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In this paper, the proof-of-concept of an optical fiber sensing technique based on a frequency shifting loop (FSL) is proposed. The system combines both a refreshing rate of the sensing measurement in the MHz range and a centimetric spatial resolution. The FSL is used as a versatile source of broadband optical chirped waveforms, with controllable chirp rate. Digital pulse compression is applied to optimize the system's signal-to-noise-ratio. The sensor system is used to monitor the phase perturbation applied to a localized transducer (an electro-optic phase modulator) placed in an optical fiber. A preliminary and promising sensitivity

The market value for the plastics manufacturing industry is projected to exceed USd700 billion in the coming decade [1]. Technology for reliable quality control is an essential component of the manufacturing process. Present technology for monitoring the thickness profile of manufactured plastics typically makes use of interferometry with a white-light (broadband or tunable-wavelength) laser source. [2]-[5]. While this method has found satisfactory implementation as a quality control mechanism to monitor deviations in the thickness of plastics, the cost and complexity of implementation can be prohibitive. In addition, laser-based time-of-flight terahertz time-domain spectroscopic (THz-TDS) tomography systems have been presented as a suitable alternative; however, a femtosecond pulsed laser is still required to render measurements on the order of a micron (mm) [6].

With the goal of persistent surveillance over a scene of interest, this paper proposes an approach for joint imaging and trajectory extraction of multiple moving objects, using circular video-SAR (ViSAR) mode. Unlike stationary SAR imaging where the phase perturbation of the received signal arises from the platform motion, the moving targets impose additional phase errors, contributing to defocusing of the moving targets’ images. Here, for proper imaging of the moving targets, specifically in low-signal-to-clutter-ratio (SCR) scenarios, their signatures are decomposed from the stationary background clutter by low rank and sparse decomposition (LRSD), before refocusing to their original positions. However, the rotation of the scene, which emerges as a consequence of circular SAR geometry, leads to undesirable decomposition results via LRSD. To facilitate the applicability of LRSD for moving target extraction in our setting, considering this rotation in our model, the decomposition is accomplished while this undesirable effect is automatically compensated for. In addition, to further guarantee that LRSD yields satisfactory decomposition results, phase errors due to platform motion are also jointly corrected along with the clutter separation process. Then, having decomposed the sequential sparse images of moving targets’ signatures, the additional phase errors caused by moving targets are compensated to refocus them to their original positions. After that, these focused sparse images of moving targets are combined to construct a single image where the trajectories of moving targets can be observed. Using this image, a composite image is also constructed, including both the moving objects’ trajectories and the stationary background, which can be used for target tracking applications. Through extensive experimental results we show the effectiveness of the proposed method on both synthetic and real SAR images.

A study on the transient behavior of a single-loop optoelectronic oscillator (OEO) under a single sinusoidal radio frequency (RF) signal injection is presented. Considering only the phase perturbation imposed by the external RF signal, the phase-dynamic equation is solved to analyze the frequency settling behavior of the loop. A closed form expression for the required time of an OEO under RF injection-locking, reaching the steady state condition, is derived in terms of the initial phase difference, beat frequency and injection signal strength. The phase modulated signal, which is responsible for the perturbation of the free running oscillation, is expanded in a Fourier series and the expression for the output RF spectrum of the injection pulled OEO is derived. The injection-pulling dynamics approach is used to describe the phase noise of the OEO and also, the influence of the phase settling time constant on the phase noise of the injection-locked OEO is studied. The experimental results corroborating the theoretical findings are given.

Grid inverters need a synchronization algorithm to connect with the grid which is often a phase-locked loop (PLL). Conventionally, small-signal models are used to tune such PLL and to assess stability in steady state; however, they can misjudge the dynamic behaviors, in particular, during large phase perturbation due to grid faults. To address this issue, a more accurate model of PLL-based synchronization of the grid inverter with second-order approximation terms valid not only for the steady state but also for phase transients has been developed in this paper. Stability criterion based on the developed model has been proposed to assess the harmonic stability during phase perturbations. The model accuracy and the effectiveness of the stability criterion have been comprehensively evaluated and validated by simulation and experiments.

