Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors

Noise effects induced by laser guide star (LGS) elongation have to be considered globally in a multi-LGS tomographic reconstruction analysis. This allows a fine estimation of performance and the comparison of different launching options. We present a modal analysis of the wavefront error with Shack-Hartmann wavefront sensors based on quasi-analytical matrix formalism. Including spot elongation and the Rayleigh fratricide effect, edge launching produces similar performance to central launching and avoids the risk of possible underestimation of fratricide scatter. Performance improves slightly with an optimized centroid estimator and is not affected by a slight field-of-view truncation of the subapertures. Finally we discuss detector characteristics for a LGS Shack-Hartmann wavefront sensor.     

Detection of phase singularities with a Shack-Hartmann wavefront sensor

While adaptive optical systems are able to remove moderate wavefront distortions in scintillated optical beams, phase singularities that appear in strongly scintillated beams can severely degrade the performance of such an adaptive optical system. Therefore the detection of these phase singularities is an important aspect of strong-scintillation adaptive optics. We investigate the detection of phase singularities with the aid of a Shack-Hartmann wavefront sensor and show that, in spite of some systematic deficiencies inherent to the Shack-Hartmann wavefront sensor, it can be used for the reliable detection of phase singularities, irrespective of their morphologies. We provide full analytical results, together with numerical simulations of the detection process.     

Study of a MEMS-based Shack-Hartmann wavefront sensor with adjustable pupil sampling for astronomical adaptive optics

We introduce a Shack-Hartmann wavefront sensor for adaptive optics that enables dynamic control of the spatial sampling of an incoming wavefront using a segmented mirror microelectrical mechanical systems (MEMS) device. Unlike a conventional lenslet array, subapertures are defined by either segments or groups of segments of a mirror array, with the ability to change spatial pupil sampling arbitrarily by redefining the segment grouping. Control over the spatial sampling of the wavefront allows for the minimization of wavefront reconstruction error for different intensities of guide source and different atmospheric conditions, which in turn maximizes an adaptive optics system's delivered Strehl ratio. Requirements for the MEMS devices needed in this Shack-Hartmann wavefront sensor are also presented.     

Hybrid wavefront sensor for the fast detection of wavefront disturbances

Strongly aberrated wavefronts lead to inaccuracies and nonlinearities in holography-based modal wavefront sensing (HMWS). In this contribution, a low-resolution Shack-Hartmann sensor (LRSHS) is incorporated into HMWS via a compact holographic design to extend the dynamic range of HMWS. A static binary-phase computer-generated hologram is employed to generate the desired patterns for Shack-Hartmann sensing and HMWS. The low-order aberration modes dominating the wavefront error are first sensed with the LRSHS and corrected by the wavefront modulator. The system then switches to HMWS to obtain better sensor sensitivity and accuracy. Simulated as well as experimental results are shown for validating the proposed method.     

Differential Shack-Hartmann curvature sensor: local principal curvature measurements

The concept of a differential Shack-Hartmann (DSH) curvature sensor was recently proposed, which yields wavefront curvatures by measuring wavefront slope differentials. As an important feature of the DSH curvature sensor, the wavefront twist curvature terms can be efficiently obtained from slope differential measurements, thus providing a means to measure the Monge-equivalent patch. Specifically, the principal curvatures and principal directions, four key parameters in differential geometry, can be computed from the wavefront Laplacian and twist curvature terms. The principal curvatures and directions provide a "complete" definition of wavefront local shape. Given adequate sampling, these measurements can be useful in quantifying the mid-spatial-frequency wavefront errors, yielding a complete characterization of the surface being measured.     

Shack-Hartmann sensor improvement using optical binning

We present a design improvement for a recently proposed type of Shack-Hartmann wavefront sensor that uses a cylindrical (lenticular) lenslet array. The improved sensor design uses optical binning and requires significantly fewer detector pixels than the corresponding conventional or cylindrical Shack-Hartmann sensor, and so detector readout noise causes less signal degradation. Additionally, detector readout time is significantly reduced, which reduces the latency for closed loop systems and data processing requirements. We provide simple analytical noise considerations and Monte Carlo simulations, we show that the optically binned Shack-Hartmann sensor can offer better performance than the conventional counterpart in most practical situations, and our design is particularly suited for use with astronomical adaptive optics systems.     

