Atmospheric Coherence Length Research Articles

Correction performance estimation of atmospheric turbulence based on eigenmode method

An eigenmode method is proposed to estimate the correction performance of atmospheric turbulence based on a deformable mirror (DM). On the basis of the eigenmode, a formula that describes the relationship among residual error, eigenmode N, and turbulence strength D/r0 (D, telescope aperture, r0, atmospheric coherence length) is derived. The eigenmode and the Zernike polynomial methods are compared, too. An experiment is conducted, and results validate the theoretical equations. Hence, the correction performance of atmospheric turbulence may be estimated with the eigenmode method. This result is helpful for conveniently designing and evaluating the adaptive optics system used for turbulence correction.

西安地区大气相干长度的实验测量及分析

西安地区大气相干长度的实验测量及分析

An Improved Method of Measuring Wavefront Aberration Based on Image with Machine Learning in Free Space Optical Communication.

In this paper, an improved method of measuring wavefront aberration based on image with machine learning is proposed. This method had better real-time performance and higher estimation accuracy in free space optical communication in cases of strong atmospheric turbulence. We demonstrated that the network we optimized could use the point spread functions (PSFs) at a defocused plane to calculate the corresponding Zernike coefficients accurately. The computation time of the network was about 6–7 ms and the root-mean-square (RMS) wavefront error (WFE) between reconstruction and input was, on average, within 0.1263 waves in the situation of D/r0 = 20 in simulation, where D was the telescope diameter and r0 was the atmospheric coherent length. Adequate simulations and experiments were carried out to indicate the effectiveness and accuracy of the proposed method.

Performance improvement of free-space continuous-variable quantum key distribution with an adaptive optics unit

We propose a method to enhance the performance of the free-space continuous-variable quantum key distribution (FSCVQKD) by utilizing an adaptive optics (AO) unit at the receiver’s side to suppress wavefront distortions caused by high-order wavefront aberrations for fault-tolerant detection. Benefiting from the AO unit, the high-order wavefront aberrations can be corrected and thus effectively improve the mixing efficiency of homodyne detection, which enhances the performance of FSCVQKD. Considering the fact that the closed-loop control bandwidth of AO unit and the atmospheric coherence length have an important effect in performance improvement for FSCVQKD, in this paper, we analyze the performance of our protocol with AO unit under different closed-loop control bandwidths and atmospheric coherence lengths, respectively. The analysis is performed by considering the three specific scenarios of turbulence which are frequent challenges in FSCVQKD protocol, namely beam wandering, randomly blocked and log-normal distribution. In addition, we also study the impact of AO-added noise on our protocol. Simulation results show that all in the beam wandering case, the randomly blocked case and the log-normal distribution, the use of AO unit can enhance the performance of FSCVQKD protocol by adjusting the closed-loop control bandwidth of AO unit and the atmospheric coherence length in appropriate ranges with the case of fixed Greenwood frequency in the presence of AO-added noise.

Modulation transfer function of an imaging system with a hexagonal pixel array detector

The modulation transfer function (MTF) is the tool most commonly used for quantifying the performance of an electro-optical imaging system. Hexagonal sampling strategy for detector arrays can provide an improvement over rectangular sampling, thus the hexagonal pixel array detector is designed with hexagonal pixel and hexagonal sampling. In this paper, firstly, two dimensional MTF model of a hexagonal pixel array detector is deduced according to its definition. Then, the MTF of an imaging system with such a detector is established. Additionally, the MTFs of detectors with other shaped pixel geometry, but with the same photosensitive areas are compared. The results show that the values of hexagonal MTF are obviously larger than those of rectangular and triangular pixel array detectors at the same frequencies. In addition, with the increase of the atmospheric coherence length, the MTF values of the system become larger, and the system imaging capability will be improved.

Performance enhancement of free-space optical communications under atmospheric turbulence using modes diversity coherent receipt.

