Adaptive Laser Beam Shaping Using a Genetic Algorithm

A low cost adaptive optical system for improving solid-state laser beam quality has been set up. This system consists of a deformable mirror, a high voltage amplifier, a set of solid-state laser system, a CCD camera, a control software and corresponding optimization algorithm. This adaptive optical system doesn't employ a wave-front sensor to detect the phase information, but optimize the light intensity within a fixed aperture in the focal plane by a 19-element piezoelectricity deformable mirror. In order to find the optimum surface profile of the deformable mirror, which is applied to correct the phase aberrations in a solid-state laser system, a global genetic algorithm is introduced. The far-field light intensity signal, which is measured by a CCD camera, is used as a fitness function of the genetic algorithm. In this paper, the performance and efficiency of this wave-front sensor-less adaptive optical system based on the genetic algorithm are presented. Both the simulation results and the experimental results are given and discussed.

The performance of laser machining systems can often be improved by adjusting the intensity profile of the beam on the target. Shaping a laser intensity profile can be efficiently accomplished by adjusting the spatial phase of the beam before propagating the beam a distance to the target. Beam shaping can be accomplished with passive diffractive elements, but this technique is only capable of creating a single intensity profile and is usually very sensitive to the input beam characteristics. Beam shaping with active optical elements like deformable mirrors can enable the system to achieve multiple shapes and compensate for non-ideal input beams, but can be very expensive. We present here a demonstration of laser beam shaping with low-cost membrane deformable mirrors.

Nearly every new large-scale laser system application at LLNL has requirements for beam control which exceed the current level of available technology. For applications such as inertial confinement fusion, laser isotope separation, laser machining, and laser the ability to transport significant power to a target while maintaining good beam quality is critical. There are many ways that laser wavefront quality can be degraded. Thermal effects due to the interaction of high-power laser or pump light with the internal optical components or with the ambient gas are common causes of wavefront degradation. For many years, adaptive optics based on thing deformable glass mirrors with piezoelectric or electrostrictive actuators have be used to remove the low-order wavefront errors from high-power laser systems. These adaptive optics systems have successfully improved laser beam quality, but have also generally revealed additional high-spatial-frequency errors, both because the low-order errors have been reduced and because deformable mirrors have often introduced some high-spatial-frequency components due to manufacturing errors. Many current and emerging laser applications fall into the high-resolution category where there is an increased need for the correction of high spatial frequency aberrations which requires correctors with thousands of degrees of freedom. The largest Deformable Mirrors currently availablemore » have less than one thousand degrees of freedom at a cost of approximately $1M. A deformable mirror capable of meeting these high spatial resolution requirements would be cost prohibitive. Therefore a new approach using a different wavefront control technology is needed. One new wavefront control approach is the use of liquid-crystal (LC) spatial light modulator (SLM) technology for the controlling the phase of linearly polarized light. Current LC SLM technology provides high-spatial-resolution wavefront control, with hundreds of thousands of degrees of freedom, more than two orders of magnitude greater than the best Deformable Mirrors currently made. Even with the increased spatial resolution, the cost of these devices is nearly two orders of magnitude less than the cost of the largest deformable mirror.« less

We investigate numerically the feasibility of phase aberration correction in a wavefront sensorless adaptive optical system, based on the imperialist competitive algorithm (ICA). Considering a 61-element deformable mirror (DM) and the Strehl ratio as the cost function of ICA, this algorithm is employed to search the optimum surface profile of DM for correcting the phase aberrations in a solid-state laser system. The correction results show that ICA is a powerful correction algorithm for static or slowly changing phase aberrations in optical systems, such as solid-state lasers. The correction capability and the convergence speed of this algorithm are compared with those of the genetic algorithm (GA) and stochastic parallel gradient descent (SPGD) algorithm. The results indicate that these algorithms have almost the same correction capability. Also, ICA and GA are almost the same in convergence speed and SPGD is the fastest of these algorithms.

