Shack-Hartmann Research Articles

Impact of Peripheral Refractive Errors in Mobility Performance.

The purpose of this study was to investigate the functional effects of peripheral refractive errors on mobility performance through a stair negotiation task. Twenty-one young, normal sighted subjects navigated through an obstacle with steps, wearing spectacles that altered only their peripheral refraction. Lenses were used to induce positive defocus (+2 diopters [D] and +4 D), negative defocus (-2 D and -4 D), or astigmatism (+1.75 D and -3.75 D, axis 45 degrees) in the periphery. Feet trajectories were analyzed, and several gait assessment parameters were obtained. Statistical tests were conducted to determine significant performance differences between the lenses. Peripheral refraction in each subject was measured using a scanning Hartmann-Shack wavefront sensor to assess the impact of intrinsic peripheral refraction on the experiment. Statistically significant differences in performance appeared when peripheral errors were superimposed. Crossing time with respect to plano lenses increased by 6.2%, 7.6%, 19.2%, and 29.6% for the -2 D, +2 D, -4 D, and +4D lenses, respectively (P<0.05 in the last 3 cases). Subjects exhibited slower walking speeds, increased step count, and adopted precautionary measures. High-power positive defocus lenses had the biggest impact on performance, and differences were observed in distance to steps between induced positive and negative defocus. In this laboratory-based study without an adaptation period, peripheral refractive errors affected stair negotiation, causing cautious behavior in subjects. Performance differences among types of peripheral defocus may result from magnification effects and intrinsic peripheral refraction. These results highlight the importance of understanding the effects of induced peripheral errors by myopia control and intraocular lenses.

Expected performance of the Pyramid wavefront sensor with a laser guide star for 40 m class telescopes

Context. The use of artificial laser guide stars (LGS) is planned for the new generation of giant segmented mirror telescopes in order to extend the sky coverage of their adaptive optics systems. The LGS, being a 3D object at a finite distance, will have a large elongation that will affect its use with the Shack–Hartmann (SH) wavefront sensor. Aims. In this paper, we compute the expected performance for a Pyramid WaveFront Sensor (PWFS) using an LGS for a 40 m telescope affected by photon noise, and also extend the analysis to a flat 2D object as reference. Methods. We developed a new way to discretize the LGS, and a new, faster method of propagating the light for any Fourier filtering wavefront sensors (FFWFS) when using extended objects. We present the use of a sensitivity model to predict the performance of a closed-loop adaptive optic system. We optimized a point-source-calibrated interaction matrix to accommodate the signal of an extended object by computing optical gains using a convolutional model. Results. We find that the sensitivity drop, given the size of the extended laser source, is large enough to make the system operate in a low-performance regime given the expected return flux of the LGS. The width of the laser beam is identified as the limiting factor, rather than the thickness of the sodium layer. Even an ideal, flat LGS will have a drop in performance due to the flux of the LGS, and small variations in the return flux will result in large variations in performance. Conclusions. We conclude that knife-edge-like wavefront sensors, such as the PWFS, are not recommended for use with LGS for a 40 m telescope, as they will operate in a low-performance regime, given the size of the extended object.

Features of Adaptive Phase Correction of Optical Wave Distortions under Conditions of Intensity Fluctuations

An analysis of the features of measurements and correction of phase distortions in optical waves propagating in the atmosphere at various levels of turbulence was performed. It is shown that with increasing intensity fluctuations, the limiting capabilities of phase correction decrease, and the phase of an optical wave that has passed through a turbulence layer consists of two components: potential and vortex. It was found that even in the region of weak fluctuations there is an overlap of spectral filtering functions for intensity and phase fluctuations. Areas of turbulence inhomogeneities have been identified that will have mutual influence and negatively affect the operation of the phase meter. It is noted that correlation functions, both phase and intensity, are less susceptible to this compared to structural functions. The results of experimental studies on the reconstruction of the wavefront of laser radiation distorted by atmospheric turbulence using a Shack–Hartmann wavefront sensor during vignetting and central screening of the entrance pupil in the optical system are presented. Studies have been carried out on the propagation of laser radiation along a horizontal atmospheric path for various levels of turbulence. The results are analyzed in terms of Zernike polynomials.