This paper numerically and experimentally investigates the performance of free-space optical receiver using modes diversity coherent receipt under moderate-to-strong turbulence. By utilizing a three-mode photonic lantern with digital maximum ratio combining, a 40 Gbps QPSK optical signal is received. The turbulence strength is measured by the ratio of beam diameter to atmospheric coherence length, D/r0. The larger the D/r0, the stronger the turbulence is, and vice versa. Compared with conventional single mode fiber based receipt, the required transmitted power can reduce by 4.6 dB and 4 dB at 10% interruption probability under turbulence strength D/r0 = 8 and 16. The required transmitted power at bit error ratio of 2.2 × 10-2 can relax by 4.2 dB and 5 dB under turbulence strength D/r0 = 8 and 16.

Analysis of aiming performance limitation for an optical system in atmospheric turbulence

In an optical system that is transmitting a laser beam through the atmosphere by phase compensation with adaptive optics, the aiming performance depends on the method of wavefront tilt detection, which can be divided into Zernike tilt detection and gradient tilt detection. A unified formulation for both methods is obtained to calculate the residual tilt angle jitter and tilt correction factor, which are defined as the evaluation indexes of the aiming performance. A parameter L0 called the equivalent atmospheric coherence length is expressed as an integral over the structure constant profile of the refraction index and is modulated by a modulation function that is determined by the ratio of the offset distance to the aperture. As a result, the tilt correction factor can be represented as (r0/L0)5/6, where r0 is the atmospheric coherence length. Simulations illustrate that the aiming performance of an optical system based on gradient tilt detection is better than that of Zernike tilt detection under identical conditions. For the two types of system, the aiming performance will be decreased as the ratio of the offset distance to the aperture increases and the atmospheric conditions worsen.

An evaluation algorithm of turbulent influence based on phase screen model

In this paper, a novel evaluation algorithm of turbulent influence is presented for influence investigation of Gaussian beam and Airy beams in atmospheric turbulence, in which a parameter to quantify the influence of turbulence is proposed and named by Intensity Variation Index. The algorithm is beneficial to analyze the distortion caused by the atmosphere. The effects of wavelength, channel condition, and the type of beams are simulated. The results show that the Intensity Variation Index of Gaussian is dually affected by atmospheric coherence length and wavelength, furthermore, the change trend is similar to the scintillation index, which shows the correctness of proposed algorithm. Meanwhile, Airy beams also affected by two factors. After performance comparison, the turbulence effect of Airy beams is greater than that of the Gaussian beam and the reason is the loss of Airy beams’ side lobes during transmission in turbulent flow. The proposed evaluation algorithm can evaluate the effects of turbulence and can accurately represent the affected trends of the beam under different conditions.

Fundamental performance of transverse wind estimator from Shack-Hartmann wave-front sensor measurements.

Real time transverse wind estimation contributes to predictive correction which is used to compensate for the time delay error in the control systems of adaptive optics (AO) system. Many methods that apply Shack-Hartmann wave-front sensor to wind profile measurement have been proposed. One of the obvious problems is the lack of a fundamental benchmark to compare the various methods. In this work, we present the fundamental performance limits for transverse wind estimator from Shack-Hartmann wave-front sensor measurements using Cramér-Rao lower bound (CRLB). The bound provides insight into the nature of the transverse wind estimation, thereby suggesting how to design and improve the estimator in the different application scenario. We analyze the theoretical bound and find that factors such as slope measurement noise, wind velocity and atmospheric coherence length r0 have important influence on the performance. Then, we introduced the non-iterative gradient-based transverse wind estimator. The source of the deterministic bias of the gradient-based transverse wind estimators is analyzed for the first time. Finally, we derived biased CRLB for the gradient-based transverse wind estimators from Shack-Hartmann wave-front sensor measurements and the bound can predict the performance of estimator more accurately.

