Shack-Hartmann Sensor Research Articles

Selection of OAM signal constellations for atmospheric channels using optimal transport theory

We describe a method for determining optimal selections of orbital angular momentum (OAM) superpositions for OAM signal modulation in free-space optical communications using a measure of distance in the context of the Optimal Transport theory. Within the range of topological charges ℓ = −20 to ℓ = 20 we design OAM constellations using 16 to 128 symbols consisting of solos, duets, trios, and quartets of OAM modes. We propose a classification strategy requiring relatively low complexity to evaluate the performance of these constellations, achieving a classification error smaller than 1/1000 in weak to strong turbulence conditions for the 16-OAM constellation. We have found that the optimal set shows some dependence on the receiver’s architecture, so we offer results for optical detectors based on the conjugate projection, the mode sorter, and the Shack-Hartmann sensor.

Automatic Compressive Sensing of Shack–Hartmann Sensors Based on the Vision Transformer

Shack–Hartmann wavefront sensors (SHWFSs) are crucial for detecting distortions in adaptive optics systems, but the accuracy of wavefront reconstruction is often hampered by low guide star brightness or strong atmospheric turbulence. This study introduces a new method of using the Vision Transformer model to process image information from SHWFSs. Compared with previous traditional methods, this model can assign a weight value to each subaperture by considering the position and image information of each subaperture of this sensor, and it can process to obtain wavefront reconstruction results. Comparative evaluations using simulated SHWFS light intensity images and corresponding deformable mirror command vectors demonstrate the robustness and accuracy of the Vision Transformer under various guide star magnitudes and atmospheric conditions, compared to convolutional neural networks (CNNs), represented in this study by Residual Neural Network (ResNet), which are widely used by other scholars. Notably, normalization preprocessing significantly improves the CNN performance (improving Strehl ratio by up to 0.2 under low turbulence) while having a varied impact on the Vision Transformer, improving its performance under a low turbulence intensity and high brightness (Strehl ratio up to 0.8) but deteriorating under a high turbulence intensity and low brightness (Strehl ratio reduced to about 0.05). Overall, the Vision Transformer consistently outperforms CNN models across all tested conditions, enhancing the Strehl ratio by an average of 0.2 more than CNNs.

Zonal shape reconstruction for Shack-Hartmann sensors and deflectometry

Some metrological means, such as Shack-Hartmann, deflectometry sensors or fringe projection profilometry, measure the shape of an optical surface indirectly from slope measurements. Zonal shape reconstruction, a method to reconstruct shape with a high number of degrees of freedom, is used for all of these applications. It has risen in interest with the use of deflectometers for the acquisition of high resolution slope data for optical manufacturing, especially because shape reconstruction is limiting in terms of shape estimation error.Zonal reconstruction methods all rely on the choice of a data formation model, a basis on which the shape will be decomposed, and an estimator. In this paper, we first study the canonical Fried and Southwell models of the literature and analyze their limitations. We show that modeling the slope measurement by a point-wise derivative as they both do can induce a bias on the shape estimation, and that the bases on which the shape is decomposed are imposed because of this assumption.In the second part of this paper, we propose to build an unbiased model of the data formation, without constraints on the choice of the decomposition basis. We then compare these models to the canonical models of Fried and Southwell.Lastly, we perform a regularized MAP reconstruction, and compare the performance in terms of total shape error of this method to the state of the art for the Southwell and Fried models, first by simulation, then on experimental data. We demonstrate that the suggested method outperforms the canonical models in terms of total shape reconstruction error on a deflectometry measurement of the high-frequency content of a freeform mirror.

