Shack-Hartmann Sensor Research Articles

Wavefront sensing for a nonuniform intensity laser beam by Shack–Hartmann sensor with modified Fourier domain centroiding

A fast and simple solution is proposed to wavefront sensing for laser beams with spatial smoothly varying intensity, where Shack–Hartmann wavefront sensor and the modified Fourier domain centroiding algorithm are applied. Detailed analysis has been conducted to Fourier domain centroiding, simplifying the origin double-frame method to work with merely single frame, and revealing its interesting property of robustness to nonuniform intensity perturbation. The key parameter is also analyzed to optimize the algorithm’s performance. Numerical simulations demonstrate that the proposed method outperforms the center of gravity algorithm, with an average phase error reduction up to approximately one order in root mean square. Application of the proposed method in joint amplitude–phase compensation system is also verified by simulation with practical models and parameters. The modified Fourier domain centroiding is promising to enhance real-time actual wavefront measurement for adaptive optics in high-power lasers, such as joint amplitude–phase compensation.

Highly sensitive Shack–Hartmann sensor for two-dimensional electron density imaging over extinguishing arc discharges

Highly sensitive Shack–Hartmann-type laser wavefront sensors incorporating meniscus microlens arrays with a long focal length of 238 or 467 mm were developed for imaging two-dimensional electron density distributions over extinguishing atmospheric arc discharges. The use of the novel microlens arrays also had the advantage of realizing the spatial synchronization of the measuring system. The highly sensitive Shack–Hartmann sensors were successfully used for the single-shot imaging of two-dimensional electron density distributions over the extinguishing arc discharges with currents of several amperes and were proven to have improved the measurement sensitivity by two orders of magnitude from 1023 to 1021 m−3. Spatiotemporal evolution of the electron density images showed that just before arc extinction the electron densities at outer radial positions with respect to the interelectrode gap were higher than those on the geometrical axis defined by the electrodes.

Bottlenecks of the wavefront sensor based on the Talbot effect

Physical constraints and peculiarities of the wavefront sensing technique, based on the Talbot effect, are discussed. The limitation on the curvature of the measurable wavefront is derived. The requirements to the Fourier spectrum of the periodic mask are formulated. Two kinds of masks are studied for their performance in the wavefront sensor. It is shown that the boundary part of the mask aperture does not contribute to the initial data for wavefront restoration. It is verified by experiment and computer simulation that the performance of the Talbot sensor, which meets established conditions, is similar to that of the Shack-Hartmann sensor.

Phase retrieval using a modified Shack–Hartmann wavefront sensor with defocus

This paper proposes a modified Shack-Hartmann wavefront sensor for phase retrieval. The sensor is revamped by placing a detector at a defocused plane before the focal plane of the lenslet array of the Shack-Hartmann sensor. The algorithm for phase retrieval is an optimization with initial Zernike coefficients calculated by the conventional phase reconstruction of the Shack-Hartmann sensor. Numerical simulations show that the proposed sensor permits sensitive, accurate phase retrieval. Furthermore, experiments tested the feasibility of phase retrieval using the proposed sensor. The surface irregularity for a flat mirror was measured by the proposed method and a Veeco interferometer, respectively. The irregularity for the mirror measured by the proposed method is in very good agreement with that measured using the Veeco interferometer.

Shack-Hartmann spot dislocation map determination using an optical flow method

We present a robust, dense, and accurate Shack-Hartmann spot dislocation map determination method based on a regularized optical flow algorithm that does not require obtaining the spot centroids. The method is capable to measure in presence of strong noise, background illumination and spot modulating signals, which are typical limiting factors of traditional centroid detection algorithms. Moreover, the proposed approach is able to face cases where some of the reference beam spots have not a corresponding one in the distorted Hartmann diagram, and it can expand the dynamic range of the Shack-Hartmann sensor unwrapping the obtained dense dislocation maps. We have tested the algorithm with both simulations and experimental data obtaining satisfactory results. A complete MATLAB package that can reproduce all the results can be downloaded from [http://goo.gl/XbZVOr].

