Deformable Mirror Surface Research Articles

Active-compensation of systematic error for the 1000 mm aperture flat interferometer.

Large-aperture elements would induce unnegligible systematic errors due to material inhomogeneity, manufacturing or gravity, that are difficult to correct in an extreme large aperture flat interferometer and result in reference wavefront distortion. We propose an active-compensation method for systematic errors by employing a deformable mirror into the interferometer to modulate reference wavefront. A mapping relationship between sag of the deformable mirror and reference wavefront error is derived by theory of matrix optics, and two interferometer optical paths are designed for whether the deformable mirror is located at the pupil or not. The algorithm for calculating and controlling the sag of a deformable mirror can eliminate the need for the deformable mirror to be positioned at the pupil in order to achieve controllable modulation of the wavefront. This algorithm has been validated through the intentional introduction of systematic errors into the 1000 mm aperture flat interferometer for effective compensation. Moreover, the optimization algorithm in Ansys Zemax is utilized to calculate the optimal solution for surface shape of the deformable mirror, treating it as a nominal value. The algorithm error is on the order of 10-6 mm, falling within the acceptable tolerance range for the deformable mirror's surface shape.

Embedded parallel-actuated technology for deformable space segmented mirror

The deployable segmented space imaging system is an important solution for future ultra-large aperture space optical systems. To achieve the imaging capability of an equivalent aperture monolithic mirror, it requires not only to ensure the positional accuracy in the cophasing process, but also to have extremely high surface accuracy and curvature consistency of the sub-mirrors. However, this work is extremely challenging due to the manufacturing error of the sub-mirrors and the complex space environment. Active optical technology can ensure the surface shape accuracy of the spliced mirror by controlling the mirror surface deformation and compensating for the wavefront aberration. This article compares and analyzes the control ability of two types of deformable mirrors actuated by vertical and parallel methods. We explored the characteristics of the influence function mathematical models of the two types of actuation forms and compared the aberration and curvature correction abilities of them through finite element analysis, summarizing the advantages of the parallel actuation forms. Finally, a 300mm aperture embedded parallel-actuated deformable mirror was designed and manufactured, and relevant experiments were conducted to verify its adjustment ability. By comparing and analyzing the experimental results with the design results, the adjustment ability of the embedded parallel-actuated deformable mirror was verified.

Shape optimization design of the offset mirror in FEL-1 beamline at S3FEL

Nowadays, due to the advantages of high peak power, high average power, ultra-short pulse, and fully coherent characteristics, the high-repetition-rate free-electron laser (FEL) is thriving in many countries around the world. The thermal load caused by high-repetition-rate FEL poses a great challenge to the mirror surface shape. Especially in the case of high average power, how to perfectly control the mirror shape to maintain the coherence of the beam has become a difficult problem in beamline design. In addition to multi-segment PZT, when multiple resistive heaters are used to compensate for the mirror shape, the heat flux (or power) generated by each heater must be optimized to obtain sub-nanometer height error. This article establishes MHCKF model for the mirror surface deformation under the combined effect of the mirror initial deformation, the thermal deformation caused by X-rays, and the deformation compensated by multiple heaters. By searching the perturbation term in the mathematical model, the least squares solution of the heat fluxes generated by all heaters can be obtained. This method can not only set multiple constraints on the heat fluxes but also quickly obtain their values when minimizing the mirror shape error. It overcomes the problem of time-consuming optimization processes encountered by traditional finite element analysis software, especially in the context of multi-parameter optimization. This article focuses on the offset mirror in the FEL-1 beamline at S3FEL. Using this method, the optimization of 25 heat fluxes generated by all resistive heaters was accomplished within a few seconds utilizing an ordinary laptop. The results indicate that the height error RMS decreased from 40 nm to 0.009 nm, and the slope error RMS reduced from 192.7nrad to 0.4nrad. Wave-optics simulations show that the wavefront quality has been significantly improved. In addition, some factors affecting mirror shape error, such as the number of heaters, higher repetition rate, film coefficient, and the length of copper tube, were analyzed. The results show that the MHCKF model and optimization algorithm can effectively solve the optimization problem of compensating for the mirror shape with multiple heaters.

