Laser beam projection with adaptive array of fiber collimators. I. Basic considerations for analysis

We present a mathematical model and provide an analysis of optical beam director systems composed of adaptive arrays of fiber collimators (subapertures), referred to here as conformal optical systems. Performances of the following two system architectures are compared: A conformal-beam director with mutually incoherent output laser beams transmitted through fiber collimators (beamlets), and a corresponding coherent system whose beamlets can be coherently combined (phase locked) at a remote target plane. The effect of the major characteristics of the conformal systems on the efficiency of laser beam projection is evaluated both analytically and through numerical simulations. The characteristics considered here are the number of fiber collimators and the subaperture and conformal aperture fill factors, as well as the accuracy of beamlet pointing.     

Decoupled stochastic parallel gradient descent optimization for adaptive optics: integrated approach for wave-front sensor information fusion

A new adaptive wave-front control technique and system architectures that offer fast adaptation convergence even for high-resolution adaptive optics is described. This technique is referred to as decoupled stochastic parallel gradient descent (D-SPGD). D-SPGD is based on stochastic parallel gradient descent optimization of performance metrics that depend on wave-front sensor data. The fast convergence rate is achieved through partial decoupling of the adaptive system's control channels by incorporating spatially distributed information from a wave-front sensor into the model-free optimization technique. D-SPGD wave-front phase control can be applied to a general class of adaptive optical systems. The efficiency of this approach is analyzed numerically by considering compensation of atmospheric-turbulence-induced phase distortions with use of both low-resolution (127 control channels) and high-resolution (256 x 256 control channels) adaptive systems. Results demonstrate that phase distortion compensation can be achieved during only 10-20 iterations. The efficiency of adaptive wave-front correction with D-SPGD is practically independent of system resolution.     

Compensation of distant phase-distorting layers. I. Narrow-field-of-view adaptive receiver system

We analyze various scenarios of adaptive wave-front phase-aberration correction in optical-receiver-type systems when inhomogeneties of the wave propagation medium are either distributed along the propagation path or localized in a few thin layers remotely located from the receiver telescope pupil. Phase-aberration compensation is performed with closed-loop control architectures based on decoupled stochastic parallel gradient descent, stochastic parallel gradient descent, and phase conjugation control algorithms. Both receiver system aperture diffraction effects and the effect of wave-front corrector position on phase-aberration compensation efficiency are analyzed.     

Foundations for low-loss fiber gradient-index lens pair coupling with the self-imaging mechanism

A fiber-optic collimator that emits a Gaussian beam with its beam waist at a certain distance after the exit face of the lens is labeled a self-imaging collimator. For such a collimator, the waist of the emitted Gaussian beam and its location are partly dependent on the properties of the gradient-index (GRIN) lens. Parameters for the self-imaging collimator are formulated in terms of the parameters of a GRIN lens (e.g., pitch, core refractive index, gradient index, length) and the optical wavelength. Next, by use of the Gaussian beam approximation, a general expression for the coupling power loss between two self-imaging-type single-mode fiber (SMF) collimators is, for the first time to our knowledge, derived as a function of three types of misalignment, namely, separation, lateral offset, and angular tilt misalignment. A coupling experiment between two self-imaging collimators with changing separation distance is successfully performed and matches the proposed self-imaging mechanism coupling loss theory. In addition, using a prism, lateral offset, as well as angular tilt, misalignments are experimentally simulated for a two self-imaging collimator coupling condition by a single collimator reflective test geometry. Experimental results agree well with the proposed loss formulas for self-imaging GRIN lenses. Hence, for the first time to our knowledge, the mathematical foundations are laid for employing self-imaging-type fiber collimators in SMF-based free-space systems allowing optimal design for ultra-low-loss coupling.     

General formula for coupling-loss characterization of single-mode fiber collimators by use of gradient-index rod lenses

A general formula for determining the coupling loss between two single-mode fiber collimators with the simultaneous existence of separation, lateral offset and angular tilt misalignments, and spot-size mismatch is theoretically derived by use of the Gaussian field approximation. Based on this general formula, the formulas for coupling losses that are due to the misalignment of insert separation, lateral offset, and angular tilt are given. The formula for the coupling loss that is due to Gaussian spot-size mismatch of two single-mode collimators is also given. Good agreement between these formulas and experimental results is demonstrated with gradient-index rod lens-based fiber collimators operating in the 1300-nm band.     

