Shack-Hartmann Wavefront Sensor Measurements Research Articles

Reference optical turbulence characteristics at the Large Solar Vacuum Telescope site

Abstract Large ground-based solar telescopes are equipped with adaptive optics systems to correct wavefront distortions induced in the turbulent atmosphere. The design of the adaptive optics system strongly depends on the vertical profiles of the optical turbulence. In particular, the characteristics of the optical turbulence determine the design of tomographic adaptive optics systems, which provide image correction within a wide field of view. In the article, a new method to estimate reference optical turbulence characteristics from Era-5 reanalysis assimilated data is presented. This method is based on the dependence of the air refractive index structure constant $C_n^2$ on the vertical shears of wind speed as well as the outer scale of turbulence L0. The L0 parameter is estimated by minimization of the dispersion between the modeled and measured values of the refractive index structure constant $C_n^2$ within the surface layer. For the first time, parametrization coefficients and reference profiles of optical turbulence averaged for the period 1940–2022 are calculated for the Large Solar Vacuum Telescope (LSVT) site. The calculated optical turbulence profiles are representative; these profiles correspond to typical changes of the measured values of the Fried parameter, the isoplanatic angle, and the outer scale of turbulence at the LSVT site. The model turbulence profiles are verified taking into account the Shack–Hartmann wavefront sensor measurements at the LSVT. The higher accuracy of estimation of the optical turbulence characteristics makes it possible to refine parameters relevant to the LSVT adaptive optics system. The obtained results can be used in order to develop high-resolution solar adaptive optics technologies as applied to ground-based telescopes including those using the principles of atmospheric tomography.

Experimental and computational investigation of Shack–Hartmann wavefront sensor measurements through a free shear layer

Experimental and computational investigation of Shack–Hartmann wavefront sensor measurements through a free shear layer

In-flight measurement of atmospheric-imposed tilt: experimental results and analysis.

The work presented here experimentally measures the tilt imposed on a laser beam by the atmosphere from Shack-Hartmann wavefront sensor measurements collected in-flight. Tip/tilt is imposed on the laser beam by propagating through optical turbulent structures larger than or of the order of the size of the beam diameter. This tip/tilt causes a dynamic, net deflection of the beam in the far field, referred to as jitter, which poses a serious problem for tracking in directed energy applications. The practical measurement of turbulence-induced tip/tilt at altitude is challenging since mechanical contamination in the form of vibrations also manifests as tip/tilt. In this paper, a procedure referred to as the stitching method is used to quantify the turbulence-induced component of tilt without the influence of mechanical corruption. It is found that the measured tilt aligns with what analytic solutions predict and that the turbulent environment through which the beam propagates has Kolmogorov-like characteristics.

Iterative wavefront reconstruction for strong turbulence using Shack-Hartmann wavefront sensor measurements.

An iterative wavefront reconstruction method using Shack-Hartmann wavefront sensor (SHWFS) measurements is presented in this paper. A new cost function for the wavefront reconstruction problem is derived and the solution is obtained iteratively using the gradient descent method. The proposed method aims to effectively handle the scintillated SHWFS measurements and to provide simpler and accurate ways to achieve branch-point-tolerant wavefront reconstruction suitable for adaptive optics compensation of strong turbulence. Simulated iterative wavefront reconstruction results show the effectiveness of the proposed method. A laboratory optical testbed is also presented to show the experimental implementation of the proposed method.

High-resolution wavefront reconstruction using multiframe Shack–Hartmann wavefront sensor measurements

High-resolution imaging with large ground-based telescopes is limited by atmospheric turbulence. The observed images are usually blurred with unknown point spread functions (PSFs) defined in terms of the wavefront distortions of light. To effectively remove the blur, numerical postprocessing with a good approximation of the wavefront is required. The gradient measurements of the wavefront recorded by Shack–Hartmann wavefront sensor (WFS) can be used to estimate the wavefront. A gradients measurement model for Shack–Hartmann WFS is built. This model is based on the frozen flow hypothesis and uses a least-squares-fit of tip and tilt across the subaperture in the WFS to genarate the averaged gradient measurements. Then a high-resolution wavefront reconstruction method using multiframe Shack–Hartmann WFS measurements is presented. The method uses high cadence WFS data in a Bayesian framework and takes into account the available a priori information of the wavefront phase. Numerical results show that the method can effectively improve the spatial resolution and accuracy of the reconstructed wavefront in different seeing conditions.

High-power 7.4W TEM00 and wavelength-tunable alexandrite laser with a novel cavity design and efficient fibre-coupled diode-pumping

We report significant improvement in the performance of TEM00 alexandrite laser operation by employing high power fibre-coupled red diode pumping, novel cavity design, and active direct Shack-Hartmann wavefront sensor measurement of pump-induced lensing. We demonstrate 12.7 W of laser power in low-order ( M 2 ∼ 5 ) mode operation from a compact double-end-pumped cavity, and with novel cavity design, a record power of 7.4 W in TEM00 operation with excellent beam quality ( M 2 ≤ 1.1 ). With single-end pumping, laser power of 4.7 W ( M 2 ∼ 1.3 ) was achieved with slope efficiencies as high as 54.9 %; a record efficiency for red-diode-pumped alexandrite. Using a birefringent filter, continuous laser wavelength tuning from 725-808 nm is achieved in diffraction-limited TEM00 mode, with laser power of 4.7 W at 765 nm, and >1 W across 730-805 nm, which is a higher tunable power than any other directly diode-pumped vibronic laser, to the best of our knowledge.

