Fast Steering Mirror Research Articles

Hysteresis Modeling and Compensation of Fast Steering Mirrors with Hysteresis Operator Based Back Propagation Neural Networks.

Fast steering mirrors (FSMs), driven by piezoelectric ceramics, are usually used as actuators for high-precision beam control. A FSM generally contains four ceramics that are distributed in a crisscross pattern. The cooperative movement of the two ceramics along one radial direction generates the deflection of the FSM in the same orientation. Unlike the hysteresis nonlinearity of a single piezoelectric ceramic, which is symmetric or asymmetric, the FSM exhibits complex hysteresis characteristics. In this paper, a systematic way of modeling the hysteresis nonlinearity of FSMs is proposed using a Madelung’s rules based symmetric hysteresis operator with a cascaded neural network. The hysteresis operator provides a basic hysteresis motion for the FSM. The neural network modifies the basic hysteresis motion to accurately describe the hysteresis nonlinearity of FSMs. The wiping-out and congruency properties of the proposed method are also analyzed. Moreover, the inverse hysteresis model is constructed to reduce the hysteresis nonlinearity of FSMs. The effectiveness of the presented model is validated by experimental results.

Experimental study on adaptive optical wavefront correction with dual mirrors in free space optical communication

The wavefront of light wave contains a tilt component after atmospheric turbulence, which increases the wavefront distortion and reduce the quality of laser communication. A fast steering mirror (FSM) must be introduced to correct the wavefront tilt. The adaptive optical closed-loop control algorithm based on Zernike mode decomposition is used to correct the wavefront distortion of light wave after indoor (0.5 m), 600 m, 1 km, 5 km, 10 km, and 100 km transmission. The experimental results show that, under the above-mentioned six different distances, the wavefront phase decreased from 9.5 µm, 15 µm, 12.5 µm, 22 µm, 35 µm, and 450–5 µm, 10 µm, 7.5 µm, 8 µm, 20 µm, and 300 µm, respectively, only after the closed-loop of the FSM; only after the closed-loop of the deformable mirror (DM), the wavefront phase decreased to 8 µm, 9 µm, 9 µm, 20 µm, 15 µm, and 300 µm, respectively. Further, when the FSM and DM are closed simultaneously, the wavefront phase decreases to 0.2 µm, 2.1 µm, 0.4 µm, 3.1 µm, 5 µm, and 200 µm. The correction effect of closed-loop of FSM and DM at the same time is better than that of either FSM or DM only.

Image Motion Measurement and Image Restoration System Based on an Inertial Reference Laser.

Satellites have many high-, medium-, and low-frequency micro vibration sources that lead to the optical axis jitter of the optical load and subsequently degrade the remote sensing image quality. To address this problem, this paper developed an image motion detection and restoration method based on an inertial reference laser, and describe edits principle and key components. To verify the feasibility and performance of this method, this paper also built an image motion measurement and restoration system based on an inertial reference laser, which comprised a camera (including the inertial reference laser unit and a Hartmann wavefront sensor), an integrating sphere, a simulated image target, a parallel light pope, a vibration isolation platform, a vibration generator, and a 6 degrees of freedom platform. The image restoration principle was also described. The background noise in the experiment environment was measured, and an image motion measurement accuracy experiment was performed. Verification experiments of image restoration were also conducted under various working conditions. The experiment results showed that the error of image motion detection based on the inertial reference laser was less than 0.12 pixels (root mean square). By using image motion data to improve image quality, the modulation transfer function (MTF) of the restored image was increased to 1.61–1.88 times that of the original image MTF. The image motion data could be used as feedback to the fast steering mirror to compensate for the satellite jitter in real time and to directly obtain high-quality images.

Coupled dynamic reaction force study of a large-aperture piezoelectric fast steering mirror.