利用标记分水岭法实现夏克-哈特曼波前传感器质心探测

As the accuracy of wave-front detection of Shack-Hartmann sensors is mainly dependent on the accuracy of centroid detection of a focal spot,this paper proposes a dynamic determination method of array spot centroid detection window based on marked watershed segmentation.This method smoothes the spot image captured by a Shack-Hartmann wave-front sensor based on the marked watershed segmentation and obtains its gradient image,firstly.Then the OTSU method is used to markthe target on the gradient image.Finally,the marked gradient image is segmented by the marked watershed method and the detection window of every spot is determined.Because the detecting window can be matched with the actual size of spot,the affection of the noise on centroid detection is effectively suppressed.The experimental results demonstrate that the precision and stability of centroid detection by this method are higher than that of traditional method.The mean values of standard deviation in every detecting window of statistic multiple images are calculated,which is 0.010 9,6times that of the traditional method(0.073 4).It can satisfy the requirement of Shack-Hartmann wave-front sensors for precision and stability of centroid calculation.

Energy efficiency of a new trifocal intraocular lens

The light distribution among the far, intermediate and near foci of a new trifocal intraocular lens (IOL) is experimentally determined, as a function of the pupil size, from image analysis. The concept of focus energy efficiency is introduced because, in addition to the theoretical diffraction efficiency of the focus, it accounts for other factors that are naturally presented in the human eye such as the level of spherical aberration (SA) upon the IOL, light scattering at the diffractive steps or the depth of focus. The trifocal IOL is tested in-vitro in two eye models: the aberration-free ISO model, and a so called modified-ISO one that uses an artificial cornea with positive spherical SA in instead. The SA upon the IOL is measured with a Hartmann-Shack sensor and compared to the values of theoretical eye models. The results show, for large pupils, a notorious reduction of the energy efficiency of the far and near foci of the trifocal IOL due to two facts: the level of SA upon the IOL is larger than the value the lens is able to compensate for and there is significant light scattering at the diffractive steps. On the other hand, the energy efficiency of the intermediate focus for small pupils is enhanced by the contribution of the extended depth of focus of the near and far foci. Thus, while IOLs manufacturers tend to provide just the theoretical diffraction efficiency of the foci to show which would be the performance of the lens in terms of light distribution among the foci, our results put into evidence that this is better described by using the energy efficiency of the foci.

Holographic wavefront sensor for fast defocus measurement

Abstract Atmospheric effects significantly influence the propagation of light. Conventional adaptive optics systems, based on Shack-Hartmann sensors (SHS), work well for vertical-path propagation. However, for more challenging scenarios like horizontal-path imaging or free-space laser communications through extended-volume turbulence and strong scintillation, the bandwidth of SHS is insufficient. A promising alternative is the holographic wavefront sensor (HWFS). Our paper deals with some dependencies and limitations of the HWFS. First, we show that the sensitivity of the HWFS is highly dependent on the detector size. The smaller the detector, the more sensitive is the sensor. This has consequences in the photon-starved regime, which would naturally occur when the sensor is operated at the intended MHz speed. Second, we show that uncorrected (or residual) tip/tilt has a large impact on the accuracy of the measurement. We present experimental results of measuring an important and also easily correctable aberration, defocus, with the HWFS.

Extended Depth of Focus With Induced Spherical Aberration in Light-Adjustable Intraocular Lenses

