Shack-Hartmann Research Articles

Higher-resolution wavefront sensing based on sub-wavefront information extraction

The limited spatial sampling rates of conventional Shack–Hartmann wavefront sensors (SHWFSs) make them unable to sense higher-order wavefront distortion. In this study, by etching a known phase on each microlens to modulate sub-wavefront, we propose a higher-resolution wavefront reconstruction method that employs a modified modal Zernike wavefront reconstruction algorithm, in which the reconstruction matrix contains quadratic information that is extracted using a neural network. We validate this method through simulations, and the results show that once the network has been trained, for various atmospheric conditions and spatial sampling rates, the proposed method enables fast and accurate high-resolution wavefront reconstruction. Furthermore, it has highly competitive advantages such as fast dataset generation, simple network structure, and short prediction time.

Head-mounted adaptive optics visual simulator.

Adaptive optics visual simulation is a powerful tool for vision testing and evaluation. However, the existing instruments either have fixed tabletop configurations or, being wearable, only offer the correction of defocus. This paper proposes a novel head-mounted adaptive optics visual simulator that can measure and modify complex ocular aberrations in real-time. The prototype is composed of two optical modules, one for the objective assessment of aberrations and the second for wavefront modulation, all of which are integrated into a wearable headset. The device incorporates a microdisplay for stimulus generation, a liquid crystal on silicon (LCoS) spatial light modulator for wavefront manipulation, and a Hartmann-Shack wavefront sensor. Miniature optical components and optical path folding structures, together with in-house 3D printed mounts and housing, were adapted to realize the compact size. The system was calibrated by characterizing and compensating the internal aberrations of the visual relay. The performance of the prototype was analyzed by evaluating the measurement and compensation of low-order and higher-order aberrations induced through trial lenses and phase masks in an artificial eye. The defocus curves for a simulated bifocal diffractive lens were evaluated in real eyes. The results show high accuracy while measuring and compensating for the induced defocus, astigmatism, and higher-order aberrations, whereas the MTF analysis shows post-correction resolution of up to 37.5 cycles/degree (VA 1.25). Moreover, the subjective test results show the defocus curves closely matched to a commercial desktop visual simulator.

Accuracy Analysis for Shack–Hartmann Wave Front Sensing with Extended Sources

Correlating the Shack–Hartmann wave front sensor (SH-WFS) with extended targets is widely used in solar adaptive optics systems. This paper aims to introduce a theoretical analysis that evaluates the accuracy of the SH-WFS on extended sources, with a specific focus on the implementation of the Normalized Cross-correlation (NCC) algorithm. To obtain an accurate error description, we utilized the calculation formula of the NCC algorithm to directly express the coordinates of the maximum value in the correlation function matrix. Furthermore, we determined the variance of the centroid position through the error transfer function, which quantifies the measurement error. In comparison with the previous findings of Michau et al., our result exhibits a coefficient disparity, specifically obtaining results 1.5 times higher than their work. The extensive solar granulation simulation and experimental results validate the theoretical error formulas. These error formulas can effectively estimate the accuracy of the SH-WFS, providing a theoretical foundation for the design of optical systems.

High-precision spherical wavefront calibration method for shack-hartmann wavefront sensor

High-precision spherical wavefront calibration method for shack-hartmann wavefront sensor

Large dynamic range Shack-Hartmann wavefront sensor based on adaptive spot matching

Large dynamic range Shack-Hartmann wavefront sensor based on adaptive spot matching

Comparison of branch-point detection approaches using a Shack–Hartmann wavefront sensor

Comparison of branch-point detection approaches using a Shack–Hartmann wavefront sensor

Light Field Acquisition Using Shack-Hartmann Wavefront Sensor and Its Application to Holographic Stereogram

Light Field Acquisition Using Shack-Hartmann Wavefront Sensor and Its Application to Holographic Stereogram

Ocular aberration measurement with and without an aperture stop using a Shack–Hartmann wavefront sensor

