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1.
Front Plant Sci ; 15: 1369696, 2024.
Article in English | MEDLINE | ID: mdl-38952847

ABSTRACT

Effectively monitoring pest-infested areas by computer vision is essential in precision agriculture in order to minimize yield losses and create early scientific preventative solutions. However, the scale variation, complex background, and dense distribution of pests bring challenges to accurate detection when utilizing vision technology. Simultaneously, supervised learning-based object detection heavily depends on abundant labeled data, which poses practical difficulties. To overcome these obstacles, in this paper, we put forward innovative semi-supervised pest detection, PestTeacher. The framework effectively mitigates the issues of confirmation bias and instability among detection results across different iterations. To address the issue of leakage caused by the weak features of pests, we propose the Spatial-aware Multi-Resolution Feature Extraction (SMFE) module. Furthermore, we introduce a Region Proposal Network (RPN) module with a cascading architecture. This module is specifically designed to generate higher-quality anchors, which are crucial for accurate object detection. We evaluated the performance of our method on two datasets: the corn borer dataset and the Pest24 dataset. The corn borer dataset encompasses data from various corn growth cycles, while the Pest24 dataset is a large-scale, multi-pest image dataset consisting of 24 classes and 25k images. Experimental results demonstrate that the enhanced model achieves approximately 80% effectiveness with only 20% of the training set supervised in both the corn borer dataset and Pest24 dataset. Compared to the baseline model SoftTeacher, our model improves mAP @0.5 (mean Average Precision) at 7.3 compared to that of SoftTeacher at 4.6. This method offers theoretical research and technical references for automated pest identification and management.

2.
Sensors (Basel) ; 23(21)2023 Oct 26.
Article in English | MEDLINE | ID: mdl-37960437

ABSTRACT

For orbital angular momentum (OAM) recognition in atmosphere turbulence, how to design a self-adapted model is a challenging problem. To address this issue, an efficient deep learning framework that uses a derived extreme learning machine (ELM) has been put forward. Different from typical neural network methods, the provided analytical machine learning model can match the different OAM modes automatically. In the model selection phase, a multilayer ELM is adopted to quantify the laser spot characteristics. In the parameter optimization phase, a fast iterative shrinkage-thresholding algorithm makes the model present the analytic expression. After the feature extraction of the received intensity distributions, the proposed method develops a relationship between laser spot and OAM mode, thus building the steady neural network architecture for the new received vortex beam. The whole recognition process avoids the trial and error caused by user intervention, which makes the model suitable for a time-varying atmospheric environment. Numerical simulations are conducted on different experimental datasets. The results demonstrate that the proposed method has a better capacity for OAM recognition.

3.
Sensors (Basel) ; 23(16)2023 Aug 09.
Article in English | MEDLINE | ID: mdl-37631574

ABSTRACT

The reliable circulation of automotive supply chain data is crucial for automotive manufacturers and related enterprises as it promotes efficient supply chain operations and enhances their competitiveness and sustainability. However, with the increasing prominence of privacy protection and information security issues, traditional data sharing solutions are no longer able to meet the requirements for highly reliable secure storage and flexible access control. In response to this demand, we propose a secure data storage and access control scheme for the supply chain ecosystem based on the enterprise-level blockchain platform Hyperledger Fabric. The design incorporates a dual-layer attribute-based auditable access control model for access control, with four smart contracts aimed at coordinating and implementing access policies. The experimental results demonstrate that the proposed approach exhibits significant advantages under large-scale data and multi-attribute conditions. It enables fine-grained, dynamic access control under ciphertext and maintains high throughput and security in simulated real-world operational scenarios.

4.
Comput Math Methods Med ; 2021: 2973108, 2021.
Article in English | MEDLINE | ID: mdl-34484414

ABSTRACT

The X-ray radiation from computed tomography (CT) brought us the potential risk. Simply decreasing the dose makes the CT images noisy and diagnostic performance compromised. Here, we develop a novel denoising low-dose CT image method. Our framework is based on an improved generative adversarial network coupling with the hybrid loss function, including the adversarial loss, perceptual loss, sharpness loss, and structural similarity loss. Among the loss function terms, perceptual loss and structural similarity loss are made use of to preserve textural details, and sharpness loss can make reconstruction images clear. The adversarial loss can sharp the boundary regions. The results of experiments show the proposed method can effectively remove noise and artifacts better than the state-of-the-art methods in the aspects of the visual effect, the quantitative measurements, and the texture details.