This article presents a detailed study of injection-locking characteristics of a single-loop optoelectronic oscillator (OEO) under strong radio frequency (RF) signal injection. We provide formulas for the steady-state phase-angle after locking, and the locking time for a higher level of a locking signal, considering only the phase perturbation. We also provide a compact expression for the main spectrum components of the pulled OEO in terms of the beat frequency, which is useful to evaluate and quantify the injection-pulling effects in the OEO. The experimental results provide partial support to the conclusion of the analysis. The analytical and experimental results are presented in design curves, which can be used to determine the required properties of an injection-locked OEO for a specific performance of the oscillator.

We report on a partially coherent power-exponent-phase vortex beam (PC-PEPV), whose spatial coherence is controllable and the initial phase exhibits a periodic power exponential change. The PC-PEPV beam was generated experimentally with various spatial coherence widths, and its propagation properties were studied both numerically and experimentally. By modulating the topological charge (TC) and power order of the PC-PEPV beam, the structure of the vortex beam can be adjusted from circular to elliptic, triangular, quadrangle, and pentagon. When the power order is odd, the PC-PEPV beam with a negative TC can be generated, and the profiles of the PC-PEPV beam can be precisely controlled via adjusting the value of the power order. For the case of high spatial coherence width, the number of the dark cores in the polygonal intensity array of the PC-PEPV beam equals the magnitude of the TC. However, when decreasing the spatial coherence width, the dark cores vanish and the intensity gradually transforms into a polygonal light spot. Fortunately, from the modulus and phase distributions of the cross-spectral density (CSD), both the magnitude and sign of the TC can be determined. In the experiment, the modulus and phase distribution of the CSD are verified by the phase perturbation method. This study has potential applications in beam shaping, micro-particle trapping, and optical tweezers.

For dynamic analysis in seismic design, selection of input ground motions is of huge importance. In the presented scheme, complex Continuous Wavelet Transform (CWT) is utilized to simulate stochastic ground motions from historical records of earthquakes with phase disturbance arbitrarily localized in time-frequency domain. The complex arguments of wavelet coefficients are determined as phase spectrum and an innovative formulation is constructed to improve computational efficiency of inverse wavelet transform with a pair of random complex arguments introduced and make more candidate wavelets available in the article. The proposed methodology is evaluated by numerical simulations on a two-degree-of-freedom system including spectral analysis and dynamic analysis with Shannon wavelet basis and Gabor wavelet basis. The result shows that the presented scheme enables time-frequency range of disturbance in time-frequency domain arbitrarily oriented and complex Shannon wavelet basis is verified as the optimal candidate mother wavelet for the procedure in case of frequency information maintenance with phase perturbation.

By developing the complex phase perturbation for vortex pulsed beams in asymmetric oceanic turbulence and the spatiotemporal orthogonal basis for Lommel-Gaussian pulsed beam, we establish the received probability model of orbital angular momentum (OAM) modes for vortex pulsed beams propagating through asymmetric oceanic turbulence. Using this new model, we investigate the received probability and the pulse broadening of OAM modes of Lommel-Gaussian pulsed beam in asymmetric oceanic turbulence. Numerical simulation results show that Lommel-Gaussian pulsed beam causes a smaller pulse broadening when it propagates through oceanic turbulence with higher asymmetric factor, lower temperature structure constant, smaller inner scale and outer scale. In addition, Lommel-Gaussian pulsed beam with lower carrier frequency propagates through the oceanic turbulence with higher asymmetric factor, larger inner scale, smaller outer scale and smaller temperature structure constant, which obtains a higher received probability of signal OAM modes. For Lommel-Gaussian pulsed beams, the change of OAM quantum number has a week effect on the pulse broadening and the received probability.

