Wave-front sensing and deformable-mirror control in strong scintillation

Recent studies of coherent wave propagation through turbulence have shown that under conditions where scintillation is significant a continuous phase function does not in general exist, owing to the presence of branch points in the complex optical field. Because of branch points and the associated branch cuts, least-squares approaches to wave-front reconstruction and deformable-mirror control can have large errors. Branch-point reconstructors are known to provide superior performance to least-squares reconstructors, but they require that branch points be explicitly detected. Detecting branch points is a significant practical impediment owing to spatial sampling and measurement noise in real wave-front sensors. Branch points are associated with real zeros in an optical field, and hence information about the phase of the field is encoded in the amplitude of the wave. We present a new wave-front-sensor processing algorithm that exploits this observation in the wave-front-reconstruction and deformable-mirror-control process. This algorithm jointly processes three intensity measurements by using light from the beacon field to develop a set of deformable-mirror actuator commands that are maximally consistent with three intensity measurements: (1) the entire wave-front-sensor image, (2) a pupil intensity image, and (3) a conventional image. Owing to the nonlinear nature of the resulting algorithm, we have used a simulation to evaluate performance. We find that in a focused laser beam projection paradigm that uses a point-source beacon, the new algorithm provides significantly improved performance over that of conventional Hartmann sensor least-squares deformable-mirror control based on centroid processing of wave-front-sensor outputs. The performance of the new algorithm approaches, the performance of an idealized branch-point reconstructor that requires pointwise phase differences for operation.     

Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration

Wave-front distortion compensation using direct system performance metric optimization is studied both theoretically and experimentally. It is shown how different requirements for wave-front control can be incorporated, and how information from different wave-front sensor types can be fused, within a generalized gradient descent optimization paradigm. In our experiments a very-large-scale integration (VLSI) system implementing a simultaneous perturbation stochastic approximation optimization algorithm was applied for real-time adaptive control of multielement wave-front correctors. The custom-chip controller is used in two adaptive laser beam focusing systems, one with a 127-element liquid-crystal phase modulator and the other with beam steering and 37-control channel micromachined deformable mirrors. The submillisecond response time of the micromachined deformable mirror and the parallel nature of the analog VLSI control architecture provide for high-speed adaptive compensation of dynamical phase aberrations of a laser beam under conditions of strong intensity scintillations. Experimental results demonstrate improvement of laser beam quality at the receiver plane in the spectral band up to 60 Hz.     

Fundamental limits on isoplanatic correction with multiconjugate adaptive optics

We investigate the performance of a general multiconjugate adaptive optics (MCAO) system in which signals from multiple reference beacons are used to drive several deformable mirrors in the optical beam train. Taking an analytic approach that yields a detailed view of the effects of low-order aberration modes defined over the metapupil, we show that in the geometrical optics approximation, N deformable mirrors conjugated to different ranges can be driven to correct these modes through order N with unlimited isoplanatic angle, regardless of the distribution of turbulence along the line of sight. We find, however, that the optimal deformable mirror shapes are functions of target range, so the best compensation for starlight is in general not the correction that minimizes the wave-front aberration in a laser guide beacon. This introduces focal anisoplanatism in the wave-front measurements that can be overcome only through the use of beacons at several ranges. We derive expressions for the number of beacons required to sense the aberration to arbitrary order and establish necessary and sufficient conditions on their geometry for both natural and laser guide stars. Finally, we derive an expression for the residual uncompensated error by mode as a function of field angle, target range, and MCAO system geometry.     

High-aspect-ratio line focus for an x-ray laser by a deformable mirror

A high-aspect-ratio line focus is required on a plane target in x-ray laser experiments for obtaining a high gain-length product. Inherent wave-front aberrations in line-focusing optics, which consist of a cylindrical lens and a spherical lens, are discussed with respect to beam diameter. The nonuniformity of the linewidth that is due to the aberrations is also calculated by the ABCD matrix method. A deformable mirror of a continuous plate type with a diameter of 185 mm provides an adequate wave-front distribution for compensating for the wave-front aberration. The wave-front control by the deformable mirror realizes a fine linewidth of 25 mum and 18.2 mm long, corresponding to the aspect ratio of 728. The linewidth is three times the diffraction limit. The intensity distribution along the line focus is also improved.     