邻域自适应选取的局部投影非线性降噪方法

局部投影降噪算法已广泛应用于非线性时间序列的分析中，但受邻域选取的影响较大。提出了一种按照自适应方式选取邻域大小的局部投影降噪算法。首先用时间延迟方法将一维时间序列重构到高维相空间。然后逐步增大每个待分析相点的领域大小，根据领域最大主方向变化过程中首次出现平稳阶段时，自适应地确定该相点的最优领域，最后再用局部几何投影的方法去除噪声成分。对洛伦兹信号和杜芬信号分别添加不同噪声水平的高斯白噪声，对领域自适应选取的局部投影算法与标准局部投影算法的降噪效果进行了比较。实验结果表明，自适应邻域选取方法，提高了局部投影算法的降噪能力和对领域参数的鲁棒性。     

Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration

Wave-front distortion compensation using direct system performance metric optimization is studied both theoretically and experimentally. It is shown how different requirements for wave-front control can be incorporated, and how information from different wave-front sensor types can be fused, within a generalized gradient descent optimization paradigm. In our experiments a very-large-scale integration (VLSI) system implementing a simultaneous perturbation stochastic approximation optimization algorithm was applied for real-time adaptive control of multielement wave-front correctors. The custom-chip controller is used in two adaptive laser beam focusing systems, one with a 127-element liquid-crystal phase modulator and the other with beam steering and 37-control channel micromachined deformable mirrors. The submillisecond response time of the micromachined deformable mirror and the parallel nature of the analog VLSI control architecture provide for high-speed adaptive compensation of dynamical phase aberrations of a laser beam under conditions of strong intensity scintillations. Experimental results demonstrate improvement of laser beam quality at the receiver plane in the spectral band up to 60 Hz.     

Generalized Fried parameter after adaptive optics partial wave-front compensation

Atmospheric turbulence imposes the resolution limit attainable by large ground-based telescopes. This limit is lambda/r(0), where r(0) is the Fried parameter or seeing cell size. Working in the visible, adaptive optics systems can partially compensate for turbulence-induced distortions. By analogy with the Fried parameter, r(0), we have introduced a generalized Fried parameter, rho(0), that plays the same role as r(0) but in partial compensation. Using this parameter and the residual phase variance, we have described the phase structure function, estimated the point-spread function halo size, and derived an expression for the Strehl ratio as a function of the degree of compensation. Finally, it is shown that rho(0) represents the diameter of the coherent cells in the pupil domain.     

Binary phase-only filtering for turbulence compensation in fiber-coupled free-space laser communication systems

Binary wavefront control in the focal plane (i.e., binary phase-only filtering) for partial compensation of atmospheric turbulence in fiber-coupled free-space laser communication systems is investigated. Numerical results from wave-optics simulations show that in an air-to-air scenario, the combination of binary phase-only filtering and centroid tracking provides mean fiber coupling efficiency close to that resulting from ideal least-squares adaptive optics, but without the requirement for direct wavefront sensing. This result suggests a simpler and less computationally demanding turbulence mitigation system that is more readily applied to tactical applications.     

Residual phase variance in partial correction: application to the estimate of the light intensity statistics

Although the wave-front correction provided by an adaptive optics system should be as complete as possible, only a partial compensation is attainable in the visible. An estimate of the residual phase variance in the compensated wave front can be used to calibrate system performance, but it is not a simple task when errors affect the compensation process. We propose a simple method for estimation of the residual phase variance that requires only the measurement of the Strehl ratio value. It provides good results over the whole range of compensation degrees. The estimate of the effective residual phase variance is useful not only for system calibration but also for determining the light intensity statistics to be expected in the image as a function of the degree of compensation introduced.     

Adaptive optics with advanced phase-contrast techniques. II. High-resolution wave-front control

A wave-front control paradigm based on gradient-flow optimization is analyzed. In adaptive systems with gradient-flow dynamics, the output of the wave-front sensor is used to directly control high-resolution wavefront correctors without the need for wave-front phase reconstruction (direct-control systems). Here, adaptive direct-control systems with advanced phase-contrast wave-front sensors are analyzed theoretically, through numerical simulations, and experimentally. Adaptive system performance is studied for atmospheric-turbulence-induced phase distortions in the presence of input field intensity scintillations. The results demonstrate the effectiveness of this approach for high-resolution adaptive optics.     

光孤子通信系统的色散控制研究

光纤色散特性是支撑光纤孤子通信的决定性因素。比较了目前的几种色散补偿方案后,着重对相位共轭控制的色散控制方式进行了分析研究,该方式利用光纤非线性四波混频产生与输入光脉冲信号相位共轭的输出光脉冲信号,光脉冲的频谱以泵浦光频为中心进行反转,构建成相位共轭器,实现了对放大自发辐射(ASE)噪声、孤子相互作用与色散波等的控制,达到提高系统传输速率、距离和通信容量的目的。     

啁啾FBG和DCF对16×10Gb/s系统进行色散补偿的性能研究

对负色散光纤法和啁啾光纤光栅法实现色散补偿的两种方案进行了模拟研究 ,结论是 :(1 )对各信道完全色散补偿的前提下 ,入纤光功率较小时 ,啁啾光纤光栅色散补偿系统误码性能较好 ;入纤光功率较高时 ,用负色散补偿光纤进行色散补偿效果更好 ;(2 )适当的欠补偿比完全补偿效果好 ,入纤光功率一定时 ,用啁啾光纤光栅比用负色散补偿光纤进行欠补偿的效果好     

