Fuzzy Proportional Integral Derivative control of a voice coil actuator system for adaptive deformable mirrors

Research on adaptive deformable mirror technology for voice coil actuators(VCAs)is an important trend in the development of large ground-based telescopes.A voice coil adaptive deformable mirror contains a large number of actuators,and there are problems with structural coupling and large temperature increases in their internal coils.Additionally,parameters of the traditional proportional integral derivative(PID)control cannot be adjusted in real-time to adapt to system changes.These problems can be addressed by introducing fuzzy control methods.A table lookup method is adopted to replace real-time calculations of the regular fuzzy controller during the control process,and a prototype platform has been established to verify the effectiveness and robustness of this process.Experimental tests compare the control performance of traditional and fuzzy proportional integral derivative(Fuzzy-PID)controllers,showing that,in system step response tests,the fuzzy control system reduces rise time by 20.25%,decreases overshoot by 78.24%,and shortens settling time by 67.59%.In disturbance rejection experiments,fuzzy control achieves a 46.09%reduction in the maximum deviation,indicating stronger robustness.The Fuzzy-PID controller,based on table lookup,outperforms the standard controller significantly,showing excellent potential for enhancing the dynamic performance and disturbance rejection capability of the voice coil motor actuator system.

High-resolution visible imaging with piezoelectric deformable secondary mirror: experimental results at the 1.8-m adaptive telescope

Integrating deformable mirrors within the optical train of an adaptive telescope was one of the major innovations in astronomical observation technology,distinguished by its high optical throughput,reduced optical surfaces,and the incorporation of the deformable mirror.Typically,voice-coil actuators are used,which require additional position sensors,internal control electronics,and cooling systems,leading to a very complex structure.Piezoelectric deformable secondary mirror technologies were proposed to overcome these problems.Recently,a high-order piezoelectric deformable secondary mirror has been developed and installed on the 1.8-m telescope at Lijiang Observatory in China to make it an adaptive telescope.The system consists of a 241-actuator piezoelectric deformable secondary mirror,a 192-sub-aperture Shack-Hartmann wavefront sensor,and a multi-core-based real-time controller.The actuator spacing of the PDSM measures 19.3 mm,equivalent to approximately 12.6 cm when mapped onto the primary mirror,significantly less than the voicecoil-based adaptive telescopes such as LBT,Magellan and VLT.As a result,stellar images with Strehl ratios above 0.49 in the R band have been obtained.To our knowledge,these are the highest R band images captured by an adaptive telescope with deformable secondary mirrors.Here,we report the system description and on-sky performance of this adaptive telescope.

Thermal stability test and analysis of a 20-actuator bimorph deformable mirror

One of the important characteristic of adaptive mirrors is the thermal stability of surface flatness. In this paper, the thermal stability from 13℃ to 25℃ of a 20-actuator bimorph deformable mirror is tested by a Shack-Hartmann wavefront sensor. Experimental results show that, the surface P-V of bimorph increases nearly linearly with ambient temperature. The ratio is 0.11 μm/℃ and the major component of surface displacement is defocused, compared with which, astigmatism, coma and spherical aberration contribute very small. Besides, a finite element model is built up to analyse the influence of thickness, thermal expansion coefficient and Young＇s modulus of materials on thermal stability. Calculated results show that bimorph has the best thermal stability when the materials have the same thermal expansion coefficient. And when the thickness ratio of glass to PZT is 3 and Young＇s modulus ratio is approximately 0.4, the surface instability behaviour of the bimorph manifests itself most severely.

A slope-based decoupling algorithm to simultaneously control dual deformable mirrors in a woofer–tweeter adaptive optics system

We propose a slope-based decoupling algorithm to simultaneously control the dual deformable mirrors （DMs） in a woofer-tweeter adaptive optics system. This algorithm can directly use the woofer＇s response matrix measured from a Shack-Hartmann wave-front sensor to construct a slope-based orthogonal basis, and then selectively distribute the large- amplitude low-order aberration to woofer DM and the remaining aberration to tweeter DM through the slope-based orthogonal basis. At the same moment, in order to avoid the two DMs generating opposite compensation, a constraint matrix used to reset tweeter control vector is convenient to be calculated with the slope-based orthogonal basis. Numeral simulation demonstrates that this algorithm has a good performance to control the adaptive optics system with dual DMs simultaneously. Compared with the typical decoupling algorithm, this algorithm can take full use of the compensation ability of woofer DM and release the stroke of tweeter DM to compensate high-order aberration. More importantly, it does not need to measure the accurate shape of tweeter＇s influence function and keeps better performance of restraining the coupling error with the continuous-dynamic aberration.

Numerical model of the influence function of deformable mirrors based on Bessel Fourier orthogonal functions

A numerical model is presented to simulate the influence function of de- formable mirror actuators. The numerical model is formed by Bessel Fourier orthog- onal functions, which are constituted of Bessel orthogonal functions and a Fourier basis. A detailed comparison is presented between the new Bessel Fourier model, the Zernike model, the Gaussian influence function and the modified Gaussian influence function. Numerical experiments indicate that the new numerical model is easy to use and more accurate compared with other numerical models. The new numerical model can be used for describing deformable mirror performances and numerical simulations of adaptive optics systems.