This paper describes the algorithm of antenna array (AA) calibration, which estimates and compensates phase lags, caused by non-identical electrical characteristics of array channels. The algorithm does not require the access to the channel signals or the channels disabling. It uses only the array output power measurements under the specific channel phase perturbations. The algorithm accuracy equals the phase shifter quantization step, i.e. it is twice less than phase shifter accuracy itself and does not depend on the number of array channels. The algorithm accuracy is compared with two similar calibration algorithms, known from publications. The compared algorithms accuracy depends on the number of array channels and is much less than the proposed algorithm. Thus, the new algorithm can be widely used for the efficient AA calibration, signal source angular position estimation and tracking by a calibrated or a non-calibrated AA with any aperture shape: linear, flat or conformal, with an arbitrary distance between neighbor AA elements and with an arbitrary antenna selected as a reference one.

The stability of a cylinder in circulation flow of an inviscid incompressible fluid is considered. The investigation of stability in the simple two-dimensional system is of considerable interest since in this problem the analytical solution can be obtained in both spectral and initial problems. The investigation of the critical layer region in which the phase perturbation velocity coincides with the velocity of mean flow is of particular interest since just in this region the perturbations are concentrated and grow indefinitely.

Joint radar-communications dual function has drawn lots of attention since it can make a better use of the scarce wireless frequency resources and expensive hardware platforms. In case of joint radar-communications signal co-use, many communication sequences have poor range sidelobes and thus are not very suitable for the radar function. In this paper, we present a single carrier joint radar-communications method operating in the pulsed radar mode. Digital communication sequences are first partitioned into blocks which are then mapped to digital phase-coded sequences, like binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK) sequences. The phases of the digital sequences are perturbed a bit such that certain degrees of freedom are available to optimize for lower range sidelobes. Insignificant phase perturbation will be deemed as phase noise by a communication receiver and then phase codes can be correctly decoded; in radar-processing channels, range compression are performed with known and optimized phase perturbation such that low-range sidelobes are obtained. An implementation scheme is presented. Numerical results with BPSK and QPSK sequences indicate that little phase perturbation can significantly drop the range sidelobe level but will insignificantly rise the bit error rate.

Injection-locking characteristics of a single-loop optoelectronic oscillator (OEO) under an independent sinusoidal RF signal injection are investigated. The mathematical model of the unlocked-driven system is developed to represent phase perturbation of the generated output RF signal caused by the RF injection signal. The closed-form expressions of the output RF spectra distorted due to RF signal injection are derived to formulate the behavior of the injection-pulled OEO. Using the phase dynamics equation, a phase noise model is developed to quantify the influence of RF injection signal on the phase noise performance of the oscillator. It is shown that our analytical model is capable of predicting the injection locking and estimating the injection pulling behavior of the single-loop OEO under RF signal injection. The theoretical results are validated by the experimental results.

In this paper, we propose an improved closed form large injection perturbation analytical model for accurately studying the phase-locking dynamics and frequency pulling phenomenon in optoelectronic oscillator (OEO) for radio frequency (RF) signal injection. We provide formulas for the lock-range, and the beat frequency, which are general and accurate in estimating the degree of phase perturbation in unlocked-driven OEO under weak as well as strong injection signal level. We also give closed form expressions for the spectral components of the unlocked-driven oscillator. It is shown that our model is capable of predicting the phase-locking and estimating the frequency pulling of RF driven OEO under weak and strong injection signal level. The accuracy of the proposed model is verified by the simulations.

A practical compact antenna test range (CATR) requires good quiet zone quality for antenna characterization. This paper addresses the phase profile of the CATR quiet zone from the known intensity pattern of spatial domain and Fourier domain based on a combined alternating projection algorithm. The proposed algorithm is composed of Gerchberg–Saxton (GS) and Hybrid Input–Output (HIO) algorithms and the two algorithms with spatial phase perturbation (SPP) work collaboratively or independently under predesigned conditions. It is observed that the algorithm with random initial phase guess can always converge to an optimal solution by performing a series of hierarchical optimizations of the problem. The numerical results are in good agreement with simulated results in different frequency bands, overcoming the phase retrieval limitation of local convergence in the iterative process. Furthermore, to validate the effectiveness and robustness of the proposed procedure, the related discussions corresponding to different sampling areas in Fourier domain and different signal to noise ratios (SNRs) are given.

