV-based FSO technology, with a specific focus on establishing robust wireless communication links to ground sites within the evolving landscape of 5G networks. The research introduces a pioneering 4-level quadrature amplitude modulation (4-QAM)-OFDM-FSO framework tailored for UAV-to-ground communication, revolutionizing the prospects for seamless and high-throughput data transmission within dynamic network environments. Through comprehensive simulations and theoretical analyses, we unveil the system's efficacy in mitigating atmospheric turbulence, achieving heightened signal integrity, and ensuring performance adaptability over varying link distances, thus significantly addressing present limitations in traditional wireless communication models. Anchored within the context of modern wireless network infrastructures, this work serves as a crucial stepping stone for the practical application of OFDM-UAV-FSO communication systems, representing a paradigm shift in fostering resilient and agile wireless connectivity in the era of 5G networks. The inception of cutting-edge wireless networks expected to outperform the capabilities of 5G necessitates an infrastructure that can handle vast amounts of data. This infrastructure must be not only cost-effective and simple to deploy but also readily scalable to accommodate the diverse demands of front-haul and backhaul applications. Motivated by the growing interest in harnessing UAVs to extend the reach and enhance the operational efficacy of conventional cellular networks, this work introduces a novel application of UAV-ground station connections. The concept employs FSO to facilitate network traffic within both the segments. To optimize throughput, resilience, and spectral efficiency, the application of OFDM is proposed. The research considers the transmission of a 20 Gbps 4-QAM data signal across various channel conditions. It thoroughly assesses the performance implications of factors such as transmission distance and beam divergence. The study explores the correlation between pointing error, scintillation, beam divergence angle, and average spectral efficiency. A slight increase in pointing error results in a rapid rise in the scintillation index, while a larger beam divergence angle can help minimize the impact of scintillation. Adapting the beam's divergence angle based on the pointing error between the optical transceivers can reduce the effects of scintillation and improve the average spectral efficiency and channel capacity. Additionally, the relationship between pointing error, scintillation, and the determination of the optical beam divergence angle in terms of beam divergence and average spectral efficiency and channel capacity is examined, and theoretical evaluations further confirm the method's effectiveness in reducing scintillation in the presence of pointing errors. Furthermore, the simultaneous use of OFDM adaptive beam divergence control and modulation could significantly enhance the data rate. This approach aims to reduce the impact of scintillation in UAV FSO links, which often experience significant losses due to unpredictable fluctuations in the atmosphere's refractive index. The results of the simulations indicate that the integrated 4-QAM-OFDM-FSO framework can realize high data transmission rates, efficiently serving front-haul and backhaul needs, thereby signifying a significant evolutionary leap for the next generation of wireless technology. The numerical findings demonstrate the significant impact of the coherent FSO OFDM optical wireless communication (OWC) setup in UAV wireless communications to ground links, particularly in mitigating the effects of strong turbulence and pointing errors (PEs). Through the integration of spatial coherence diversity and adaptive modulation OFDM in the coherent OWC, there has been a noticeable enhancement in the average spectral efficiency (ASE). Notably, our results indicate an ASE of 53 bits/s/Hz and 37 bits/s/Hz achieved at an average transmitted optical power of 10 dBm for an aperture diameter of 10 cm, without and with PEs for the coherent OWC-FSO OFDM UAV technique, respectively. The proposed method was validated through simulations, demonstrating both improved average spectral efficiency and effective reduction of the scintillation effect. This approach holds promise for mitigating scintillation effects in UAV-FSO links.

Modeling the atmospheric refractive index structure parameter using macrometeorological observations

The dynamic fluctuations in the atmospheric refractive index, commonly referred to as optical turbulence, cause phase distortions of the electromagnetic waves propagating through the atmosphere. The consequent scintillations have large implications for free-space optical communication, laser remote sensing, and directed energy applications. The refractive index structure parameter (C n 2), quantifying the strength of these fluctuations, is usually estimated using high-frequency micrometeorological measurements, employing sonic anemometer-thermometers or scintillometers. Despite providing highly accurate information, these systems are immensely complex and costly, especially for frequent field applications and remote locations. In this study, we have developed an empirical multinomial model for estimating C n 2 using three-year macrometeorological data and validated it against collocated and concurrent micrometeorological measurements, from a tropical semi-arid location. This simpler model would be handy for applications in remote locations having weather station measurements alone.