To evaluate the quality of vision and depth of focus induced by controlled amounts of negative spherical aberration in patients implanted bilaterally with light-adjustable intraocular lenses. Prospective, nonrandomized clinical trial. Seventeen patients were implanted and treated with appropriate spatial irradiance light profiles. One eye was set for emmetropia, and the fellow eye received an additional aspheric light treatment to induce controlled amounts of negative spherical aberration. We used a Hartmann-Shack sensor to measure the eye's refraction and aberrations for a 4-mm pupil diameter. Decimal visual acuity (VA) was measured using a micro-display placed at 10 m, 60 cm, 40 cm, and 30 cm. Eyes treated with aspheric profiles were divided into 2 groups depending on the final amount of induced negative spherical aberration: low [-0.05, -0.10 μm] and high [-0.13, -0.23 μm]. In both groups, the mean uncorrected decimal VA at 60 cm was over 0.90. In the first group, distance VA was 0.97 ± 0.16, but in the second group it was lower (0.76 ± 0.16). As expected, the VA for nearer distances is higher in the eyes with a larger magnitude of spherical aberration (P value < .01): 0.94 ± 0.10 and 0.73 ± 0.16 at 40 and 30 cm, respectively, in comparison with 0.71 ± 0.15 and 0.50 ± 0.14. Binocular summation with the fellow eye, adjusted for emmetropia, produces an excellent binocular distance VA (>1.10) in both groups. Controlled amounts of negative spherical aberration and defocus can be induced in eyes implanted with adjustable intraocular lenses to enhance near vision.

Creating microlens arrays in K8 glass for wave-front sensors

Electrically stimulated migration of silver ions has been used to fabricate microlens arrays in K8 glasses. A theoretical model has been developed for the dependence of the parameters of the microlenses on the technological regimes for fabricating them. These microlens arrays were used in Shack–Hartmann sensors to determine the wave-front distortions.

Myopic aberrations: Simulation based comparison of curvature and Hartmann Shack wavefront sensors

In comparison with a Hartmann Shack wavefront sensor, the curvature wavefront sensor is known for its higher sensitivity and greater dynamic range. The aim of this study is to numerically investigate the merits of using a curvature wavefront sensor, in comparison with a Hartmann Shack (HS) wavefront sensor, to analyze aberrations of the myopic eye. Aberrations were statistically generated using Zernike coefficient data of 41 myopic subjects obtained from the literature. The curvature sensor is relatively simple to implement, and the processing of extra- and intra-focal images was linearly resolved using the Radon transform to provide Zernike modes corresponding to statistically generated aberrations. Simulations of the HS wavefront sensor involve the evaluation of the focal spot pattern from simulated aberrations. Optical wavefronts were reconstructed using the slope geometry of Southwell. Monte Carlo simulation was used to find critical parameters for accurate wavefront sensing and to investigate the performance of HS and curvature sensors. The performance of the HS sensor is highly dependent on the number of subapertures and the curvature sensor is largely dependent on the number of Zernike modes used to represent the aberration and the effective propagation distance. It is shown that in order to achieve high wavefront sensing accuracy while measuring aberrations of the myopic eye, a simpler and cost effective curvature wavefront sensor is a reliable alternative to a high resolution HS wavefront sensor with a large number of subapertures.

Sub-3-cycle vortex pulses of tunable topological charge

Novel types of reflective spiral micro-electro-mechanical systems were used to generate few-cycle vortex pulses of variable topological charge from a Ti:sapphire laser oscillator. The phase profile of these components was controlled by varying the temperature. The temporal properties of the pulses were characterized with spatially resolved nonlinear autocorrelation. The beam structure resembles a slightly distorted Laguerre-Gaussian distribution. The different topological charges were indicated by detecting Poynting-vector maps with a programmable Shack-Hartmann sensor of enhanced angular sensitivity.

A new cumulative wavefront reconstructor for the Shack–Hartmann sensor

Abstract. We present a new direct algorithm for the reconstruction of the optical wavefront from the Shack–Hartmann sensor measurements in Single Conjugate Adaptive Optics (SCAO) systems. The computational complexity of this method which is based on linear triangular finite elements is linear in the number of unknowns. Moreover, due to its simple structure, the cumulative reconstructor is pipelinable and parallelizable, which makes the effective computation even faster. Error estimates are given in dependence of the number of the subapertures and the data noise.

Wavefront reconstruction based on the results of light-field conversion by a Shack-Hartmann sensor

The efficiency of adaptive correction of turbulent distortions of optical radiation depends on corrector control using information obtained by a wavefront sensor. A wavefront reconstruction algorithm based on analyzing the spatial transformations of the wavefront during passage of the light field through a Shack-Hartmann wavefront sensor and controlling the operation of the system is proposed.