Subject(s)
Radiographic Image Interpretation, Computer-Assisted/statistics & numerical data , Tomography, X-Ray Computed/statistics & numerical data , Algorithms , Computational Biology , Databases, Factual/statistics & numerical data , Humans , Neural Networks, Computer , Radiation Dosage , Radiographic Image Enhancement/methods , Signal-To-Noise Ratio
5.
Appl Opt ; 60(35): 10901-10913, 2021 Dec 10.
Article in English | MEDLINE | ID: mdl-35200852

ABSTRACT

Three-dimensional (3D) registration plays a pivotal step in augmented reality (AR) systems. Traditional 3D registration methods have the disadvantages of poor accuracy and robustness. This paper proposes a novel registration method, we believe, for AR systems based on the AKAZE and Tanimoto similarity measurement method. In this paper, the image feature points are extracted and matched by combining the AKAZE algorithm and the Tanimoto similarity measurement method. Then, the camera pose is estimated by calculating the constraint relationship of the feature points. Finally, the 3D registration and real-time tracking of the virtual objects are realized by the Lucas-Kanade (LK) optical flow tracking algorithm. We use Tanimoto to determine the similarity of feature points to improve the matching accuracy of the AKAZE algorithm, and this method not only retains the advantages of strong scale adaptation but also has the advantage of high-precision matching. Experiments show that the method proposed in this paper has the benefits of high registration accuracy, low time consumption, and strong robustness. Under the premise of ensuring accuracy, when the marker is rotated or blocked, it can be accurately registered. In addition, when the external environment changes, for example, the light intensity or the size of the parallax, the registration can still be stable.

6.
Opt Express ; 28(10): 14280-14299, 2020 May 11.
Article in English | MEDLINE | ID: mdl-32403470

ABSTRACT

Optical spatial-mode reception has a physical nature quite different from that of the traditional optical power-in-the-bucket (PIB) reception. The former belongs to coherent reception scheme while the latter pertains to incoherent reception scheme. Under weak-turbulence conditions, the statistical correlation between turbulence-impacted optical signals collected by a pair of adjacent spatial-mode receivers is mathematically formulated in terms of a new theoretical framework that takes into account the distinctive nature of the spatial-mode reception. The aperture Fresnel number, coherence Fresnel number, separation Fresnel number and mode Fresnel number are identified as fundamental determinative parameters in evaluation of the correlation coefficient. With the help of the obtained formulations, two analytical asymptotic formulae for the correlation coefficient are further derived under the conditions that the aperture Fresnel number is much smaller than the coherence Fresnel number and separation Fresnel number, respectively. Despite the use of asymptotic approximations in the theoretical derivation, it is found that the two asymptotic formulae indeed have utility in many situations of practical interest to us. Furthermore, Monte-Carlo-simulation-based calculations are carried out to examine the accuracy of employing the two asymptotic formulae to approximate the correlation coefficient. It is shown that the ranges of applicability of these two asymptotic formulae are mainly determined by the coherence Fresnel number and the ratio of the separation Fresnel number to the aperture Fresnel number, basically irrespective of the mode Fresnel number.

7.
Comput Math Methods Med ; 2020: 5487168, 2020.
Article in English | MEDLINE | ID: mdl-32104203

ABSTRACT

Multimodal medical images are useful for observing tissue structure clearly in clinical practice. To integrate multimodal information, multimodal registration is significant. The entropy-based registration applies a structure descriptor set to replace the original multimodal image and compute similarity to express the correlation of images. The accuracy and converging rate of the registration depend on this set. We propose a new method, logarithmic fuzzy entropy function, to compute the descriptor set. It is obvious that the proposed method can increase the upper bound value from log(r) to log(r) + ∆(r) so that a more representative structural descriptor set is formed. The experiment results show that our method has faster converging rate and wider quantified range in multimodal medical images registration.