Frequency-dependent effects of 0.05% atropine eyedrops on myopia progression and peripheral defocus: a prospective study

BackgroundAtropine, specifically 0.05% eyedrops, has proven effective in slowing myopia progression. This study aims to investigate peripheral refraction (PR) characteristics in myopic children treated with 0.05% atropine eyedrops at different frequencies.MethodsOne hundred thirty-eight myopic children completed this one-year prospective study, randomly assigned to once daily (7/7), twice per week (2/7), or once per week (1/7) groups. Spherical equivalent (SE) and axial length (AL) were measured. PR was assessed using a custom-made Hartmann-Shack wavefront peripheral sensor, covering a visual field of horizontal 60° and vertical 36°. Relative peripheral refraction (RPR) was calculated by subtracting central from peripheral measurements.ResultsAfter one year, SE increased more significantly in the 1/7 group compared to the 7/7 group (P < 0.001) and 2/7 group (P = 0.004); AL elongation was also greater in the 1/7 group compared to the 7/7 group (P < 0.001). In comparison with higher frequency groups, 1/7 group exhibited more myopic PR in the fovea and its vertical superior, inferior, and nasal retina; and less myopic RPR in the periphery retina after one-year (P < 0.05). Additionally, RPR in the 7/7 group demonstrated myopic shift across the entire retina, the 2/7 group in temporal and inferior retina, while the 1/7 group showed a hyperopic shift in the superior retina (P < 0.05). Moreover, myopic shift of RPR in the temporal retina is related to less myopia progression, notably in the 7/7 group (P < 0.05).ConclusionsAtropine inhibits myopia progression in a frequency-dependent manner. The once-daily group showed the slowest myopia progression but exhibited more myopic shifts in RPR. Additionally, RPR in the temporal retina was related to myopia progression in all groups.Trial registrationChinese Clinical Trial Registry, ChiCTR2100043506. Registered 21 February 2021, https://www.chictr.org.cn/showproj.html?proj=122214

The induced defocus by Defocus Incorporated Soft Contact lenses is dependent on visual distance and ambient illuminance.

Defocus Incorporated Soft Contact (DISC) lenses, a commonly used type of multifocal lens in clinical practice, may slow down myopia progression by inducing myopic retinal defocus. The purpose of this study was to explore whether the induced defocus across the retina could be affected by visual environments encountered in the real world, such as differences in viewing distance and ambient illuminance. In this cross-over trial, 30 myopic adults wore both DISC lenses and single vision contact (SVC) lenses in random order. An open-view Hartmann-Shack scanning wavefront sensor was used to measure defocus at different retinal locations along the horizontal meridian under four experimental conditions: far target (3 m) and near targets (0.33 m) under scotopic (<1 lux) or photopic (~300 lux) conditions. The results showed that DISC lenses induced more myopic retinal defocus than SVC lenses in all conditions (all p < 0.05), except for the scotopic near target. In addition, for DISC lenses, the defocus was greater in the photopic than the scotopic conditions for both the far and near targets (both p < 0.05). In conclusion, the retinal defocus induced by these multifocal lenses was dependent on both visual distance and ambient illuminance, indicating that the visual conditions might affect the anti-myopia efficacy of these devices.

Striving towards robust phase diversity on-sky

Context. The recent IRLOS upgrade for VLT/MUSE narrow field mode (NFM) introduced a full-pupil mode to enhance sensitivity and sky coverage. This involved replacing the 2 × 2 Shack-Hartmann sensor with a single lens for full-aperture photon collection, which also enabled the engagement of the linearized focal-plane technique (LIFT) wavefront sensor instead. However, initial on-sky LIFT experiments have highlighted a complex point spread function (PSF) structure due to strong and polychromatic non-common path aberrations (NCPAs), complicating the accurate retrieval of tip-tilt and focus using LIFT. Aims. This study aims to conduct the first on-sky validation of LIFT on VLT/UT4, outline challenges encountered during the tests, and propose solutions for increasing the robustness of LIFT in on-sky operations. Methods. We developed a two-stage approach to focal-plane wavefront sensing, where tip-tilt and focus retrieval done with LIFT is preceded by the NCPA calibration step. The resulting NCPA estimate is subsequently used by LIFT. To perform the calibration, we proposed a method capable of retrieving the information about NCPAs directly from on-sky focal-plane PSFs. Results. We verified the efficacy of this approach in simulated and on-sky tests. Our results demonstrate that adopting the two-stage approach has led to a significant improvement in the accuracy of the defocus estimation performed by LIFT, even under challenging low-flux conditions. Conclusions. The efficacy of LIFT as a slow and truth focus sensor in practical scenarios has been demonstrated. However, integrating NCPA calibration with LIFT is essential to verifying its practical application in the real system. Additionally, the proposed calibration step can serve as an independent and minimally invasive approach to evaluate NCPA on-sky.