The M² factor could be decomposed as amplitude term and phase term. A method to improve the beam quality of laser beams is proposed. In our method, the amplitude and phase of a laser beam are both compensated in order to improve the beam quality completely. In experiment, a laser amplifier is set to modulate the amplitude to Gaussian type, and a deformable mirror is used to compensate the phase aberration. The laser beam is well compensated by our method; the beam quality factor of the laser is improved from 1.7 to 1.1.

Using ultra-short laser pulses for the generation of microstructures results in a high flexible tool for free form geometries in the micro range. Increasing laser power and repetition rates increase as well the demand of high flexible and efficient process strategies. To increase the ablation efficiency the optimal fluency can be determined, which is a material specific value. By varying the beam shape, the ablation efficiency can be enhanced. In this study a deformable mirror was used to vary the beam shape. This mirror is built by combining a piezo-electric ceramic and a mirror substrate. The ceramic is divided into several segments, which can be controlled independently. This results in a high flexible deformable mirror which influences the beam shape and can be used to vary the spot size or generate line geometries. The ablation efficiency and roughness of small generated cavities were analyzed in this study as well as the dimensions of the cavity. This can be used to optimize process strategies to combine high volume ablation and fine detail generation.

The goal of directly imaging Earth-like planets in the habitable zone of other stars has motivated the design of coronagraphs for use with large segmented aperture space telescopes. In order to achieve an optimal trade-off between planet light throughput and diffracted starlight suppression, we consider coronagraphs comprised of a stage of phase control implemented with deformable mirrors (or other optical elements), pupil plane apodization masks (gray scale or complex valued), and focal plane masks (either amplitude only or complex-valued, including phase only such as the vector vortex coronagraph). The optimization of these optical elements, with the goal of achieving 10 or more orders of magnitude in the suppression of on-axis (starlight) diffracted light, represents a challenging non-convex optimization problem with a nonlinear dependence on control degrees of freedom. We develop a new algorithmic approach to the design optimization problem, which we call the ”Auxiliary Field Optimization” (AFO) algorithm. The central idea of the algorithm is to embed the original optimization problem, for either phase or amplitude (apodization) in various planes of the coronagraph, into a problem containing additional degrees of freedom, specifically fictitious ”auxiliary” electric fields which serve as targets to inform the variation of our phase or amplitude parameters leading to good feasible designs. We present the algorithm, discuss details of its numerical implementation, and prove convergence to local minima of the objective function (here taken to be the intensity of the on-axis source in a ”dark hole” region in the science focal plane). Finally, we present results showing application of the algorithm to both unobscured off-axis and obscured on-axis segmented telescope aperture designs. The application of the AFO algorithm to the coronagraph design problem has produced solutions which are capable of directly imaging planets in the habitable zone, provided end-to-end telescope system stability requirements can be met. Ongoing work includes advances of the AFO algorithm reported here to design in additional robustness to a resolved star, and other phase or amplitude aberrations to be encountered in a real segmented aperture space telescope.

A general approach is presented for evaluating and optimizing the degree of atmospheric turbulence compensation achieved by an adaptive optics system employed as part of a extended field-of-view astronomical telescope. This method applies to an adaptive optics system incorporating either one or multiple natural and/or laser guide stars sensed by wave-front slope sensors, a wave-front reconstruction algorithm equivalent to a matrix multiply, a servo control law to temporally filter the output of the wave-front reconstructor, and one or several deformable mirrors optically conjugate to different ranges along the telescope’s line-of-sight. The degree of atmospheric turbulence compensation achieved by such a configuration is evaluated in terms of the residual mean-square phase distortion and turbulence-induced optical transfer function at each point in the telescope’s field-of-view. This evaluation accounts for the combined, interacting effects of the atmospheric turbulence C n 2 ( h ) profile and wind velocity profile, wave-front sensor and deformable mirror fitting error, wave-front sensor noise, finite control system bandwidth, and the net anisoplanatism associated with a given constellation of natural and/or laser guide stars. Optimal wave-front reconstruction algorithms are derived which minimize the telescope’s field-of-view-averaged residual mean-square phase distortion. These evaluation and optimization results are first-order in the sense that they neglect diffraction effects and assume that all adaptive optics components are strictly linear. Results for the case of a finite servo bandwidth also require the wave-front reconstruction algorithm coefficients to satisfy a set of linear constraints; the reconstructor must precisely predict the deformable mirror actuator command vector in the absense of sensor noise and atmospheric turbulence. Numerical results are presented for a variety of adaptive optics configurations incorporating either a single guide star, multiple guide stars and a single deformable mirror, or multiple guide stars and two deformable mirrors.