2-D inverse synthetic aperture Ladar imaging and tracking of maneuvering extended Micro-Doppler UAVs in atmospheric turbulence with skewness

The inverse synthetic aperture Ladar (ISAL) is an important system for observation of space objects. Here, a 2-D ISAL imaging and tracking algorithm is proposed for low observable maneuvering extended objects tracking (M−EOT) such as small space UAVs. When imaging maneuvering objects with ISAL, dispersion and Doppler frequency time-variation exist in the range and cross-range echo signal, respectively. Additionally, the ISAL system can achieve high-resolution images for long-range moving objects, while its performance is affected by atmospheric turbulence. Atmospheric turbulence is a very complicated random state formed by the instability of regular laminar flow at a high maneuvering velocity, which is caused by the random motion of the atmosphere and lead to the random fluctuation of the atmospheric refractive index. Therefore, in real-time M−EOT scenario, the measurements distribution over the whole object is not symmetrical but distributed and skewed in some portions while a target maneuvers due to the unbalanced of reflection that caused by the atmospheric turbulence. In practice, the micro Doppler effect caused by micro moving components such as drone rotors will seriously affect the focused ISAL imaging of the M−EOT’s rigid body. To solve these problems in real-time low observable M−EOTs imaging and tracking from 2-D ISAL system, a novel robustness measurement model and recursion multi-Bernoulli track-before-detect filter based on a multiple model skewed non-symmetrically normal distribution is represented with more than one ellipse and lower complexity. In this paper, the Radon-Laplace method is presented to reduce this micro-Doppler effect in ISAL imaging. Additionally, we will eliminate the effect of atmospheric turbulence in ISAL Imaging by using the network-based variance–covariance estimation (NVCE) weighting method. In particular, we describe the M−EOT’s state through the random matrices model (RMM). In RMM, the extent is applied by one ellipse, which often lose information about size, heading, and shape, when the scatter centers are distributed symmetrically around the M−EOT’s centroid. In this paper, a new observation model used to modify a sub-RMM by considering the characteristics of 2-D ISAL data is proposed. Simulation results demonstrates the proposed robustness algorithm with the influence of the atmospheric turbulence and micro-Doppler.

Enhanced Fiber Long‐Range Surface Plasmon Sensing Enabled by Resonance Coupling to Surface Plasmon Polaritons

A tunable fiber optic (FO) long‐range surface plasmon (LRSP) sensor with strong coupling is developed and demonstrated theoretically in this article. The sensor consists of a square lattice array of Ag nanodisks resting on the FO end face. Utilizing nanodisks with small diameters leads to the pronounced excitation of two distinct and independent resonant modes: surface plasmon polaritons (SPP) and LRSP. A systematic investigation is performed to evaluate the sensing performance and capabilities of the sensor, focusing on its bulk and surface sensitivity. Significantly, the LRSP mode demonstrates high sensitivity and favorable linearity in response to refractive index (RI) changes, with an exceptionally high figure of merit (FOM). On the contrary, the SPP mode is regarded as an ideal self‐referencing mode due to its immunity to RI fluctuations. The enlargement of nanodisks diameters results in a swift redshift in the LRSP wavelength, leading to a strong coupling with the SPP mode. This coupling facilitates the transfer of electric fields within the SPP mode, promotes sensing capabilities, and enables the realization of dual‐channel sensing functionality. The occurrence of strong coupling phenomena along with the use of FO substrates provides an innovative option for achieving multifunctionality and miniaturization in sensor platforms.