10Gbit/s色散补偿系统中自相位调制效应的研究

首先讨论了单模光纤中自相位调制对系统色散的影响。数值计算和实验结果表明。增加入纤功率能在一定程度上抑制色散效应 ,当入纤功率为 1 5dBm时 ,对于 4 0 .0km的单模光纤 ,自相位调制效应和色散恰好抵消 ,功率代价接近为零。然后比较了前、后置色散补偿系统的性能。理论分析和实验表明 ,在入纤光功率较大的情况下 ,采取前置、完全色散补偿系统具有较低的误码率。前置补偿最佳入纤功率比后置补偿最佳入纤功率高约 1 0 .0dB。这表明 ,采取前置、完全色散补偿 ,系统具有较长的中继距离和较高的接收端光信噪比 ,对 (1 6 0× 1 0Gbit/s)DWDM系统 30 0 0km超长距离传输中光放大和色散补偿问题的整体优化具有重要现实意义。     

A hyperstable neural network for the modelling and control of nonlinear systems

A multivariable hyperstable robust adaptive decoupling control algorithm based on a neural network is presented for the control of nonlinear multivariable coupled systems with unknown parameters and structure. The Popov theorem is used in the design of the controller. The modelling errors, coupling action and other uncertainties of the system are identified on-line by a neural network. The identified results are taken as compensation signals such that the robust adaptive control of nonlinear systems is realised. Simulation results are given.     

Dual-fiber collimator with elliptical spot for optical MEMS devices

Fiber collimators are widely used in optical communication components and fiber-optic sensors. Ordinary fiber collimators are made with a circular beam waist radius from 100?μm to 300?μm. The circular beam waist is too large to switch or shut the beam for certain micro-electro-mechanical system (MEMS) actuators (such as MEMS linear mirrors). In this paper, a dual-fiber collimator with an elliptical spot is proposed to meet the demands of MEMS optical devices. The elliptical spot collimator has been designed and fabricated, the beam waist spot of which is an elliptical spot with a 231.6?μm long-axis radius and a 12.87?μm short-axis radius, and its coupling loss is 0.37?dB.     

Adaptive demodulation of dynamic signals from fiber Bragg gratings using two-wave mixing technology

A two-wave mixing (TWM) interferometer using photorefractive (PRC) InP:Fe crystal is configured to demodulate the spectral shift of a fiber Bragg grating (FBG) sensor. The FBG is illuminated with a broadband source, and any strain in the FBG is encoded as a wavelength shift of the light reflected by the FBG. The wavelength shift is converted into phase shift by means of an unbalanced TWM interferometer. TWM wavelength demodulation is attractive for monitoring dynamic strains because it is adaptive and multiplexable. Adaptivity implies that it can selectively monitor dynamic strains without active compensation of large quasi-static strains and large temperature drifts that otherwise would cause system to drift. Multiplexability implies that several FBG sensors can be simultaneously demodulated using a single demodulator. TWM wavelength demodulation is therefore a cost-effective method of demodulating several spectrally encoded FBG sensors.     

Partial correction for turbulent distortions in telescopes

To provide complete compensation for turbulent distortions in the visible range at aperture dimensions typical for modern telescopes (6-10 m), one needs to develop adaptive systems with hundreds of control channels. More simple adaptive systems that provide complete compensation in the infrared range can give an essential advantage in angular resolution in the visible range too. In this case the image brightness characterized by the Strehl ratio remains much less than that in the diffraction-limited case, i.e., the system provides only partial compensation. We present the results of numerical calculations of the partially corrected point-spread function and discuss possible approaches to composing the adaptive system configuration.     

Effect of wavefront corrugations on fringe motion in an astronomical interferometer with spatial filters

Numerical simulations of atmospheric turbulence and adaptive optics (AO) wavefront correction are performed to investigate the time scale for fringe motion in optical interferometers with spatial filters. These simulations focus especially on partial AO correction, where only a finite number of Zernike modes are compensated. The fringe motion is found to depend strongly on both the aperture diameter and the level of AO correction used. In all the simulations the coherence time scale for interference fringes is found to decrease dramatically when the Strehl ratio provided by the AO correction is < or = 30%. For AO systems that give perfect compensation of a limited number of Zernike modes, the aperture size that gives the optimum signal for fringe phase tracking is calculated. For AO systems that provide noisy compensation of Zernike modes (but are perfectly piston neutral), the noise properties of the AO system determine the coherence time scale of the fringes when the Strehl ratio is < or = 30%.     

Convergence rates for iterative vector space projection methods for control of two deformable mirrors for compensation of both amplitude and phase fluctuations

The control of two deformable mirrors for compensation of time-varying fluctuations in the complex field that results from wave propagation through a turbulent medium is considered. Iterative vector space projection methods are utilized to determine the control commands to be applied to the two deformable mirrors. Convergence of the iterative algorithm is accelerated when the algorithm is initialized, at each measurement period, with the values for the phase commands obtained from the previous measurement period. Furthermore, it is found that, if the sample frequency is sufficiently greater than the Greenwood frequency, then only a single iterative step at each measurement period is required to obtain good compensation of both amplitude and phase fluctuations.