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.     

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%。     

Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing

Adaptive optics provides a real-time compensation for atmospheric turbulence that severely limits the resolution of ground-based observation systems. The correction quality relies on a key component, that is, the wavefront sensor (WFS). When observing extended sources, WFS precision is limited by anisoplanatism effects. Anisoplanatism induces a variation of the turbulent phase and of the collected flux in the field of view. We study the effect of this phase and scintillation anisoplanatism on wavefront analysis. An analytical expression of the error induced is given in the Rytov regime. The formalism is applied to a solar and an endoatmospheric observation. Scintillation effects are generally disregarded, especially in astronomical conditions. We shall prove that this approximation is not valid with extended objects.     

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.     

Measuring the centroid gain of a Shack-Hartmann quad-cell wavefront sensor by using slope discrepancy

Shack-Hartmann wavefront sensors (SH WFS) are used by many adaptive optics (AO) systems to measure the wavefront. In this WFS, the centroid of the spots is proportional to the wavefront slope. If the detectors consist of 2 x 2 quad cells, as is the case in most astronomical AO systems, then the centroid measurement is proportional to the centroid gain. This quantity varies with the strength of the atmospheric turbulence and the angular extent of the beacon. The benefits of knowing the centroid gain and current techniques to measure it are discussed. A new method is presented, which takes advantage of the fact that, in a SH-WFS-based AO system, there are usually more measurements than actuators. Centroids in the null space of the wavefront reconstructor, called slope discrepancy measurements, contain information about the centroid gain. Tests using the W. M. Keck Observatory AO system demonstrate the accuracy of the algorithm.     

Binocular open-view Shack-Hartmann wavefront sensor with consecutive measurements of near triad and spherical aberration

We have developed a binocular open-view Shack-Hartmann wavefront sensor for measuring time variation of binocular accommodation, vergence, pupil sizes (i.e., the binocular near triad), and monochromatic aberrations. The device measures these values16 times per second for up to 1 min. Our purpose is to introduce the new instrument. We have confirmed the accuracy of the device. Refractions for a 4 mm pupil were accurate across the range of measurements of model eyes and normal human eyes. We measured binocular dynamics of accommodation, vergence, and spherical aberrations.     

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.     

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.     

Shack-Hartmann wavefront estimation with extended sources: anisoplanatism influence

Anisoplanatism limits the correction field of adaptive optics (AO). In the case of Shack-Hartmann measurement performed on extended sources it may also strongly affect wavefront estimation accuracy. An analytical formalism has been previously proposed to quantify anisoplanatism slope measurement error. It is exploited here to derive the most relevant quantity in AO, the wavefront error. Analytical and end-to-end simulation results are compared in three cases: solar observation, weakly perturbed near-to-ground observation, and strongly perturbed near-to-ground observation. In every case, anisoplanatism wavefront error takes significant values. The accuracy of the analytical model is investigated in detail. Three contributions to the slope error previously identified are considered: phase anisoplanatism, scintillation anisoplanatism, and coupling between scintillation and phase anisoplanatism. The influence of both scintillation and coupling contributions to the wavefront error is confirmed here.     

Efficient implementation of a spatial light modulator as a diffractive optical microlens array in a digital Shack-Hartmann wavefront sensor

A traditional Shack-Hartmann wavefront sensor (SHWS) uses a physical microlens array to sample the incoming wavefront into a number of segments and to measure the phase profile over the cross section of a given light beam. We customized a digital SHWS by encoding a spatial light modulator (SLM) with a diffractive optical lens (DOL) pattern to function as a diffractive optical microlens array. This SHWS can offer great flexibility for various applications. Through fast-Fourier-transform (FFT) analysis and experimental investigation, we studied three sampling methods to generate the digitized DOL pattern, and we compared the results. By analyzing the diffraction efficiency of the DOL and the microstructure of the SLM, we proposed three important strategies for the proper implementation of DOLs and DOL arrays with a SLM. Experiments demonstrated that these design rules were necessary and sufficient for generating an efficient DOL and DOL array with a SLM.     

Optimization of scanning strategy of digital Shack-Hartmann wavefront sensing

In the traditional Shack-Hartmann wavefront sensing (SHWS) system, a lenslet array with a bigger configuration is desired to achieve a higher lateral resolution. However, practical implementation limits the configuration and this parameter is contradicted with the measurement range. We have proposed a digital scanning technique by making use of the high flexibility of a spatial light modulator to sample the reflected wavefront [X. Li, L. P. Zhao, Z. P. Fang, and C. S. Tan, "Improve lateral resolution in wavefront sensing with digital scanning technique," in Asia-Pacific Conference of Transducers and Micro-Nano Technology (2006)]. The lenslet array pattern is programmed to laterally scan the whole aperture. In this paper, the methodology to optimize the scanning step for the purpose of form measurement is proposed. The correctness and effectiveness are demonstrated in numerical simulation and experimental investigation.     

Propagation of optical vortices embedded with multiple wavefront singularities

Optical vortices with the embedded wavefront singularities have attracted intensive attentions in many branches of modern physics, due to their important applications in optical tweezers, quantum entangles, optical testing, atmospheric propagations, etc. In this paper, optical vortices are generated by new types of custom designed wavefronts and their propagation in free-space is reported. Huygens–Fresnel diffraction integral is directly solved using the Gauss–Legendre quadrature method to estimate the diffraction pattern at some arbitrary plane. The variation of vorticity is demonstrated under diffraction. Evolution of phase singularities in wavefronts as the wavefront propagate is predicted for various near field distances. Simulations reveal that the exchange of the nature of topological charge occurs at a finite distance. Experimentally, the wavefronts have been generated using the phase-only spatial light modulator and their far-field diffraction patterns are recorded. The experimental result has been validated with the numerical simulation.     

Measuring seeing with a Shack-Hartmann wave-front sensor during an active-optics experiment

We describe the measurement of atmospheric enclosure seeing along a 120-m light path by use of a Shack-Hartmann wave-front sensor (S-H WFS) for the first time to our knowledge in the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) outdoor active-optics experiment system, based on the differential image motion method and a S-H WFS. Seeing estimates that were gained with the S-H WFS were analyzed and found to be in close agreement with the actual seeing conditions, the estimates of refractive-index structure constant, and the thin-mirror active optics results, which usually include the shape sensing precision and the active correction precision of the experimental system. Finally, some countermeasures against poor seeing conditions were considered and adopted.     

Misalignment effects of the Shack-Hartmann sensor

The Shack-Hartmann sensor uses a microlens array and a CCD camera for wave-front measurements. To obtain wave-front measurements with high accuracy, an accurate relative alignment of both is essential. The different states of misalignment of the Shack-Hartmann sensor are divided into groups and are treated theoretically and experimentally. Their effect on the accuracy of wave-front measurements is evaluated. In addition, a practical method for proper alignment of the Shack-Hartmann sensor is proposed.     

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.     

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.     

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.     

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.     

Shack-Hartmann sensor for fast infrared wave-front testing

Abstract

A Shack-Hartmann sensor has been designed for testing the wave front of CO₂ lasers. Fabrication of a lens array and a detector array with tight tolerances on position accuracy are essential steps. Parallel electronics allow for high-speed wave-front measurements with 1 kHz sampling frequency. The device has been used to investigate the behaviour of a high-power CO₂ laser. Besides the expected thermal drifts of beam direction at the beginning of laser action, periodic changes of beam direction, have been detected. The Shack-Hartmann sensor seems the appropriate device for controlling adaptive optics in high-power laser applications.     

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.