Hartmann Wavefront Sensor Research Articles

Large-aperture adaptive optical system for correcting wavefront distortions of a petawatt Ti : sapphire laser beam

This paper reports a large-aperture adaptive optical system with a bimorph deformable mirror and Shack – Hartmann wavefront sensor for aberration correction and beam focusing improvement in state-of-the-art petawatt Ti : sapphire lasers. We consider methods for providing feedback to the wavefront sensor and obtaining an objective wavefront that optimises beam focusing onto a target. The use of an adaptive system with a controlled 127-channel 320-mm-aperture mirror in a Ti : sapphire laser with an output power of 4.2 PW has made it possible to obtain a record high laser beam intensity: 1.1 × 1023 W cm−2.

Wide-Aperture Bimorph Deformable Mirror for Beam Focusing in 4.2 PW Ti:Sa Laser

The bimorph deformable mirror with a diameter of 320 mm, including 127 control electrodes, has been developed and tested. The flatness of the initial mirror surface of about 1 μm (P-V) was achieved by mechanically adjusting the mirror substrate fixed in the metal mount. To correct for the aberrations and improve the beam focusing in the petawatt Ti:Sa laser, the wide-aperture adaptive optical system with the deformable mirror and Shack–Hartmann wavefront sensor was developed. Correction of the wavefront aberrations in the 4.2 PW Ti:Sa laser using the adaptive system provided increases the intensity in the focusing plane to a value of 1.1 × 1023 W/cm2

Radial shearing dynamic wavefront sensor based on a geometric phase lens pair.

A radial shearing dynamic wavefront sensor is theorized and experimentally verified. The proposed sensor is based on a geometric phase lens pair that generates two radially sheared wavefronts. A polarization pixelated camera instantaneously obtains polarization-multiplexed phase maps from a single acquired image using a spatial phase-shifting technique. Experimental tests applied several wavefront shapes with a deformable mirror. The results were compared with a Shack-Hartmann wavefront sensor to evaluate the performance.

Characterizing turbulence profile layers through celestial single-source observations.

Future spacecraft missions aim to communicate with the Earth using near-infrared lasers. The possible bit rate of free-space optical communication (FSOC) is orders of magnitude greater when compared to current radio frequency transmissions. The challenge of ground-space FSOC is that atmospheric turbulence perturbs optical wavefront propagation. These wavefront aberrations can be measured using a Shack-Hartmann wavefront sensor (SHWFS). A ground-based adaptive optics (AO) system can mitigate these aberrations along the optical path by translating wavefront measurements into deformable mirror commands. However, errors result from atmospheric turbulence continuously evolving, and there are unavoidable delays during AO wavefront correction. The length of an acceptable delay is referred to as the coherence time-a parameter dependent on the strength of turbulence profile layers and their corresponding wind-driven velocity. This study introduces a novel technique, to the best of our knowledge, for using SHWFS single-source observations, e.g., the downlink signal from a geostationary satellite, to measure the strength and velocity of turbulence profile layers. This work builds upon previous research and demonstrates that single-source observations can disentangle turbulence profile layers through studying the cross-covariance of temporally offset SHWFS centroid measurements. Simulated data are used to verify that the technique can recover the coherence time. The expected and measured results have a correlation coefficient of 0.95.

Reconstruction of coherence matrix in x-representation using nonclassical Hartmann sensor

We show the coherence properties of a signal can be measured by a Hartmann wavefront sensor in a nonclassical regime. Recasting the detection theory of the classical Hartmann sensor in the sense of quantum tomography enables to measure the coherence function, which is an analogy to the density matrix of mixed quantum states. Two methods were tested for the reconstruction of the coherence matrix from the intensity scan in the nonclassical mode of the Hartmann sensor. The reconstruction was performed in a classic way using the POVM matrix and using data pattern tomography.

High-Sensitivity X-ray Phase Imaging System Based on a Hartmann Wavefront Sensor

The Hartman wavefront sensor can be used for X-ray phase imaging with high angular resolution. The Hartmann sensor is able to retrieve both the phase and absorption from a single acquisition. The system calculates the shift in a series of apertures imaged with a detector with respect to their reference positions. In this article, the impact of the reference image on the final image quality is investigated using a laboratory setup. Deflection and absorption images of the same sample are compared using reference images acquired in air and in water. It can be easily coupled with tomographic setups to obtain 3D images of both phase and absorption. Tomographic images of a test sample are shown, where deflection images revealed details that were invisible in absorption. The findings reported in this paper can be used for the improvement of image reconstruction and for expanding the applications of X-ray phase imaging towards materials characterization and medical imaging.