Structural strength of iso-polyhedral beryllium alloy rotating mirror for ultra-high-speed camera

This study aims to examine the influence law of polyhedron structure on the spatial mechanical properties of ultra-high-speed rotating mirrors. To this end, polyhedral beryllium alloy rotating mirrors are investigated on the basis of elastoplastic theory and finite element method. The maximum stress is located at the end position of the contact between the shaft and the mirror body. Stress increases with the number of mirror faces. The different structures have a negative stress gradient. The structural strength of rotating mirror is affected by the strength of the mirror body material in high-speed rotation of the tensile force of centrifugal force. The lateral deformation of the mirror surface is caused by the combined effect of compression of centrifugal force generated by the material of sharp-corner and the tretching of tensile force caused by the material at the centre of the mirror at high-speed rotation. The amount of mirror surface deformation is not proportional to the number of faces. The rotating mirror with iso-quadrangular structure has the best lateral deformation effect. This research provides a theoretical basis for the research and design of rotating mirrors with high potential value.

Description method with automatically configurable Gaussian radial basis function for complex freeform surface.

The description of deformable mirror (DM) surface, which is usually a complex freeform surface, affects the measurement speed and accuracy in a real-time interferometric measurement system with a DM as the dynamic compensator. We propose an accurate and fast description method with automatically configurable Gaussian radial basis function. The distribution and shape factors of GRBFs are related to the complexity of the surface with sufficient flexibility to improve the accuracy, and the fitting results are automatically obtained using a traversal optimization algorithm, which can improve the fitting speed by reducing the number of time-consuming calculations. The feasibility is verified by numerical and practical experiment.

High-precision assembly process of large-aperture laser transport mirror in the high-energy laser facility

Aiming to minimize the surface distortion of large-aperture laser transport mirrors in high-power laser facilities, an assembly design and mounting method are proposed for the mirror. First, a theoretical model on the mirror surface deformation is established. With a new assembly design, the mirror is fastened on its neutral plane and its optical surface distortion can be precisely compensated through several adjustable forces on the sides, which will generate bending moments on the mirror body. Furthermore, a dynamic kinematic joint is designed, in which a corresponding relationship between spring compression and screw rotation ensures the accurate control of the magnitude of mirror preload. Finally, the performance of the presented method has been validated through field experiments and numerical simulations. This transport mirror assembly and mounting design have obvious technical advantages on simple mechanical structure, high operational efficiency, and precise preload control. The results show that the assembly design and optimized mounting strategy can keep the total surface distortion of the mirror within 350 nm (peak-valley).

Contoured thermal deformation of mirror surface for detuning parametric instability in an optical cavity

Independent mode frequency control will improve the ability to suppress parametric instabilities in gravitational wave detectors. In this article we investigate a formalism that allows multiple cavity optical modes to be thermally tuned independently based on the transformation between the change in mode spacing and the mirror surface deformation. An FFT based cavity simulation software is used to demonstrate the effectiveness of the formalism. A case study showed that it is possible to tune the HG03 mode spacing by 100 Hz while maintaining other mode spacings with minimum change. Our investigation also indicates that the desired mirror surface deformation is experimentally realisable with a matrix heater.

Small-phase retrieval using single focused far-field intensity

We develop a method to retrieve small wave-front aberrations from a single far-field intensity. The solution specifies the even and odd parts of the unknown phase T in two separate equations. Both the odd part and the even part require only one focus intensity measurement with a given phase diversity produced by the deformable mirror or active surface system. We take the solution, the approximation of T, zero and random phase distributions as the initial guesses of GS (Gerchberg & Saxton) algorithm respectively, the final recovered TR is chosen from the one with the minimum amplitude Root Mean Squared Error (RMSE). Numerical simulation results show that the method works well when the root mean squared (RMS) of the phase error is less than 3.14 rad, and it is effective when the signal-to-noise ratio(SNR)>10. Phase ambiguity is solved by moving the deformable mirror twice according to the twin images TR and TR’ TR*, and the image with higher peak intensity is selected as the final estimation of T.

Study on the correction method of the deformable mirror surface profile

Before using the deformable mirror (DM) for wavefront beam shaping, it is necessary to correct its surface profile to reduce the high-order aberrations, because the DM surface profile is different from the original set plane. In this paper, we demonstrate a simple method to correct the DM surface profile. The method is verified experimentally by using He-Ne laser. Results show that the DM surface profile is corrected to be near flat-topped by using the method. The output peak-to valley value changes from 2.38 λ to 0.21 λ of the He-Ne laser and the RMS value changes from 0.49 λ to 0.04 λ after correcting the DM surface.