Performance analysis of an adaptive optics system for free-space optics communication through atmospheric turbulence

The performance of free-space optics communication (FSOC) is greatly degraded by atmospheric turbulence. Adaptive optics (AO) is an effective method for attenuating the influence. In this paper, the influence of the spatial and temporal characteristics of turbulence on the performance of AO in a FSOC system is investigated. Based on the Greenwood frequency (GF) and the ratio of receiver aperture diameter to atmospheric coherent length (D/r0), the relationship between FSOC performance (CE) and AO parameters (corrected Zernike modes number and bandwidth) is derived for the first time. Then, simulations and experiments are conducted to analyze the influence of AO parameters on FSOC performance under different GF and D/r0. The simulation and experimental results show that, for common turbulence conditions, the number of corrected Zernike modes can be fixed at 35 and the bandwidth of the AO system should be larger than the GF. Measurements of the bit error rate (BER) for moderate turbulence conditions (D/r0 = 10, fG = 60 Hz) show that when the bandwidth is two times that of GF, the average BER is decreased by two orders of magnitude compared with fG/f3dB = 1. These results and conclusions can provide important guidance in the design of an AO system for FSOC.

Numerical calculation and discussion on return photons of polychromatic laser guide stars by a laser beam with 330 nm wavelength

The properties of return photons of polychromatic laser guide stars excited by a modeless laser with 330 nm wavelength are investigated in this paper by numerical simulation. The repetition rate, linewidth, initial diameter of laser spot and atmospheric transmittance have great influences on the return photons at 330 nm and 2207 nm from polychromatic laser guide stars. First, the laser linewidth is optimized by solving the rate equations of interaction between laser and sodium atoms. We find that the 0.6 GHz linewidth for the continuous wave laser and the 1.0 GHz linewidth for the pulse laser are beneficial to obtaining the higher excited probability of sodium atoms. Based on the fitted relation between the excitation probability of sodium atoms and laser intensity, considering the random distributions of laser intensity at the mesosphere due to the influence of atmospheric turbulence, the return photons from polychromatic laser guide stars are numerically calculated. The results show that the return photons at 330 nm excited by the continuous-wave laser are more than those excited by the pulse laser. And the return photons excited by continuous-wave laser almost do not fluctuate when laser power arriving at sodium layer is 1 W. Furthermore, effects of the repetition rate of pulse laser and the laser initial diameter on the return photons at 330 nm are studied. The two results are obtained as follows. The first result is that the increment of return photons at 330 nm will converge to a constant value when the repetition rate of pulse laser is over 50 kHz. The second result is that the initial diameter of continuous wave laser has no effect on the return photons but the effect of pulse laser is more obvious. Particularly, the atmospheric transmittance is an important factor of influence because it causes a severe loss of light power at 330 nm wavelength. Under the conditions of 5 km atmospheric visibility and 12.8 cm atmospheric turbulence coherence length, the launched power of pulse laser with 50 ns duration should be more than 34 W for obtaining enough return photons required for the effective detection of atmospheric turbulence tip-tilt with the natural stars. But for the continuous-wave laser, the launched power should be more than 20 W. In the case of 10 km atmospheric visibility, if the same return photons at 330 nm are required, the launched power of pulse laser will also be more than that of the continuous-wave laser under the same conditions. Therefore, the continuous-wave laser has more advantages than the pulse laser in exciting the polychromatic laser guide stars. We hope that the above results will be beneficial to the further experimental research.

A New CMTF Evaluation Model for Dynamic Target in Photoelectric Imaging System

To evaluate the reliability of photoelectric imaging system, it is essential to research the influences of the illumination contrast and the modulation transfer functions (MTF) to the system imaging capability. This paper deduces a new illumination contrast model based on the optical geometry structure and the optical reflection characteristics of dynamic target; according to the photoelectric imaging principle, defines the system’s MTF by the form of some imaging links, including the optical characteristics, the CCD detector, and the atmospheric characteristics; establishes a new contrast modulation transfer functions (CMTF) mathematical model based on the analysis of the illumination contrast and MTF; obtains the expression of magnitude to evaluate the effects of some key factors to imaging capability. Through the calculation and analysis, under various conditions, with the increasing of target reflectivity, relative aperture, atmospheric coherence length, and optical transmittance, the system imaging capability shows a general trend of rising; with the increasing of background radiation illumination, target distance, standard deviation, and the system imaging capability shows attenuation trend; the results show that different factors have a great impact on the imaging capability, which proves the suitability of CMTF model for evaluating the performance photoelectric system.

