Hartmann Wavefront Sensor Research Articles

Traceable calibration of Shack–Hartmann wavefront sensors employing spherical wavefronts

Traceable, highly accurate calibration of wavefront sensors such as Shack–Hartmann sensors is a challenging task and an active field of research. We have developed a measurement system for the traceable calibration of wavefront sensors employing spherical wavefronts and a point light source in combination with a three-axis linear stage. We obtain an absolute calibration of sensor errors, including the reference spot position and wavefront gradient-dependent errors for each microlens individually. We discuss the main error influences and present an initial measurement uncertainty budget for the calibration. The calibration can be performed with an expanded measurement uncertainty (95% coverage interval) of better than 5 μrad for the wavefront gradient deviation.

Highly multimodal structure of high topological charge extreme ultraviolet vortex beams

Optical beams carrying orbital angular momentum are a very active field of research for their prospective applications, especially at short wavelengths. We consider here such beams produced through high-harmonic generation (HHG) in a rare gas and analyze the characterization of their high-charge vortex structure by an extreme ultraviolet Hartmann wavefront sensor. We show that such HHG beams are generally composed of a set of numerous vortex modes. The sensitivity of the intensity and phase of the HHG beam to the infrared laser aberrations is investigated using a deformable mirror.

Reflective binary amplitude grating for soft x-ray shearing and Hartmann wavefront sensing.

We demonstrate a reflective wavefront sensor grating suitable for the characterization of high-quality x-ray beamlines and optical systems with high power densities. Operating at glancing incidence angles, the optical element is deeply etched with a two-level pattern of shearing interferometry gratings and Hartmann wavefront sensor grids. Transverse features block unwanted light, enabling binary amplitude in reflection with high pattern contrast. We present surface characterization and soft x-ray reflectometry of a prototype grating array to demonstrate function prior to wavefront measurement applications. A simulation of device performance is shown.

High fill factor microlens array fabrication using direct laser writing and its application in wavefront detection

We fabricate 100% fill factor microlens arrays (MLAs) using femtosecond laser direct writing. The array consists of periodical hexagonal plano-convex microlens units with a diameter of 9 µm. The focusing efficiency of each microlens is measured to be 92%. Combined with a CCD camera, the MLA works as a Shack-Hartmann wavefront sensor. We use it to detect wavefronts of both oblique incident plane beams and vortex beams. The experimental results match well with theoretical ones.

High numerical aperture Hartmann wave front sensor for extreme ultraviolet spectral range.

We present a novel, to the best of our knowledge, Hartmann wave front sensor for extreme ultraviolet (EUV) spectral range with a numerical aperture (NA) of 0.15. The sensor has been calibrated using an EUV radiation source based on gas high harmonic generation. The calibration, together with simulation results, shows an accuracy beyond λ/39 root mean square (rms) at λ=32nm. The sensor is suitable for wave front measurement in the 10 nm to 45 nm spectral regime. This compact wave front sensor is high-vacuum compatible and designed for in situ operations, allowing wide applications for up-to-date EUV sources or high-NA EUV optics.

Deep learning assisted Shack-Hartmann wavefront sensor for direct wavefront detection.

The conventional Shack-Hartmann wavefront sensor (SHWS) requires wavefront slope measurements of every micro-lens for wavefront reconstruction. In this Letter, we applied deep learning on the SHWS to directly predict the wavefront distributions without wavefront slope measurements. The results show that our method could provide a lower root mean square wavefront error in high detection speed. The performance of the proposed method is also evaluated on challenging wavefronts, while the conventional approaches perform insufficiently. This Letter provides a new approach, to the best of our knowledge, to perform direct wavefront detection in SHWS-based applications.