Deep tomography for the three-dimensional atmospheric turbulence wavefront aberration

Multiconjugate adaptive optics (MCAO) can overcome atmospheric anisoplanatism to achieve high-resolution imaging with a large field of view (FOV). Atmospheric tomography is the key technology for MCAO. The commonly used modal tomography approach reconstructs the three-dimensional atmospheric turbulence wavefront aberration based on the wavefront sensor (WFS) detection information from multiple guide star (GS) directions. However, the atmospheric tomography problem is severely ill-posed. The incomplete GS coverage in the FOV coupled with the WFS detection error significantly affects the reconstruction accuracy of the three-dimensional atmospheric turbulence wavefront aberration, leading to a nonuniform aberration detection precision over the whole FOV. We propose an efficient approach for achieving accurate atmospheric tomography to overcome the limitations of the traditional modal tomography approach. We employed a deep-learning-based approach to the tomographic reconstruction of the three-dimensional atmospheric turbulence wavefront aberration. We propose an atmospheric tomography residual network (AT-ResNet) that is specifically designed for this task, which can directly generate wavefronts of multiple turbulence layers based on the Shack-Hartmann (SH) WFS detection images from multiple GS directions. The AT-ResNet was trained under different turbulence intensity conditions to improve its generalization ability. We verified the performance of the proposed approach under different conditions and compared it with the traditional modal tomography approach. The well-trained AT-ResNet demonstrates a superior performance compared to the traditional modal tomography approach under different atmospheric turbulence intensities, various turbulence layer distributions, higher-order turbulence aberrations, detection noise, and reduced GSs conditions. The proposed approach effectively addresses the limitations of the modal tomography approach, leading to a notable improvement in the accuracy of atmospheric tomography. It achieves a highly uniform and high-precision wavefront reconstruction over the whole FOV. This study holds great significance for the development and application of the MCAO technology.

Flow Field Estimation with Distortion Correction Based on Multiple Input Deep Convolutional Neural Networks and Hartmann–Shack Wavefront Sensing

The precise estimation of fluid motion is critical across various fields, including aerodynamics, hydrodynamics, and industrial fluid mechanics. However, refraction at complex interfaces in the light path can cause image deterioration and lead to severe measurement errors if the aberration changes with time, e.g., at fluctuating air–water interfaces. This challenge is particularly pronounced in technical energy conversion processes such as bubble formation in electrolysis, droplet formation in fuel cells, or film flows. In this paper, a flow field estimation algorithm that can perform the aberration correction function is proposed, which integrates the flow field distribution estimation algorithm based on the Particle Image Velocimetry (PIV) technique and the novel actuator-free adaptive optics technique. Two different multi-input convolutional neural network (CNN) structures are established, with two frames of distorted PIV images and measured wavefront distortion information as inputs. The corrected flow field results are directly output, which are divided into two types based on different network structures: dense estimation and sparse estimation. Based on a series of models, a corresponding dataset synthesis model is established to generate training datasets. Finally, the algorithm performance is evaluated from different perspectives. Compared with traditional algorithms, the two proposed algorithms achieves reductions in the root mean square value of velocity residual error by 84% and 89%, respectively. By integrating both flow field measurement and novel adaptive optics technique into deep CNNs, this method lays a foundation for future research aimed at exploring more intricate distortion phenomena in flow field measurement.

