Controlling an active bimorph deformable mirror with sub-nanometre resolution

Piezoelectric bimorph deformable mirrors (`bimorphs') are routinely used on many synchrotron and free-electron laser beamlines to provide active variation in the size and shape of the X-ray beam. However, the time-domain potential of such optics has never been fully exploited. For the first time, the fast dynamic bending response of bimorphs is investigated here using Fizeau interferometry. Automated scripts for acquisition and analysis were developed to collect Fizeau data at a rate of 0.1 Hz to record dynamic changes in the optical surface as voltages were applied to the electrodes of the piezoelectric actuators. It is demonstrated that residual drift in the tangential radius of curvature of a bimorph can be significantly reduced using enhanced opto-mechanical holders and a fast programmable high-voltage power supply. Further improvements are achieved by applying small opposing voltages to compensate for piezoelectric creep. The present study shows that bimorphs can truly be used as high-speed adaptive optics for the X-ray domain, even without closed-loop feedback correction. This opens the possibility for relatively simple real-time tuning of the profile of X-ray bimorphs. Part II of this study [Alcock, Nistea, Signorato, Owen, Axford, Sutter, Foster & Sawhney (2019), J. Synchrotron Rad. 26, 45-51] builds upon these results and demonstrates how bimorphs can rapidly provide customisable sizes and shapes of synchrotron X-ray beams, specifically tailored to suit the experimental samples being investigated.

Harmonic lasing in a free electron laser with a planar undulator (under the condition that the fundamental frequency is suppressed) might be a cheap and efficient way of extension of wavelength ranges of existing and planned x-ray free electron laser (FEL) facilities. Contrary to nonlinear harmonic generation, harmonic lasing can provide much more intense, stable, and narrow-band FEL beam which is easier to handle due to the suppressed fundamental frequency. In this paper we perform a parametrization of the solution of the eigenvalue equation for lasing at odd harmonics, and present an explicit expression for FEL gain length, taking into account all essential effects. We propose and discuss methods for suppression of the fundamental harmonic. We also suggest a combined use of harmonic lasing and lasing at the retuned fundamental wavelength in order to reduce bandwidth and to increase brilliance of x-ray beam at saturation. Considering 3rd harmonic lasing as a practical example, we come to the conclusion that it is much more robust than usually thought, and can be widely used in the existing or planned x-ray FEL (XFEL) facilities. In particular, Linac Coherent Light Source (LCLS) after a minor modification can lase to saturation at the 3rd harmonic up to the photon energy of 25--30 keV providing multigigawatt power level and narrow bandwidth. As for the European XFEL, harmonic lasing would allow one to extend operating range (ultimately up to 100 keV), to reduce FEL bandwidth and to increase brilliance, to enable two-color operation for pump-probe experiments, and to provide more flexible operation at different electron energies. Similar improvements can be realized in other x-ray FEL facilities with gap-tunable undulators like FLASH II, SACLA, LCLS II, etc. Harmonic lasing can be an attractive option for compact x-ray FELs (driven by electron beams with a relatively low energy), allowing the use of the standard undulator technology instead of small-gap in-vacuum devices. Finally, in this paper we discover that in a part of the parameter space, corresponding to the operating range of soft x-ray beam lines of x-ray FEL facilities (like SASE3 beam line of the European XFEL), harmonics can grow faster than the fundamental wavelength. This feature can be used in some experiments, but might also be an unwanted phenomenon, and we discuss possible measures to diminish it.

Deformable, piezo bimorph mirrors are often used to expand X-ray beams to a continuous range of sizes. However, optical polishing errors present on all X-ray mirrors introduce striations into the reflected beam. To counteract them, reentrant surface modifications with alternating concave and convex curvature have been proposed and applied to mirrors of fixed shape or bimorph mirrors. For the latter, a new method of constructing re-entrant surface modifications on segments of unequal length is described. This allows the re-entrant modification required for a desired beam size at the focal point to be matched to the bimorph mirror’s polishing errors, thus reducing the voltage variations. Optical profilometry using the Diamond-NOM showed that a 5-segment and a 7-segment modification could be suitably applied to a deformable bimorph mirror. X-ray tests showed that striations caused by the 5-segment modification in the beam at the focus are concentrated at the beam edges, while the beam center is left clear. This is in contrast to simple defocusing, in which a strong side shoulder appears. The 7-segment modification produces a pattern of evenly spaced striations. The intensity spikes seen with the re-entrant modifications are caused chiefly by the finite curvature of the mirror at the turning points. The question of whether deformable bimorph mirrors with different piezo response functions could sharpen the curvature changes will be investigated. Optimal modifications of continuous curvature, which could more realistically be applied, will be sought.