This paper deals with the design of the constant modulus sequence set for MIMO radar in an effort to achieve the desired correlation properties and favorable Doppler tolerance. In particular, the phase perturbation terms are forced in LFM waveforms with different frequency modulation disturbance to provide the optimization degree of freedom to achieve low correlation sidelobe level. To this end, the Weighted Integrated Sidelobe Level (WISL) of auto-and cross-correlation functions is formulated as a figure of merit to minimize. Besides, to obtain good Doppler tolerance, the similarity constraint between the devised waveforms and these LFM waveforms is involved. To cope with the resultant NP-hard problem, the Coordinate Descent (CD) framework is introduced along with a quartic problem with a closed-form solution in each iteration. Numerical results are provided to assess the designed waveform set in terms of Doppler tolerance and compatibility of detecting weak targets and high speed targets.

A kind of Michelson interference structure is used to improve the round-trip phase correction method and realize the feedback phase stabilization control. In the system, the phase shifter pre-compensation control, 1/4 wave plate debirefringence and Faraday rotator de-polarization sensitivity effectively avoid the polarization fading phenomenon existing in photoelectric detection by external factors, and realize the signal arm carrying phase jitter. At the same time, the AOFS driven by the intermediate frequency signal realizes the construction of the reference arm of the interferometer. Through photoelectric detector to beat frequency of two arms mutual interference signal, the beat frequency signal and intermediate frequency reference signal phase matching, can get the phase perturbation of optical fiber transmission system, the phase discriminator output signal processing can be used as the bias current of SOA control signal, realize the purpose of the feedback control signal phase, has solved the traditional approach to the problem of high frequency signal phase is not convenient to monitor.

This paper describes an analytical model of an injection-synchronized single-loop optoelectronic oscillator (OEO) under the influence of radio frequency (RF) interfering signal to study the performance of the system considering only the phase perturbation imposed by the RF injection signal. We derive the phase dynamic equation of the system, which is used to derive compact expression for the lock-range and investigates the influence of interfering signal on the lock-range considering both weak and strong interfering signal strength. We provide formula for the lock-range of the OEO under RF injection-locking in the presence of interfering signal, to reach the steady-state. It is shown that the injection-synchronized OEO under the influence of strong interfering signal exhibits frequency jump phenomena. The experimental results corroborating the theoretical findings are given.

In interference lithography, the environmental disturbances will lead to a phase drift of the interference fringes during the exposure process, resulting in a decrease of exposure contrast. Feedback control is usually used to stabilize the phase, and the choice of control algorithm will affect the exposure effect. In this paper, a linear-quadratic-Gaussian (LQG) controller combined with a Kalman filter is applied to provide an optimal feedback control by solving the problem of minimizing the variance of the residual phase errors. The phase control method is described using a state-space approach. The simulation results show that the proposed control method can effectively suppress the low-frequency phase drift, as well as the phase perturbation caused by mechanical vibrations.

The applicability limits of the small complex phase perturbation (Rytov) theory for laser light propagation in soft biological tissues have been tackled. We have found that for typical coherent opt...

In this study, a novel method is proposed to deal with the problem of altitude measurement of a low-elevation target for very high frequency radars in complex terrains. The problem typically concerns about the direction-of-arrival (DOA) estimation method for closely spaced and correlated signals arose by multipath propagation, in which the multipath signal would be modulated by the rough and irregular reflecting surface, result in amplitude and phase perturbation and energy fluctuations of the receiving signals. A perturbation multipath propagation model is derived where the influence of irregular reflecting in complex terrain is taken as a random perturbation of the multipath signal. The spatial sparsity of the receiving signal is then exploited, and a weighted sparse Bayesian learning method is proposed to estimate both the random perturbation coefficients and DOA of the incident signal with high precision. Both the computer simulations and real data analysis indicate the efficiency and superior performance of the proposed method in dealing with altitude measurement in complex terrain.