Subject(s)
Brain/diagnostic imaging , Fuzzy Logic , Image Processing, Computer-Assisted/methods , Multimodal Imaging , Algorithms , Brain Mapping , Entropy , Humans , Image Interpretation, Computer-Assisted/methods , Magnetic Resonance Imaging , Models, Statistical , Neuroimaging , Normal Distribution , Reproducibility of Results , Tomography, X-Ray Computed
8.
Opt Express ; 27(20): 28968-28982, 2019 Sep 30.
Article in English | MEDLINE | ID: mdl-31684639

ABSTRACT

The instantaneous transmission coefficient, i.e., instantaneous transmittance, of a turbulent optical orbital-angular-momentum (OAM) channel is mathematically formulated as a weighted integration and is found to range between 0 and 1. Common probability distribution models for optical irradiance fluctuations with a support from 0 to ∞ are not strictly proper for statistical description of the fluctuating transmission coefficient. The novel dual Johnson S B distribution is proposed to model the statistical behavior of the fluctuating transmission coefficient. Its applicability is verified by making comparisons between the histograms of transmission-coefficient samples generated by Monte Carlo simulations and the corresponding fitted probability density functions; the values for its four independent control parameters under different conditions are obtained by the fit of the dual Johnson S B distribution to relevant simulated transmission-coefficient samples. It is found that each of the four independent control parameters of the dual Johnson S B distribution can be considered as a function of three quantities, viz., the OAM index, the Fried's atmospheric coherence width, and the ratio of the root-mean-square (RMS) OAM-beam radius to the Fried's atmospheric coherence width. The results demonstrate that the statistical distribution of the fluctuating transmission coefficient depends less on the first two quantities than on the last one. Finding a model for direct mapping from these three quantities to the four control parameters of the dual Johnson S B distribution deserves future study.

9.
Biomed Eng Online ; 17(1): 181, 2018 Dec 04.
Article in English | MEDLINE | ID: mdl-30514298

ABSTRACT

BACKGROUND: Imbalanced data classification is an inevitable problem in medical intelligent diagnosis. Most of real-world biomedical datasets are usually along with limited samples and high-dimensional feature. This seriously affects the classification performance of the model and causes erroneous guidance for the diagnosis of diseases. Exploring an effective classification method for imbalanced and limited biomedical dataset is a challenging task. METHODS: In this paper, we propose a novel multilayer extreme learning machine (ELM) classification model combined with dynamic generative adversarial net (GAN) to tackle limited and imbalanced biomedical data. Firstly, principal component analysis is utilized to remove irrelevant and redundant features. Meanwhile, more meaningful pathological features are extracted. After that, dynamic GAN is designed to generate the realistic-looking minority class samples, thereby balancing the class distribution and avoiding overfitting effectively. Finally, a self-adaptive multilayer ELM is proposed to classify the balanced dataset. The analytic expression for the numbers of hidden layer and node is determined by quantitatively establishing the relationship between the change of imbalance ratio and the hyper-parameters of the model. Reducing interactive parameters adjustment makes the classification model more robust. RESULTS: To evaluate the classification performance of the proposed method, numerical experiments are conducted on four real-world biomedical datasets. The proposed method can generate authentic minority class samples and self-adaptively select the optimal parameters of learning model. By comparing with W-ELM, SMOTE-ELM, and H-ELM methods, the quantitative experimental results demonstrate that our method can achieve better classification performance and higher computational efficiency in terms of ROC, AUC, G-mean, and F-measure metrics. CONCLUSIONS: Our study provides an effective solution for imbalanced biomedical data classification under the condition of limited samples and high-dimensional feature. The proposed method could offer a theoretical basis for computer-aided diagnosis. It has the potential to be applied in biomedical clinical practice.


Subject(s)
Biomedical Research , Data Analysis , Machine Learning
10.
Comput Math Methods Med ; 2018: 6213264, 2018.
Article in English | MEDLINE | ID: mdl-30356395

ABSTRACT

To solve the problem of scoliosis recognition without a labeled dataset, an unsupervised method is proposed by combining the cascade gentle AdaBoost (CGAdaBoost) classifier and distance regularized level set evolution (DRLSE). The main idea of the proposed method is to establish the relationship between individual vertebrae and the whole spine with vertebral centroids. Scoliosis recognition can be transferred into automatic vertebral detection and segmentation processes, which can avoid the manual data-labeling processing. In the CGAdaBoost classifier, diversified vertebrae images and multifeature descriptors are considered to generate more discriminative features, thus improving the vertebral detection accuracy. After that, the detected bounding box represents an appropriate initial contour of DRLSE to make the vertebral segmentation more accurate. It is helpful for the elimination of initialization sensitivity and quick convergence of vertebra boundaries. Meanwhile, vertebral centroids are extracted to connect the whole spine, thereby describing the spinal curvature. Different parts of the spine are determined as abnormal or normal in accordance with medical prior knowledge. The experimental results demonstrate that the proposed method cannot only effectively identify scoliosis with unlabeled spine CT images but also have superiority against other state-of-the-art methods.


