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A metrological device—Hartmannometer—based on a Shack-Hartmann wavefront sensor for measuring the flatness of optical surfaces was developed and researched, and the results were compared with the results obtained from measurements using a Fizeau interferometer. The paper presents a method for calibrating a Hartmannometer, and also compares the results of measuring a test optical surface using the developed device and a classical Fizeau interferometer. The total amplitude of wavefront distortions measured using a Fizeau interferometer was 0.127 μm (standard deviation 0.022 μm). The Hartmannometer showed distortions amplitude of 0.131 µm (standard deviation 0.024 µm). [ABSTRACT FROM AUTHOR]

The 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The widely used Shack–Hartmann wavefront sensor (SHWFS) is a wavefront measurement system. Its measurement accuracy is limited by the reference wavefront used for calibration and also by various residual errors of the sensor itself. In this study, based on the principle of spherical wavefront calibration, a pinhole with a diameter of 1 µm was used to generate spherical wavefronts with extremely small wavefront errors, with residual aberrations of 1.0 × 10−4 λ RMS, providing a high-accuracy reference wavefront. In the first step of SHWFS calibration, we demonstrated a modified method to solve for three important parameters (f, the focal length of the microlens array (MLA), p, the sub-aperture size of the MLA, and s, the pixel size of the photodetector) to scale the measured SHWFS results. With only three iterations in the calculation, these parameters can be determined as exact values, with convergence to an acceptable accuracy. For a simple SHWFS with an MLA of 128 × 128 sub-apertures in a square configuration and a focal length of 2.8 mm, a measurement accuracy of 5.0 × 10−3 λ RMS was achieved across the full pupil diameter of 13.8 mm with the proposed spherical wavefront calibration. The accuracy was dependent on the residual errors induced in manufacturing and assembly of the SHWFS. After removing these residual errors in the measured wavefront results, the accuracy of the SHWFS increased to 1.0 × 10−3 λ RMS, with measured wavefronts in the range of λ/4. Mid-term stability of wavefront measurements was confirmed, with residual deviations of 8.04 × 10−5 λ PV and 7.94 × 10−5 λ RMS. This study demonstrates that the modified calibration method for a high-accuracy spherical wavefront generated from a micrometer-scale pinhole can effectively improve the accuracy of an SHWFS. Further accuracy improvement was verified with correction of residual errors, making the method suitable for challenging wavefront measurements such as in lithography lenses, astronomical telescope systems, and adaptive optics.

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 μ m, 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. [ABSTRACT FROM AUTHOR]

Achieving a high-quality wavefront sensing light spot and accurate wavefront estimation of the rat eye is still challenging due to its large ocular aberrations and the back reflections from fundus multilayer. Simulation and experiments of rat eye wavefront sensing are conducted to improve the quality of sensing spot for accurate wavefront estimation. The simulation results show that a smaller pupil diameter leads to a high quality of wavefront sensing light spot, and the model rat eye reaches diffractive limitation when the pupil diameter is 0.8 mm. However, the experimental results indicate a different conclusion. Consistent with the simulation results, the quality of the sensing light spot significantly improves when the pupil diameter decreases from 3.6 mm to 1.8 mm. The full width at half maximum (FWHM) of the sensing light spots decreases from 77.36 ± 8.95 μm to 26.78 ± 3.25 μm, and the calculated Strehl ratio increases from 0.007 to 0.396. As the pupil diameter continues to decrease to 1.2 mm, the sensing spot and calculated Strehl ratio continue to improve, while the detected low-order aberrations exhibit a significant increase in both value and variance. This observation suggests that using a half-filled pupil for rat wavefront detection may be a more favorable choice, which assists in obtaining high-resolution retinal images in the rat eye using adaptive optics technology. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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.