Optical solution to spot elongation in laser guide stars wavefront sensors for Extremely Large Telescopes

ABSTRACTLaser guide stars have been proposed to overcome a widely recognized limitation of adaptive optics: the need for bright reference sources for wavefront sensing nearby the scientific field of interest. The laser guide stars foreseen for the future Extremely Large Telescopes are based on the resonant back-scattering of a laser beam by the Sodium atoms concentrated in a ∼13 km thick layer at about 90 km above the ground. Such an artificial source, observed from a position laterally offset from the laser projector, appears elongated due to the finite thickness of the Sodium layer: on a 40-m class telescope with laser projector located on the primary mirror edge the image elongation may exceed 13 arcsec. In a Shack–Hartmann wavefront sensor, the elongated spots require the use of large detectors to avoid spot truncation and impose demanding requirements in terms of photon flux return with respect to smaller telescopes. We propose an alternative wavefront sensor concept intrinsically insensitive to the spot elongation, measuring the local wavefront slope in the direction orthogonal to the elongation itself; the full 2D slope measurements are retrieved by combining the signals from different laser guide stars, projected from different positions at the edge of the telescope. The performance of the new wavefront sensor is analysed in the framework of a ground-layer adaptive optics application. A possible extension to multiconjugate adaptive optics is also qualitatively described.

Deep phase retrieval for astronomical Shack–Hartmann wavefront sensors

ABSTRACT We present a high-speed deep learning-based phase retrieval approach for Shack–Hartmann wavefront sensors used in astronomical adaptive optics. It reconstructs the Zernike modal coefficients from the image captured by the wavefront sensor with a lightweight convolutional neural network. Compared to the traditional slope-based wavefront reconstruction, the proposed approach uses the image captured by the sensor directly as inputs for more high-order aberrations. Compared to the recently developed iterative phase retrieval methods, the speed is much faster with the computation time less than 1 ms for a 100-aperture configuration, which may satisfy the requirement of an astronomical adaptive optics system. Simulations have been done to demonstrate the advantages of this approach. Experiments on a 241-unit deformable-secondary-mirror AOS have also been done to validate the proposed approach.

High-precision Shack-Hartmann wavefront sensing with a multi-focal diffraction Taiji-lenslet array

A Hartmann wavefront sensor is a type of wavefront detection instrument that has been widely used in various fields. Traditional Hartmann wavefront sensors usually comprise a monofocal refraction lenslet array to segment the wavefront at the entrance pupil. Each wavelet is focused at the focal plane along the projection of the lenslet, forming the foci array. Unlike the multifocal self-interference Taiji-lenslet array, a type of multifocal diffraction Taiji-lenslet array was proposed in this study to improve the measurement accuracy using the weighted centroid location algorithm of these multifocal spots, where the latter is more easily designed than the former. An optical experiment was implemented using the multifocal diffraction Taiji-lenslet array to verify its effectiveness. As a type of diffractive lens, a large-aperture Taiji-lenslet array can be easily fabricated via lithography, which has great potential for application in the measurement of large-scale laser beams and optical elements.

Investigation of spatial and temporal characteristics of turbulent-distorted laser radiation during its dynamic phase correction in an adaptive optical system

We report the results of the analysis of experiments on dynamic phase correction of laser radiation distorted by a turbulent airflow in an adaptive optical system (AOS) with a Shack–Hartmann wavefront sensor (WFS). A field-programmable gate array is used as the main AOS control element, which provides a closed loop AOS bandwidth of up to 2000 Hz. The WFS is used to estimate the characteristic bandwidth of the generated turbulence ν turb. Changes in the spatial and temporal spectra of the laser radiation phase, as well as the quality of the beam during its dynamic phase correction at various AOS frequencies, are analysed. It is shown experimentally and by calculation that to ensure a high efficiency of the wavefront correction, the AOS frequency should be at least 20 times higher than ν turb.

Measurement techniques to improve the accuracy of x-ray mirror metrology using stitching Shack-Hartmann wavefront sensors.