Canonical and Poynting currents in propagation and diffraction of structured light: tutorial

The local propagation and the energy flux in structured optical fields are often associated with the Poynting vector. However, the local phase gradient (i.e., local wavevector) in monochromatic fields in free space is described by another fundamental quantity: the canonical momentum density. Distributions of the Poynting and canonical momentum densities can differ significantly from each other in structured fields. We examine the role of these quantities in the propagation and diffraction of structured optical fields, exemplified by various circularly polarized vortex beams carrying orbital angular momentum. We describe the canonical and Poynting momentum distributions in such beams, experimentally measure the local transverse momentum density by a Shack-Hartmann wavefront sensor, and investigate fine features of the diffraction of various vortex beams on a knife-edge aperture. In all cases, the measured local momentum density and local beam evolution are consistent with the canonical momentum distribution rather than the Poynting vector. Furthermore, we introduce the local angular velocity in vortex beams and determine the universal integral π angle of azimuthal rotation in an arbitrary (yet circularly symmetric) propagating and diffracting vortex beam. Finally, we discuss the “supermomentum” and “backflow” effects; both of these phenomena are examples of superoscillations and are related to the properties of the canonical momentum. Our results reveal the profound role of the canonical momentum in the evolution of light and demonstrate the importance of distinguishing between it and the Poynting vector in structured light.

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.

The 85-electrode adaptive optics system of the Swedish 1-m Solar Telescope

We discuss the chosen concepts, detailed design, implementation and calibration of the 85-electrode adaptive optics (AO) system of the Swedish 1-meter Solar Telescope (SST), which was installed in 2013. The AO system is unusual in that it uses a combination of a monomorph mirror with a Shack-Hartmann (SH) wavefront sensor (WFS) and a second high-resolution SH microlens array to aid the characterization, calibration, and modal control of the deformable mirror. An Intel PC workstation performs the heavy image processing associated with cross-correlations and real-time control at a 2 kHz update rate with very low latency. The computer and software continue the successful implementation since 1995 of earlier generations of correlation tracker and AO systems at SST and its predecessor, the 50-cm Swedish Vacuum Solar Telescope, by relying entirely on work-station technology and an extremely efficient algorithm for implementing cross-correlations with the large field of view of the WFS. We describe critical aspects of the design, calibrations, software, and functioning of the AO system. The exceptionally high performance is testified through the highest Strehl ratio (inferred from the measured granulation contrast) of existing meter-class solar telescopes, as demonstrated here at wavelengths shorter than 400 nm and discussed in more detail in a previous separate publication We expect that some aspects of this AO system may also be of interest outside the solar community.

Large-Dynamic-Range Ocular Aberration Measurement Based on Deep Learning with a Shack-Hartmann Wavefront Sensor.

The Shack-Hartmann wavefront sensor (SHWFS) is widely utilized for ocular aberration measurement. However, large ocular aberrations caused by individual differences can easily make the spot move out of the range of the corresponding sub-aperture in SHWFS, rendering the traditional centroiding method ineffective. This study applied a novel convolutional neural network (CNN) model to wavefront sensing for large dynamic ocular aberration measurement. The simulation results demonstrate that, compared to the modal method, the dynamic range of our method for main low-order aberrations in ocular system is increased by 1.86 to 43.88 times in variety. Meanwhile, the proposed method also has the best measurement accuracy, and the statistical root mean square (RMS) of the residual wavefronts is 0.0082 ± 0.0185 λ (mean ± standard deviation). The proposed method generally has a higher accuracy while having a similar or even better dynamic range as compared to traditional large-dynamic schemes. On the other hand, compared with recently developed deep learning methods, the proposed method has a much larger dynamic range and better measurement accuracy.

Convolutional neural network for improved event-based Shack-Hartmann wavefront reconstruction

