Information propagation of focus wave mode localized waves in anisotropic turbulent seawater.

The evolution of the information transfer capability of an optical system for underwater focused wave mode localized wave (FWMLW) in anisotropic weakly turbulent absorbing seawater is studied. By developing the probability distribution function as well as the detection probability of the vortex modes carried by the FWMLW and the average bit error rate of the FWMLW underwater system, the information capacity of the FWMLW system with a pointing error is modeled. Through a numerical analysis of the effects of turbulent seawater and optical system parameters on the built light intensity, the detection probability, and the information capacity models, we find that the FWMLW system has an optimal delay time determined by the spectrum bandwidth when the spectrum bandwidth is greater than 1. The information capacity of the FWMLW system is higher than that of the X localized wave system under the same turbulent seawater channel condition, and FWMLW is a better optical signal source for vortex mode division multiplexing underwater systems than a Bessel-Gaussian beam.

High-bandwidth tilt-tip mirror with octagonal prism flexible mechanism.

The adaptive optical system requires a tilt-tip mirror (TTM) with high bandwidth to compensate for optical beam jitter caused by atmospheric turbulence in real time. This paper introduces a novel, to the best of our knowledge, design of a voice coil TTM using an octagonal flexible mechanism and optimizes its parameters through theoretical analysis and finite element simulations. The results show that its resonance frequency in the non-working direction is up to 1005.2 Hz, representing a 19.4% improvement in theoretical calculations and a 13.8% improvement in simulations compared to traditional cylindrical flexible mechanisms. Additionally, the non-working direction stiffness of the flexible support structure has been optimized, enhancing the third-order and higher resonance frequencies of the system to meet the high bandwidth requirements. A prototype of the TTM was developed based on this design, and its deflection angles and responses were measured in the laboratory, confirming the design's reliability. This low-cost, high-bandwidth TTM design facilitates miniaturization of adaptive optical systems, making it beneficial for applications in astronomical observations, laser communication, laser weapons, laser processing, and more.

High-precision calculation and experiments on the thermal blooming of high-energy lasers.

Thermal blooming (TB) is one of the important factors affecting the quality of high-energy laser beams. Reasonable simulation of thermal blooming is important to the application of a high-energy laser. However, reported investigations on TB simulation are mainly based on one method, such as the perturbation method or the phase screen method, which often leads to obvious errors in some conditions. In the paper, the reasonable ranges of optical generalized distortion parameters for both methods are determined based on the reported experimental data, which solves the problem of accurate TB simulations for the first time. In addition, the dynamic effect of thermal blooming is also calculated. Finally, the formula method is presented to extract the phase of thermal blooming distortion. We then use LC-SLM (Liquid crystal spatial light modulator) to emulate thermal blooming effect in the lab. The experimental results are more consistent with the numerical simulation results than conventional phase extraction methods. Our work provides a quantitatively and programmable way to accurately simulate TB with LC-SLM in the lab.

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

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

Bit-error rate and average capacity of an absorbent and turbulent underwater wireless communication link with perfect Laguerre-Gauss beam.

The proper selection of signal source structure and parameters is one of the effective methods to suppress the random disturbance of underwater channel and enhance the performance of link communication. In this paper, the bit error probability and average capacity of a weakly turbulent absorbing seawater link with a perfect Laguerre-Gaussian beam are studied. The bit error rate of orbital angular momentum (OAM) channel under on-off key modulation is derived. The average capacity model of the optical wireless communication link is established on the basis that the OAM channel formed by vortex carrier of topological charge m is symmetric channel. The relationship between OAM channel capacity, carrier wavelength and seawater absorption is numerically analyzed by seawater spectral absorption coefficient, and it is concluded that in the range of "window transmission wavelength" and long channel, the conclusion of the longer signal source wavelength is beneficial to the performance of non-absorptive turbulent channel is no longer valid. Some other numerical results are worked out to show that the underwater communication link with perfect Laguerre-Gaussian beam can obtain high channel capacity by adopting low OAM topological charge, smaller aperture of transmitter as well as receiver.

Wander and spread of a perfect Laguerre-Gauss beam under turbulent absorbent seawater.

The wander and long-term spread of a beam caused by turbulence are two important factors affecting channel targeting and information receiving in optics communication systems. In this paper, the wander and long-term spread of a perfect Laguerre-Gauss (PLG)/circular perfect Laguerre-Gauss (CPLG) beam in turbulent absorbing seawater are studied. The analytical expression of the wander for a CPLG beam in the weak turbulent fluctuation region and the analytical expression of the long-term spread for a CPLG beam in a weak to strong turbulent fluctuation region are derived by using the Rytov approximation and the generalized Huygens-Fresnel integral, respectively. Through numerical analysis, we find that the optimal beam diameter and self-convergence effect of the PLG beam exist under given communication link conditions, the long-term spread of PLG beam is smaller than that of the LG beam, but the wander evolution trend of the PLG beam with increasing propagation distance is opposite to that of the LG beam. PLG and CPLG beams have stronger resistance disturbance of turbulence than that of Laguerre-Gauss and circular Laguerre-Gauss beams, respectively.