Pupil size is an important parameter since it governs the magnitude of ocular aberrations. The pupil size of a human eye has significant individual differences and varies with light level and accommodation. In order to accurately measure ocular aberrations under different pupil sizes using a Shack–Hartmann wavefront sensor (SHWFS), two types of relationship matrices R(1) and R(2) were proposed, which corresponded to wavefront reconstruction with and without an aperture stop, respectively. The numerical and experimental results indicated that matrix R(2) can significantly improve the accuracy of wavefront restoration when the incident beam size is inconsistent with the wavefront reconstruction aperture. Meanwhile, the impact of the aperture stop on the reconstruction accuracy will become smaller and smaller as the ratio ρ of the outer area to the detection aperture decreases. This study not only can be used for accurately measuring ocular aberrations under different pupil sizes, but also for other variable aperture aberrations measurement in other applications.

Potential vision tester using adaptive optics, Maxwellian view, and small pupil.

We demonstrate a free-space, trolley-mounted potential vision tester (PVT), designed to study and improve the accuracy of visual acuity (VA) measurements in the aging eye. Key features include a high-resolution visual display presented in Maxwellian view, a 3 mm pupil to limit wavefront (WF) aberrations, and a moderate cost deformable mirror to induce or correct higher order optical aberrations. The visual display supported accurate measurement of visual acuities down to 20/5. The moderate cost, piezo deformable mirror induced seven nominal aberrations, calibrated as 0, -0.32, -0.23, + 0.27, and +0.39 microns spherical aberration; + 0.49 microns Y coma; and -0.51 microns X coma. A custom Hartmann Shack (HS) calibration (HSc) system demonstrated that induced aberrations were repeatable and stable. A Badal optometer provided the coarse focus. WF aberrations were measured for five normal subjects with a commercially available HS device (HSP) (OCULUS Pentacam AXL Wave), providing estimates of WF errors for 3 mm and other pupil sizes. VA was measured using four alternative forced-choice for a single black on white E stimulus in each trial. Using the method of constant stimuli yielded robust standard deviation measurements. The 50% fit for VA plotted against induced aberration resulted in linear functions for each subject for the range of our positive and negative spherical aberration data. Subjects differed, but higher order terms were unnecessary to describe data across spherical aberrations.

Highly Stable Spatio-Temporal Prediction Network of Wavefront Sensor Slopes in Adaptive Optics.

Adaptive Optics (AO) technology is an effective means to compensate for wavefront distortion, but its inherent delay error will cause the compensation wavefront on the deformable mirror (DM) to lag behind the changes in the distorted wavefront. Especially when the change in the wavefront is higher than the Shack-Hartmann wavefront sensor (SHWS) sampling frequency, the multi-frame delay will seriously limit its correction performance. In this paper, a highly stable AO prediction network based on deep learning is proposed, which only uses 10 frames of prior wavefront information to obtain high-stability and high-precision open-loop predicted slopes for the next six frames. The simulation results under various distortion intensities show that the prediction accuracy of six frames decreases by no more than 15%, and the experimental results also verify that the open-loop correction accuracy of our proposed method under the sampling frequency of 500 Hz is better than that of the traditional non-predicted method under 1000 Hz.

Atmospheric Turbulence Aberration Correction Based on Deep Learning Wavefront Sensing.

In this paper, research was conducted on Deep Learning Wavefront Sensing (DLWS) neural networks using simulated atmospheric turbulence datasets, and a novel DLWS was proposed based on attention mechanisms and Convolutional Neural Networks (CNNs). The study encompassed both indoor experiments and kilometer-range laser transmission experiments employing DLWS. In terms of indoor experiments, data were collected and training was performed on the platform built by us. Subsequent comparative experiments with the Shack-Hartmann Wavefront Sensing (SHWS) method revealed that our DLWS model achieved accuracy on par with SHWS. For the kilometer-scale experiments, we directly applied the DLWS model obtained from the indoor platform, eliminating the need for new data collection or additional training. The DLWS predicts the wavefront from the beacon light PSF in real time and then uses it for aberration correction of the emitted laser. The results demonstrate a substantial improvement in the average peak intensity of the light spot at the target position after closed-loop correction, with a remarkable increase of 5.35 times compared to the open-loop configuration.