The reaction force of a large-aperture piezoelectric fast steering mirror (PFSM) has adverse coupling interference for the stability and pointing accuracy of laser beams, and the dynamic characteristics of the reaction force are coupled with the inner components of the PFSM. In order to compensate for and eliminate the reaction force, it is essential to accurately analyze the dynamic characteristics. In this paper, a simplified piezoelectric-coupling model of PFSM is established. The coupling mathematical equations for investigating the characteristics of the reaction force are deducted based on the piezoelectric constitutive equation and Hamiltonian's principle. Then the coupling characteristics of the reaction force are probed by a finite element (FE) piezoelectric-coupling method. The simulations for three large apertures' (250, 320, and 400 mm) FE models show that the reaction force has a linear positive correlation with the actuating voltage, and coupled with the materials of the central flexure hinge, the relationship between the reaction force and driving frequency is not completely quadratic. Experiments with the 320 mm aperture are completed, and the testing results are consistent with the mathematical model and the FE piezoelectric-coupling simulation. The dynamic characteristics of the reaction force demonstrated in this paper are significance for the accurate estimation of the reaction force, the design of compensation structure, and the optimization of algorithm for beam jitter controlling.

Development of a novel two-DOF piezo-driven fast steering mirror with high stiffness and good decoupling characteristic

A novel two-DOF piezo-driven fast steering mirror (PFSM) with high stiffness and good decoupling characteristic was proposed. This PFSM could realize rotary motions around X-axis and Y-axis by differential push–pull structure with four piezoelectric stack actuators (PSAs) arranged in cross and orthogonal state, and its lateral stiffness was high enough to overcome the problem that PSA was easy to be destroyed by large lateral force. The PFSM was designed and its working principle was described in detail. The static model was established to analyze the stiffness characteristic of the structure and precisely predict the output angles. The finite element method (FEM) was performed to verify the effectiveness of the proposed structure and static model. A prototype of the PFSM was fabricated, and an experimental setup was established. The experiments showed that the proposed PFSM could achieve rotary motion ranges of 2.33 mrad around X-axis and 2.25 mrad around Y-axis under the voltage of 120 V, respectively. And the resolution was measured as high as 0.28 μrad with the voltage increment of 0.2 V. Furthermore, the first order resonance frequency was measured as 4578 Hz and a good decoupling characteristic was obtained, the coupling errors of both two axes were below 0.75%. The two-DOF PFSM could be applied to the laser communication and the adaptive optics system based on its merits of high stiffness, high resolution and good decoupling characteristic.

Laser Beam Pointing Stabilization Control through Disturbance Classification

In laser systems, beam pointing usually drifts as a consequence of various disturbances, e.g., inherent drift, airflow, transmission medium variation, mechanical vibration, and elastic deformation. In this paper, we develop a laser beam pointing control system with Fast Steering Mirrors (FSMs) and Position Sensitive Devices (PSDs), which is capable of stabilizing both the position and angle of a laser beam. Specifically, using the ABCD matrix, we analyze the kinematic model governing the relationship between the rotation angles of two FSMs and the four degree-of-freedom (DOF) beam vector. Then, we design a Jacobian matrix feedback controller, which can be conveniently calibrated. Since disturbances vary significantly in terms of inconsistent physical characteristics and temporal patterns, great challenges are imposed to control strategies. In order to improve beam pointing control performance under a variety of disturbances, we propose a data-driven disturbance classification method by using a Recurrent Neural Network (RNN). The trained RNN model can classify the disturbance type in real time, and the corresponding type can be subsequently used to select suitable control parameters. This approach can realize the universality of the beam stabilization pointing system under various disturbances. Experiments on beam pointing control under several typical external disturbances are carried out to verify the effectiveness of the proposed control system.