Derivation of Rytov variance for jet engine-induced turbulence

In this study, we analytically derived the Rytov variance and scintillation index value of turbulence caused by jet engines. In addition, we analyzed the variation characteristics of the Rytov variance and scintillation index values numerically depending on the variations in turbulence strength, experimental data, and wavelength. We observe that Rytov variance reaches up to high values due to the strong turbulence resulting from high refractive index fluctuations. This result brings high-intensity fluctuations regardless of the anisotropy of the turbulence. Rytov variance is directly proportional to turbulence strength. We present scintillation index curves considering the aperture averaged case. We plot our results considering the variations in the operating wavelength, turbulence strength, and the scaling parameter. According to our results, we think that it will be useful for a system such as directed infrared countermeasure (DIRCM), which is highly sensitive and should be exposed to minimum turbulence in the field of use. Since DIRCMs transmit codes to paralyze the missile’s seeker, intensity fluctuations play a vital role during this transmission. It could reduce the performance of these systems when intensity fluctuations are high.

Design and analysis of a photonic crystal nanocavity based bio-sensor for blood componentdetection.

A design of a photonic crystal nanocavity based bio-sensor having a footprint of 12×8µm 2 is proposed to detect different blood components. A finite difference time domain (FDTD) numerical technique has been used to characterize the sensor by evaluating its frequency response. The shift in resonant wavelength of the proposed cavity is utilized to detect blood refractive index fluctuation due to the presence of various components. The obtained numerical findings show that the maximum sensitivity for a shift in resonant wavelength is reported as 760nm/RIU for various blood components. Moreover, the fabrication of PhC is always prone to the fabrication induced disorders. Hence, the impact of fabrication imperfections on the sensor's performance also has been included in the analysis.

Angular width and beam quality of a partially coherent standard Laguerre-Gaussian vortex beam in turbulent plasma.

Analytical formulas for the angular width and propagation factor of a partially coherent standard Laguerre-Gaussian (sLG) vortex beam through anisotropic turbulent plasma were derived based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function. The evolution properties of the angular width and propagation factor of partially coherent sLG vortex beams propagating in anisotropic turbulent plasma were investigated numerically. The numerical results demonstrate the influence of the source and turbulence parameters on the normalized angular width and normalized propagation factor of the partially coherent sLG vortex beams. It can be observed that in a partially coherent sLG vortex beam with a lower beam order, topological charge, and wavelength, or a higher correlation coefficient of the source plane, and with increasing propagation distance and refractive index fluctuation variance or decreasing anisotropy parameters, the outer and inner scales of the turbulent plasma have a large angular width and propagation factor (i.e.,the beam quality is worse). The results of this study will be beneficial for applications in remote sensing and optical communications.

The Elusive Nature of “Seeing”

Atmospheric image blur, “seeing”, is one of the key parameters that influences the selection of observatory sites and the performance of ground-based telescopes. In this review, the common definition of seeing based on the Kolmogorov turbulence model is recalled. The ability of this model to represent real, non-stationary fluctuations of the air refractive index is discussed. Even in principle, seeing (a model parameter) cannot be measured with arbitrary accuracy; consequently, describing atmospheric blur by a single number, seeing, is a crude approximation. The operating principles of current seeing monitors are outlined. They measure optical effects caused by turbulence, sampling certain regions of spatial and temporal spectrum of atmosphreic optical disturbances, and interpret their statistics in the framework of the standard model. Biases of seeing monitors (measurement noise, propagation, finite exposure time, optical defects, wind shake, etc.) should be quantified and corrected using simulations, while instrument comparison campaigns serve as a check. The elusive nature of seeing follows from its uniqueness (a given measurement cannot be repeated or checked later), its non-stationarity (dependence on time, location, and viewing direction), a substantial role of the highly variable surface layer, and a potential bias caused by the air flow in the immediate vicinity of the seeing monitors. The results of seeing measurements are outside the scope of this review.

Non-linear optical scattering PUF: enhancing security against modeling attacks for authentication systems.