Subject(s)
Image Processing, Computer-Assisted/methods , Imaging, Three-Dimensional/methods , Scoliosis/diagnostic imaging , Spine/diagnostic imaging , Tomography, X-Ray Computed/methods , Adolescent , Adult , Algorithms , Female , Humans , Male , Middle Aged , Models, Statistical , Pattern Recognition, Automated , Probability , Reproducibility of Results , Young Adult
11.
Opt Express ; 26(13): 16422-16441, 2018 Jun 25.
Article in English | MEDLINE | ID: mdl-30119474

ABSTRACT

Common randomness arising from turbulence-induced signal fading in reciprocal optical wireless channels is a beneficial resource that can be used to generate secret keys shared by two legitimate parties. The concept of optical wireless channels using common-transverse-spatial-mode coupling (CTSMC) that can maintain perfect fading reciprocity in atmospheric turbulence is first developed in a general manner. Subsequently, by performing Monte Carlo simulations, the Johnson SB probability distribution is demonstrated to be appropriate for statistical description of turbulence-induced signal fading in an optical wireless channel constructed by use of two identical CTSMC transceivers, and the nature of correlation between signal fadings detected by two contiguous reception spatial modes is further quantitatively characterized, revealing that rapid spatial decorrelation between signal fadings observed by a legitimate party and an eavesdropper holds for scenarios of practical interest. Finally, the information theoretic capacity for generating secret keys from CTSMC-based optical wireless channels is theoretically formulated and quantitatively examined under different conditions, manifesting that the turbulence strength and average electrical signal-to-noise ratio have a noticeable combined impact on the secret key capacity, especially in the far-field case.

12.
Opt Lett ; 42(23): 4933, 2017 Dec 01.
Article in English | MEDLINE | ID: mdl-29216148

ABSTRACT

This publisher's note corrects a typo in the title in Opt. Lett.38, 1887 (2013)OPLEDP0146-959210.1364/OL.38.001887.

13.
J Opt Soc Am A Opt Image Sci Vis ; 34(11): 2070-2076, 2017 Nov 01.
Article in English | MEDLINE | ID: mdl-29091659

ABSTRACT

The root-mean-square (RMS) bandwidth of temporal light-flux fluctuations is formulated for both plane and spherical waves propagating in the turbulent atmosphere with location-dependent transverse wind. Two path weighting functions characterizing the joint contributions of turbulent eddies and transverse winds at various locations toward the RMS bandwidth are derived. Based on the developed formulations, the roles of variations in both the direction and magnitude of transverse wind velocity with locations over a path on the RMS bandwidth are elucidated. For propagation paths between ground and space, comparisons of the RMS bandwidth computed based on the Bufton wind profile with that calculated by assuming a nominal constant transverse wind velocity are made to exemplify the effect that location dependence of transverse wind velocity has on the RMS bandwidth. Moreover, an expression for the weighted RMS transverse wind velocity has been derived, which can be used as a nominal constant transverse wind velocity over a path for accurately determining the RMS bandwidth.

14.
PLoS One ; 12(9): e0184586, 2017.
Article in English | MEDLINE | ID: mdl-28910349

ABSTRACT

Both symmetric and asymmetric color image encryption have advantages and disadvantages. In order to combine their advantages and try to overcome their disadvantages, chaos synchronization is used to avoid the key transmission for the proposed semi-symmetric image encryption scheme. Our scheme is a hybrid chaotic encryption algorithm, and it consists of a scrambling stage and a diffusion stage. The control law and the update rule of function projective synchronization between the 3-cell quantum cellular neural networks (QCNN) response system and the 6th-order cellular neural network (CNN) drive system are formulated. Since the function projective synchronization is used to synchronize the response system and drive system, Alice and Bob got the key by two different chaotic systems independently and avoid the key transmission by some extra security links, which prevents security key leakage during the transmission. Both numerical simulations and security analyses such as information entropy analysis, differential attack are conducted to verify the feasibility, security, and efficiency of the proposed scheme.