Performance analysis of a coherent free space optical communication system based on experiment

Based on our previous study and designed experimental AO system with a 97-element continuous surface deformable mirror, we conduct the performance analysis of a coherent free space optical communication (FSOC) system for mixing efficiency (ME), bit error rate (BER) and outage probability under different Greenwood frequency and atmospheric coherent length. The results show that the influence of the atmospheric temporal characteristics on the performance is slightly stronger than that of the spatial characteristics when the receiving aperture and the number of sub-apertures are given. This analysis result provides a reference for the design of the coherent FSOC system.

Advancement of adaptive optics in astronomical observation

Adaptive optics is used to compensate the atmospheric turbulence aberration for diffractive limit images, which makes the angular resolution of large aperture telescope not limited by the seeing or atmospheric coherence length. The continuous improvements of wavefront sensing, correctors and enlarged FOV for adaptive optics accelerate the development of astronomy. The main adaptive optics techniques include classical FOV and high resolution astronomical observation, extro-planet observation and solar observations and so on. And they have different technique requirements for adaptive optics. In the paper, we give some summarization and expectation of the advancement in the above three fields, especially in some new elemental techniques in detail, which will be helpful for our national adaptive optics development in large aperture telescopes.

Linearization theory of small scale thermal blooming effect in non-Kolmogorov turbulent atmosphere

High energy laser beams propagating in the atmosphere are subjected to a variety of effects, such as the absorption and scattering of molecule and aerosol, atmospheric turbulence effects, thermal blooming effects, and the interaction between turbulence and thermal blooming. In general, these atmospheric propagation effects degrade laser beam quality and reduce the beam power concentration at the target. With adaptive optics compensation, the beam quality can be modified. But small-scale perturbation has developed and the phase compensation becomes unstable in some conditions. The performance of adaptive-optics system is degraded, which effects can be well explained by small-scale linear theory of thermal blooming. However previous theoretical studies of small-scale thermal blooming focused on the Kolmogorov turbulence. In the past decade, experimental evidence has shown significant deviations from Kolmogorov model in certain portions of the atmosphere. An generalized power-law of non-Kolmogorov turbulence model has been introduced, which becomes quite popular in the optical propagation community. Numerous theoretical and developmental efforts have been made based on non-Kolmogorov turbulence model in recent years. Thus it is very meaningful and imperative to explore the theoretical mechanism of high energy laser phase compensation with non-Kolmogorov turbulence.In this study, the Strehl ratio of the thermal blooming phase compensation is generalized with the non-Kolmogorov turbulence spectrum, and the analytical expression is obtained based on the linear theory of small-scale thermal blooming. The influence of the turbulence spectrum on the phase compensation of the high energy laser is analyzed. The results show that the turbulence spectrum has an important influence on the phase compensation of turbulent thermal blooming effect. Under the same turbulence Fresnel number condition, the compensation effect is worse when the spectral index is closer to 3 and the compensation effect is better when the spectral index is close to 4. Under the same atmospheric coherence length condition or under the same turbulence refractive index constant condition, the Strehl ratio decreases with the increase of the thermal blooming effect when the spectral index is close to 3 and the decline rate of the Strehl ratio is slower when the turbulence spectrum index is close to 4. This is because as the turbulence spectrum exponent increases, the logarithmic amplitude fluctuation slows down due to the interaction between turbulence and thermal blooming. These theoretical results can provide some scientific bases and theoretical guidance for the practical applications of high energy laser transmission.