Adaptive optics system simulator

In this paper we present the development of a computational tool that simulates the behavior of the basic devices in an adaptive optics system. These elements are a deformable mirror, a Shack-Hartmann wavefront sensor and a basic control system. To represent the wavefront and the deformable mirror surface, Zernike polynomials and Gaussian profiles as influence functions, respectively, were used. The Shack-Hartmann sensor was represented by a lenslet array and the irradiance pattern was obtained using the Fourier Optics theory. The developed programs enable calculation of the reconstruction and influence matrices, as well as estimation of the Zernike coefficients and vector voltages required for the actuators of the deformable mirror. In the programs the user can change the number of lenslets in the Shack Hartmann sensor as well as the number of actuators in the deformable mirror. This simulation system can be used as support tool with a real system or alone to improve the understanding of the elements in the Adaptive Optics system when there is no access to an experimental setup.

Beam alignment based on the imaging properties of the spatial filter by controlling the deformable mirror in a high power laser

Deformable mirror placed in the front-end is widely used for wavefront correction in high power solid-state lasers. However, the laser beam is usually partly blocked by the spatial filter pinhole when the deformable mirror surface is improper. In this paper, this beam alignment problem is solved based on the imaging properties of the spatial filter by controling the defocusing value of the deformable mirror surface. Experimental results show that the spatial filter pinhole is passed through successfully and a relatively complete laser beam nearfield is achieved after beam alignment in the output of the laser system.

A control algorithm for an adaptive optics system based on the focal spot radius minimization

A control algorithm for adaptive optics systems using the focal spot of a light beam is suggested. The algorithm is based on the analytical relationship between the spot radius and a change in shape of the deformable mirror surface. A numerical simulation has been carried out, which verifies this relationship and its applicability to the wavefront correction. Some experimental results confirm the algorithm applicability for practical use.

Thermal optics property study and athermal design on optical window of IR aiming device reliability testing system

Optical window is used as optical interface connecting the reliability texting system for infrared aiming device with external infinite infrared simulation target which runs in acute axial temperature field, excellent thermal optics performance of optical window is the fundamental guarantee for testing system being in normal operation. In order to decrease the deformation of mirror surface caused by thermal stress, an athermal design decreasing thermal stress of optical window is put forward, a mathematical model of the deformation of optical window under axial temperature load is established and rigid body displacement after thermal deformation is analyzed by means of finite element method, the mirror surface is fitted by Zernike polynomial and introduced into optical analysis software to provide the analysis result of image quality and luminance uniformity of optical system. The rigid body displacement of optical window after athermal design decreases 0.164mm, MTF keeps invariant basically at 20lp/mm special frequency, the PV value and RMS value of IR optical window is just 0.342λ and 0.043λ, and uniformity of exit beam is raised up more significantly than without athermal design. The ZYGO interferometer is adopted as testing equipment detecting surface shape error (PV/RMS) of optical parallel of IR optical window. The experimental results show that the simulation results are in good agreement with the experimental results.

Analysis and experimental investigation for collimator reflective mirror surface deformation adjustment

Analysis and experimental investigation for collimator reflective mirror surface deformation adjustment

Optimization of lightweight structure and supporting bipod flexure for a space mirror.

This article presents an optimization process for integrated optomechanical design. The proposed optimization process for integrated optomechanical design comprises computer-aided drafting, finite element analysis (FEA), optomechanical transfer codes, and an optimization solver. The FEA was conducted to determine mirror surface deformation; then, deformed surface nodal data were transferred into Zernike polynomials through MATLAB optomechanical transfer codes to calculate the resulting optical path difference (OPD) and optical aberrations. To achieve an optimum design, the optimization iterations of the FEA, optomechanical transfer codes, and optimization solver were automatically connected through a self-developed Tcl script. Two examples of optimization design were illustrated in this research, namely, an optimum lightweight design of a Zerodur primary mirror with an outer diameter of 566mm that is used in a spaceborne telescope and an optimum bipod flexure design that supports the optimum lightweight primary mirror. Finally, optimum designs were successfully accomplished in both examples, achieving a minimum peak-to-valley (PV) value for the OPD of the deformed optical surface. The simulated optimization results showed that (1)the lightweight ratio of the primary mirror increased from 56% to 66%; and (2)the PV value of the mirror supported by optimum bipod flexures in the horizontal position effectively decreased from 228 to 61nm.