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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Achieving a high-quality wavefront sensing light spot and accurate wavefront estimation of the rat eye is still challenging due to its large ocular aberrations and the back reflections from fundus multilayer. Simulation and experiments of rat eye wavefront sensing are conducted to improve the quality of sensing spot for accurate wavefront estimation. The simulation results show that a smaller pupil diameter leads to a high quality of wavefront sensing light spot, and the model rat eye reaches diffractive limitation when the pupil diameter is 0.8 mm. However, the experimental results indicate a different conclusion. Consistent with the simulation results, the quality of the sensing light spot significantly improves when the pupil diameter decreases from 3.6 mm to 1.8 mm. The full width at half maximum (FWHM) of the sensing light spots decreases from 77.36 ± 8.95 μm to 26.78 ± 3.25 μm, and the calculated Strehl ratio increases from 0.007 to 0.396. As the pupil diameter continues to decrease to 1.2 mm, the sensing spot and calculated Strehl ratio continue to improve, while the detected low-order aberrations exhibit a significant increase in both value and variance. This observation suggests that using a half-filled pupil for rat wavefront detection may be a more favorable choice, which assists in obtaining high-resolution retinal images in the rat eye using adaptive optics technology.

• The proposed method can be applied to the measurement of focal length, radius of curvature and refractive index of a positive and negative lenses. • The proposed method does not need to reconstruct wavefront, and is resistant to interference. • Measurement of focal length does not require determination of the position of the principal plane. The focal length, radius of curvature, and refractive index are key parameters of a spherical lens. Here, an approach for measuring lens parameters based on the Shack-Hartmann wavefront sensor (SHS) is proposed. Firstly, the position of the reference point for measuring focal length is determined by the figure-of-merit function, called the least square sum of centroids shifts (LSSCS), from the spot array formed by the microlens array of SHS. The focal length is estimated by measuring radii of curvatures of two spherical waves. Each spherical wave is caused by the distance between the focal point of the lens and the determined reference. Secondly, the radius of curvature is the difference between two coordinate locations of the lens. Each location, corresponding to a collimated beam reflected from the lens, is determined by the figure-of-merit function LSSCS. Thirdly, the refractive index can be further estimated by lens maker's equation through the measured focal length and radius of curvature. A positive and a negative lens are both tested by the proposed method. Experimental results show that the lens parameters measured by the proposed method are in good agreement with the nominal values. The proposed method does not require wavefront reconstruction, and is simple, accurate and noise-resistant. [ABSTRACT FROM AUTHOR]

The accuracy of centroiding algorithms in Shack-Hartmann wavefront sensing is limited by the implicit approximation of uniform pixel illumination. Iterative centroiding algorithms are further limited by the consideration of full pixels to define the image domain for centroiding. Here, we demonstrate two practical and complementary approaches to mitigate both these sources of error. First, we consider partial or 'fractional' pixels to maintain centroiding area symmetry around the center of mass. Secondly, we propose methods to perform piece-wise polynomial interpolation to calculate intensity distribution within pixels, which is then used to estimate the centroid within each pixel area. This approach that accounts for intensity non-uniformity across pixels notably reduces centroid errors up to a factor of 5 across lenslet image widths ranging from 1.33 to 3.10 pixels full-width-half-maximum (FWHM). Consequently, wavefront sensing errors decrease from 14 % to 4 %, on average, for FWHM = 1.35 pixels, demonstrating a substantial benefit when the number of pixels per lenslet is minimized to enhance the signal-to-noise ratio or increase frame rate. [ABSTRACT FROM AUTHOR]

Conventional high spatial resolution Shack-Hartmann wavefront sensors have difficulty realizing high-precision wavefront detection under extreme-few-pixel conditions. A method of Shack-Hartmann wavefront sensor based on tilt modulation is proposed. The proposed method first increases the amount of sub-spot image information. Then, the corresponding wavefront detection accuracy can be improved by tuning parameters such as modulation amplitude, modulation angle, and modulation number. Finally, the detection accuracy for different parameter settings is fitted statistically. As observed in numerical simulations and experiments, the tilt modulation-based method effectively improves detection accuracy. Moreover, there are obvious advantages over the conventional Shack-Hartmann wavefront sensors in 4 × 4 sub-aperture pixels and a short focal length of the microlens array, which improves detection accuracy by about 84% in the experiments. Realization of the need for high spatial resolution and high detection accuracy of Shack-Hartmann wavefront sensors. • The tilt modulation-based method of Shack-Hartmann wavefront sensor under under extreme-few-pixel conditions is proposed. • There are obvious advantages over the conventional Shack-Hartmann wavefront sensors in 4 × 4 sub-aperture pixels. • Realization of the need for high spatial resolution and high detection accuracy of Shack-Hartmann wavefront sensors. [ABSTRACT FROM AUTHOR]