Two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere

A two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere is presented. This system uses a deformable mirror and a Fourier-transforming mirror to adjust the amplitude of the wave front in the telescope pupil, similar to kinoforms used in laser beam shaping. A second deformable mirror is used to correct the phase of the wave front before it leaves the aperture. The phase applied to the deformable mirror used for controlling the beam amplitude is obtained with a technique based on the Fienup phase-retrieval algorithm. Simulations of propagation through a single turbulent layer sufficiently distant from the beacon observation and laser beam transmission aperture to cause scintillation shows that, for an ideal deformable-mirror system, this field-conjugation approach improves the on-axis field amplitude by a factor of approximately 1.4 to 1.5 compared with a conventional phase-only correction system.     

Wave-front design algorithm for shaping a quasi-far-field pattern

To design a fully continuous wave-front distribution suitable for focused beam shaping by a deformable mirror, we modify the phase-retrieval algorithm by employing a uniformly distributed phase as a starting phase screen and spatial filtering for the near-field phase retrieved during the iteration process. A special phase unwrapping algorithm is not required to obtain a continuous phase distribution from the retrieved phase since the boundary of the 2pi-phase-jumped region in the designed phase distribution is perfectly closed. From the computational result producing a uniform square beam transformation from a circular defocused beam, this algorithm has provided a fully continuous wave-front distribution with a lower spatial frequency for a deformable mirror. The transformed square beam has a normalized intensity nonuniformity of varsigma(rms) = 0.14 with respect to a desired flat-topped square beam pattern. This beam-shaping method also provides a high energy-concentration rate of more than 98%.     

The influence of high-frequency phase and correction distance on the phase correction effect

By studying the propagation characteristics of the wavefront phase of laser beams in adaptive optics systems, the influence of the high-frequency phase on the correction effect has been analyzed and the variations of correction effect with the position of optical deformable mirror have been analyzed quantitatively. The results show that the beam quality of the corrected beam in far field obviously degrades with an increase of high-frequency phase in a distorted wavefront, and the correction effect becomes worse and worse. In addition, the correction effect is related to the position of the deformable mirror; with an increase of the distance between the deformable mirror and the output mirror of the laser the correction effect is better. For a deformable mirror with a given unit size, when the distance of correction is more than 20?m the correction effect is perfect.     

Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation

The nonlinear response and strong coupling of control channels in micromachined membrane deformable mirror (MMDM) devices make it difficult for one to control the MMDM to obtain the desired mirror surface shapes. A closed-loop adaptive control algorithm is developed for a continuous-surface MMDM used for aberration compensation. The algorithm iteratively adjusts the control voltages of all electrodes to reduce the variance of the optical wave front measured with a Hartmann-Shack wave-front sensor. Zernike polynomials are used to represent the mirror surface shape as well as the optical wave front. An adaptive experimental system to compensate for the wave-front aberrations of a model eye has been built in which the developed adaptive mirror-control algorithm is used to control a deformable mirror with 19 active channels. The experimental results show that the algorithm can adaptively update control voltages to generate an optimum continuous mirror surface profile, compensating for the aberrations within the operating range of the deformable mirror.     

Improved compensation of turbulence-induced amplitude and phase distortions by means of multiple near-field phase adjustments

An approach for compensation of turbulence-induced amplitude and phase distortions is described. Two deformable mirrors are placed optically conjugate to the collecting aperture and to a finite range from this aperture. Two control algorithms are presented. The first is a sequential generalized projection algorithm (SGPA) that is similar to the Gerchberg-Saxton phase retrieval algorithm. The second is a parallel generalized projection algorithm (PGPA) that introduces constraints that minimize the number of branch points in the control commands for the deformable mirrors. These approaches are compared with the approach of placing the second deformable mirror conjugate to the far field of the collecting aperture and using the Gerchberg-Saxton algorithm to determine the optimal mirror commands. Simulation results show that placing the second deformable mirror at a finite range can achieve near-unity Strehl ratio regardless of the strength of the scintillation induced by propagation through extended paths, while the maximum Strehl ratio of the far-field approach drops off with increasing scintillation. The feasibility of the solutions is evaluated by counting the branch points contained in the deformable mirror commands. There are large numbers of branch points contained in the control commands that are generated by the Gerchberg-Saxton SGPA-based algorithms, irrespective of where the second deformable mirror is located. However, the control commands generated by the PGPA with branch point constraints achieves excellent Strehl ratio and minimizes the number of branch points.     