Application of eigenmode in the adaptive optics system based on a micromachined membrane deformable mirror

The construction process and characteristics of a deformable mirror eigenmode are introduced. The eigenmode of a 37-element micromachined membrane deformable mirror (MMDM) from OKO, Ltd. is analyzed. The Gaussian-Seidel low-order aberrations are fitted with eigenmodes as basic functions. An experimental adaptive optics (AO) system is constructed with the MMDM as the wavefront corrector, a deformable mirror eigenmode as the wavefront control algorithm, and a Shack-Hartmann wavefront sensor as the wavefront detector. The experimental results demonstrate that the deformable mirror eigenmode can act as the wavefront control algorithm for the AO system based on the MMDM.     

Dipole influence on Shack-Hartmann vortex detection in scintillated beams

Optical vortices can appear in an optical beam that propagates over a long distance through a turbulent atmosphere. A Shack-Hartmann wavefront sensor can be used to detect such vortices. However, the morphology of these vortices, which changes with beam propagation, and nearby oppositely charged vortices will affect this vortex detection. The influence of the morphology and the separation distance from oppositely charged vortices on the Shack-Hartmann vortex detection is studied. Numerical simulations for vortex detection under these turbulent atmospheric circumstances are also provided.     

High-speed Shack-Hartmann wavefront sensor design with commercial off-the-shelf optics

Several trade-offs relevant to the design of a two-dimensional high-speed Shack-Hartmann wavefront sensor are presented. Also outlined are some simple preliminary experiments that can be used to establish critical design specifications not already known. These specifications include angular uncertainty, maximum measurable wavefront tilt, and spatial resolution. A generic design procedure is then introduced to enable the adaptation of a limited selection of CCD cameras and lenslet arrays to the desired design specifications by use of commercial off-the-shelf optics. Although initially developed to aid in the design of high-speed (i.e., megahertz-frame-rate) Shack-Hartmann wavefront sensors, our method also works when used for slower CCD cameras. A design example of our procedure is provided.     

Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering

We describe modeling and simulation results for the Thirty Meter Telescope on the degradation of sodium laser guide star Shack-Hartmann wavefront sensor measurement accuracy that will occur due to the spatial structure and temporal variations of the mesospheric sodium layer. By using a contiguous set of lidar measurements of the sodium profile, the performance of a standard centroid and of a more refined noise-optimal matched filter spot position estimation algorithm is analyzed and compared for a nominal mean signal level equal to 1000 photodetected electrons per subaperture per integration time, as a function of subaperture to laser launch telescope distance and CCD pixel readout noise. Both algorithms are compared in terms of their rms spot position estimation error due to noise, their associated wavefront error when implemented on the Thirty Meter Telescope facility adaptive optics system, their linear dynamic range, and their bias when detuned from the current sodium profile.     

Wavefront error measurement of high-numerical-aperture optics with a Shack-Hartmann sensor and a point source

We developed a new, to the best of our knowledge, test method to measure the wavefront error of the high-NA optics that is used to read the information on the high-capacity optical data storage devices. The main components are a pinhole point source and a Shack-Hartmann sensor. A pinhole generates the high-NA reference spherical wave, and a Shack-Hartmann sensor constructs the wavefront error of the target optics. Due to simplicity of the setup, it is easy to use several different wavelengths without significant changes of the optical elements in the test setup. To reduce the systematic errors in the system, a simple calibration method was developed. In this manner, we could measure the wavefront error of the NA 0.9 objective with the repeatability of 0.003 lambda rms (lambda = 632.8 nm) and the accuracy of 0.01 lambda rms.     

Wavefront sensor based on the Talbot effect with the precorrected holographic grating

A holographic wavefront sensor based on the Talbot effect is proposed. Optical wavefronts are measured by sampling the light amplitude distribution with a two-dimensional (2D) precorrected holographic grating. The factors that allow changing an angular measurement range and a spatial resolution of the sensor are discussed. A comparative analysis with the Shack-Hartmann sensor is illustrated with some experimental results.     

Sampling error analysis of Shack–Hartmann wavefront sensor with variable subaperture pixels

Abstract

The sampling error of a Shack–Hartmann wavefront sensor with variable subaperture pixels is analysed under the consideration of various threshold values and detecting dynamic ranges. A generalized expression, which is used for fitting the sampling error of a Shack-Hartmann wavefront sensor with variable subaperture pixels, is presented. The computational results of the sampling error of a Shack–Hartmann wavefront sensor with different pixel numbers per subaperture, different detecting dynamic ranges, different atmospheric coherence length, different extended degree of the object and the different threshold values are also given. The results indicate that the sampling error of the Shack–Hartmann wavefront sensor is sensitive to the dynamic range of the subaperture, the pixel numbers per subaperture, the extended degree of the object and the coherent length of atmosphere, but not sensitive to the threshold value.     