Shack-Hartmann wavefront sensor plays a key role in adaptive optics (AO) systems, which detect the aberrant wavefront by an array of micro-lenslets across the aperture pupil. However, some sub-apertures would be a lack of light induced by the imperfectness of micro-lenslets or pupil shift away from the optical path. Thus, the wavefront detection would be under-sampled and the performance of wavefront reconstruction would be severely degraded. It is therefore important to evaluate the influence of under-sampling on the wavefront reconstruction. In this paper, an AO system was established by the OOMAO simulation platform. For dynamical turbulence aberrations or statistic defocus aberrations, three cases including a single sub-aperture, a row of sub-apertures, and a quadrant sub-apertures lack of light were simulated. Compared with the uncorrected aberrant wavefront, our results showed that the RMS of the residual wavefront for a typical atmospheric condition (Fried parameter (r0) ranges from 5 cm to 15 cm) can be reduced by a factor of 5~8, 4~6, and 2~3 with these three cases of under-sampling, respectively. [ABSTRACT FROM AUTHOR]

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.

With the successful application of the Shack–Hartmann wavefront sensor in measuring aberrations of the human eye, researchers found that, when the aberration is large, the local wavefront distortion is large, and it causes the spot corresponding to the sub-aperture of the microlens to shift out of the corresponding range of the sub-aperture. However, the traditional wavefront reconstruction algorithm searches for the spot within the corresponding range of the sub-aperture of the microlens and reconstructs the wavefront according to the calculated centroid, which leads to wavefront reconstruction errors. To solve the problem of the small dynamic range of the Shack–Hartmann wavefront sensor, this paper proposes a wavefront reconstruction algorithm based on the autocorrelation method and a neural network. The autocorrelation centroid extraction method was used to calculate the centroid in the entire spot map in order to obtain a centroid map and to reconstruct the wavefront by matching the centroid with the microlens array through the neural network. This method breaks the limitation of the sub-aperture of the microlens. The experimental results show that the algorithm improves the dynamic range of the first 15 terms of the Zernike aberration reconstruction to varying degrees, ranging from 62.86% to 183.87%. [ABSTRACT FROM AUTHOR]

Aiming at the problem that it is difficult for the conventional Shack–Hartmann wavefront sensor to achieve high-precision wavefront reconstruction with low spatial sampling, a kind of Shack–Hartmann wavefront sensing technology based on four-quadrant binary phase modulation is proposed in this paper. By introducing four-quadrant binary phase modulation into each subaperture, the technology is able to use an optimization algorithm to reconstruct wavefronts with high precision. The feasibility and effectiveness of this method are verified at extreme low spatial frequency by a series of numerical simulations, which show that the proposed method can reliably reconstruct wavefronts with high accuracy with rather low spatial sampling. In addition, the experiment demonstrates that with a 2 × 2 microlens array, the four-quadrant binary phase-modulated Shack–Hartmann wavefront sensor is able to achieve approximately 54% reduction in wavefront reconstitution error over the conventional Shack–Hartmann wavefront sensor. [ABSTRACT FROM AUTHOR]

The effect of limited operation speed of an adaptive optics system with a Shack–Hartmann wavefront sensor (WFS) on the efficiency of correction of dynamic laser beam phase distortions due to atmospheric turbulence is numerically studied. We suggest estimating the frequency bandwidth of significant turbulent distortions with a WFS, which is convenient from a practical point of view. [ABSTRACT FROM AUTHOR]