Comparative Analysis of Image-shift Measurement Algorithms for Solar Shack–Hartmann Wavefront Sensors

Observations of the Sun provide unique insights into its structure, evolution, and activity, with significant implications for space weather forecasting and solar energy technologies. Ground-based telescopes offer cost-effective and flexible solutions for high-resolution solar observations, but image quality can be affected by atmospheric turbulence. Adaptive optics (AO) systems equipped with Shack–Hartmann wave front sensors (SH-WFS) enable real-time image correction to mitigate these effects. The accuracy of SH-WFS relies on correlation algorithms that measure wave front shifts, but reaching consistent conclusions regarding their accuracy remains challenging. In this study, we conducted an evaluation and comparison of standard correlation algorithms (the Square Difference Function, Normalized Cross-Correlation, Absolute Difference Function, Absolute Difference Function-Squared, and the Covariance Function in the frequency domain (CFF)) using simulated and authentic solar images. We optimized the algorithms through pre-processing techniques and carefully selected the most suitable window function for the CFF algorithm. Additionally, we analyzed the influence of various factors, such as shift ranges, bias, and the size of live images on the accuracy of algorithms. The consistent findings revealed that the CFF algorithm demonstrates superior measurement accuracy and robustness compared to the others. Choosing the CFF algorithm for solar observations can significantly enhance measurement accuracy, AO system performance, and the overall quality of solar research findings, thereby providing crucial support for space weather forecasting and other related scientific fields.

Adaptive Optics Microscopy with Wavefront Sensing Based onNeighbor Correlation.

Complex structures in living cells and tissues induce wavefront errors when light waves pass through them, and images observed with optical microscopes are undesirably blurred. This problem is especially serious for living plant cells because images are strikingly degraded even within a single cell. Adaptive optics (AO) is expected to be a solution to this problem by correcting such wavefront errors, thus enabling high-resolution imaging. In particular, scene-based AO involves wavefront sensing based on the image correlation between subapertures in a Shack-Hartmann wavefront sensor and thus does not require an intense point light source. However, the complex 3D structures of living cells often cause low correlation between subimages, leading to loss of accuracy in wavefront sensing. This paper proposes a novel method for scene-based sensing using only image correlations between adjacent subapertures. The method can minimize changes between subimages to be correlated and thus prevent inaccuracy in phase estimation. Using an artificial test target mimicking the optical properties of a layer of living plant cells, an imaging performance with a Strehl ratio of approximately 0.5 was confirmed. Upon observation of chloroplast autofluorescence inside living leaf cells of the moss Physcomitrium patens, recovered resolution images were successfully obtained even with complex biological structures. Under bright-field illumination, the proposed method outperformed the conventional method, demonstrating the future potential of this method for label- and damage-free AO microscopy. Several points for improvement in terms of the effect of AO correction are discussed.

Complex amplitude extraction from a set of interferograms by simultaneous modulation of amplitude and phase steps

The measurement of an optical field arises in various fields of science and engineering, including holography, crystallography, microscopy, and many others. Nowadays, there are several methods to estimate amplitude and phase including Shack–Hartman wavefront sensor, algorithms type Gerchberg–Saxton, algorithm-based on the transport of irradiance equation, holographic, interferometric, among others. This paper introduces an interferometric method for retrieving the complex amplitude from a set of interferograms modulated simultaneously in visibility and phase steps. Instead of phase only as the method of so-called phase-shifting interferometry. This approach is based on the modulation of amplitude and phase steps and is presented for the case of synchronous detection and coherence light. It is validated with a numerical noise study, turning out to be accurate and robust to detuning errors, with low distortion, and a very high signal-to-noise. The experiment is carried out on a Mach–Zehnder interferometer adapted to modulate the reference amplitude, and the phase steps by modulation of polarization, instead of phase steps only as in phase-shifting interferometry.