Exact ray-trace beam for an off-axis paraboloid surface

When an off-axis paraboloidal mirror focuses a parallel beam, the image is formed on one side of the optical axis. For a tilted beam focused by an off-axis paraboloidal mirror, the focus is no longer pointlike (not considering the diffraction effect); rather, it is a distorted spot. This is due to the inherent aberrations of the surface. In addition, there is a change in the focus position. We calculate by exact ray-trace equations the modified wave-front aberration and express it in power series. Our formulation uses the optical path variation along a defined principal ray that we relate to the parameter that describe the surface and the beam angle of incidence. We designate this ray as that reflected by the center of the entrance pupil and field of view. We employ the direction cosines of the principal ray to compute the wave-front aberration function of a beam reflected by an off-axis paraboloid.     

Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror

We investigate the characteristics of a 37-channel micromachined membrane deformable mirror for wave-front generation. We demonstrate wave-front generation of the first 20 Zernike polynomial modes, using an iterative algorithm to adjust driving voltages. The results show that lower-order-mode wave fronts can be generated with good accuracy and large dynamic range, whereas the generation of higher-order modes is limited by the number of the actuator channels and the working range of the deformable mirror. The speed of wave-front generation can be as fast as several hundred hertz. Our results indicate that, in addition to generation of wave fronts with known aberrations, the characteristics of the micromachined membrane deformable mirror device can be useful in adaptive optics systems for compensating the first five orders of aberration.     

Multiconjugate adaptive optics for large telescopes: analytical control of the mirror shapes

We present an analytical algorithm for deriving the shapes of the deformable mirrors to be used for multiconjugate adaptive correction on a large telescope. The algorithm is optimal in the limit where the overlap of the wave-front contributions from relevant atmospheric layers probed by the guide stars is close to the size of the pupil. The fundamental principle for correction is based on a minimization of the sum of the residual power spectra of the phase fluctuations seen by the guide stars after correction. On the basis of the expressions for the mirror shapes, so-called layer transfer functions describing the distribution of the correction of a single atmospheric layer among the deformable mirrors and the resulting correction of that layer have been derived. It is shown that for five guide stars distributed in a regular cross, two- and three-mirror correction will be possible only up to a maximum frequency defined by the largest separation of the conjugate altitudes of the mirrors and by the angular separation of the guide stars. The performance of the algorithm is investigated in the K band by using a standard seven-layer atmosphere. We present results obtained for two guide-star configurations: a continuous distribution within a given angular radius and a five-star cross pattern with a given angular arm length. The wave-front fluctuations are subjected to correction using one, two, and three deformable mirrors. The needed mirror dynamic range is derived as required root-mean-square stroke and actuator pitch. Finally the performance is estimated in terms of the Strehl ratio obtained by the correction as a function of field angle. No noise has been included in the present analysis, and the guide stars are assumed to be at infinity.     

星载自适应光学系统信标技术与理论

由于重力场、温度场、光学器件等产生波前误差,造成航空详查相机的分辨力和测量精度降低,用自适应光学钠导星信标系统对这种波前误差进行校正是一种理想的方法。通过对钠导星信标产生原理进行分析,提出了钠导星信标理论模型,并且在该模型的基础上进行了仿真实验,在实验中得到相机高度在250-400km高空时激光器最佳脉冲能量值在597-1530mJ之间,激光脉宽则在5.4-7.1ns之间,这些实验数据对实际应用有一定的参考价值。     

Model of structure of hollow searchlight laser beam: low-frequency approximation

We introduce a powerful but simple methodology for numerical modeling of the far field of a hollow searchlight laser beam that is produced by passing a laser beam through a reflaxicon. Such a beam can be used in remote sensing as a space beacon. The far field is described by a Fourier-Bessel transform over an aperture function that includes a conical phase term introduced by the reflaxicon. Computations of the far field of the reflaxicon are difficult. The conventional approach for calculating the far field of such ideal aperture distributions as a plane wave or a Gaussian beam is to find exact solutions in the form of hypergeometric series and determine their asymptotic approximations for large values of some parameter. This approach does not extend to more complicated aperture distributions. We modify the transform by using the asymptotic form for the Bessel function as well as by limiting this form to include only the low-frequency (difference frequency) term. This approach is easily related to a one-dimensional Fourier transform of the aperture distribution, and thus numerical evaluations that make use of this approach can use the fast Fourier transform.     