Shack-Hartmann wavefront sensor plays a key role in adaptive optics (AO) systems, which detect the aberrant wavefront by an array of micro-lenslets across the aperture pupil. However, some sub-apertures would be a lack of light induced by the imperfectness of micro-lenslets or pupil shift away from the optical path. Thus, the wavefront detection would be under-sampled and the performance of wavefront reconstruction would be severely degraded. It is therefore important to evaluate the influence of under-sampling on the wavefront reconstruction. In this paper, an AO system was established by the OOMAO simulation platform. For dynamical turbulence aberrations or statistic defocus aberrations, three cases including a single sub-aperture, a row of sub-apertures, and a quadrant sub-apertures lack of light were simulated. Compared with the uncorrected aberrant wavefront, our results showed that the RMS of the residual wavefront for a typical atmospheric condition (Fried parameter (r0) ranges from 5 cm to 15 cm) can be reduced by a factor of 5~8, 4~6, and 2~3 with these three cases of under-sampling, respectively.

Laser Guide Star (LGS) reference sources, articially generated at an altitude of 90 km at the atmospheric sodiumlayer, are mandatory to ensure large sky coverage of astronomical Adaptive Optics (AO) systems developed for8m and Extremely Large Telescope (ELT) class telescopes. As a result of the projection eect of an object locatedat a nite distance from the telescope, the AO wavefront sensor (WFS) perceives the LGS as elongated. Thiselongation is a few arcseconds for the 8m class telescopes and can be more than 10 arcseconds for the ELTs. Thiscan pose several challenges when using a Shack-Hartmann wavefront sensor (SHS) such as truncation eects,the requirement for large detectors, and/or the requirement for detectors with geometry that corresponds to thesource shape. In this work, we report the results of numerical simulations focused on the pyramid wavefrontsensor (PWFS) sensitivity when used with a LGS, in this case, a 2D extended object. In addition, the closed-loopperformance of both PWFS and SHS are estimated.

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. • A new optical sensing technique is developed for fracture characterization. • This technique measures the surface slope variation around a propagating crack tip. • This technique achieves micrometer spatial and sub-microsecond temporal resolution. • A fitting procedure is developed taking the measured surface slope data as the input. • The apparent stress intensity factor is extracted using the developed fitting procedure. • The technique is demonstrated using Macor, a commercially available glass ceramic. • The setup is flexible in optics arrangement and compact in space. • It can thus work with synchrotron radiation sources for multi-modal characterization. [ABSTRACT FROM AUTHOR]

An intraocular lens (IOL) is a lens implanted in the eye to correct refractive errors after cataract surgery. It plays a crucial role in ocular biomechanics since it is frequently used to replace the natural eye lens. Understanding the mechanical behavior of the eye and its effect on the IOL after implantation is essential to ensure surgical success and long-term stability. In addition, the precise analysis of IOL parameters, such as spherical power, is a critical task. Therefore, the current study aims to propose a non-contact optical method for the accurate measurement of the spherical power of monofocal IOLs. The proposed method is based on sensing the wavefront transmitted from the IOL being tested using a phase gradient-based approach. The approach relies on using an adaptive optical system consisting of a Shack-Hartmann wavefront sensor (SHWFS) and a deformable mirror (DM). The system evaluates the phase gradient and subsequently reconstructs the wavefront transmitted by the tested IOL. The DM is used to compensate for the aberrations induced by the illumination laser beam, the wet cell containing the IOL and all the optical components integrated in the system. Three monofocal IOLs have been tested using two wavelengths: λ G = 531.2 nm and λ R = 634.449 nm. The results reveal that there is a difference between the measurements before and after aberrations compensation, indicating the impact of the existing aberrations on the measurements. Furthermore, the repeatability of the measurements was evaluated to determine the stability of the repeated measures, and the dynamic range of the proposed system was estimated. • An adaptive phase gradient-based metrology system was proposed for precise spherical power measurement of monofocal IOLs. • The aberrations associated with the laser beam, the wet cell, and the lenses in the measurement system were compensated. • Dispersion and Abbe number of the IOLs materials (hydrophobic acrylic) were estimated to evaluate the refractive efficiency. • The proposed system yields repeatable measurements and an extended dynamic range to precisely evaluate a wide range of IOLs. [ABSTRACT FROM AUTHOR]