Vertical Distribution of Optical Turbulence at the Peak Terskol Observatory and Mount Kurapdag

Atmospheric turbulence characteristics are essential in determining the quality of astronomical images and implementing adaptive optics systems. In this study, the vertical distributions of optical turbulence at the Peak Terskol observatory (43.27472°N 42.50083°E, 3127 m a.s.l.) using the Era-5 reanalysis and scintillation measurements are investigated. For the closest reanalysis grid node to the observatory, vertical profiles of the structural constant of the air refractive index turbulent fluctuations Cn2 were obtained. The calculated Cn2(z) vertical profiles are compared with the vertical distribution of turbulence intensity obtained from tomographic measurements with a Shack–Hartmann sensor. The atmospheric coherence length at the location of Terskol Peak was estimated. Using a combination of atmospheric models and paramaterization schemes of turbulence, Cn2(z) profiles at Mt. Kurapdag were obtained. The values of atmospheric coherence length at Peak Terskol are compared with estimated values of this length at the ten astronomical sites, including Ali, Lenghu and Daocheng.

High-accuracy determination of the beam divergence error in free-fall absolute gravimeters

We investigate the bias due to the beam divergence of the collimator in a free-fall absolute gravimeter of type FG5X. First, we measure the beam parameters with a Shack-Hartmann sensor. Then, we use the parameters to simulate the relative gravitational acceleration error of an FG5X gravimeter, which employs an unbalanced Mach-Zehnder laser interferometer. This investigation we do with four different commercial collimators, providing different divergence angles. We compare the results to real gravity measurements using the same collimators. The larger the divergence angle, and the bigger the relative length error, the bigger is the bias in the gravity measurements. A good agreement between theory and experiment is found, resulting in a relative bias of −2.77(24)⋅10−9 ( −2.72(24) μGal) for our standard collimator of type Thorlabs TC25APC, which is usually used for free-fall acceleration determinations. The outcome is also important for the realization of the SI unit kilogram via Kibble balance experiments that, on one side, employ laser interferometers for velocity measurements, and, on the other side, require accurate values of the gravitational acceleration. For example, if this divergence error is not corrected in the Kibble balance, then the mass determination would be biased by 2.77(24) μg kg−1 (numbers are valid only for our gravimeter with our collimator and fiber).

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.

Evaluation of atmospheric coherent length of free-space optical links by using phase fluctuation.

Atmospheric coherence length is one of the most crucial parameters for free-space optical (FSO) links, which can reflect the level of phase and amplitude fluctuations caused by the atmospheric turbulence. In this paper, we study the evaluation of the atmospheric coherence length of the FSO links. The analytical expression of atmospheric coherence length is rendered based on the phase fluctuation resulting from atmospheric turbulence by using the most realistic Bump model. The proposed method is validated theoretically with the Monte Carlo phase screen. Also, the experimental setup with respect to FSO links is established with the spatial light modulator to validate the method experimentally, wherein the fluctuated phase is collected by Shack-Hartmann sensor. The results show that the evaluation of atmospheric coherence length by the analytical expression is consistent with the theoretical prediction as well as the experimental measurement. Thus, the proposed method enables the accurate evaluation of atmospheric coherence length under various turbulence conditions, which can assist the performance analysis as well as design of free-space optical communication systems.