Preprocessed cumulative reconstructor with domain decomposition: a fast wavefront reconstruction method for pyramid wavefront sensor

We present a fast method for the wavefront reconstruction from pyramid wavefront sensor (P-WFS) measurements. The method is based on an analytical relation between pyramid and Shack-Hartmann sensor (SH-WFS) data. The algorithm consists of two steps--a transformation of the P-WFS data to SH data, followed by the application of cumulative reconstructor with domain decomposition, a wavefront reconstructor from SH-WFS measurements. The closed loop simulations confirm that our method provides the same quality as the standard matrix vector multiplication method. A complexity analysis as well as speed tests confirm that the method is very fast. Thus, the method can be used on extremely large telescopes, e.g., for eXtreme adaptive optics systems.

Registration of vortex beam parameters in a turbulent atmosphere

In this paper detection of vortex beam parameters in a turbulent atmosphere is considered numerically. The characteristics of singular radiation were obtained with the use of wavefront gradients, i.e. an ideal system was simulated. After that, a model of a Shack–Hartmann sensor was included in the calculation schematic which allowed us to assess the influence of the device limitations on the precision of registration and optimize its parameters.

Off-Axis Aberration Measurement Based on the Hartmann-Shack Sensor

Human eyes is an imperfect imaging system that has various aberrations such as on axis and off axis aberrations, which often affect the imaging quality of retina. However, the available aberration methods are mainly concerned with on-axis aberration measurement, which include defocusing, astigmation, and some higher order aberration measurements. Therefore, off-axis aberration measurement under the principle of Hartmann-Shack sensor is proposed in this paper with an empirical study, the results of which showed that the imaging quality of human eyes’ peripheral field decreased with the enlargement of off axis angle. The enlargement of human eyes’ off axis aberration and the decrease of photosensory cell density of the peripheral field are two reasons for such a result.

Study of atmospheric turbulence with Shack Hartmann wavefront sensor

In order to understand adaptive optics technology in detail, it is essential to understand the propagation of light through atmospheric turbulence. In this context, we have attempted to understand this behaviour by simulating atmospheric turbulence environment both numerically and experimentally. Results of such simulation studies are presented. Wavefront sensing is an important component in any adaptive optics system. The performance of the Shack Hartmann wavefront sensor in the presence of atmospheric turbulence is extensively dealt and reported. Finally, the results of laboratory simulation of atmospheric turbulence and its effect on the Shack Hartmann sensor and recalculation of the Fried’s parameter from the laboratory data also presented.

Correspondence of chaos in binocular aberration dynamics

We used a binocular Shack-Hartmann sensor to measure the aberration dynamics of six participants at a rate of 21 Hz. Chaos theory analysis was used to determine the Lyapunov exponent for the time evolution of the rms wavefront error, accommodation, and each individual Zernike coefficient up to and including the fifth radial order. In all cases there was no statistically significant difference between the Lyapunov exponents between the two eyes, suggesting that the level of chaos is common between them. The mean Lyapunov exponent averaged across both eyes of all participants was 0.42±0.14 μm/s for the rms wavefront error, 0.37±0.06 D/s for accommodation, and 0.32±0.09 μm/s averaged across Zernike coefficients. We found no statistically significant correlation per se between the eyes, except for horizontal coma. The correlation may be masked by the impact of differing tear film dynamics. Understanding the nature of aberration dynamics has utility in optimizing the performance of adaptive optics systems for the human eye.

Recent measurements of aero-optical effects caused by subsonic boundary layers

Results of recent experimental measurements of aero-optical distortions caused by turbulent boundary layers at subsonic speeds M=0.4…0.6 are presented. Measurements were performed using a high-speed Shack-Hartmann sensor to collect instantaneous wavefronts with high spatial and temporal resolution, accompanied by wavefront measurements with a Malley probe. Effects of different aperture sizes on levels of aero-optical aberrations and detailed statistical analysis of spatial and temporal spectra of aero-optical distortions for both wavefront sensors are presented and discussed.