Aiming at the problem that it is difficult for the conventional Shack–Hartmann wavefront sensor to achieve high-precision wavefront reconstruction with low spatial sampling, a kind of Shack–Hartmann wavefront sensing technology based on four-quadrant binary phase modulation is proposed in this paper. By introducing four-quadrant binary phase modulation into each subaperture, the technology is able to use an optimization algorithm to reconstruct wavefronts with high precision. The feasibility and effectiveness of this method are verified at extreme low spatial frequency by a series of numerical simulations, which show that the proposed method can reliably reconstruct wavefronts with high accuracy with rather low spatial sampling. In addition, the experiment demonstrates that with a 2 × 2 microlens array, the four-quadrant binary phase-modulated Shack–Hartmann wavefront sensor is able to achieve approximately 54% reduction in wavefront reconstitution error over the conventional Shack–Hartmann wavefront sensor.

The biocompatible hydrogel materials are used for the fabrication of artificial cornea. The refractive index of the hydrogel material can affect the optical quality of the artificial cornea. It is challenging to measure the refractive index of the hydrogel material because it is between solid and liquid status during the fabrication processes. In this work, we propose using the Shack–Hartmann wavefront sensor system to measure the wavefront images and to calculate the corresponding aberrations of optical material. The wavefront aberrations can be used to estimate the refractive index of the optical material. To prove the concept, the standard N-BK7 bi-convex lenses with focal lengths of 100 and 150 mm at wavelengths 780, 532, and 450 nm have been measured, and the results show that the relative errors of the average measured refractive indices are about 0.1%–0.17%. We used this proposed method to measure the refractive index of the P407-DA hydrogel material. We found that the average measured refractive indices of the P407-DA hydrogel material are 1.3175, 1.3516, and 1.3645 at wavelengths 780, 532, and 450 nm, respectively. Compared with the refractive index of human cornea, the P407-DA hydrogel can be used as the artificial cornea material. The Cauchy dispersion formula can be used to calculate the Abbe number of the P407-DA hydrogel material, which is about 11, lower than the human cornea’s Abbe number. It means that the P407-DA hydrogel material has higher chromatic dispersion than the human cornea material. Moreover, the elasmobranch (shark) corneas, which are known as the suitable material for xenotransplantation, are measured by the Shack–Hartmann wavefront sensor system. The ABBE refractometer (ATAGO DR-M4) is used to measure the flat P407-DA hydrogel sample and it is found that the refractive index is slightly different when compared with the measured results by the Shack–Hartmann wavefront sensor system. The refractive indices of other biocompatible hydrogels poly(acrylic acid) (PAA) and poly(2-hydroxyethyl methacrylate) (PHEMA) are also measured by our proposed method, and it is found that the refractive index of P407-DA is more suitable for designing corneal samples than other hydrogels. It is found that the refractive indices of the elasmobranch corneas are similar to the P407-DA material. Our proposed method to measure the refractive index of hydrogel material using the Shack–Hartmann wavefront sensor system is useful. It is a non-contact, minimally invasive, and time-efficient method for shaped structures. The results can be used as a guide for developing better biocompatible material for artificial cornea. [ABSTRACT FROM AUTHOR]

In this article, a Shack–Hartmann wavefront sensor is combined with a mechatronic positioning system to overcome the limited dynamic range of the Shack–Hartmann sensor (SHS) by repositioning and reorienting the SHS. Feedback loops to ensure a tangential orientation of the wavefront sensor in every measurement position and a measurement strategy that compensates for tip and tilt between wavefront and sensor are described and implemented. A framework that estimates the admissible measurement trajectories by relating the positioning errors caused by misalignments of the stages to the parameters of the wavefront sensor is developed. It is demonstrated that the setup is capable of directly measuring a highly divergent optical wavefront by combining wavefront data and positioning data acquired along the wavefront generated by a microscope objective with numerical aperture (NA) of 0.45. [ABSTRACT FROM AUTHOR]

Abstract Compressed sensing leverages the sparsity of signals to reduce the amount of measurements required for its reconstruction. The Shack-Hartmann wavefront sensor meanwhile is a flexible sensor where its sensitivity and dynamic range can be adjusted based on applications. An investigation is done by using compressed sensing in surface measurements with the Shack-Hartmann wavefront sensor. The results show that compressed sensing paired with the Shack-Hartmann wavefront sensor can reliably measure surfaces accurately. The performance of compressed sensing is compared with those of the iterative modal-based wavefront reconstruction and Fourier demodulation of Shack-Hartmann spot images. Compressed sensing performs comparably to the modal based iterative wavefront reconstruction in both simulation and experiment while performing better than the Fourier demodulation in simulation.