SHARPEST: the atmospheric turbulence profiling experiment using Shack–Hartmann sensor at the Subaru telescope

ABSTRACT Atmospheric turbulence profile plays an important role in designing and operating adaptive optics (AO) systems with multiple laser guide stars. To obtain representative free atmospheric profiles and resolved ground layer profiles for future AO systems at the Subaru telescope, we are conducting the Shack–Hartmann Atmospheric tuRbulence Profiling Experiment at the Subaru Telescope project. In this project, we develop a turbulence profiler comprising two Shack–Hartmann (SH) sensors to observe a pair of bright stars through the Subaru telescope with high spatial sampling by 2 cm subapertures. We perform two analyses on the SH spot data: variance analysis on the spot scintillation for free atmospheric profiles, and on the spot slope for ground layer profiles. This paper introduces the initial results of free atmospheric profiles as well as total seeing values and wind profiles obtained by the first two engineering runs. The free atmospheric profiles reconstructed by the two independent SH sensors show good agreement. The results are also consistent with simultaneous measurements by another profiler except for turbulence strength at ∼1 km, which is explained by an overestimation problem of scintillation-based profilers. Measured total seeing values are also smaller than the simultaneous measurements, possibly due to the difference in ground layer turbulence between the two sites. The wind profiles show good consistency with the direct measurements by a rawinsonde. Through this study, we establish a method to constrain the free atmospheric profile, the total seeing, and the wind profile by analysing data from a single SH sensor with fine subapertures.

Method for testing freeform surfaces based on a Shack-Hartmann sensor with plane wavefront scanning and stitching.

Currently, the surface error measurement technology for freeform faces a significant contradiction between measurement accuracy and dynamic range. The study proposes a non-null testing method for measuring freeform surfaces by utilizing a Shack-Hartmann wavefront sensor to emit a small aperture parallel beam and scan along the normal direction at the center of subapertures for stitching (SHPSS). A mathematical model based on ray tracing and the reflection theorem is established to calculate the sampling points on an ideal freeform surface, the reference spot array on CCD, and the corresponding relationship between microlens array and spots. An algorithm is proposed to iteratively calculate the wavefront aberration and gradually approach the actual sampling points using the established model. Theoretical analysis and numerical simulation results indicate that SHPSS can increase the dynamic range and improve the accuracy of wavefront reconstruction. The error analysis of the SHPSS method is carried out, the measurement accuracy of full aperture freeform surface is 11.45 nm. A testing system is set up and experiments are conducted on a 100 mm aperture freeform reflective mirror. The RMS of the SHPSS test results is less than λ/30 (λ=635 nm) compared to the interferometric test results. By analyzing five groups of repeated measurement experiments, the repeatability accuracy of SHPSS method is less than 1/80 λ (RMS). This demonstrates the feasibility and measurement capabilities of the method for freeform surface testing.

Two-Dimensional Peripheral Refraction and Higher-Order Wavefront Aberrations Induced by Orthokeratology Lenses Decentration.

The purpose of this study was to explore two-dimensional peripheral refraction and higher-order aberrations (HOAs) induced by orthokeratology lens decentration. Two-dimensional peripheral refraction and HOAs in a rectangular field (horizontally 60 degrees and vertically 36 degrees) were obtained using an open-view Hartmann-Shack wavefront sensor. The peripheral field was divided into 8 regions according to a combination of superior (UZ) or inferior (LZ) and a value, 1 (T25 to T30), 2 (T20 to T25), 3 (N20 to N25), or 4 (N25 to N30). The decentration of the lens was evaluated based on the change of power in the front of the tangential corneal map. All measurements were taken at the baseline and 1 month after lens fitting. In total, 134 myopic children (age = 12.47 ± 1.70 years, SER = -2.44 ± 1.10 diopters [D]) were recruited. In general, horizontally asymmetrical change was observed in relative peripheral refraction (RPR), spherical aberration (SA), and horizontal coma. The root-mean square of higher order aberration (RMSHOA) and vertical coma demonstrated radial symmetrical change and vertically asymmetric change, respectively. Relative peripheral myopia was significantly increased after the treatment, with more myopic refraction in the temporal side. RPR changes in UZ2, UZ3, UZ4, LZ1, and LZ2 were related to the amount of lens decentration (r ≈ 0.4, P<0.05). All HOAs increased after lens fitting (around 0.03 um, 0.02 um, 0.04 um, and 0.41 um for SA, horizontal COMA, vertical COMA, and RMSHOA in the periphery region). RPR and HOAs are related to lens decentration, which might contribute to the efficacy of orthokeratology. The study found a decentration-related optical feature after 1 month of lens wear, which is a suggested protective factor in myopia treatment. The findings might provide new insights for customized contact lens myopia treatment based on optics.