Algorithm based on the optimal block zonal strategy for fast wavefront reconstruction.

Fast wavefront reconstruction is crucial for improving the temporal frequency of adaptive optics systems, in which a mass of subapertures is used. In this paper, we present a novel block zonal reconstruction algorithm based on Southwell geometry to speed up the wavefront reconstruction from Shack-Hartmann wavefront sensor measurements. Therein, we use the theory of computational complexity to install a novel optimal block zonal strategy to get the best size of the subwavefront and give the verification through simulations. Compared with the classical Southwell entire wavefront reconstruction algorithm, the algorithm based on the optimal block zonal strategy needs only a few milliseconds to finish the reconstruction process from 100×100 subapertures. Moreover, we analyze the superiority to use our algorithm to realize the phase reconstruction of the unconnected subwavefront, which cannot be reconstructed via traditional methods. Further, the simulation and experiments show that the precision of the algorithm based on the proposed optimal block zonal strategy is comparable with the commercial wavefront sensor HASO, the time consumption is much less than that of the traditional zonal reconstruction, and it is applicable to the square wavefront, circular wavefront, and local unconnected wavefront. Our proposed algorithm can be widely utilized in astronomical observation, laser transmission, and remote sensing.

Fundamental performance of transverse wind estimator from Shack-Hartmann wave-front sensor measurements.

Real time transverse wind estimation contributes to predictive correction which is used to compensate for the time delay error in the control systems of adaptive optics (AO) system. Many methods that apply Shack-Hartmann wave-front sensor to wind profile measurement have been proposed. One of the obvious problems is the lack of a fundamental benchmark to compare the various methods. In this work, we present the fundamental performance limits for transverse wind estimator from Shack-Hartmann wave-front sensor measurements using Cramér-Rao lower bound (CRLB). The bound provides insight into the nature of the transverse wind estimation, thereby suggesting how to design and improve the estimator in the different application scenario. We analyze the theoretical bound and find that factors such as slope measurement noise, wind velocity and atmospheric coherence length r0 have important influence on the performance. Then, we introduced the non-iterative gradient-based transverse wind estimator. The source of the deterministic bias of the gradient-based transverse wind estimators is analyzed for the first time. Finally, we derived biased CRLB for the gradient-based transverse wind estimators from Shack-Hartmann wave-front sensor measurements and the bound can predict the performance of estimator more accurately.

Method of calculating the cross-wind speed at the entrance aperture of an adaptive system based on Shack–Hartmann wavefront sensor measurements

This paper presents a method for calculating the cross-wind speed at the entrance aperture of an adaptive system from the coordinates of the energy centers of gravity of the focal spots measured by a Shack–Hartmann wavefront sensor. The range of applicability of the method are determined for data obtained in an experiment on an atmospheric path depending on the intensity of turbulent distortions and the optical parameters of the sensor.

Creation of photonic orbital angular momentum by distributed volume turbulence

In previous work, we presented theory of how atmospheric turbulence can impart orbital angular momentum to propagating optical waves. In this paper we provide the first experimental demonstration of the detection of orbital angular momentum from distributed volume turbulence through the identification of well-defined, turbulence-induced, optical vortex trails in Shack-Hartmann wave front sensor measurements.

Advanced adaptive correction of turbulent distortions based on a Shack-Hartmann wavefront sensor measurements

The propagation of laser radiation through the atmosphere is accompanied by a change in the light field under the influence of turbulence and is a random process. An adaptive system that includes a Shack-Hartmann wavefront sensor and a flexible mirror corrects distortions found at the previous time but changed before being corrected by the system. Analysis of turbulence within a given time period allows one to predict turbulent distortions at the subsequent time and use it to make a correction in the radiation phase distribution. The adaptive correction performance can also be improved by preparing the reflective surface of the adaptive mirror based on predictions of the state of the wavefront at the next time by the turbulence parameters and the transverse component of the wind speed found in previous Hartmann-Shack sensor measurements.

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.

Real-time turbulence profiling with a pair of laser guide star Shack–Hartmann wavefront sensors for wide-field adaptive optics systems on large to extremely large telescopes

Real-time turbulence profiling is necessary to tune tomographic wavefront reconstruction algorithms for wide-field adaptive optics (AO) systems on large to extremely large telescopes, and to perform a variety of image post-processing tasks involving point-spread function reconstruction. This paper describes a computationally efficient and accurate numerical technique inspired by the slope detection and ranging (SLODAR) method to perform this task in real time from properly selected Shack-Hartmann wavefront sensor measurements accumulated over a few hundred frames from a pair of laser guide stars, thus eliminating the need for an additional instrument. The algorithm is introduced, followed by a theoretical influence function analysis illustrating its impulse response to high-resolution turbulence profiles. Finally, its performance is assessed in the context of the Thirty Meter Telescope multi-conjugate adaptive optics system via end-to-end wave optics Monte Carlo simulations.

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.

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.

Improvement of Shack–Hartmann wave-front sensor measurement for extreme adaptive optics

The development of high-performance adaptive optics systems requires the optimization of wave-front sensors (WFSs) working in the high-order correction regime. We propose a new method to improve the wave-front slope estimation of a Shack-Hartmann WFS in such a regime. Based on a detailed analysis of the different errors in the slope estimation with a classical centroid and with the new method, the gain in terms of wave-front-sensing accuracy in both the detector and the photon noise regimes is stressed. This improvement is proposed without major system disruption.