H∞ controller design for the mitigation of atmospheric effects on the laser beam pointing

In this paper, the control of a fast steering mirror, which is the core element of an adaptive optics system, is investigated to suppress the beam jitter. The main source of the jitter is taken as the atmospheric turbulence. The effect of the atmospheric turbulence on the beam jitter is experimentally determined with respect to the two different refractive index structure parameters. The mathematical model of the fast steering mirror based on the atmoshperic turbulence data is obtained using the system identification. In order to overcome implementation problems, the low order proportional-integral-derivative (PID) type controllers, which minimize the [Formula: see text] norm of the closed loop system, are designed in the centralized and the decentralized settings. In addition to this, the fixed order weighted [Formula: see text] controller is based on the frequency characteristics of the atmospheric turbulence that is determined experimentally. Then, in order to show the effectiveness of the proposed low order PID type controller, the designed controllers are compared on the experimental setup. Finally, the simulation and the experimental results are presented. Comparison of advantageous and disadvantageous of centralized and decentralized controller architectures are discussed.

Design and characterisation of a compact 4-degree-of-freedom fast steering mirror system based on double Porro prisms for laser beam stabilization

This paper proposes a 4-degree-of-freedom (DOF) actuator for a fast steer mirror (FSM) compensation system in order to compensate for 4-DOF laser errors. The mathematic system modeling was built to design and predict the performance of the proposed 4-DOF FSM. Finite element analysis was performed by using a commercial software to analyze the characteristics of the electromagnetic structure and mechanical structure for the proposed 4-DOF FSM. This study further verifies the properties of the proposed 4-DOF FSM by using a laboratory-built prototype. The proposed 4-DOF FSM has the travel range of ±5 mrad and ±0.04 mm along X and Y axes with accuracy of 0.025 mrad and 0.0012 mm and the bandwidth of rotational part and translational part are 10 Hz and 39 Hz, respectively.

Numerical analysis of multi-scale pressure pulsation on the energy accumulation for submarine-based tracking and pointing systems

One of the main goals of submarine designers and researchers is to estimate the influence of submarine fluid dynamics for submarine-based optical tracking and pointing systems. In this study, firstly, based on the basic flow governing equation and hierarchical grids, the numerical simulation method of DNS (direct numerical simulation) is adopted to simulate the seawater flow around the submarine at 6° yaw angle and 107 Reynolds number. Secondly, the transformation equations from the earth coordinate system to the optical axis system have been deduced and the ultimate influence of pressure torques on the tracking system is studied. Transfer functions of the coarse channel direct current (DC) torque motor and fine channel fast steering mirror (FSM) also have been modeled and deduced. On this basis, the time domain step responses of both subsystems are analyzed by MATLAB Simulink. Finally, performance analyses have been deduced by comparing the error variation and vortices evolution. It revealed that the frequency characteristics of multi-scale pressure pulsation mainly depended on the lengths of submarine hull or its appendage, as well as the fluid dissipation and random interaction. In general, the coarse channel appears a good compensation performance at low frequency and large amplitude error that caused by the middle-scale pressure pulsation. Contrarily, the FSM fine channel exerts an excellent control effect for higher frequency and small amplitude error caused by small-scale pressure pulsations.

Numerical Simulation of the Fast Steering Mirror

According to the structural characteristic and working properties, the finite element analysis model of the fast steering mirror (FSM) is established. The numerical simulation is conducted for the FSM. The resonance frequency by use of the modal analysis is compared with the measured result. It is concluded that the resonance frequency of the mirror has the least influence on the mirror in the entire steering mirror structure. The theoretical basis is provided for the structural design of the steering mirror.

Strategies for achieving high key rates in satellite-based QKD

Quantum key distribution (QKD) is a pioneering quantum technology on the brink of widespread deployment. Nevertheless, the distribution of secret keys beyond a few 100 km at practical rates remains a major challenge. One approach to circumvent lossy terrestrial transmission of entangled photon pairs is the deployment of optical satellite links. Optimizing these non-static quantum links to yield the highest possible key rate is essential for their successful operation. We therefore developed a high-brightness polarization-entangled photon pair source and a receiver module with a fast steering mirror capable of satellite tracking. We employed this state-of-the-art hardware to distribute photons over a terrestrial free-space link with a distance of 143 km, and extracted secure key rates up to 300 bits per second. Contrary to fiber-based links, the channel loss in satellite downlinks is time-varying and the link time is limited to a few minutes. We therefore propose a model-based optimization of link parameters based on current channel and receiver conditions. This model and our field test will prove helpful in the design and operation of future satellite missions and advance the distribution of secret keys at high rates on a global scale.