In a sky-wave radar, the strong ocean clutter may cover up the echo signal of slow-speed targets. This letter proposed a knowledge-aided ocean clutter suppression method for the sky-wave radar. The proposed method uses the radar carrier frequency and the pulse repetition interval as prior knowledge to reconstruct the prior ocean clutter. This reconstructed clutter is combined with the ionosphere phase perturbation model. The resulting prior clutter is included in the optimal filter design. The simulation results show that the output signal-to-clutter plus noise ratio of this proposed method is 2.507 dB larger than the methods proposed by others.

The matrix reconstruction technique can effectively estimate the direction-of-arrival (DOA) of coherent signals with a relatively small computational complexity. However, the existing methods are affected by the phase perturbation or the fact that the eigenvalue ratio of the signal subspace to noise subspace is linearly related to the square of input signal-to-noise ratio (SNR). This results in a significant decrease in the DOA estimation performance for the cases with a low SNR. To address these problems, we propose a new method for DOA estimation of coherent signals based on the beamspace matrix reconstruction. The array is firstly divided into multiple subarrays, and the data received is transformed from the element space into the beamspace via beamforming, which can eliminate the phase perturbation caused by the mutual impact between the coherent signals and improve the SNR. Then, we add the output covariance matrices from several beam directions to realize the beamspace matrix reconstruction, this results in the eigenvalue ratio of the signal subspace to the noise subspace is the linear transformation of the input SNR in the beamspace domain, which can enhance the eigenvalue ratio of beamspace signal to noise at low SNRs. Finally, the DOAs can be resolved by combining it with the subspace-based methods. Theoretical analysis and simulation results verify the effectiveness of the proposed method at low input SNRs due to beamspace processing, even in the cases where the DOAs between the coherent signals are closely spaced and low snapshot number, our proposed method significantly provides better performance on estimation and resolution.

Rotary traveling wave oscillators use a transmission line connected as a closed loop as their resonant element. This allows the use of spatial degrees of freedom, not available in typical L–C oscillator topologies, in the design of the amplifier needed to sustain the oscillating mode. Here, we present a novel amplifier design that takes advantage of this extra degree of freedom to improve performance of RTWOs in two ways. If no precautions are taken then the oscillation can start in either a clockwise or anti-clockwise direction. The Phased amplifier, introduced here, forces one direction of oscillation with a measured probability of reverse oscillation of less than 0.43 ppm with a confidence level of 99%. No reverse oscillations were observed in 107 trials. This is accomplished by adding additional phase-dependent degeneration transistors and phase shifting the various amplifier inputs by taking them from different locations on the transmission line. Additionally, this amplifier design reduces the phase noise by reducing the amplifier noise during the time that the oscillator is most sensitive to phase perturbation, resulting in a 1.2-dB reduction in phase noise measured 1 MHz from the peak and a 2.9-dB improvement in the figure of merit.

The traditional direction of arrival (DOA) estimation method is very sensitive to the array perturbation, but there are often various errors or perturbations in application, which directly influence the estimation seriously. Therefore, we address the problem of direction of arrival (DOA) estimation to mixed far-filed and near-field signals in the presence of gain-phase perturbation, which can effectively calculate the DOA of far-field signal (FS) and location of near-field signal (NS). First, the spatial spectrum of FS is simplified according to the structure of the array, thus, the DOA can be obtained by finding the roots of the corresponding determinant. Second, gain-phase perturbation is determined based on the orthogonality between noise subspace and signal subspace of FS. Finally, DOA of NS is skillfully acquired through matrix transformation, and then their location can also be decided in the open space. Simulation results demonstrate the effectiveness of the proposed method.