We describe the development of specific measurement protocols to improve the accuracy of surface metrology of x-ray mirrors using a dedicated commercial instrument based on wavefront sensing techniques. This instrument, SHARPeR, uses measurements from a Shack-Hartmann wavefront sensor combined with a sub-aperture stitching method to provide two-dimensional maps of the surface slope errors and can measure curved mirrors above 1m radii. In this paper, we describe the results of measurement methods developed on a SHARPeR system installed at the European Synchrotron (ESRF) to reduce the contribution of systematic errors to measurements of strongly curved spherical and aspherical x-ray mirrors with intrinsic slope errors of the order of 100-200 nrad rms. We demonstrate how this commercial integrated instrument can provide measurements of these mirrors with comparable accuracy to those measured with a long trace profiler.

Issues of wavefront tilt measurement

Different realizations of methods for estimation of random tilts of wavefront are considered. Dispersions of tilt estimates are demonstrated to practically coincide for different methods of their determination. Possibilities of measuring the Fried parameter for adaptive optics applications are determined. The parameters of a Shack–Hartmann wavefront sensor are analytically calculated for operation under different conditions in terms of turbulence level and for radiation at different wavelengths.

Detecting momentum weak value: Shack-Hartmann versus a weak measurement wavefront sensor.

The task of wavefront sensing is to measure the phase of the optical field. Here, we demonstrate that the widely used Shack-Hartmann wavefront sensor detects the weak value of transverse momentum, usually achieved by the method of quantum weak measurement. We extend its input states to partially coherent states and compare it with the weak measurement wavefront sensor, which has a higher spatial resolution but a smaller dynamic range. Since weak values are commonly used in investigating fundamental quantum physics and quantum metrology, our work would find essential applications in these fields.

Tomography of a seeded free-electron laser focal spot: qualitative and quantitative comparison of two reconstruction methods for spot size characterization.

Performing experiments at free-electron lasers (FELs) requires an exhaustive knowledge of the pulse temporal and spectral profile, as well as the focal spot shape and size. Operating FELs in the extreme ultraviolet (EUV) and soft X-ray (SXR) spectral regions calls for designing ad-hoc optical layouts to transport and characterize the EUV/SXR beam, as well as tailoring its spatial dimensions at the focal plane down to sizes in the few micrometers range. At the FERMI FEL (Trieste, Italy) this task is carried out by the Photon Analysis Delivery and Reduction System (PADReS). In particular, to meet the different experimental requests on the focal spot shape and size, a proper tuning of the optical systems is required, and this should be monitored by means of dedicated techniques. Here, we present and compare two reconstruction methods for spot characterization: single-shot imprints captured via ablation on a poly(methyl methacrylate) sample (PMMA) and pulse profiles retrieved by means of a Hartmann wavefront sensor (WFS). By recording complementary datasets at and nearby the focal plane, we exploit the tomography of the pulse profile along the beam propagation axis, as well as a qualitative and quantitative comparison between these two reconstruction methods.

Supersonic Aerothermoelastic Experiments of Aerospace Structures

The U.S. Air Force Research Laboratory Structural Sciences Center recently started an experimental campaign in the Arnold Engineering Development Center von Kármán Facility Tunnel C to investigate the aerothermoelastic (combined aerodynamics, heat transfer, and structural mechanics) behavior of a flight-weight stiffened aerostructure at high-supersonic flow conditions. Optical measurement techniques were employed to record simultaneously the panel deformation (three-dimensional digital image correlation), panel surface temperature, and the boundary-layer state/dynamics (high-speed schlieren and Shack–Hartmann wavefront sensor). Panel transient behavior, including a dynamic snap-through event, was captured using these full-field measurement techniques. Importantly, panel surface deformation on the order of 8 mm, or five times the panel thickness, was realized. Maximum pressure and heat flux amplifications of about 1.7 and 1.5, respectively, were measured/estimated across a rigid article that mimicked, and closely matched, the expected thin panel deformation. The unique results and knowledge gained from this campaign will be provided to the aerospace community for the purpose of calibrating and validating coupled aerothermoelastic simulation methods.

Extended-aperture Hartmann wavefront sensor with raster scanning.