Shack-Hartmann wavefront sensing is a technique for measuring wavefront aberrations, whose use in adaptive optics relies on fast position tracking of an array of spots. These sensors conventionally use frame-based cameras operating at a fixed sampling rate to report pixel intensities, even though only a fraction of the pixels have signal. Prior in-lab experiments have shown feasibility of event-based cameras for Shack-Hartmann wavefront sensing (SHWFS), asynchronously reporting the spot locations as log intensity changes at a microsecond time scale. In our work, we propose a convolutional neural network (CNN) called event-based wavefront network (EBWFNet) that achieves highly accurate estimation of the spot centroid position in real time. We developed a custom Shack-Hartmann wavefront sensing hardware with a common aperture for the synchronized frame- and event-based cameras so that spot centroid locations computed from the frame-based camera may be used to train/test the event-CNN-based centroid position estimation method in an unsupervised manner. Field testing with this hardware allows us to conclude that the proposed EBWFNet achieves sub-pixel accuracy in real-world scenarios with substantial improvement over the state-of-the-art event-based SHWFS. An ablation study reveals the impact of data processing, CNN components, and training cost function; and an unoptimized MATLAB implementation is shown to run faster than 800 Hz on a single GPU.

Laboratory study of aberration calculation in underwater turbulence using Shack-Hartmann wavefront sensor and Zernike polynomials

This paper presents a laboratory study of the aberrations calculation in underwater turbulence using the Shack-Hartmann wavefront sensor. The wavefront decomposition method and Zernike polynomials determine the aberration parameters. In our experimental setup, the turbulent phase screen generator is located in two locations: near the transmitter and therefore far from the receiver, and near the receiver and consequently far from the transmitter. Additionally, we investigate the impact of aperture diameter on turbulence-induced aberrations in the optical receiver system. However, it is essential to note that the coefficients of Zernike polynomials obtained using this method are subject to errors caused by receiver sensor noise and correlation between the polynomials. To address this, we first calculate the coefficients in different arrangements and then correct measurement errors arising from sensor noise and polynomial coefficient correlation.

Shack–Hartmann wavefront sensing: A new approach to time-resolved measurement of the stress intensity factor during dynamic fracture

The stress intensity factor describes the stress state around a crack tip in a solid material and is important for understanding crack initiation and propagation. Because stresses cannot be measured directly, the characterization of the stress intensity factor relies on the measurement of deformation around a crack tip. Such measurements are challenging for dynamic fracture of brittle materials where the deformation is small and the crack tip velocity can be high. Digital gradient sensing (DGS) is capable of full-field measurement of surface deformation with a sub-micrometer sensitivity and a sub-microsecond temporal resolution, but it has only been demonstrated on centimeter-scale specimens with a spatial resolution of ∼ 1 mm. This makes it challenging to measure deformations close to the crack tip. Here, we demonstrate the potential of Shack–Hartmann wavefront sensing (SHWFS), as an alternative to DGS, for measuring surface deformation during dynamic brittle fracture of millimeter-scale specimens. Using an opaque commercial glass ceramic as an example material, we demonstrate the capability of SHWFS to measure the surface slope evolution induced by a propagating crack with a micrometer spatial resolution and a sub-microsecond temporal resolution. The SHWFS apparatus has the additional advantage of being physically more compact than a typical DGS apparatus. We interpret our SHWFS measurements of the surface slope by comparing them with 2D analytical predictions and phase-field simulations as well as 3D linear-elastic FEM simulations, based on which we discuss the relevance of 3D effects around the crack tip. Then, we introduce our procedure for extracting the apparent stress intensity factor associated with the propagating crack tip using SHWFS measurements. We conclude by discussing potential future enhancements of this technique and how its compactness could enable the integration of SHWFS with other characterization techniques including x-ray phase-contrast imaging (XPCI) for multi-modal characterization of dynamic fracture.