Efficiency analysis of homodyne detection for a coherent lidar with adaptive optics

For a coherent lidar, the efficiency of homodyne detection is a significant factor. Adaptive optics (AO) is an effective way to correct the turbulence-induced wavefront distortions. Based on our previous works, an expression for the homodyne detection efficiency is given. The results of the numerical simulation show that the atmospheric coherent length has an influence on the homodyne detection efficiency for a fixed atmospheric Greenwood frequency and a closed-loop control bandwidth. In addition, an experimental AO system is employed to verify the effect of the AO on the coherent lidar. The results show that the homodyne detection efficiency is obviously improved after aberrations are corrected. The conclusion of this paper provides a reference for designing an AO system for a coherent lidar.

Field experiment and image reconstruction using a Fourier telescopy imaging system over a 600-m-long horizontal path.

To confirm the effect of uplink atmospheric turbulence on Fourier telescopy (FT), we designed a system for far-field imaging, utilizing a T-type laser transmitting configuration with commercially available hardware, except for a green imaging laser. The horizontal light transmission distance for both uplink and downlink was ∼300 m. For both the transmitting and received beams, the height upon the ground was below 1 m. The imaging laser's pointing accuracy was ∼9.3 μrad. A novel image reconstruction approach was proposed, yielding significantly improved quality and Strehl ratio of reconstructed images. From the reconstruction result, we observed that the tip/tilt aberration is tolerated by the FT system even for Changchun's atmospheric coherence length parameter (r0) below 3 cm. The resolution of the reconstructed images was ∼0.615 μrad.

Spatial light coupled into a single-mode fiber by a Maksutov-Cassegrain antenna through atmospheric turbulence.

Maksutov-Cassegrains are widely used in free-space optical communication. The coupling efficiency and variance of a Maksutov-Cassegrain fiber (single-mode) system distorted by atmospheric turbulence are numerically evaluated using second-order and fourth-order moments under a Von Karman spectrum. Considering the limited cost and size of the equipment, the Maksutov-Cassegrain aperture should satisfy DA/ρS≈7 (ρS approximates the characteristic atmospheric coherence length), and the obscuration ratio should be no more than 0.2.

Theoretical and experimental study of atmospheric turbulence measurement using two-aperture differential scintillation method

We report the basic theory and first horizontal results of a method called two-aperture differential scintillation method which is aimed at monitoring the vertical profile of atmospheric optical turbulence strength. The method is based on irradiance fluctuation of active light source, but can extract the optical turbulence information in the single-passage path. In this paper, the theoretical principle of two-aperture differential scintillation method is derived in detail. A concise expression is proposed for irradiance fluctuation structure function with differential aperture in the Rytov approximation under a weak fluctuation regime based on the cross-path theory. The mathematic relationship between irradiance fluctuation structure function and atmospheric optical turbulence strength is then developed. The effects of beacon aperture and beacon altitude on path weighting function of this method are analyzed for Kolmogorov turbulence. In order to test the validity of the new method, the experiments are conducted to compare the two-aperture differential scintillation method and single-aperture scintillation method in atmospheric boundary layer over 2 km horizontal single-passage path. In this arrangement, we employ a differential image motion monitor system to measure differential scintillation. Simultaneously, a large aperture scintillation instrument is placed 5 m away at the same altitude to measure the single-aperture scintillation. It is shown that the results of atmospheric refractive index structure constant deduced from the two methods are in good agreement. The measurements of atmospheric coherence length for spherical wave corresponding to the two methods indicate a linear correction factor (R2) of 0.96, in a slope of 0.98 with an offset of -0.09 cm. Feasibility and effectiveness of two-aperture differential scintillation method are thus verified experimentally. The novel method can separate single-passage scintillation information of active beacon double-passage propagation, thereby providing an accurate technique for measuring the atmospheric turbulence of active beacon.

大气相干长度的瞬时测量

大气相干长度的瞬时测量