It is well known that using two or more deformable mirrors (DMs) can improve the compensation ability of an adaptive optics (AO) system. However, to keep the stability of an AO system, the correlation between the multiple DMs must be suppressed during the correction. In this paper, we proposed a slope-based decoupling algorithm to simultaneous control the multiple DMs. In order to examine the validity and practicality of this algorithm, a typical woofer-tweeter (W-T) AO system was set up. For the W-T system, a theory model was simulated and the results indicated in theory that the algorithm we presented can selectively make woofer and tweeter correct different spatial frequency aberration and suppress the cross coupling between the dual DMs. At the same time, the experimental results for the W-T AO system were consistent with the results of the simulation, which demonstrated in practice that this algorithm is practical for the AO system with dual DMs.

Unimorph deformable mirrors are attractive in adaptive optics system due to their advantages of simplicity, compact, low cost and large stroke. In this paper, a double drive modes unimorph deformable mirror is presented, which comprises a 200 μm thick PZT layer and a 400 μm thick silicon layer. This deformable has 214 inner actuators in the 50-mm active aperture, which are for the aberration correction and a outer ring actuator for generating an overall defocus bias. An analytical model based on the theory of plates and shells is built to predict the behavior of the deformable mirror. The stroke of the deformable mirror is tested in the experiments. In order to test the performance for aberration correction, the deformable mirror is used to correct the aberration from its imperfect initial mirror surface in the close-loop manner. The root-mean-square value of the mirror surface after the close-loop correction for ten iterations is about λ/40, which indicates this deformable mirror has a good aberration correction performance. This DM has the potential to be used for astronomical adaptive optics.

Arbitrary spatial beam shaping was demonstrated with a membrane electrostatic actuator type deformable mirror (DM). An automatic closed loop system must optimize such beam shapes as flattop. Well-characterized short pulse laser beam is widely required for a photocathode RF gun or for microscopic processing, etc. We propose a new sophisticated optimizing method based on a genetic algorithm (GA) for spatial shaping. A membrane type DM is driven by electrostatic attraction power, and applied electrode voltages vs displacement of membrane surface have a square function relationship. We prepare discrete electrode voltages to linearly change displacement as a utilized gene of the initial population in GA. Using uniform crossover without mutation in this method, we can make an arbitrary spatial beam shape quasi-flattop.

High-power laser plays an important role in many fields, such as directed energy weapon, optoelectronic contermeasures, inertial confinement fusion, industrial processing and scientific research. The uniform nearfield and wavefront are the important part of the beam quality for high power lasers, which is conducive to maintaining the high spatial beam quality in propagation. We demonstrate experimentally that the spatial intensity and wavefront distribution at the output is well compensated simultaneously in the complex high-power solid-state laser system by using the small-aperture spatial light modulator (SLM) and deformable mirror (DM) in the front stage. The experimental setup is a hundred-Joule-level Nd:glass laser system operating at three wavelengths at 1053 nm (1ω), 527 nm (2ω) and 351 nm (3ω) with 3 ns pulse duration with the final output beam aperture of 60 mm. While the clear arperture of the electrically addressable SLM is less than 20 mm and the effective diameter of the 52-actuators DM is about 15 mm. In the beam shaping system, the key point is that the two front-stage beam shaping devices needs to precompensate the gain nonuniform and wavefront distortion of the laser system. The details of the iterative algorithm for improving the beam quality and the strategy of achiving high beam quality on spatial intensity and wavefront simultaneously are presented. Experimental results show that the output wavefront RMS value is 0.06, and simultaneously the output near-field modulation is 1.38:1 and the fluence contrast is 10.5% at 3 ns at 1053nm with 40-Joule-level energy.