High average power operation of the Mercury Laser induces dynamic aberrations to the laser beam wavefront. Analysis of recent data indicates that up to 4 waves of low order aberration (mainly focus error or power, with spatial resolution < 0.5 cm{sup -1}) could be expected at each pass. Because of the magnitude of the wavefront error, the logical position is to place a deformable mirror (DM) at the M11 position, where the DM will correct the beam between passes 1 & 2 and 3 & 4. Currently, there are only two established commercial vendors offering complete adaptive optic (AO) systems that can accommodate the Mercury beam size (45 x 75 mm) which are compatible with high damage threshold coatings. Xinetics (MA, USA) offers a complete AO system along with a Shack-Hartmann wavefront sensor. The Xinetics DM is based on lead magnesium niobate (PMN) technology. A number of US aerospace firms as well as NIF use Xinetics PMN technology for their DMs. Phasics (Paris, France) offers a complete AO solution with its proprietary SID-4, a four-way shearing interferometric wavefront sensor capable of high resolution (over 100 x 100 sampling points). The Phasics system includes a bimorph deformable mirror from Night-n-Opt (Moscow, Russia) that uses lead zirconate titanate (PZT) technology. Various high power laser laboratories around the world such as LULI (France), HELEN (UK), and GEKKO (Japan) are using the PZT-based bimorph DM in their system. While both DM technologies are equivalent and have been deployed in high-energy laser systems, the PZT based bimorph DM offers two distinct features that makes it more attractive for high average power laser systems. The bimorph DM uses two layers of PZT actuators with the outer layer acting as power correctors, capable of correcting up to 20 waves of power. The Xinetics DM offers a maximum stroke of 4 waves. In addition, Night-N-Opt has also designed a water-cooled DM with a silicon based substrate (as opposed to a glass substrate) specifically for high average power laser systems--an option that is currently not available for PMN based DMs.

High-energy and high-intensity lasers are essential for pushing the boundaries of science. Their development has allowed leaps forward in basic research areas, including laser–plasma interaction, high-energy density science, metrology, biology and medical technology. The Helmholtz International Beamline for Extreme Fields user consortium contributes and operates two high-peak-power optical lasers using the high energy density instrument at the European X-ray free electron laser (EuXFEL) facility. These lasers will be used to generate transient extreme states of density and temperature to be probed by the X-ray beam. This paper introduces the ReLaX laser, a short-pulse high-intensity Ti:Sa laser system, and discusses its characteristics as available for user experiments. It will also present the first experimental commissioning results validating its successful integration into the EuXFEL infrastructure and viability as a relativistic-intensity laser driver.

In our previous works, we presented a zoom system and image stabilization design based on deformable mirrors (DMs). According to the high bandwidth and free edge characteristics of the piezoelectric deformable mirror (PDM), we tested the system’s image-stable capability. We found the PDM could realize some tilt displacements while keeping a certain stable surface shape, it could obtain higher image stabilizing precision when integrated with the traditional mechanical image stabilization systems. In the design of the image stabilization system, the PDM’s tilt displacement range is a key factor for consideration. So in this paper, we carried out a tilt displacement range testing experiment by using the OKO’s 37-channel PDM. We measured and analyzed the variation of the tilt displacements in optical image stabilization process, and calculated the maximum tilt angle as the PDM surface shape was stabilized. We built an experimental platform consisting of a fixed target, an imaging system based on PDM, and a CCD camera. We used the ZYGO interferometer as an evaluation instrument to measure the surface shape stability. When the PDM surface had a tilt displacement, the image point of the fixed target on the camera sensor shifted correspondingly. The tilt angle of the PDM could be obtained by calculating this shift. The results showed that the maximum tilt angle of the PDM was 0.2mrad. The paper also analyzed the experiment errors when concerning about the off-axis error of the PDM deflection center.

To compensate for the wavefront distortions in high-power laser setups we developed stacked-actuator deformable mirror with aperture of 120 mm and 121 control actuators and bimorph deformable mirror with size of 410×468 mm. Design of the stacked-actuator mirror provides substitution of broken piezoactuators. Also, we can provide thermostabilization of the mirror surface through actuator body. Bimorph mirror has high surface amplitude deformation (about 20 um) and good flatness of the initial surface of the mirror (0.03 um RMS). Also, there is a possibility of preliminary adjustment by the piezostacks, which situated on the edge of the mirror.

The wave front corrector is one of the three key elements in adaptive optics, along with the wave front sensor and the control computer. Low cost, compact deformable mirrors are increasingly available. We have tested the AOptix bimorph deformable mirror, originally developed for ultra-high bandwidth laser communication systems, to determine its suitability for vision science applications, where cornea and lens introduce optical aberrations. Measurements of the dynamic response of the mirror to a step input were obtained using a commercial Laser Doppler Vibrometer (LDV). A computer-controlled Twyman-Green interferometer was constructed to allow the surface height of the deformable mirror to be measured using Phase-Shifting Interferometry as a function of various control voltages. A simple open-loop control method was used to compute the control voltages required to generate aberration mode shapes described by the Zernike polynomials. Using this method, the ability of the deformable mirror to generate each mode shape was characterized by measuring the maximum amplitude and RMS error of each Zernike mode shape up to the fifth radial order. The maximum deformation amplitude was found to diminish with the square of the radial order of the Zernike mode, with a measured deformation of 8 microns and 1.5 microns achieved at the second-order and fifth-order Zernike modes, respectively. This deformation amplitude appears to be sufficient to allow the mirror to correct for aberrations up to the fifth order in the human eye.