Implementing a Hybrid Method for Shack–Hartmann Wavefront Spots Labeling on FPGA

This paper presents a real-time implementation of a hybrid connected component labeling method for processing the Shack–Hartmann wavefront sensor’s images for an adaptive optics (AO) system. The output image of a wavefront sensor is an image of spots. During the sensor’s operation, it can happen that highly distorted wavefronts (WF) may cause the spots to shift outside of their sub-aperture, which may lead to the reduction of the AO system performance. This article explains the benefits of high-performance computing and parallel processing of a field programmable gate array (FPGA). The objective is to calculate the centroids of these spots. A hybrid labeling method was investigated to fulfill this purpose. First, this method was implemented using a forward and backward scan with a respective mask for each scan. Additionally, a relabeling process is applied after labeling each line, and it is carried out in both directions. After labeling, several processing units were implemented in parallel to calculate centroids. Each unit is responsible for calculating the centroid of one label. The system runs in real time with a latency of one frame, which means the output image is a fusion of a current frame and the centroids of the previous frame. Forward and backward labeling requires a large amount of memory, which is the reason for limiting the investigation to forward labeling only. The forward labeling was successfully implemented, and the centroids were detected under minimum spot distortion conditions. This forward labeling implementation also runs in real time with significant latency reduction to calculate the centroids, which leads to minimizing the overall AO system latency, enabling faster computation and correction in addition to reducing the memory usage to 1% when compared to the forward and backward labeling usage of 81% as an advantage for the hardware implementation.

Pitch‐Switchable Metalens Array for Wavefront Profiling at Multiwavelength

AbstractThe wavefront sensor is a crucial component in the adaptive optics system (AOS), responsible for detecting aberrated wavefronts. However, The Shack–Hartmann wavefront sensor with single‐pitch microlens array is limited in its adaptability to different observing conditions, affecting wavefront reconstruction accuracy. And conventional microlens arrays are wavelength‐specific. Here, a polarization‐dependent pitch‐switchable metalens array based on non‐interleaved silicon metasurfaces is proposed, capable of working at multiple wavelengths. By controlling the incident and outgoing light polarization, three metalens arrays with customized pitches can be switched at will. Furthermore, achromatic performance is achieved in the 950 nm and 1030 nm wavelengths through structural dispersion engineering. Finally, wavefront detection experiments are finally conducted to demonstrate the phase reconstruction with variable spatial resolution. The metalens array with high flexibility in wavefront sensor can further enhance the adaptability of AOS and has great potential for applications in light‐field imaging, and machine vision, etc.

Wavelength-switching performance and thermal lens effect of cryogenic Yb:YAG lasers

Wavelength-switching performance and thermal lens effect of cryogenic Yb:YAG lasers pumped by a 940 nm laser diode are presented. A maximum continuous wave output power is reached 13.16 W at 80 K with an optic-optic efficiency of 25.6% at an incident pump power of 60 W. The wavelength-switching performance is observed and explained by absorbed pump power threshold behavior as temperature. Moreover, we directly characterize the thermal lens effect by wavefront measurement with a Shack-Hartmann wavefront sensor. The wavefront peak-to-valley value (PV) is 0.338 µm (about 0.33λ) at 80 K, corresponding to a thermal lens dioptric power of 0.15 m-1. The substantial decrease of the thermal lens effect contributes to the significant improvement of laser performance, which is consistent with the brilliant beam quality factor M2 of about 1.10 at both x and y directions.

Deep learning-based optical aberration estimation enables offline digital adaptive optics and super-resolution imaging

Optical aberrations degrade the performance of fluorescence microscopy. Conventional adaptive optics (AO) leverages specific devices, such as the Shack–Hartmann wavefront sensor and deformable mirror, to measure and correct optical aberrations. However, conventional AO requires either additional hardware or a more complicated imaging procedure, resulting in higher cost or a lower acquisition speed. In this study, we proposed a novel space-frequency encoding network (SFE-Net) that can directly estimate the aberrated point spread functions (PSFs) from biological images, enabling fast optical aberration estimation with high accuracy without engaging extra optics and image acquisition. We showed that with the estimated PSFs, the optical aberration can be computationally removed by the deconvolution algorithm. Furthermore, to fully exploit the benefits of SFE-Net, we incorporated the estimated PSF with neural network architecture design to devise an aberration-aware deep-learning super-resolution model, dubbed SFT-DFCAN. We demonstrated that the combination of SFE-Net and SFT-DFCAN enables instant digital AO and optical aberration-aware super-resolution reconstruction for live-cell imaging.