Study on fatigue damage characteristics of deformable mirrors under thermal-mechanical coupling effect.

In a wavefront correction process, both the mechanical effect and the irradiation of a high-power continuous-wave laser distort the deformable mirror (DM) surface, which inevitably speeds up the fatigue damage of the DM. By utilizing the stress analysis model for the fatigue damage of the DM, the fatigue damage effects are analyzed quantitatively on the consideration of thermal-mechanical coupling effects, and the fatigue life prediction model has further been proposed based on the S-N curve and Miner cumulative damage theory. On this basis, thermal-mechanical conditions have been analyzed, and the influence of laser parameters on the fatigue life of the DM has also been discussed in detail. The results indicate that the increasing of maximum temperature rise of the DM leads to the increasing of stress, and further brings about the decreasing of the fatigue life. Meanwhile, the position at the rear surface of the DM subjected to the maximum stress always presents the minimum fatigue life. Furthermore, the laser irradiation makes the DM more easily damaged when the DM is correcting a distorted wavefront, and the fatigue life decreases with the increasing of irradiation time and power density for a given peak and valley (PV) value of the corrected wavefront. Additionally, the fatigue life also decreases with the increasing of power density and the decreasing of spot radius for a certain total irradiation. On the other hand, for the given laser parameters, the influence of the mechanical effect on fatigue life is gradually apparent with increasing PV value of the corrected wavefront, and when the PV value is more than 2λ, the mechanical effect instead of the thermal effect becomes the key factor for fatigue damage of the DM.

Study of a wide-aperture combined deformable mirror for high-power pulsed phosphate glass lasers

A deformable mirror with the size of controlled by bimorph piezoceramic plates and multilayer piezo stacks is developed. The response functions of individual actuators and the measurements of the flatness of the deformable mirror surface are presented. The study of mirrors with an interferometer and a wavefront sensor has shown that it is possible to improve the surface flatness down to a residual roughness of (RMS). The possibility of correction of beam aberrations in an ultra-high-power laser using the created bimorph mirror is demonstrated.

Feasibility of Constrained Receding Horizon Control Implementation in Adaptive Optics

Adaptive optics (AO) provide real-time compensation for atmospheric turbulence to improve the resolution of images acquired by ground-based optical telescopes. The actuators in deformable mirrors, which are used as correctors, are constrained by a maximal allowable movement. The control techniques used in current AO systems do not account for these constraints, leading to inferior performance and a risk of damage of the deformable mirror's surface. This paper presents a feasibility study for receding horizon control (RHC) with online constrained quadratic programming (QP). The results of numerical simulations provided in this paper are based on realistic models obtained from an optical test-bench. We compare QP algorithms that represent three main methods for convex optimization: 1) interior point; 2) active set (AS); and 3) gradient-based algorithms. It is shown that constrained RHC is computationally feasible for moderate-size AO systems using hot-started structure-exploiting AS QP solvers with bound constraints. An evaluation of performance indicates that RHC is advantageous in terms of atmospheric turbulence rejection in the case of active constraints.

Erratum to: Measurement of copper vapour laser-induced deformation of dielectric-coated mirror surface by Michelson interferometer

A Michelson interferometer-based technique has been used to measure the deformation of dielectric-coated mirror, caused by an incident repetitive pulsed laser beam with high average power. Minimum measurable deformation of 17 nm is reported.

Faulty actuator tolerance in deformable mirrors for Extremely Large Telescope multi-object adaptive optics

Planned instruments utilizing multi-object adaptive optics systems on the forthcoming extremely large telescopes require large numbers of high order deformable mirrors. These devices are a significant cost driver, particularly if specifications regarding the number of faulty actuators are stringent. Here, we investigate the effect on adaptive optics performance that such faulty actuators have, and draw conclusions about how far faulty actuator specifications (and hence cost) can be relaxed without having a significant effect on adaptive optics performance. We also provide performance estimates using a map of faulty actuators from an existing deformable mirror. We investigate the effect of faulty actuators using an end-to-end Monte Carlo adaptive optics simulation code. We find that for actuators stuck at a fixed height above the deformable mirror surface, between 1 and 2 per cent of actuators can be faulty before significant performance degradation occurs. For actuators that are a coupled to nearest neighbours, up to about 5 per cent, can be faulty before adaptive optics (AO) performance begins to be affected.