Wavefront prediction using artificial neural networks for open-loop adaptive optics

ABSTRACT Latency in the control loop of adaptive optics (AO) systems can severely limit performance. Under the frozen flow hypothesis linear predictive control techniques can overcome this; however, identification and tracking of relevant turbulent parameters (such as wind speeds) is required for such parametric techniques. This can complicate practical implementations and introduce stability issues when encountering variable conditions. Here, we present a non-linear wavefront predictor using a long short-term memory (LSTM) artificial neural network (ANN) that assumes no prior knowledge of the atmosphere and thus requires no user input. The ANN is designed to predict the open-loop wavefront slope measurements of a Shack–Hartmann wavefront sensor (SH-WFS) one frame in advance to compensate for a single-frame delay in a simulated 7 × 7 single-conjugate adaptive optics system operating at 150 Hz. We describe how the training regime of the LSTM ANN affects prediction performance and show how the performance of the predictor varies under various guide star magnitudes. We show that the prediction remains stable when both wind speed and direction are varying. We then extend our approach to a more realistic two-frame latency system. AO system performance when using the LSTM predictor is enhanced for all simulated conditions with prediction errors within 19.9–40.0 nm RMS of a latency-free system operating under the same conditions compared to a bandwidth error of 78.3 ± 4.4 nm RMS.

Wavefront reconstruction of a Shack-Hartmann sensor with insufficient lenslets based on an extreme learning machine.

In a standard Shack-Hartmann wavefront sensor, the number of effective lenslets is the vital parameter that limits the wavefront restoration accuracy. This paper proposes a wavefront reconstruction algorithm for a Shack-Hartmann wavefront sensor with an insufficient microlens based on an extreme learning machine. The neural network model is used to fit the nonlinear corresponding relationship between the centroid displacement and the Zernike model coefficients under a sparse microlens. Experiments with a 6×6 lenslet array show that the root mean square (RMS) relative error of the proposed method is only 4.36% of the initial value, which is 80.72% lower than the standard modal algorithm.

Testing of the stochastic parallel radient descent algorithm for the alignment of a two-mirror telescope

The precise alignment of a high-performance, wide-field telescope is a key factor to ensure its imaging quality. The sharpness function of far-field images combined with an optimization algorithm is one of the most commonly used telescope alignment methods because of its advantages of having a concise measurement system, a simple calculation process, and wide application fields. In this paper, a Cassegrain telescope with two mirrors is aligned by maximizing the sharpness function of far-field images using the stochastic parallel gradient descent algorithm. To verify the effects of this method, both numerical simulations and experiments are implemented. The misalignments are corrected only after a few iterations, indicating that the stochastic parallel gradient descent algorithm can align the telescope rapidly. What’s more, wavefront errors are measured using a Shack–Hartmann wavefront sensor to confirm the accuracy. The results show that this method can align a telescope that is in a misaligned working state with large misalignment errors rapidly and accurately, and the image quality after correction is improved greatly.

Analysis of the wavefront reconstruction error of the spot location algorithms for the Shack–Hartmann wavefront sensor

Spot location algorithms greatly influence the wavefront measurement error of the Shack–Hartmann wavefront sensor. Based on numerical simulations and experiments, we compare the wavefront reconstruction error of several spot location algorithms under different signal-to-noise ratio (SNR) conditions. We solve the problem of how to select the most suitable spot location algorithm and optimal parameters under different SNR conditions, which mimic the realistic working environment of the adaptive optics system changes. We find the optimal threshold and optimal window setting rules of the center of gravity (COG), intensity weighted centroiding, and weighted center of gravity (WCOG) algorithms. The correctness of our recommendation of spot location algorithms under different SNR conditions is supported by numerical simulations and experiments. We find that when the SNR is extremely low, that is the SNR is lower than 2, the cross-correlation algorithm and the thresholding WCOG algorithm are the best choices. When the SNR is moderately low, that is the SNR ranges from 2 to 10, the best choice is the thresholding WCOG algorithm. When the SNR is high, that is, the SNR is higher than 10, the simple algorithm of thresholding COG is the best choice.

Shack–Hartmann wavefront sensors based on 2D refractive lens arrays and super-resolution multi-contrast X-ray imaging

Different approaches of 2D lens arrays as Shack-Hartmann sensors for hard X-rays are compared. For the first time, a combination of Shack-Hartmann sensors for hard X-rays (SHSX) with a super-resolution imaging approach to perform multi-contrast imaging is demonstrated. A diamond lens is employed as a well known test object. The interleaving approach has great potential to overcome the 2D lens array limitation given by the two-photon polymerization lithography. Finally, the radiation damage induced by continuous exposure of an SHSX prototype with a white beam was studied showing a good performance of several hours. The shape modification and influence in the final image quality are presented.