Extended scene deep-phase-retrieval Shack-Hartmann wavefront sensors

Context. Strong atmospheric turbulence has been a challenge for high-resolution imaging of solar telescopes. Adaptive optics (AO) systems are capable of improving the quality of imaging by correcting partial aberrations. Thus, the performance of Shack-Hartmann sensors in measuring aberrations generally determines the upper performance bound of AO systems. In solar AO, classic correlation Shack-Hartmann sensors only correct a small number of modal aberrations. Moreover, strong aberrations are difficult to measure stably by correlation Shack-Hartmann. In this context, the improvement in the performance of Shark-Hartmann sensors promises to enable higher-resolution imaging of extended objects for ground-based telescopes or Earth observation. Aims. We propose a new extended scene deep-phase-retrieval Shack-Hartmann wavefront sensing approach to improve the image quality of solar telescopes. It is capable of achieving high-accuracy measurements of high-spatial-resolution wavefronts on extended scene wavefront sensing. Moreover, it has great generalization when observing unknown objects from different fields of view of the telescope. Methods. Our proposed approach can extract features resembling the sub-aperture point spread function (PSF) from a Shack-Hartmann sensor image without any prior information. Then a convolutional neural network is used to establish a nonlinear mapping between the feature image and the wavefront modal coefficients. The extracted feature greatly eliminates the shape information of the extended object while maintaining more information related to aberrations. We verified the performance of the proposed method through simulations and experiments. Results. In the indoor experiment on the ground layer adaptive optics (GLAO) of the 1 m New Vacuum Solar Telescope, compared to the Shack-Hartmann correlation method, the proposed method reduces the correction errors by more than one third. When observing objects from different fields of view in the GLAO that differ from the object in the training data, the relative errors fluctuate within the range of 20% to 26%. The AO system with the proposed wavefront measurement method can obtain higher-resolution focal images of the simulated solar granulation after a round of offline correction. The average latency of the proposed method is about 0.6 ms.

Wavefront reconstruction based on ASH-Net with less lenslets SHWFS

Generally, the number of lenslets in Shack–Hartman wavefront sensor (SHWFS) determines its spatial sampling frequency. However, increasing the number of lenslets is limited by the data processing delay time and low sensitivity in the adaptive optics system. In this paper, a wavefront reconstruction method based on ASH-Net for SHWFS is presented to recover the distorted wavefront from the light spots array with high accuracy with a spatial sampling frequency than traditionally required. The results show that the maximum number of Zernike modes recovered by the method is 36, 54, and 70 for 4 × 4, 6 × 6, and 8 × 8 lenslets arrays, respectively. Residual wavefront root mean square values are as low as about 0.02 μm, corresponding to a Strehl Ratio of 0.99. This method breaks the limitation that the number of reconstructed Zernike modes in the traditional wavefront reconstruction algorithm must be less than the number of effective lenslets. Experiments in lab are used to validate the method. Additionally, fewer lenslets is valuable to improve the detection capability of SHWFS for faint targets. This is important for applications of adaptive optics in areas such as astronomy and retinal imaging.

Large dynamic range Shack–Hartmann wavefront sensor based on holographic multipoint generation and pattern correlation

Large dynamic range Shack–Hartmann wavefront sensor based on holographic multipoint generation and pattern correlation

Spectral characterization of optical aberrations in fluidic lenses

We report an extensive numerical study and supporting experimental results on the spectral characterization of optical aberrations in macroscopic fluidic lenses with tunable focal distance and aperture shape. By using a Shack–Hartmann wavefront sensor, we experimentally reconstruct the near-field wavefront transmitted by the fluidic lenses, and we characterize the chromatic aberrations in terms of Zernike polynomials in the visible range. Moreover, we further classify the spectral response of the lenses using clustering techniques, in addition to correlation and convolution measurements. Experimental results are in agreement with numerical results based on our theoretical model of the nonlinear deformation of thin elastic membranes.