Mapping Local Climate Zones in the Urban Environment: The Optimal Combination of Data Source and Classifier.

The novel concept of local climate zones (LCZs) provides a consistent classification framework for studies of the urban thermal environment. However, the development of urban climate science is severely hampered by the lack of high-resolution data to map LCZs. Using Gaofen-6 and Sentinel-1/2 as data sources, this study designed four schemes using convolutional neural network (CNN) and random forest (RF) classifiers, respectively, to demonstrate the potential of high-resolution images in LCZ mapping and evaluate the optimal combination of different data sources and classifiers. The results showed that the combination of GF-6 and CNN (S3) was considered the best LCZ classification scheme for urban areas, with OA and kappa coefficients of 85.9% and 0.842, respectively. The accuracy of urban building categories is above 80%, and the F1 score for each category is the highest, except for LCZ1 and LCZ5, where there is a small amount of confusion. The Sentinel-1/2-based RF classifier (S2) was second only to S3 and superior to the combination of GF-6 and random forest (S1), with OA and kappa coefficients of 64.4% and 0.612, respectively. The Sentinel-1/2 and CNN (S4) combination has the worst classification result, with an OA of only 39.9%. The LCZ classification map based on S3 shows that the urban building categories in Xi'an are mainly distributed within the second ring, while heavy industrial buildings have started to appear in the third ring. The urban periphery is mainly vegetated and bare land. In conclusion, CNN has the best application effect in the LCZ mapping task of high-resolution remote sensing images. In contrast, the random forest algorithm has better robustness in the band-abundant Sentinel data.

Received probability of perfect optical vortex in absorbent and weak turbulent seawater links.

We investigated the effects of absorbent and weak turbulent seawater channels on the orbital angular momentum (OAM) mode carried by perfect optical vortex (POV) based on the Rytov approximation. After deriving the received probability of OAM modes, some numerical results are worked out to show that the receiving probability of OAM modes decreases linearly with the increase of virtual refractive index of the water body. An underwater communication link with POV as the signal carrier can obtain high receiving probability by adopting long signal wavelength in intervals of "seawater window wavelength," low OAM quantum number, a POV with a larger ring radius, and a transmitter as well as receiver with a smaller aperture. The transmission distance of OAM mode carried by POV in four kinds of seawater is better than that of a Bessel-Gaussian beam.

Multiple-image optical encryption based on phase retrieval algorithm and fractional Talbot effect.

A new multiple-image optical encryption scheme based on phase retrieval algorithm and fractional Talbot effect is proposed. In encryption process, by using Fresnel domain phase retrieval algorithm, each image is encoded into a pure phase distribution with different spatial constraints. The spatial constraints are chosen as complementary square aperture array. A Talbot illuminator is designed according to the fractional Talbot effect, which is treated as a decoder to obtain the designed square aperture array. Then all obtained phase distributions are combined into the final ciphertext image. In decryption process, the images can be decoded from the ciphertext by using the Talbot illuminator and keys. Benefit from the use of fractional Talbot effect, the demultiplexing setup of the cryptosystem is very simple and straightforward, with no need of lens. The simulation results prove that the multiplexing capability is considerably enhanced. At the same time, the security analysis proves that the system can resist various attacks.

Precise calibration of pupil images in pyramid wavefront sensor.

The pyramid wavefront sensor (PWFS) is a novel wavefront sensor with several inspiring advantages compared with Shack-Hartmann wavefront sensors. The PWFS uses four pupil images to calculate the local tilt of the incoming wavefront. Pupil images are conjugated with a telescope pupil so that each pixel in the pupil image is diffraction-limited by the telescope pupil diameter, thus the sensing error of the PWFS is much lower than that of the Shack-Hartmann sensor and is related to the extraction and alignment accuracy of pupil images. However, precise extraction of these images is difficult to conduct in practice. Aiming at improving the sensing accuracy, we analyzed the physical model of calibration of a PWFS and put forward an extraction algorithm. The process was verified via a closed-loop correction experiment. The results showed that the sensing accuracy of the PWFS increased after applying the calibration and extraction method.

More Zernike modes' open-loop measurement in the sub-aperture of the Shack-Hartmann wavefront sensor.