Subject(s)
Image Processing, Computer-Assisted/methods , Algorithms , Color , Entropy , Neural Networks, Computer , Nonlinear Dynamics
15.
Opt Express ; 25(11): 12779-12795, 2017 May 29.
Article in English | MEDLINE | ID: mdl-28786631

ABSTRACT

Expressions for the correlation coefficient between light-flux fluctuations of two waves counter-propagating along a common path in weak turbulence are developed. Only the aperture and inner-scale Fresnel parameters are needed for evaluation of the correlation coefficient if the turbulence spectrum has no path dependence, and of the path weighting functions for the cross-covariance and variances of normalized light-flux fluctuations if the turbulence spectrum is dependent on path locations. Under the condition that atmospheric turbulence is statistically homogeneous over a path, although good correlation between light-flux fluctuations of two counter-propagating spherical waves may be achieved for a relatively small aperture Fresnel parameter or relatively large inner-scale Fresnel parameter, the correlation coefficient between light-flux fluctuations of two counter-propagating plane waves is always lower than 1 obviously. When the aperture Fresnel parameter becomes larger than the inner-scale Fresnel parameter, the inner scale of turbulence tends to play an unimportant role in determining the correlation coefficient.

16.
Opt Express ; 24(17): 19713-27, 2016 Aug 22.
Article in English | MEDLINE | ID: mdl-27557248

ABSTRACT

The changes in the radial content of orbital-angular-momentum (OAM) photonic states described by Laguerre-Gaussian (LG) modes with a radial index of zero, suffering from turbulence-induced distortions, are explored by numerical simulations. For a single-photon field with a given LG mode propagating through weak-to-strong atmospheric turbulence, both the average LG and OAM mode densities are dependent only on two nondimensional parameters, i.e., the Fresnel ratio and coherence-width-to-beam-radius (CWBR) ratio. It is found that atmospheric turbulence causes the radially-adjacent-mode mixing, besides the azimuthally-adjacent-mode mixing, in the propagated photonic states; the former is relatively slighter than the latter. With the same Fresnel ratio, the probabilities that a photon can be found in the zero-index radial mode of intended OAM states in terms of the relative turbulence strength behave very similarly; a smaller Fresnel ratio leads to a slower decrease in the probabilities as the relative turbulence strength increases. A photon can be found in various radial modes with approximately equal probability when the relative turbulence strength turns great enough. The use of a single-mode fiber in OAM measurements can result in photon loss and hence alter the observed transition probability between various OAM states. The bit error probability in OAM-based free-space optical communication systems that transmit photonic modes belonging to the same orthogonal LG basis may depend on what digit is sent.

17.
Opt Express ; 24(7): 6959-75, 2016 Apr 04.
Article in English | MEDLINE | ID: mdl-27136990

ABSTRACT

The radial average-power distribution and normalized average power of orbital-angular-momentum (OAM) modes in a vortex Gaussian beam after passing through weak-to-strong atmospheric turbulence are theoretically formulated. Based on numerical calculations, the role of the intrinsic mode index, initial beam radius and turbulence strength in OAM-mode variations of a propagated vortex Gaussian beam is explored, and the validity of the pure-phase-perturbation approximation employed in existing theoretical studies is examined. Comparison between turbulence-induced OAM-mode scrambling of vortex Gaussian beams and that of either Laguerre-Gaussian (LG) beams or pure vortex beams has been made. Analysis shows that the normalized average power of OAM modes changes with increasing receiver-aperture size until it approaches a nearly stable value. For a receiver-aperture size of practical interest, OAM-mode scrambling is severer with a larger mode index or smaller initial beam radius besides stronger turbulence. Under moderate-to-strong turbulence condition, for two symmetrically-neighboring extrinsic OAM modes, the normalized average power of the one with an index closer to zero may be greater than that of the other one. The validity of the pure-phase-perturbation approximation is determined by the intrinsic mode index, initial beam radius and turbulence strength. It makes sense to jointly control the amplitude and phase of a fundamental Gaussian beam for producing an OAM-carrying beam.