Remote focusing with dynamic aberration elimination by model-based adaptive optics

Remote focusing using a deformable mirror (DM) provides a rapid and responsive technique for performing axial scanning. However, to maintain the laser focusing quality, the aberrations within the system must be adequately controlled. Accordingly, the present study proposes a low control complexity model-based adaptive optics (AO) approach for remote focusing with zero aberrations. Based on the Zernike coefficients measured by a self-built Shack-Hartmann wavefront sensor (SHWS), 15 independent closed-loop controllers (one for each Zernike mode according to Wyant expansion scheme) execute a three-step DM identification process to determine the control vectors required to actuate the DM in such a way as to restore the Zernike coefficients of the wavefront to their required values. The experimental results show that the controllers converge within four time steps (20 ms) and reduce the converged wavefront variance by nearly 475 times. Moreover, the controller used to manipulate the Z3 (defocus) Zernike coefficient converges within just three time steps (15 ms). Given a static disturbance of the wavefront, the proposed AO control method enables the defocus laser spot to be driven precisely along a target sinusoidal trajectory while maintaining all the other Zernike modes at zero. The control system shows a similar performance in compensating the dynamic aberrations produced by a low-frequency thermal disturbance within the system. Overall, the results indicate that the proposed model-based AO controller facilitates remote focusing with simultaneous aberration elimination and improves the central intensity of the focus laser spot by around 3.1 times compared to the case in which the controller is not applied.

Expanded Scene Image Preprocessing Method for the Shack–Hartmann Wavefront Sensor

Due to the influence of atmospheric turbulence, the detector, and background noise, the subaperture image of an extended scene Shack–Hartmann wavefront sensor will have a low signal-to-noise ratio, which will introduce errors to the offset estimation and reduce the accuracy of the slope measurement. To solve this problem, this paper proposes a cross-correlation subaperture image preprocessing method, which uses the generalized Anscombe transform to convert the Gauss–Poisson noise into Gaussian noise and introduces residual feedback on the basis of BM3D to achieve the efficient denoising of subaperture images. The simulation results show that compared with the three commonly used denoising algorithms, the proposed method improves the relative error of the subaperture offset calculation by 51.96% and the corresponding Zernike coefficient of distorted reconstruction wavefront by 85.56%, which realizes the improvement in the detection accuracy on the basis of effectively retaining image details.

Estimation of Crystalline Lens Material Properties From Patient Accommodation Data and Finite Element Models.

The mechanical properties of the crystalline lens are related to its optical function of accommodation, and their changes with age are one of the potential causes for presbyopia. We estimated the mechanical parameters of the crystalline lens using quantitative optical coherence tomography (OCT) imaging and wavefront sensing data from accommodating participants and computer modeling. Full-lens shape data (from quantitative swept-source OCT and eigenlens representation) and optical power data (from Hartmann-Shack wavefront sensor) were obtained from 11 participants (22-30 years old) for relaxed accommodation at infinity and -4.5 D accommodative demand. Finite element models of lens, capsular bag, zonulae, and ciliary body were constructed using measured lens geometry and literature data, assuming a 60-mN radial force. An inverse modeling scheme was used to determine the shear moduli of the nucleus and cortex of the lens, such that the simulated deformed (maximally stretched) lens matched the participant's lens at -4.5 D. The shear moduli of the nucleus and cortex were 1.62 ± 1.32 and 8.18 ± 5.63 kPa, on average, respectively. The shear modulus of the nucleus was lower than that of the cortex for all participants evaluated. The average of the two moduli per participant was statistically significantly correlated with age (R2 = 0.76, P = 0.0049). In vivo imaging and mechanical modeling of the crystalline lens allow estimations of the crystalline lens' mechanical properties. Differences between nuclear and cortical moduli and their dependency with age appear to be critical in accommodative function and likely in its impairment in presbyopia.