Modeling the combined effect of static and varying phase distortions on the performance of adaptive optical systems

The end-to-end performance achieved by an adaptive optical (AO) imaging system is determined by a combination of the residual time-varying phase distortions associated with atmospheric turbulence and the quasi-static unsensed and uncorrectable aberrations in the optical system itself. Although the effects of these two errors on the time-averaged Strehl ratio and the time-averaged optical transfer function (OTF) of the AO system are not formally separable, such an approximation is found to be accurate to within a few percent for a range of representative residual wave-front errors. In these calculations, we combined static optical system aberrations and time-varying residual phase distortion characteristics of a deformable mirror fitting error, wave-front sensor noise, and anisoplanatism. The static aberrations consist of focus errors of varying magnitudes as well as a combination of unsensed and uncorrectable mirror figure errors derived from modeling by the Gemini 8-Meter Telescopes Project. The overall Strehl ratios and OTF's that are due to the combined effect of these error sources are well approximated as products of separate factors for the static and time-varying aberrations, as long as the overall Strehl ratio that is due to both errors is greater than approximately 0.1. For lower Strehl ratios, the products provide lower bounds on the actual values of the Strehl ratio and the OTF. The speckle transfer function is also well approximated by a product of two functions, but only where AO compensation is sufficiently good that speckle imaging techniques are usually not required.     

Methods for the characterization of deformable membrane mirrors

We demonstrate two methods for the characterization of deformable membrane mirrors and the training of adaptive optics systems that employ these mirrors. Neither method employs a wave-front sensor. In one case, aberrations produced by a wave-front generator are corrected by the deformable mirror by use of a rapidly converging iterative algorithm based on orthogonal deformation modes of the mirror. In the other case, a simple interferometer is used with fringe analysis and phase-unwrapping algorithms. We discuss how the choice of singular values can be used to control the pseudoinversion of the control matrix.     

Tilt Estimation in Moderate-to-Strong Scintillation

Adaptive optics systems are being applied in ever more challenging environments, for example, the projection of lasers over long horizontal paths through the atmosphere. These long atmospheric paths corrupt the signal received from the beacon and typically yield highly scintillated received wave fronts. Tilt estimation for controlling the fast steering mirror in these systems is complicated by the presence of branch points in the scintillated received wave fronts. In particular, correlation between the tilt and the projected beam's centroid error at the target has been observed in horizontal laser beam projection experiments. The presence of this correlation indicates that better tracking performance should be achievable. We compare the performance of four estimation schemes applied to tilt estimation in a horizontal laser projection system. It is demonstrated that all four schemes underestimate the tilt required to return the laser beam to a target in highly scintillated environments. A method of correcting this tilt is presented, and the expected performance improvement is quantified.     

Adaptive helical mirror for generation of optical phase singularity

We report a specially designed adaptive mirror that can be bent into a helical shape for generation of an optical phase singularity. The adaptive helical mirror (AHM) reported here is a reflective device that can provide a continuous phase variation of the optical field in the azimuthal direction. The construction details and evaluation of the AHM are presented. A Michelson interferometer is used for the detection of the phase singularity. The AHM can be used for generation of a singular beam having multiple topological charges, positive or negative, just by controlling the excitation voltage of the AHM.     

Shack Hartmann wave-front measurement with a large F-number plastic microlens array

A new plastic microlens array, consisting of 900 lenslets, has been developed for the Shack Hartmann wave-front sensor.The individual lens is 300 μm × 300μm and has a focal length of 10 mm, which provides the same focal size, 60 μm in diameter, with a constant peak intensity. One can improve thewave-front measurement accuracy by reducing the spot centroiding error by averaging a few frame memories of an image processor. A deformable mirror for testing the wave-front sensor gives anappropriate defocus and astigmatism, and the laser wave front is measured with a Shack Hartmann wave-front sensor. The measurement accuracy and reproducibility of our wave-front sensor are better than λ/20 and λ/50 (λ = 632.8 nm),respectively, in rms.