18.
Perception ; 44(3): 232-42, 2015 Mar.
Article in English | MEDLINE | ID: mdl-26562250

ABSTRACT

Sensory information is multimodal; through audiovisual interaction, task-irrelevant auditory stimuli tend to speed response times and increase visual perception accuracy. However, mechanisms underlying these performance enhancements have remained unclear. We hypothesize that task-irrelevant auditory stimuli might provide reliable temporal and spatial cues for visual target discrimination and behavioral response enhancement. Using signal detection theory, the present study investigated the effects of spatiotemporal relationships on auditory facilitation of visual target discrimination. Three experiments were conducted where an auditory stimulus maintained reliable temporal and/or spatial relationships with visual target stimuli. Results showed that perception sensitivity (d') to visual target stimuli was enhanced only when a task-irrelevant auditory stimulus maintained reliable spatiotemporal relationships with a visual target stimulus. When only reliable spatial or temporal information was contained, perception sensitivity was not enhanced. These results suggest that reliable spatiotemporal relationships between visual and auditory signals are required for audiovisual integration during a visual discrimination task, most likely due to a spread of attention. These results also indicate that auditory facilitation of visual target discrimination follows from late-stage cognitive processes rather than early stage sensory processes.


Subject(s)
Auditory Perception/physiology , Signal Detection, Psychological/physiology , Space Perception/physiology , Time Perception/physiology , Visual Perception/physiology , Adult , Humans , Male , Young Adult
19.
Opt Express ; 23(19): 24657-68, 2015 Sep 21.
Article in English | MEDLINE | ID: mdl-26406667

ABSTRACT

The mean-square angle-of-arrival (AOA) difference between two counter-propagating spherical waves in atmospheric turbulence is theoretically formulated. Closed-form expressions for the path weighting functions are obtained. It is found that the diffraction and refraction effects of turbulent cells make negative and positive contributions to the mean-square AOA difference, respectively, and the turbulent cells located at the midpoint of the propagation path have no contributions to the mean-square AOA difference. If the mean-square AOA difference is separated into the refraction and diffraction parts, the refraction part always dominates the diffraction one, and the ratio of the diffraction part to the refraction one is never larger than 0.5 for any turbulence spectrum. Based on the expressions for the mean-square AOA difference, formulae for the correlation coefficient between the angles of arrival of two counter-propagating spherical waves in atmospheric turbulence are derived. Numerical calculations are carried out by considering that the turbulence spectrum has no path dependence. It is shown that the mean-square AOA difference always approximates to the variance of AOA fluctuations. It is found that the correlation coefficient between the angles of arrival in the x or y direction of two counter-propagating spherical waves ranges from 0.46 to 0.5, implying that the instantaneous angles of arrival of two counter-propagating spherical waves in atmospheric turbulence are far from being perfectly correlated even when the turbulence spectrum does not vary along the path.

20.
Appl Opt ; 54(18): 5797-804, 2015 Jun 20.
Article in English | MEDLINE | ID: mdl-26193032

ABSTRACT

A theoretical formulation of the spherical-wave two-frequency mutual coherence function (MCF) for a propagation path characterized by a complex ABCD matrix with anisotropic atmospheric turbulence existing somewhere is developed. A specialization of this formulation leads to an expression for the two-frequency MCF of an equivalent pulsed Gaussian beam propagating in weak anisotropic atmospheric turbulence along a horizontal line-of-sight path; relevant closed-form analytical solutions under both near- and far-field conditions are obtained. The small- and large-scale solutions for both the plane- and spherical-wave spatial-coherence radii in either horizontal or vertical direction are derived. Analysis shows that the formula for the on-axis two-frequency MCF of a pulsed Gaussian beam under the weak-turbulence condition in both the near- and far-field regions is distinguished from that applicable in the strong-turbulence limit only by whether the turbulence-induced beam broadening can be thought of as negligible. Under both the near- and far-field conditions, the turbulence-induced increment of the mean-square temporal-pulse half-width is proportional to the effective anisotropy factor of turbulence. The MCF becomes statistically anisotropic due to the anisotropy of turbulence. For the spatial coherence radius of either a plane or spherical wave propagating along a horizontal line-of-sight path in anisotropic atmospheric turbulence, the corresponding small-scale solution is proportional to that for the plane-wave spatial-coherence radius in the isotropic-turbulence case with a proportionality coefficient depending only on the effective anisotropy factor of turbulence. The corresponding large-scale solution is proportional to that for the plane-wave spatial-coherence radius in the isotropic-turbulence case with a proportionality coefficient that depends on both the effective anisotropy factor and spectral index of turbulence.

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