A low-cost and duplicable portable solar adaptive optics system based on LabVIEW hybrid programming

Abstract We have developed a portable solar adaptive optics (PSAO) for diffraction-limited imaging based on today’s multi-core personal computer. Our PSAO software is written in LabVIEW code, which features block-diagram function based programming and can dramatically speed up the software development. The PSAO can achieve a ~1000 Hz open-loop correction speed with a Shack–Hartmann Wave-front Sensor (SH-WFS) in 11 × 11 sub-aperture configuration. The image shift measurements for solar wave-front sensing are the most time-consuming computations in a solar adaptive optics (AO) system. Since our current LabVIEW program does not fully support multi-core techniques for the image shift measurements, it cannot fully take advantage of the multi-core computer’s power for parallel computation. In order to accelerate the AO system’s running speed, a dedicated message passing interface/open multi-processing parallel programming technique is developed for our LabVIEW-based AO program, which fully supports multi-core parallel computation in LabVIEW programming. Our experiments demonstrate that the hybrid parallel technique can significantly improve the running speed of the solar AO system, and this work paves the way for the applications of a low-cost and duplicable PSAO system for large solar telescopes.

Shack-Hartmann versus reverse Hartmann wavefront sensors: experimental results.

With respect to the classical Shack-Hartmann (SH) wavefront sensor (WFS), the recently proposed reverse Hartmann (RH) sensor inverts the locations of the filtering and observation planes and forms a direct image of the pupil on a detector array. The slopes of the wavefront error (WFE) are then reconstructed by using a double Fourier transform algorithm. It turns out that the same algorithm can also be applied to the raw data acquired by SH sensors. This Letter presents the first, to the best of our knowledge, experimental results obtained with a simplified RH WFS and their comparison to those provided by a reference SH sensor, in both classical and double Fourier transform modes. They demonstrate that similar WFE measurement accuracy is achievable when using the three techniques, at least within the limit of our test bench that is estimated around $\lambda/10$λ/10 RMS.

Intensity-enhanced deep network wavefront reconstruction in Shack–Hartmann sensors

The Shack-Hartmann wavefront sensor (SH-WFS) is known to produce incorrect measurements of the wavefront gradient in the presence of non-uniform illumination. Moreover, the most common least-squares phase reconstructors cannot accurately reconstruct the wavefront in the presence of branch points. We therefore developed the intensity/slopes network (ISNet), a deep convolutional-neural-network-based reconstructor that uses both the wavefront gradient information and the intensity of the SH-WFS's subapertures to provide better wavefront reconstruction. We trained the network on simulated data with multiple levels of turbulence and compared the performance of our reconstructor to several other reconstruction techniques. ISNet produced the lowest wavefront error of the reconstructors we evaluated and operated at a speed suitable for real-time applications, enabling the use of the SH-WFS in stronger turbulence than was previously possible.

Systematic Characterization of Near-Index-Matched Optics Based Atmospheric Turbulence Simulator

In the present communication, a systematic characterization of atmospheric turbulence simulator (ATS) based on near-index-matched optics is reported. Characteristics of the propagating laser beam in actual turbulence can be realized in the laboratory by employing such types of turbulence simulators. Such simulators are necessarily required to evaluate the performance of an adaptive optics sensor and compensator modules in the laboratory. Various strengths of atmospheric turbulence can be generated by selecting the different speeds of rotation and the diameters of the beam-interacting area of ATS. A MATLAB-based high-speed video processing method is developed and used for estimating the various turbulence parameters such as angle-of-arrival fluctuations, Fried parameter, Hurst exponent, turbulence frequencies and the scintillation index from the generated turbulence. Also, the maximum transmitted wavefront error produced by this turbulence simulator is measured by an in-house developed Shack–Hartmann wavefront sensor.

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.