By the use of phase perturbation theory we show that if a single realization of a one-dimensional randomly rough interface between two dielectric media is illuminated at normal incidence from either medium by a broadband Gaussian beam, it produces a scattered field whose differential reflection coefficient closely matches the result produced by averaging the differential reflection coefficient produced by a monochromatic incident beam over the ensemble of realizations of the interface profile function., 10 pages, 7 figures

This works presents a reconstruction algorithm to recover the complex object information for an off-axis digital holographic microscope (DHM) operating in the telecentric regimen. We introduce an automatic and fast method to minimize a cost function that finds the best numerical conjugated reference beam to compensate the filtered object information, eliminating any undesired phase perturbation due to the tilt between the reference and object waves. The novelties of the proposed approach, to the best of our knowledge, are a precise estimation of the interference angle between the object and reference waves, reconstructed phase images without phase perturbations, and reduced processing time. The method has been validated using a manufactured phase target and biological samples.

Practical orbital angular momentum (OAM)-based free-space optical (FSO) communications commonly experience serious performance degradation and crosstalk due to atmospheric turbulence. In this paper, we propose a wave-front sensorless adaptive optics (WSAO) system with a modified Gerchberg–Saxton (GS)-based phase retrieval algorithm to correct distorted OAM beams. We use the spatial phase perturbation (SPP) GS algorithm with a distorted probe Gaussian beam as the only input. The principle and parameter selections of the algorithm are analyzed, and the performance of the algorithm is discussed. The simulation results show that the proposed adaptive optics (AO) system can significantly compensate for distorted OAM beams in single-channel or multiplexed OAM systems, which provides new insights into adaptive correction systems using OAM beams.

We demonstrate the influence on mode features with introducing typical intracavity perturbation and results of aberrated wavefront compensation in a folded-type unstable resonator used in high energy lasers. The mode properties and aberration coefficient with intracavity misalignment are achieved by iterative calculation and Zernike polynomial fitting. Experimental results for the relation of intracavity maladjustment and mode characteristics are further obtained in terms of S-H detection and model wavefront reconstruction. It indicates that intracavity phase perturbation has significant influence on out coupling beam properties, and the uniform and symmetry of the mode is rapidly disrupted even by a slight misalignment of the resonator mirrors. Meanwhile, the far-field beam patterns will obviously degrade with increasing the distance between the convex mirror and the phase perturbation position even if the equivalent disturbation is inputted into such the resonator. The closed-loop device for compensating intracavity low order aberration is successfully fabricated. Moreover, Zernike defocus aberration is also effectively controlled by precisely adjusting resonator length, and the beam quality is noticeably improved.

In this paper, we analyze the phase-locking phenomenon in a single-loop optoelectronic microwave oscillator, when subjected to the influence of small radio-frequency (RF) signal. We derive the differential equations for the amplitude and phase variations in the oscillator. Using quasi-linear approximation, analytical expressions for the lock range and phase-shift after phase-locking are presented. In addition, beat frequency of the unlocked-driven optoelectronic oscillator (OEO) is obtained and the phase-locking dynamics of the driven oscillator is discussed. Also, the spectrum components of the pulled OEO is derived as a function of the frequency detuning, lock range, beat-frequency, and frequency-shift induced by the phase perturbation of the injection signal. It is shown that all the analytical closed-form expressions clearly demonstrate the phase-locking mechanism starting from the fast-beat state through the quasi-locked state to the locked state of the pulled OEO. Finally, the simulation results are given to validate the analytical results.