With the rapid expansion of the Internet of Things (IoT), ensuring the security of personal and group information has become increasingly crucial. However, conventional optical scattering physical unclonable function (OS-PUF) faces challenges due to its linear scattering behavior. In this article, we propose a non-linear OS-PUF (NOS-PUF) that integrates electro-optic materials. By leveraging random refractive index fluctuations generated by the NOS-PUF, we mitigate modeling attacks based on the OS-PUF and bolster the overall security of the authentication process. Moreover, we introduce a novel modeling attack methodology based on scattering invariant modes (SIMs) that poses a significant threat to conventional OS-PUF and NOS-PUF authentication systems. Through extensive simulations, we demonstrate that our NOS-PUF achieves a remarkably lower false accept rate for modeling attacks utilizing SIMs, surpassing the entropy limit imposed by the Gabor filtering algorithm by more than five orders of magnitude. These results highlight the heightened security and increased information entropy offered by the proposed NOS-PUF, making it particularly suitable for applications demanding robust and high-security authentication measures.

Correlations of multimode optical incidences in a turbulent biological tissue.

In a turbulent biological tissue, field correlations at the observation plane are found when a multimode optical incidence is used. For different multimode structures, variations of the multimode field correlations are evaluated against the biological tissue turbulence parameters, i.e.,the strength coefficient of the refractive-index fluctuations, fractal dimension, characteristic length of heterogeneity, and the small length-scale factor. Using a chosen multimode content, for specific biological tissue types of liver parenchyma (mouse), intestinal epithelium (mouse), upper dermis (human), and deep dermis (mouse), field correlations are evaluated versus the strength coefficient of the refractive-index fluctuations and small length-scale factor. Again, with a chosen multimode content, behavior of the field correlations is studied against the strength coefficient of the refractive-index fluctuations for various diagonal lengths and the transverse coordinate at the observation plane. Finally, the field correlation versus the strength coefficient of the refractive-index fluctuations is reported for different single modes, which are special cases of multimode excitation. This topic is being reported in the literature for the first time, to our knowledge, and the presented results can be employed in many important biological tissue applications.

Atmospheric Turbulence with Kolmogorov Spectra: Software Simulation, Real-Time Reconstruction and Compensation by Means of Adaptive Optical System with Bimorph and Stacked-Actuator Deformable Mirrors

Atmospheric turbulence causes refractive index fluctuations, which in turn introduce extra distortions to the wavefront of the propagated radiation. It ultimately degrades telescope resolution (in imaging applications) and reduces radiation power density (in focusing applications). One of the possible ways of researching the impact of turbulence is to numerically simulate the spectrum of refractive index fluctuations, to reproduce it using a wavefront corrector and to measure the resultant wavefront using, for example, a Shack–Hartmann sensor. In this paper, we developed turbulence simulator software that generates phase screens with Kolmogorov spectra. We reconstructed the generated set of phase screens using a stacked-actuator deformable mirror and then compensated for the introduced wavefront distortions using a bimorph deformable mirror. The residual amplitude of the wavefront reconstructed by the 19-channel stacked-actuator mirror was 0.26 λ, while the residual amplitude of the wavefront compensated for by the 32-channel bimorph mirror was 0.08 λ.

Spatial and temporal distributions of atmospheric refractive-index structure parameter measured by moiré deflectometry

Random fluctuation of refractive index distorts the wavefront of light propagation in the atmosphere, which destroys the coherence of the light waves, as well as has an impact on optical detection and communication, etc. In this paper, a phase-based measurement method for synchronously temporal and spatial distributions of atmospheric refractive-index structure parameter is applied. First of all, the depended relation between phase and refractive-index structure parameter is established, based on which an experiment is adopted. In experiment, 3600 frames of moiré fringes were obtained within an hour. And then, the phase and deflection angles distributions of moiré fringes are obtained by Fourier analysis and multi-grid method. Finally, the temporal and spatial distributions of refractive-index structure parameter are yielded according to the deduced theoretical relationship. The results show that both the temporal and spatial distributions refractive-index structure parameter could be measured by moiré deflectometry, and they are in good agreement with the existing methods. In a word, the related results could provide some references for studying the refractive-index structure parameter and the influence of atmosphere on optical detection and communication.