Optical Adjustment of the FITE Interferometer

We have developed a balloon-borne far-infrared interferometer, the Far-infrared Interferometric Telescope Experiment (FITE). The final goal of spatial resolution was one arcsec at 100[Formula: see text][Formula: see text]m. As a first step, we aimed to achieve a spatial resolution of five arcsecs at 155[Formula: see text][Formula: see text]m with a 6-m baseline. FITE is a two-beam interferometer like Michelson’s stellar interferometer. Positions and attitudes of all mirrors required to have their alignment checked and possibly adjusted before launch and were checked during observation. We had to satisfy three requirements: the coincidence of the phases of each beam (wavefront error), image quality of the two beams at the (common) focus, and no optical path difference between the two beams for celestial objects. In order to achieve the former two requirements, we developed an interferometer adjustment system that used a newly-developed interferometer measurement instrument. This instrument adopted a Shack–Hartmann wavefront sensor to measure wavefront errors of the two off-axis parabolic mirrors, simultaneously. With this system, the adjustment of the FITE interferometer was carried out at the Alice Springs balloon base in Australia as the JAXA’s Australia balloon experiment campaign of 2018. On-site adjustment was successful; wavefront errors of the two off-axis parabolic mirrors were 1.78[Formula: see text][Formula: see text]m and 4.99[Formula: see text][Formula: see text]m (peak-to-valley), and the Hartmann constant was 13 arcsecs. As for the optical path difference, we achieved the requirement by step-wise displacement of a folding plane mirror. Results satisfied the requirements for an interferometer designed for a wavelength of 155[Formula: see text][Formula: see text]m. Improvement of spatial resolution at far-infrared wavelengths is undoubtedly important for research on protoplanetary disks, circumstellar dust shells of late-type stars, and star-forming galaxies. The method we have developed is also useful for future space interferometers.

Single-shot, high sensitivity X-ray phase contrast imaging system based on a Hartmann mask

Significant efforts are currently ongoing in X-Ray imaging to provide multimodal imaging systems, targeting better sensitivity and specificity for both biomedical or non-destructive testing (NDT) applications. X-Ray Phase Contrast Imaging (X-PCI) shows great capability to differentiate elements with similar absorption. For example, in the medical field, knowing the chemical composition of breast microcalcifications would help to differentiate malign and benign tumors. The composition can be determined from the measurement of the phase as the optical index of materials is directly related to the composition. We propose a novel, high-sensitivity X-ray quantitative phase imaging system based on a Hartmann wavefront sensor. The system provides high resolution (20?m without magnification) and high sensitivity (~100 nrad), and is compatible with tomographic experiments using both synchrotron beamlines or laboratory sources. We present here our first X-PCI prototype as well as the first images obtained. We also present an alternative design based on the same approach, providing larger field-of-view at the cost of some trade-off regarding resolution and sensitivity and the first tomographic results obtained with this imaging system.

Improved adaptive-optics performance using polychromatic speckle mitigation.

Adaptive-optics (AO) systems correct the optical distortions of atmospheric turbulence to improve resolution over long paths. In applications such as remote sensing, object tracking, and directed energy, the AO system's beacon is often an extended beacon reflecting off an optically rough surface. This situation produces speckle noise that can corrupt the wavefront measurements of the AO system, degrading its correction of the turbulence. This work studies the benefits of speckle mitigation via polychromatic illumination. To quantify the benefits over a wide range of conditions, this work uses a numerical wave-optics model with the split-step method for turbulence and the spectral-slicing method for polychromatic light. It assumes an AO system based on a Shack-Hartmann wavefront sensor. In addition, it includes realistic values for turbulence strength, turbulence distribution along the path, coherence length, extended-beacon size, and object motion. The results show that polychromatic speckle mitigation significantly improves AO system performance, increasing the Strehl ratio by 180% (from 0.10 to 0.28) in one case.

A new temporal control approach for SCAO systems

Adaptive optics (AO) systems for ground-based telescopes use deformable mirrors to physically correct wavefront distortions induced by atmospheric turbulence. Due to time delays caused by different parts of the AO system, the process of turbulence correction becomes even more difficult since the earth’s atmosphere changes continuously. In this paper we propose a new temporal control approach for the computation of optimal mirror configurations based on the solution of a sequence of inverse problems for the wavefront sensor operator. Our mathematical formulation of the underlying problem allows the incorporation of computationally efficient wavefront reconstruction methods and a wavefront prediction step. Based on the frozen flow assumption, the prediction of a future wavefront relies on a suitable shift of the reconstructed wavefront. The performance of our temporal control algorithm is demonstrated in the context of a single conjugate adaptive optics system on a 37 meter telescope using a Shack–Hartmann wavefront sensor. Numerical results of the proposed control method are provided using OCTOPUS, the official end-to-end simulation tool of the European Southern Observatory.