(abridged) Extreme adaptive optics (XAO) encounters severe difficulties to cope with the high speed (>1kHz), high accuracy and high order requirements for future extremely large telescopes. An innovative high order adaptive optics system using a self-referenced Mach-Zehnder wavefront sensor (MZWFS) allows counteracting these limitations. This sensor estimates very accurately the wavefront phase at small spatial scale by measuring intensity differences between two outputs, with a $\lambda /4$ path length difference between its two legs, but is limited in dynamic range due to phase ambiguity. During the past few years, such an XAO system has been studied by our team in the framework of 8-meter class telescopes. In this work, we report on our latest results with the XAO testbed recently installed in our lab, and dedicated to high contrast imaging with 30m-class telescopes (such as the E-ELT or the TMT). After reminding the principle of a MZWFS and describing the optical layout of our experiment, we will show the results of the assessment of the woofer-tweeter phase correctors, i.e., a Boston Micromachine continuous membrane deformable mirror (DM) and a Boulder Nonlinear Systems liquid crystal spatial light modulator (SLM). In particular, we will detail the calibration of the DM using Zygo interferometer metrology. Our method consists in the precise measurement of the membrane deformation while applying a constant deformation to 9 out of 140 actuators at the same time. By varying the poke voltage across the DM operating range, we propose a simple but efficient way of modeling the DM influence function using a Gaussian model. Finally, we show the DM flattening on the MZWFS allowing to compensate for low order aberrations.

We present a direct slope-based correction algorithm to simultaneously control two deformable mirrors (DMs) in a woofer-tweeter adaptive optics system. A global response matrix was derived from the response matrices of each deformable mirror and the voltages for both deformable mirrors were calculated simultaneously. This control algorithm was tested and compared with a 2-step sequential control method in five normal human eyes using an adaptive optics scanning laser ophthalmoscope. The mean residual total root-mean-square (RMS) wavefront errors across subjects after adaptive optics (AO) correction were 0.128 ± 0.025 μm and 0.107 ± 0.033 μm for simultaneous and 2-step control, respectively (7.75-mm pupil). The mean intensity of reflectance images acquired after AO convergence was slightly higher for 2-step control. Radially-averaged power spectra calculated from registered reflectance images were nearly identical for all subjects using simultaneous or 2-step control. The correction performance of our new simultaneous dual DM control algorithm is comparable to 2-step control, but is more efficient. This method can be applied to any woofer-tweeter AO system.

NRC’s NEW-EARTH Lab has demonstrated in the laboratory a Self-Coherent Camera (SCC) concept combined with a Tilt-Gaussian-Vortex focal plane mask (FPM). This speckle suppression technique, a.k.a. Fast Atmospheric SCC Technique (FAST), can enhance the contrast up to 100 times. Based on this success, NRC is now building SPIDERS, a visitor instrument for Subaru telescope to be installed on the infrared Nasmyth platform behind AO188 and the new Subaru Beam Switcher. The beam can be either shared between SPIDERS and SCExAO for simultaneous observations or sent entirely to only one instrument. SPIDERS should also benefit from the upcoming AO188 deformable mirror (DM) upgrade (64x64 actuators) turning A188 to AO3k. The key-components of SPIDERS are an ALPAO DM468, used as a second-stage AO correction, a pupil apodizer mask, a Tilt-Gaussian FPM, a Lyot stop, a beam-splitter feeding (i), a C-RED2 camera imaging a 5” FoV in narrow bands and (ii), an imaging Fourier-Transform Spectrograph and a SAPHIRA camera for spectroscopy up to R~20,000 over a 3.3” FoV. SPIDERS optical design is fully reflective up to the FPM to avoid chromatic aberrations and reduce the number of surfaces. Two off-axis ellipsoid mirrors are enough to form the pupil planes required on the DM and the apodizer mask, and the f/64 focus on the FPM. Only lenses are used from the FPM up to the C-RED2 camera to mitigate the sensitivity of the SCC to vibrations. The Lyot stop reflects the blocked light to a camera acting as a Low-Order Wavefront Sensor complementing the SCC focal plane wavefront sensing.