The effective beam width of a partially coherent rectangular mul-ti-Gaussian Schell-model vortex beam propagating in a turbulent plasma

Based on the derived analytical formulae for the optical intensity and effective beam width of a partially coherent rectangular multi-Gaussian Schell-model (RMGSM) vortex beam, we analyzed the evolution of the effective beam width of a partially coherent RMGSM vortex beam propagating in an anisotropic turbulent plasma using numerical examples. The numerical results demonstrated that the effective beam widths in the x and y directions were similar. In studies on the influences of the source parameters, one can see that an RMGSM vortex beam with a larger topological charge and beam waist or a smaller correlation coefficient σ evolves into a beam with a larger effective beam width. However, the influence of beam order was not evident. In addition, numerical examples proved that the effective beam width increases with increasing propagation distance and refractive index fluctuation variance or decreasing anisotropy parameter , outer scale , and inner scale . This study's results will be beneficial for applications in free-space optical communications.

Π-ML: a dimensional analysis-based machine learning parameterization of optical turbulence in the atmospheric surface layer.

Turbulent fluctuations of the atmospheric refraction index, so-called optical turbulence, can significantly distort propagating laser beams. Therefore, modeling the strength of these fluctuations (C n2) is highly relevant for the successful development and deployment of future free-space optical communication links. In this Letter, we propose a physics-informed machine learning (ML) methodology, Π-ML, based on dimensional analysis and gradient boosting to estimate C n2. Through a systematic feature importance analysis, we identify the normalized variance of potential temperature as the dominating feature for predicting C n2. For statistical robustness, we train an ensemble of models which yields high performance on the out-of-sample data of R2 = 0.958 ± 0.001.

Physics-based scintillations for outdoor sound auralization.

The sound propagating in a turbulent atmosphere fluctuates in amplitude and phase. This phenomenon, known as acoustic scintillation, is caused by random fluctuations in the acoustic refractive index of the air induced by atmospheric turbulence. Auralization techniques should consider this phenomenon to increase the realism of the synthetic sound. This paper proposes a physics-based formulation to model sequences of log-amplitude and phase fluctuations of a sound propagating in a turbulent atmosphere. This method applies to slanted and vertical propagation of the sound, which is useful for simulating elevated noise sources such as aircraft, drones, and wind turbines. The theoretical framework is based on the spatial correlation functions for the log-amplitude and phase fluctuations for spherical waves, the von Kármán spectrum, and similarity theories to model atmospheric turbulence. Two applications with audio files are presented to demonstrate the applicability of this method to tonal and broadband noise.

Stochastic quantization of laser propagation models

This paper identifies certain interesting mathematical problems of stochastic quantization type in the modeling of Laser propagation through turbulent media. In some of the typical physical contexts, the problem reduces to stochastic Schrödinger equation with space–time white noise of Gaussian or Poisson or Lévy type. We identify their mathematical resolution via stochastic quantization. Nonlinear phenomena such as Kerr effect can be modeled by a stochastic nonlinear Schrödinger equation in the focusing case with space–time white noise. A treatment of stochastic transport equation, the Korteweg–De Vries equation as well as a number of other nonlinear wave equations with space–time white noise is also given. The main technique is the S-transform (we will actually use the closely related Hermite transform) which converts the stochastic partial differential equation (PDE) with space–time white noise to a deterministic PDE defined on the Hida–Kondratiev white noise distribution space. We then utilize the inverse S-transform/Hermite transform known as the characterization theorem combined with the infinite-dimensional implicit function theorem for analytic maps to establish local existence and uniqueness theorems for path-wise solutions of this class of problems. The particular focus of this paper on singular white noise distributions is motivated by practical situations where the refractive index fluctuations in the propagation medium in space and time are intense due to turbulence, ionospheric plasma turbulence, marine-layer fluctuations, etc. Since a large class of PDEs, that arise in nonlinear wave propagation, have polynomial-type nonlinearities, white noise distribution theory is an effective tool in studying these problems subject to different types of white noises.