The development of laser technique and various applications of laser radiation requires the use of devices that can modify as well as correct for the wavefront of laser beams. In these cases, the use of deformable mirrors is simply very important. In the high-power laser setups, the task of correction of laser aberrations assumes the use of thermally stabilized optical elements. We consider that two types of wavefront correctors are the most well-suitable for such an application: bimorph deformable mirrors and stacked-actuator (SADM) ones. Bimorph deformable mirrors proved their reliability and could be used in high-power industrial lasers. They can perfectly correct for low-order and are simple in manufacturing. On the contrary stacked-actuator mirror can reproduce high-order wavefront aberrations and thus have high spatial resolution of control elements and might be applied in fast adaptive optical systems to correct for laser radiation distributed through turbulent media.

The bimorph deformable mirror with a diameter of 320 mm, including 127 control electrodes, has been developed and tested. The flatness of the initial mirror surface of about 1 μm (P-V) was achieved by mechanically adjusting the mirror substrate fixed in the metal mount. To correct for the aberrations and improve the beam focusing in the petawatt Ti:Sa laser, the wide-aperture adaptive optical system with the deformable mirror and Shack–Hartmann wavefront sensor was developed. Correction of the wavefront aberrations in the 4.2 PW Ti:Sa laser using the adaptive system provided increases the intensity in the focusing plane to a value of 1.1 × 1023 W/cm2

PZT-glued bimorph deformable mirrors are widely used in hard X-ray regimes; however, they haven’t been used in soft X-ray regimes because they are less compatible for usage under high vacuum. Therefore we have developed a glue-free bimorph deformable mirror, in which silver nano-particles were employed to bond PZT actuators to mirror substrates. However at long type, precise shape control had been hard since its mirror size was longer than PZT plate length whose gap between each PZT enevitablly existed. These gap area cannot be bended. In this study, we developed deformable mirror using triangle shaped PZT which aim is to reduce gap effect even at long mirror. At the simulation result, the gap effect would be reduced to be under 0.01 nm even at maximum bending. Also, vacuum tests of PZT glue-free bimolph mirror were also conducted. The final degree of vacuum obtained 9×10-8 Pa that was same as background level.

A four-group stabilized zoom lens design of two focal-length-variable elements was discussed in our early work. The focal-length of the zoom system could be adjusted by tuning the surface shape of focal-length-variable element. In this paper, we propose to use the deformable mirror (DM) as the focal-length-variable device, and then we need to control the DM to forming the required surface shape and analyze the errors between actual surface and theoretic surface. This lays the foundation for analyzing the focusing zoom errors of the stabilized zoom lens in the zoom process. This paper firstly introduces a DM flatten method applied for using OKO Technologies’ Piezoelectric Deformable Mirror (PDM) and analyzes the high order errors of flattened surface with the help of ZYGO interferometer. Then we study the method of DM control to form sphere surfaces with different curvature. The analyses of the high order error of the actual surface and the measurement of the curvature range of the sphere surface are also included in this paper.

We describe the development of flexi-circuit addressed, high resolution small aperture Bimorph Deformable Mirror (BDM) suitable for a satellite to ground optical communications system. In the first phase, the base of an existing BDM was modified to enable integration onto a commercially available tip-tilt stage. Evaluation demonstrated that there was no reduction in performance as a result of the integration. In the current phase, a 100 element BDM with a 10mm optical aperture suitable for integration onto a bespoke tip-tilt platform has been designed and assembled. The results of initial tests are presented.

In the development process of satellite control systems and solar sensors, conventional solar simulators can"t show variations in the solar shape and intensity in the state of solar occultation, so we set up a solar simulation and test platform. A method is put forward to simulate the wavefront error based on deformable mirror (DM). In this paper, the main relevant parameters which describe the atmospheric turbulence are introduced. The statistic characteristics of optical wavefront phase influenced by atmospheric turbulence are presented, and analyzed by the method of Zernike modes. A piezoelectric DM with 109 electrodes manufactured by OKO is used as the wavefront phase modulator. The important technology parameter about the deformable mirror is tested. Owing to the linear superposition, we have a research in the optical influence function and voltage deflection. The method of Karhunen-Loeve function is used in the simulation of optical wavefront, because it is statistically independent and can be expanded into the form of Zernike polynomials. We can get the coefficient matrix of random turbulence wavefront, and then link up with surface of the mirror. According to the relationship between deformation of the mirror and the voltage, we can deduce the voltage control matrix, and change the surface of the mirror as we conceive. The numerical results indicate that wavefront error can be introduced to the distribution maps of solar shape and intensity in different orbital position and any tangent point by DM in the light path.

We describe a closed-loop adaptive optical system with bimorph deformable mirror to obtain good focused laser beam. This adaptive system can correct for the wavefront aberrations without any measurements of the wavefront: we use M2-meter as a sensor for the feedback. Closed-loop software allows to measure focal spot with M2-meter and then to calculate voltages to be applied to corrector. The best focal spot can be reached by use of combined method based on genetic and hill-climbing algorithms. We demonstrate the use of such a system with water-cooled bimorph deformable mirror as a wavefront corrector on CW solid state Nd:YAG 1kW CW laser system.