小波滤波在Shack-Hartmann传感器上的应用

在使用Shack-Hartmann传感器进行大口径非球面镜面检测中,外部环境的各种振动影响以及气流、温差的干扰都会使检测精度下降。针对这个问题,提出了一种新的时域小波滤波技术。这项技术可以对传感器的信号干扰在时间域上进行不同层次的小波分析,提取干扰信号的先验特征,对测量数据进行有效的滤波,减小波前的扰动起伏,以更准确地探测质心。实验结果表明,采用这种技术后,Shack-Hartmann波前传感器对光学镜面检测的静态测量精度提高了50%以上,离散性减少到原来的20%-30%。     

Adaptive optics technique to overcome the turbulence in a large-aperture collimator

A collimator with a long focal length and large aperture is a very important apparatus for testing large-aperture optical systems. But it suffers from internal air turbulence, which may limit its performance and reduce the testing accuracy. To overcome this problem, an adaptive optics system is introduced to compensate for the turbulence. This system includes a liquid crystal on silicon device as a wavefront corrector and a Shack-Hartmann wavefront sensor. After correction, we can get a plane wavefront with rms of about 0.017 lambda (lambda=0.6328 microm) emitted out of a larger than 500 mm diameter aperture. The whole system reaches diffraction-limited resolution.     

Cumulative Reconstructor: fast wavefront reconstruction algorithm for Extremely Large Telescopes

The Cumulative Reconstructor (CuRe) is a new direct reconstructor for an optical wavefront from Shack-Hartmann wavefront sensor measurements. In this paper, the algorithm is adapted to realistic telescope geometries and the transition from modified Hudgin to Fried geometry is discussed. After a discussion of the noise propagation, we analyze the complexity of the algorithm. Our numerical tests confirm that the algorithm is very fast and accurate and can therefore be used for adaptive optics systems of Extremely Large Telescopes.     

Calibration of a Shack-Hartmann sensor for absolute measurements of wavefronts

We demonstrate a method with which to calibrate a Shack-Hartmann sensor for absolute wavefront measurement of collimated laser beams. Nearly perfect spherical wavefronts originating from a single-mode fiber were used as references. After the calibration, the uncertainty of the wavefront was less than lambda/100 peak to valley across a diameter of 6 mm. For example, this method allowed us to balance aberrations and prepare collimated beams with wavefronts that are plane to lambda/500 across 1 mm.     

Error propagation: a comparison of Shack-Hartmann and curvature sensors

Phase estimates in adaptive-optics systems are computed by use of wavefront sensors, such as Shack-Hartmann or curvature sensors. In either case, the standard error of the phase estimates is proportional to the standard error of the measurements; but the error-propagation factors are different. We calculate the ratio of these factors for curvature and Shack-Hartmann sensors in dependence on the number of sensors, n, on a circular aperture. If the sensor spacing is kept constant and the pupil is enlarged, the ratio increases as n(0.4). When more sensing elements are accommodated on the same aperture, it increases even faster, namely, proportional to n(0.8). With large numbers of sensing elements, this increase can limit the applicability of curvature sensors.     

Shack-Hartmann wavefront sensor measurement for dynamic temperature profiles in heat-capacity laser rods

A Shack-Hartmann sensor nonintrusive measurement for the temperature profile in a heat-capacity neodymium-doped glass rod is proposed. This technique is possible because the optical path length of the rod changes with temperature linearly over a wide range. The temperature change of the solid-state laser rod is often recorded by using a thermocouple, thermal camera, or phase-shifting interferometer. Based on an analysis of temperature-induced changes in length and index of refraction, we can get the temperature profiles from the wavefront reconstructions in real time. The results suggest the Shack-Hartmann sensors could replace microbolometer-based thermal cameras and phase-shifting interferometers for dynamic temperature profiles in heat-capacity laser rods with particular advantages. A strange temperature chaos of the Nd:glass rod just after the pump cycle is discovered.     

Intrinsic limitations of Shack-Hartmann wavefront sensing on an extended laser guide source

In this paper we investigate the behavior of various centroiding methods (weighted center of gravity, matched filtering, and correlation) classically used in Shack-Hartmann wavefront sensing when dealing with an elongated asymmetric spot. We study the impact of model errors on these centroiding methods at high signal-to-noise ratios, and, using a one-dimensional formalism, we show that the associated estimates all suffer from a bias uncorrelated with the actual spot displacement if its shape is not known precisely. Additionally, we show that the correlation method provides an estimate with a unitary gain whatever the parameters used, while the other two methods introduce a non-unitary gain in the estimation process. Finally, we show that the sampling of the spot structures after filtering by some convolution kernels is crucial to get an unbiased estimate of the spot displacement.