In this paper, we propose an extended-aperture Hartmann wavefront sensor (HWFS) based on raster scanning. Unlike traditional HWFS, where there is a trade-off between the dynamic range and spatial resolution of wavefront measurement, our extended-aperture HWFS breaks the trade-off and thus could achieve a large dynamic range and high spatial resolution simultaneously. By applying a narrow-beam raster-scanning scheme, the detection aperture of our HWFS is extended to 40 × 40 mm2 without using the enlarging 4f relay system. The spatial resolution of our setup depends on the scanning step, the pinhole size, and the wavelength. The sensitivity and dynamic range can be adjusted flexibly by varying the axial distance between the pinhole plane and the imaging sensor plane, because our decoupled large dynamic range could be reasonable traded-off to achieve better sensitivity. Furthermore, compared with tradition HWFS, our method does not need to compute the positions of a two-dimensional spots array where complicated spots tracking algorithms are necessary to achieve high dynamic range, thus remarkably reduces the spots aliasing issue and the computational cost. It should be noted that this scheme is not only applicable for HWFS but also for Shack-Hartmann wavefront sensor (SHWFS) with microlens array to achieve higher accuracy and better power efficiency. Experiments were performed to demonstrate the capability of our method.

Wavefront Coherent Compensation Technology Under Direct Sunlight in Free Space Optical Communication System

The charge-coupled device-based Shaker–Hartmann wavefront sensor has been widely used to compensate for wavefront distortion in coherent optical communication. However, the influence of strong background light causes large errors when restoring the signal light wavefront. This study proposes a wavefront recovery method by combining a detector array with an optical nutation of the local oscillator. By adding a small rotation angle to the local oscillator, the wavefront slope is estimated according to the output of the change law of the mixed signal and the local oscillator light, and the multi-order Zernike mode is used to reconstruct the signal light wavefront. Simulation studies show that the root-mean-square value (RMS) and the coherence efficiency of the signal light wavefront were significantly optimized. Under direct sunlight, the estimation compensation error of the wavefront slope reached 0.008. Under strong turbulence, the mixing efficiency was increased by nearly 97.5 times, and the RMS was reduced to the original value of 0.048 The designed system has good background light compensation and wavefront recovery capabilities and is suitable for coherent optical communication under direct sunlight.

Aero-Optical Measurements of the Response of a Thin Panel at Mach 6

An experiment was recently conducted in the Air Force Research Laboratory Mach 6 High Reynolds Number Facility to observe the response of a generic vehicle wedge-mounted, thin metallic panel. A Shack–Hartmann wavefront sensor was used to measure aero-optical distortions in the boundary layer developing over the flexible panel. Localized buckling and fixed-frequency oscillations of the panel were detected using the wavefront sensor. The root mean square and power spectral density of the optical path difference obtained over the flexible panel resembled freestream measurements for deformations toward the cavity. This work introduces a novel application of a Shack–Hartmann wavefront sensor, providing wall-normal variation of the aero-optical distortions in the boundary layer developing over a flexible model. The initial findings of this study indicate that a Shack–Hartmann wavefront sensor can be used to nonintrusively detect fluid–structure coupling.

COACH-based Shack-Hartmann wavefront sensor with an array of phase coded masks.

Shack-Hartmann wavefront sensors (SHWS) are generally used to measure the wavefront shape of light beams. Measurement accuracy and the sensitivity of these sensors are important factors for better wavefront sensing. In this paper, we demonstrate a new type of SHWS with better measurement accuracy than the regular SHWS. The lenslet array in the regular SHWS is replaced with an array of coded phase masks, and the principle of coded aperture correlation holography (COACH) is used for wavefront reconstruction. Sharper correlation peaks achieved by COACH improve the accuracy of the estimated local slopes of the measured wavefront and consequently improve the reconstruction accuracy of the overall wavefront. Experimental results confirm that the proposed method provides a lower mean square wavefront error by one order of magnitude in comparison to the regular SHWS.

Application of the Gaussian modeling algorithm to a Shack-Hartmann wavefront sensor for daylight adaptive optics.

Daytime use of Shack-Hartmann wavefront sensor (SHWS)-based adaptive optics (AO) at a telescope is hindered by the fluctuating bright sky background. Therefore, we propose a Gaussian modeling centroid extraction algorithm that performs real-time daylight AO closed-loop corrections. The algorithm is executed in the process of modeling and updating each pixel of the consecutive SHWS images. The simulation results show that our method can provide a lower centroid estimation error (CEE) for bright sky background conditions. We also performed a field experiment on a 2 m ground-based telescope and achieved a daylight AO correction of 2.1 times diffraction limit for a star with a visual magnitude of 4.7 (HIP113116) when the elevation angle of the sun was 7.7°. This represents the first publicly reported daylight natural guide star AO correction result on a 2 m class telescope.