Reconstructing highly divergent wavefronts from sparse measurements

The paper presents a concept for the sparse measurement and reconstruction of highly divergent wavefronts enabling measurements at high throughputs and beyond the dynamic range of the wavefront sensor. In the proposed concept, a direct measurement of the wavefront is carried out, where a few segments of the wavefront are measured with Shack–Hartmann sensors (SHSs). In total about 1% of the wavefront is measured and used for the reconstruction of the entire wavefront, which makes the concept suitable for applications where low measurement times are needed. A simulation analysis and an experimental validation of the concept are carried out, and results show that a wavefront with a divergence of 62° can be reconstructed with a root-mean-square error of about 200 nm.

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.

Atmospheric Turbulence with Kolmogorov Spectra: Software Simulation, Real-Time Reconstruction and Compensation by Means of Adaptive Optical System with Bimorph and Stacked-Actuator Deformable Mirrors

Atmospheric turbulence causes refractive index fluctuations, which in turn introduce extra distortions to the wavefront of the propagated radiation. It ultimately degrades telescope resolution (in imaging applications) and reduces radiation power density (in focusing applications). One of the possible ways of researching the impact of turbulence is to numerically simulate the spectrum of refractive index fluctuations, to reproduce it using a wavefront corrector and to measure the resultant wavefront using, for example, a Shack–Hartmann sensor. In this paper, we developed turbulence simulator software that generates phase screens with Kolmogorov spectra. We reconstructed the generated set of phase screens using a stacked-actuator deformable mirror and then compensated for the introduced wavefront distortions using a bimorph deformable mirror. The residual amplitude of the wavefront reconstructed by the 19-channel stacked-actuator mirror was 0.26 λ, while the residual amplitude of the wavefront compensated for by the 32-channel bimorph mirror was 0.08 λ.

Optical Quality and Higher Order Aberrations of Refractive Extended Depth of Focus Intraocular Lenses.

To compare the optical quality and higher order aberrations of four different refractive extended depth of focus intraocular lens (EDOF IOL) models (Lentis Comfort [Teleon Surgical BV], MiniWell (SIFI), LuxSmart [Bausch & Lomb], and AcrySof IQ Vivity [Alcon Laboratories, Inc]) and a monofocal IOL (Tecnis ZCB00; Johnson & Johnson Surgical Vision, Inc). An optical metrology instrument (OptiSpheric IOL PRO2; Trioptics GmbH) was used to study image quality metrics of the different IOLs. The modulation transfer function (MTF) was measured at pupil sizes 1 to 5 mm in 1-mm steps. Area under the MTF and simulated visual acuity were calculated for different pupil diameters. Wavefront aberrations were measured with the SHS Ophthalmic device (Optocraft GmbH), which features a Hartmann-Shack sensor. All EDOF lenses yielded a simulated far visual acuity of 0.00 logMAR (20/20 Snellen) or better. At the 0.20 logMAR visual acuity level, the EDOF IOLs showed an increased depth of focus of at least 0.75 diopters compared to the monofocal IOL. Pupil dependency was more pronounced with the MiniWell, LuxSmart, and Vivity, whereas the Lentis showed a more consistent behavior at different apertures. The wavefront measurement revealed increased central aberrations for the MiniWell, LuxSmart, and Vivity IOL compared to the monofocal control. All EDOF IOLs demonstrated increased depth of focus while maintaining good simulated visual acuity at the far focus. Pupil dependency differed between the IOL models. The wavefront analysis revealed the complex design of the different EDOF IOLs with several zones with varying aberrations. [J Refract Surg. 2023;39(10):668-674.].

Fast modal reconstruction of large plane wavefronts from sparse measurements using Shack-Hartmann sensors.

A concept for the fast measurement and reconstruction of optical wavefronts using Shack-Hartmann sensors (SHSs) is presented. For wavefronts with a diameter at the scale of several tens of millimeters, hundreds of measurements with an SHS may be necessary to cover the wavefront. In the proposed concept, a few SHSs are used to measure about 2% of the entire wavefront, providing sufficient measurement data for its successful reconstruction. The small number of SHSs mounted in parallel makes the concept suitable for time-critical applications. A simulation analysis is performed, and an experimental validation of the concept is presented, demonstrating that the wavefront can be reconstructed with an RMS error of about 100nm.