The centroid-based Shack-Hartmann wavefront sensor (SHWFS) treats the sampled wavefronts in the sub-apertures as planes, and the slopes of the sub-wavefronts are used to reconstruct the whole pupil wavefront. The problem is that the centroid method may fail to sense the high-order modes for strong turbulences, decreasing the precision of the whole pupil wavefront reconstruction. To solve this problem, we propose a sub-wavefront estimation method for SHWFS based on the focal plane sensing technique, by which more Zernike modes than the two slopes can be sensed in each sub-aperture. In this paper, the effects on the sub-wavefront estimation method of the related parameters, such as the spot size, the phase offset with its set amplitude and the pixels number in each sub-aperture, are analyzed and these parameters are optimized to achieve high efficiency. After the optimization, open-loop measurement is realized. For the sub-wavefront sensing, we achieve a large linearity range of 3.0 rad RMS for Zernike modes Z2 and Z3, and 2.0 rad RMS for Zernike modes Z4 to Z6 when the pixel number does not exceed 8 × 8 in each sub-aperture. The whole pupil wavefront reconstruction with the modified SHWFS is realized to analyze the improvements brought by the optimized sub-wavefront estimation method. Sixty-five Zernike modes can be reconstructed with a modified SHWFS containing only 7 × 7 sub-apertures, which could reconstruct only 35 modes by the centroid method, and the mean RMS errors of the residual phases are less than 0.2 rad2, which is lower than the 0.35 rad2 by the centroid method.

Wavefront detection method of a single-sensor based adaptive optics system.

In adaptive optics system (AOS) for optical telescopes, the reported wavefront sensing strategy consists of two parts: a specific sensor for tip-tilt (TT) detection and another wavefront sensor for other distortions detection. Thus, a part of incident light has to be used for TT detection, which decreases the light energy used by wavefront sensor and eventually reduces the precision of wavefront correction. In this paper, a single Shack-Hartmann wavefront sensor based wavefront measurement method is presented for both large amplitude TT and other distortions' measurement. Experiments were performed for testing the presented wavefront method and validating the wavefront detection and correction ability of the single-sensor based AOS. With adaptive correction, the root-mean-square of residual TT was less than 0.2 λ, and a clear image was obtained in the lab. Equipped on a 1.23-meter optical telescope, the binary stars with angle distance of 0.6″ were clearly resolved using the AOS. This wavefront measurement method removes the separate TT sensor, which not only simplifies the AOS but also saves light energy for subsequent wavefront sensing and imaging, and eventually improves the detection and imaging capability of the AOS.

Simple and robust algorithm to extend the dynamic range of tip-tilt for a Shack-Hartmann sensor.

We propose an algorithm to extend the dynamic range of tip-tilt (TT) for a Shack-Hartmann wave-front sensor. With this method, the dynamic range of TT is determined by the size of the whole CCD pixel array rather than the size of the sub-aperture. Thus the separate TT sensor in adaptive optics (AO) systems for optical telescope can be saved, which will simplify the systems and enhance the light energy efficiency. The proposed algorithm is computationally effective and appropriate for the real-time TT computation of AO systems. The simulated and experimental results show that the algorithm is robust to realistic scintillation and photon noise and can work well under poor observing conditions. For the given condition with r0 of 5 cm at 550 nm and average flux of 100 photons per sub-aperture, the ultimate measurement accuracy of TT is about 5% pixels (peak-to-valley value).

Time delay compensation method for tip-tilt control in adaptive optics system.

The time delay engendered by wavefront sampling and data processing inevitability exists in almost all the wavefront sensor (WFS) based adaptive optics (AO) systems. Also, when WFS is used for tip-tilt aberration detection, the time delay significantly reduces the tip-tilt correction performance of the AO system. In this paper, we focus on researching time delay in a tip-tilt (TT) control system and introduce a predicted signal compensation method (PSCM) to compensate the time delay by modifying the WFS detected signals. Based on a precise model of a TT dynamic control system, the detection delay of TT corrections included in a WFS detected signal can be compensated. Experiments are conducted in the lab: the pure integrator (I), proportional and integral (PI) wavefront TT controllers, and these controllers with PSCM are compared to test the efficiency of the PSCM for TT corrections. For the PI controller, the rejection bandwidth increases from 52 to 62 Hz by using PCSM; meanwhile, the open-loop phase margin increases from 45 to 60 deg. In addition, astronomical observation results are also given based on the PI wavefront TT controller. The PSCM improves the Strehl ratio by a factor of 1.3. The new method is proven to improve the AO system closed-loop performance not only for increasing the closed-loop rejection bandwidth but also in favor of the error attenuation at low frequency. Furthermore, the method does not introduce more noise to the system.

Improve the accuracy of interaction matrix measurement for liquid-crystal adaptive optics systems.