In this paper, a novel method is proposed to deal with altitude measurement of low-elevation target for very high frequency (VHF) radars in complex terrain. In VHF radars, the altitude measurement of low elevation target is unstable and unfavorable owing to the presence of multipath phenomenon. The multipath signal, reflected by the ground, is highly correlated with the direct signal. Moreover, the direct and multipath signal always fall within the same beamwidth. Especially, in complex terrain, the multipath signal is modulated by the rough and irregular reflecting, which results in performance depravation of the exiting direction-of-arrival (DOA) estimation methods, and makes the altitude measurement of low elevation target difficult. To resolve this problem, a perturbation multipath propagation model for low-angle tracking and localization is developed to simulate the echo of the low elevation target in complex terrain, where the effect of irregular reflecting is considered as random amplitude and phase perturbation of the multipath signal. Then a novel method is proposed to resolve the model and estimate the DOA of the low elevation target. Both computer simulations and real data analysis results illustrate that the proposed method can estimate the DOA with higher accuracy in comparison with the existing methods.

The cylindrical vector beams (CVBs) compose two circularly polarized vortex beams carrying orbital angular momentum (OAM) states with the opposite topological charge. We derived the probabilities for OAM of high-order CVB propagation through turbulent atmosphere. The calculated probabilities of OAM are based on the polarization insensitive element detection and phase perturbation coherence function assumption. The numerical calculation results show that the probabilities of OAM state spreading to neighbor states of CVBs through turbulent atmosphere increase with the propagation distance increase. Under the same conditions, the spreading of OAM for CVBs are weaker than Laguerre-Gaussian beam propagation through turbulent atmosphere. The results show that the OAM state of CVBs could improve the performance of optical communications systems in atmospheric turbulence.

International audience; The estimation of the misalignment of an active telescope, from aberrations measured in its focal plane, is a tomographic issue. MMSE-based estimation is successfully used in optical tomography issues, like multiconjugate adaptive optics, where the problem is linear, and the phase perturbation spectrum rapidly decreasing. The implementation of MMSE developed in the case of multiconjugate adaptive optics has been applied to the alignment of active telescopes, although the forward problem is not linear, and the aberration spectrum different. Its performance is characterized by numerical modeling in the case of a TMA type large-field imaging space telescope, and compared to the classical Least-Square approach. The MMSE estimation brings a significant gain in terms of robustness and accuracy.; L'estimation du désalignement d'un télescope actif, à partir d'aberrations mesurées dans son plan focal, est un problème tomographique. L'estimation basée sur le MMSE est utilisée avec succès dans les problèmes de tomographie optique, comme l'optique adaptative à conjugaisons multiples, où le problème est linéaire et le spectre de perturbation de phase décroissant rapidement. L’implémentation du MMSE développée dans le cas de l’optique adaptative à conjugaisons multiples a été appliquée à l’alignement des télescopes actifs, bien que le problème de l’avenir ne soit pas linéaire et que le spectre des aberrations soit différent.Ses performances sont caractérisées par une modélisation numérique dans le cas d'un télescope spatial à imagerie grand champ de type TMA, et comparée à l'approche classique des moindres carrés. L'estimation MMSE apporte un gain significatif en termes de robustesse et de précision.

The paper presents an algorithm of antenna array calibration, which estimates and compensates phase lags, caused by non-identical electrical characteristics of the array channels. To estimate the phase lags, the algorithm uses only the array output power measurements under the specific channel phase perturbations. The estimation accuracy equals phase shifter quantization step and does not depend on the number of the array channels. The algorithm is compared with two similar calibration algorithms, known from publications, whose accuracy depends on the number of the array channels and is much less compared with that of the proposed algorithm. For this reason, the algorithm, presented in this paper, can be widely used for efficient arrays calibration, signal source angular position estimation and tracking by a calibrated or a non-calibrated array with any aperture shape: linear, flat or conformal and with an arbitrary channel, selected as a reference one.

16-core photonic crystal fiber (PCF) was designed. In order to obtain spatially flat in-phase modes, the super-mode near- field properties were studied through method of numerical simulation calculation and according to coupled mode theory. On the based of the scalar Fraunhofer Diffraction, a far- field in-phase super-mode theoretical modeling was presented. According to the modeling, one discussed the influence of the random phase perturbation, the random amplitude perturbation and the polarization direction perturbation on the far-filed intensity distribution, in detail. The results show that both phase perturbation and amplitude perturbation sharply impact the far-filed distribution of interference intensity and contrast. However, the influence of the polarization direction perturbation is not obvious. When the parameterδ, μ and u increases, the field center intensity decreases and the power of the central spot also does, which means the profile of the spot will blur and the beam quality drop.