Efficacy of estimations of Hartmann-Shack sensors in small pupil sizes.

The purpose of this study was to evaluate the in vivo efficacy of the estimations of wavefront analyzers using Hartmann-Shack technology to measure optical aberrations when the pupil size is smaller than the evaluated pupil area. Patients implanted with the monofocal ZCB00 intraocular lens (Johnson and Johnson) were examined with the KR-1W Wavefront Analyzer (Topcon) without pharmacological mydriasis and with it afterward. Optical aberrations were analyzed considering a 4-mm pupil and a 6-mm pupil for both examinations. Sixty-six eyes of 33 patients with a mean axial length of 23.35 ± 0.91 mm were assessed. The mean pupil diameter at the baseline examination was 5.05 ± 0.88 mm and under pharmacological mydriasis, it was 6.29 ± 0.84 mm. Outcomes were similar with and without dilation in the 4-mm comparison. However, there was a great disparity in the 6-mm comparison. Most of the values obtained under mydriasis were statistically lower than at baseline (P < 0.05). The iris interferes with measurements of wavefront aberrations, and therefore, real pupil size should always be checked before evaluating optical aberrations with Hartman-Shack sensors. When pupil size is smaller than the analyzed diameter, ocular, and internal, and sometimes, corneal aberrations are estimated far more positive than real values.

A method to determine the M2 beam quality from the electric field in a single plane

Laser beam quality is a key parameter for both industry and science. However, the most common measure, the M2 parameter, requires numerous intensity spatial-profiles for its determination. This is particularly inconvenient for modelling the impact of photonic devices on M2, such as metalenses and thin-film stacks, since models typically output a single electric field spatial-profile. Such a profile is also commonly determined in experiments from e.g., Shack-Hartmann sensors, shear plates, or off-axis holography. We introduce and test the validity and limitations of an explicit method to calculate M2 from a single electric field spatial-profile of the beam in any chosen transverse plane along the propagation direction.

Real-Time Wavefront Sensing at High Resolution with an Electrically Tunable Lens.

We have designed, assembled, and evaluated a compact instrument capable of capturing the wavefront phase in real time, across various scenarios. Our approach simplifies the optical setup and configuration, which reduces the conventional capture and computation time when compared to other methods that use two defocused images. We evaluated the feasibility of using an electrically tunable lens in our camera by addressing its issues and optimizing its performance. Additionally, we conducted a comparison study between our approach and a Shack-Hartmann sensor. The camera was tested on multiple targets, such as deformable mirrors, lenses with aberrations, and a liquid lens in movement. Working at the highest resolution of the CMOS sensor with a small effective pixel size enables us to achieve the maximum level of detail in lateral resolution, leading to increased sensitivity to high-spatial-frequency signals.

Comparison of optical myopia control interventions: effect on peripheral image quality and vision.

This study compares the effects on peripheral vision and image quality of four myopia control interventions: a) Perifocal spectacles/ArtOptica, b) Stellest spectacles/Essilor), c) MiyoSmart spectacles/Hoya and d) MiSight contact lenses/CooperVision. Five subjects participated with habitual or no correction as reference. Three techniques were used: 1) Hartmann-Shack sensors for wavefront errors, 2) double-pass imaging system for point-spread-functions (PSF), and 3) peripheral acuity evaluation. The results show that multiple evaluation methods are needed to fully quantify the optical effects of these myopia control interventions. Perifocal was found to make the relative peripheral refraction (RPR) more myopic in all subjects and to interact with the natural optical errors of the eye, hence showing larger variations in the effect on peripheral vision. MiSight had a smaller effect on RPR, but large effect on peripheral vision. Stellest and MiyoSmart also showed small effects on RPR but had broader double-pass PSFs for all participants, indicating reduced retinal contrast. Reduction in peripheral retinal contrast might thereby play a role in slowing myopia progression even when the peripheral refraction does not turn more myopic.