We present a novel method to measure the interaction matrix of liquid-crystal adaptive optics systems, by applying least squares method to mitigate the impact of measurement noise. Experimental results showed a dramatic gain in the accuracy of interaction matrix, and a considerable improvement in image resolution with open loop adaptive optics correction.

Optimal energy-splitting method for an open-loop liquid crystal adaptive optics system.

A waveband-splitting method is proposed for open-loop liquid crystal adaptive optics systems (LC AOSs). The proposed method extends the working waveband, splits energy flexibly, and improves detection capability. Simulated analysis is performed for a waveband in the range of 350 nm to 950 nm. The results show that the optimal energy split is 7:3 for the wavefront sensor (WFS) and for the imaging camera with the waveband split into 350 nm to 700 nm and 700 nm to 950 nm, respectively. A validation experiment is conducted by measuring the signal-to-noise ratio (SNR) of the WFS and the imaging camera. The results indicate that for the waveband-splitting method, the SNR of WFS is approximately equal to that of the imaging camera with a variation in the intensity. On the other hand, the SNR of the WFS is significantly different from that of the imaging camera for the polarized beam splitter energy splitting scheme. Therefore, the waveband-splitting method is more suitable for an open-loop LC AOS. An adaptive correction experiment is also performed on a 1.2-meter telescope. A star with a visual magnitude of 4.45 is observed and corrected and an angular resolution ability of 0.31″ is achieved. A double star with a combined visual magnitude of 4.3 is observed as well, and its two components are resolved after correction. The results indicate that the proposed method can significantly improve the detection capability of an open-loop LC AOS.

Advanced single-frame overdriving for liquid-crystal spatial light modulators.

A single-frame overdriving scheme was employed to improve the temporal response of the active matrix addressing liquid-crystal spatial light modulator used in an open-loop adaptive optics system (OLAOS). Optimal time distribution giving minimum wavefront residual error for the OLAOS was demonstrated. As a result, the measured -3 decibels rejection frequency was increased from 26 to 35 Hz, and the image quality was significantly improved.

Analysis of Dynamic Evolution and Spatial-Temporal Heterogeneity of Carbon Emissions at County Level along "The Belt and Road"-A Case Study of Northwest China.

Northwest region is the main energy supply and consumption area in China. Scientifically estimating carbon emissions (CE) at the county level and analyzing the spatial-temporal characteristics and influencing factors of CE in a long time series are of great significance for formulating targeted CE reduction plans. In this paper, Landscan data are used to assist NPP-VIIRS-like data to simulate the CE from 2001 to 2019. Spatial-temporal heterogeneity of CE was analyzed by using a two-stage nested Theil index and geographically and temporally weighted regression model (GTWR). The CE in northwest China at the county increases yearly while the growth rate slows down from 2001 to 2019. The spatial pattern forms a circle expansion centered on the high-value areas represented by the provincial capital, which is also obvious at the border between Shaanxi and Ningxia. Axial expansion along the Hexi Corridor is conspicuous. The spatial pattern of CE conforms to the Pareto principle; the spatial correlation of CE in northwest counties is increasing year by year, and the high-high agglomeration areas are expanding continuously. It is an obvious high carbon spillover effect. Restricted by the ecological environment, the southwest of Qinghai and the Qinling-Daba Mountain area are stable low-low agglomeration areas. The spatial pattern of CE in northwest China shows remarkable spatial heterogeneity. The difference within regions is greater than that between regions. The "convergence within groups and divergence between groups" changing trend is obvious. According to the five-year socioeconomic indicators, the economic scale (GDP), population scale (POP), and urbanization level (UR) are the main influencing factors. The direction and intensity of the effect have changed in time and space. The same factor shows different action intensities in different regions.

Zonal slope prediction for open-loop adaptive optics.

We present what we believe to be the first results that obtained with the recursive least square zonal slope predictor working on an open-loop liquid-crystal adaptive optics system operating on astronomical implementation at visible and near infrared wavelength on a 1.23 m telescope. The system produces substantially better results than a direct open-loop correction based on previous measurement. A 27% relative gain in full-width at half-maximum and 30% relative gain in Strehl ratio are obtained.

Improvement of the switching frequency of a liquid-crystal spatial light modulator with optimal cell gap.

In the application of a nematic liquid-crystal (LC) spatial light modulator, we derived the formula of retardation dynamic response of the device by solving the Erickson-Leslie equation. Then, the response time of the 2π phase change can be expressed as a function of the LC cell gap. The theoretical and experimental results all indicate that the response time of 2π first decreases and then increases with the LC cell gap increasing, and there is an optimal cell gap to obtain the shortest response time. Therefore, the method of optimizing the cell gap shows potential to improve the switching frequency for all type of nematic LC optical device with specific modulation quantity.