Eigenmode of resonators with asymmetric circular mirrors based on misalignment passive positive-branch unstable resonator is investigated in the paper. To do so, we use iterative algorithm to simulate the effect of intracavity phase perturbation on eigenmode structure properties of the passive confocal unstable resonator. On this basis, further experiment of output beam properties on a misaligned passive unstable laser resonator has been performed by adopting Hartmann–Shack (H–S) method and Zernike modal wavefront reconstruction. Wavefront distribution and the first 35-order Zernike coefficient included in the wavefront are obtained. The results show that intracavity tilt perturbation notablely affects outcoupled beam intensity distribution, and will also increase some high-order aberrations of beam phase properties. However, low-order Zernike tilt aberration is the main component with phase-tilted perturbation is introduced into resonator cavity. Defocus, low-order astigmatism and coma aberration will all be brought with the augument of phase tilt aberration, which will obviously degrade output beam quality. When intracavity compensating elements are adopted for optical aberration correction, the correction of tilt aberration should be considered first.

Some representative factors of intracavity perturbation will obviously degrade output power and beam mode properties for crystal passive Q-modulated solid-state lasers. In this paper, eigenmode of resonators using general asymmetric circular mirrors in solid-state lasers is briefly discussed, moreover, experiment analysis of the output beam quality on a passive Q-switched zig-zag slab Nd:YAG laser has been presented by adopting Hartmann–Shack (H–S) method and Zernike mode reconstruction theory. In this way, the PV and RMS errors of the wavefront aberration, each order Zernike aberrations can be acquired accurately, distribution of circle energy in far-field and other beam evaluation factors can also be obtained by further calculation, so beam mode properties and quality can be analyzed comprehensively. Experimental results illuminate that wavefront aberration of the laser is concentrated in the frontal 10 ranks of Zernike aberration, mainly including the defocus Z3, the low-order astigmatism Z5, the coma aberration Z6 and the spherical aberration Z10 because of the crystal thermal effect and the intracavity phase perturbation.

We develop a rapidly converging algorithm for stabilizing a large channel-count diffractive optical coherent beam combination. An 81-beam combiner is controlled by a novel, machine-learning based, iterative method to correct the optical phases, operating on an experimentally calibrated numerical model. A neural-network is trained to detect phase errors based on interference pattern recognition of uncombined beams adjacent to the combined one. Due to the non-uniqueness of solutions in the full space of possible phases, the network is trained within a limited phase perturbation/error range. This also reduces the number of samples needed for training. Simulations have proven that the network can converge in one step for small phase perturbations. When the trained neural-network is applied to a realistic case of 360 degree full range, an iterative scheme exploits random walking at the beginning, with the accuracy of prediction on phase feedback direction, to allow the neural-network to step into the training range for fast convergence. This neural-network-based iterative method of phase detection works tens of times faster than the commonly used stochastic parallel gradient descent approach (SPGD) using a single-detector and random dither when both are tested with random phase perturbations.

We report on the realization of an optical phase noise cancellation technique by passively embedding the optical phase noise information into a radio frequency signal and creating a copy of the optical frequency signal, which is pre-corrected by the amount of phase noise introduced by optical phase perturbations. Neither phase discrimination nor an active servo controller is required due to the open-loop design, mitigating some technical problems, such as the limited compensation speed and finite phase/timing jitter, in conventional phase noise cancellation. We experimentally demonstrate that this technique maintains the same delay-limited bandwidth and phase noise suppression capability as in conventional techniques, but significantly shortens the response speed and phase recovery time. Passive decoupling optical phase perturbation represents a powerful technique in the domains of optical frequency standard comparisons and tools for future optical atomic clocks, which are now under investigation for a potential redefinition of the International Time Scale.