Design and application of bi-axial half-butterfly flexure hinges in fast steering mirrors

Design and application of bi-axial half-butterfly flexure hinges in fast steering mirrors

Multi-objective optimal design of elliptic flexible hinge in fast steering mirror

Multi-objective optimal design of elliptic flexible hinge in fast steering mirror

Piston Error Evaluation and Correction for Multi-aperture Imaging System

In this paper, the imaging quality of a three-aperture Golay3 imaging system is studied. The formula of point spread function (PSF) is derived when piston errors exist among each subaperture. The 1951 resolution target is used to analyze the imaging quality under the influence of different piston errors. To evaluate the imaging quality quantificationally, the Tenengrad function based on image gradient definition is employed. The fast steering mirror (FSM) controlled by PZT is used to eliminate the phase error in the optical structure of the Golay3 imaging system. The principle and formula of piston error correction are introduced. Using the Tenengrad function, the relationship between the movement of PZT and the image sharpness is obtained. Through the simulation of piston error correction, the piston error p = λ/2 in the system can be completely corrected when the PZT movement p’ = 0.35λ.

Multi-Objective Optimization Design of Natural Frequency of Two-Degree-of-Freedom Fast Steering Mirror System

In the design of two-degree-of-freedom (2-DOF) fast steering mirror (FSM) system, in order to improve the control bandwidth of the system, the low-order natural frequency in the working direction should be reduced as much as possible, and the high-order natural frequency in the non-working direction should be increased. In this paper, a deep-cut flexure hinge mirror system was studied. Firstly, the motion direction of the first to third order natural vibration mode of the system was analyzed. Next, the working stiffness in the third vibration mode direction was deduced to solve the problem that the traditional stiffness calculation method is not suitable for the third vibration mode direction. Then, the energy method and the Castigliano’s second theorem were used to analyze the working stiffness of the deep-cut flexure hinge. Next, the formula for calculating the relationship between the thickness of the mirror and the moment of inertia in the direction of the vibration mode was derived. Combined with the calculation formula of working stiffness in the vibration mode direction, the formula of the first to third order natural frequencies was derived, and the finite element verification and sensitivity analysis of structural parameters were carried out. Finally, by using NSGA-II, a multi-objective optimization design was carried out on the first to third natural frequencies of the system with hinge structure parameters and reflector thickness as independent variables, and the optimization results were analyzed by theoretical calculation and finite element simulation verification. The results show that the first and second-order natural frequencies of fast steering mirror system are reduced by 7.8% and 7.11%, and the third-order natural frequencies are increased by 139.8%. It proves that the optimized structure is much better than the original structure, and the optimal calculation can effectively increase the control bandwidth of the system

Active disturbance rejection controller of fast steering mirror based on improved dragonfly algorithm

Active disturbance rejection controller of fast steering mirror based on improved dragonfly algorithm

Structure Design of Compact Piezoelectric Fast Steering Mirror with High Performance

Structure Design of Compact Piezoelectric Fast Steering Mirror with High Performance

Decoupling control of fast steering mirror based on dual feedforward + dual neural network adaptive

Decoupling control of fast steering mirror based on dual feedforward + dual neural network adaptive

Design of flexible support for fast steering mirror via kinematic principles

Design of flexible support for fast steering mirror via kinematic principles

Optimal design of natural frequency of two-degree-of-freedom fast steering mirror system

Optimal design of natural frequency of two-degree-of-freedom fast steering mirror system