Laser beam shaping with magnetic fluid-based liquid deformable mirrors

A new controllable laser beam shaping technique is demonstrated, where a magnetic fluid-based liquid deformable mirror is proposed to redistribute the laser phase profile and thus change the propagation property of the beam. The mirror is driven by an inner miniature actuator array along with a large outer actuator. The inner actuator array is used for deforming the magnetic fluid surface, while the outer actuator is used to linearize the fluid surface response and amplify the magnitude of the deflection. In comparison to other laser beam shaping techniques, this technique offers the advantages such as simplicity, low cost, large shape deformation, and high adaptability. Based on a fabricated prototype of the liquid deformable mirror, an experimental AO system was set up to produce a desired conical surface shape that shaped the incident beam into a Bessel beam. The experimental results show the effectiveness of the proposed technique for laser beam shaping.

Wavefront correction of Ti:sapphire terawatt laser with varying precision of phase conjugation between deformable mirror and wavefront sensor

The phase conjugation between the deformable mirror and the wavefront sensor in the aberration correction of a terawatt Ti：sapphire laser is studied experimentally and theoretically in this paper. At varying values of phase- conjugation precision, we focus the corresponding beams into spots of the same size of 5.1 μm × 5.3 μm with a f/4 parabola in the 32 TW/36 fs Ti：sapphire laser system. The results show that the precision of conjugation can induce an intensity modulation but does not significantly affect the wavefront correction.

Performance of an Adaptive Optics System with Dual Deformable Mirrors

One deformable mirror （DM） in conventional adaptive optics system can not meet the needs of large scale and high order aberration compensation. In this paper, a dual DMs way is presented, which needs the decoupling of dual DMs. In dual DMs adaptive optics （AO） system, the decoupling algorithm of dual DMs is deduced. Stroke of one of DMs is large, spatial frequency of the other is high. According to the algorithm, the large stroke DM （LSDM） corrects low order aberration only, and the high spatial frequency DM （HSFDM） corrects other aberration. The experimental result for two 61-DM AO system is presented. The result indicates that the experimental performance of dual DMs AO system is almost the same with that of the conventional AO system using single DM with ideal stroke and equivalent spatial frequency.

Conformal optical design with combination of static and dynamic aberration corrections

Conformal domes that are shaped to meet aerodynamic requirements can increase range and speed for the host platform. Because these domes typically deviate greatly from spherical surface descriptions, a variety of aberrations are induced which vary with the field-of-regard （FOR） angle. A system for correcting optical aberrations created by a conformal dome has an outer surface and an inner surface. Optimizing the inner surface is regard as static aberration correction. A deformable mirror is placed at the position of the secondary mirror in the two-mirror all reflective imaging system, which is the dynamic aberration correction. An ellipsoidal MgF2 conformal dome with a fineness ratio of 1.0 is designed as an example. The FOR angle is 0°-30°, and the design wavelength is 4μm. After the optimization at 7 zoom positions by using the design tools Code V, the root-mean-square （RMS） spot size is reduced to approximately 0.99 to 1.48 times the diffraction limit. The design results show that the performances of the conformal optical systems can be greatly improved by the combination of the static correction and the dynamic correction.

Correcting dynamic residual aberrations of conformal optical systems using AO technology

This paper analyses the dynamic residual aberrations of a conformal optical system and introduces adaptive optics （AO） correction technology to this system. The image sharpening AO system is chosen as the correction scheme.Communication between MATLAB and Code V is established via ActiveX technique in computer simulation.The SPGD algorithm is operated at seven zoom positions to calculate the optimized surface shape of the deformable mirror.After comparison of performance of the corrected system with the baseline system,AO technology is proved to be a good way of correcting the dynamic residual aberration in conformal optical design.

Monochrome HUD’s Imaging Projector Based on Laser-DMD System

Design and tolerance of a new head up display’s projector system is reported. It is based on laser-micro display modules. We designed optical diffraction limited modules and some of our novelties were compactness, using common material and spherical lenses in optical design, easy and economical manufacturing process, uniform intensity and minimum aberrations of final image, economical and repairable designed system. Projector magnification is 10.0X and diagonal of image plane is 76.2 mm. ZEMAX software is employed for optical design and tolerance.

Bimorph deformable mirror based adaptive optics scanning laser ophthalmoscope for retina imaging in vivo

A bimorph deformable mirror （DM） with a large stroke of more than 30 μm using 35 actuators is presented and characterized for an adaptive optics （AO） confocal scanning laser ophthalmoscope application. Facilitated with a Shack-Hartmann wavefront sensor, the bimorph DM-based AO operates closed-loop AO corrections for hu- man eyes and reduces wavefront aberrations in most eyes to below 0.1 μm rms. Results from living eyes, including one exhibiting ~5D of myopia and ~2D of astigmatism along with notable high-order aberrations, reveal a prac- tical efficient aberration correction and demonstrate a great benefit for retina imaging, including improving resolution, increasing brightness, and enhancing the contrast of images.