The optical radiation wavefront distorted by turbulence is reconstructed based on the Hartmann method by approximating the wave function by Zernike polynomials according to estimates of local tilts. The reconstruction is analyzed for high-intensity turbulent distortions. Relying on results of statistical analysis of information on phase distortions of radiation by a hartmannogram formed in the plane of the receiving device, a method is suggested which allows one to reduce the residual reconstruction error caused by the presence of high-intensity phase fluctuations in the wavefront distribution. [ABSTRACT FROM AUTHOR]

• Three-step deformable mirror identification is proposed to solve channel coupling problem. • Deformable mirror is identified to generate 15 Zernike modes with over 20 dB contrast. • 200 Hz parallel model-based closed-loop controllers manipulate Zernike modes independently. • Axial remote focusing is achieved while eliminating aberrations in presence of heat flow. 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 Z 3 (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. [ABSTRACT FROM AUTHOR]

The Shack–Hartmann wavefront sensor (SHWFS) has been used to measure wavefronts. However, the dynamic range and measurement accuracy limits the application of the SHWFS. A new centroid estimation algorithm based on image segmentation and related techniques to expand the dynamic range based on search strategy is presented in this paper. In this study, each spot is segmented from a spot array image and the centroid of each spot is calculated only in regions of segmented spots. To compute the slope between the spot centroid and the sub-aperture centre, the calculated centroids are assigned to their corresponding sub-apertures using a search method. The proposed method overcomes the limitations that the centroid must be calculated in its corresponding detection area and reduces the measurement errors caused by noise, expanding the dynamic range significantly without any change to the SHWFS setup as well as improving the measurement accuracy under strong noise. Moreover, the proposed method provides a unit linear coefficient response of centroid estimation. The dynamic range for the proposed method is evaluated by numerical simulations and experiments. Applications include measurement accuracy and linearity. [ABSTRACT FROM AUTHOR]

Compressed sensing leverages the sparsity of signals to reduce the amount of measurements required for its reconstruction. The Shack-Hartmann wavefront sensor meanwhile is a flexible sensor where its sensitivity and dynamic range can be adjusted based on applications. An investigation is done by using compressed sensing in surface measurements with the Shack-Hartmann wavefront sensor. The results show that compressed sensing paired with the Shack-Hartmann wavefront sensor can reliably measure surfaces accurately. The performance of compressed sensing is compared with those of the iterative modal-based wavefront reconstruction and Fourier demodulation of Shack-Hartmann spot images. Compressed sensing performs comparably to the modal based iterative wavefront reconstruction in both simulation and experiment while performing better than the Fourier demodulation in simulation. [ABSTRACT FROM AUTHOR]

The European Extremely Large Telescope (ELT) is a 39m large, ground-based optical and near- to mid-infrared telescope under construction in the Chilean Atacama desert. Operation is planned to start around the middle of the next decade. All first light instruments will come with wavefront sensing devices that allow control of the ELT's intrinsic M4 and M5 wavefront correction units, thus building an adaptive optics (AO) system. To take advantage of the ELT's optical performance, full diffraction-limited operation is required and only a high performance AO system can deliver this. Further technically challenging requirements for the AO come from the exoplanet research field, where the task to resolve the very small angular separations between host star and planet, has also to take into account the high-contrast ratio between the two objects. We present in detail the results of our simulations and their impact on high-contrast imaging in order to find the optimal wavefront sensing device for the METIS instrument. METIS is the mid-infrared imager and spectrograph for the ELT with specialised high-contrast, coronagraphic imaging capabilities, whose performance strongly depends on the AO residual wavefront errors. We examined the sky and target sample coverage of a generic wavefront sensor in two spectral regimes, visible and near-infrared, to pre-select the spectral range for the more detailed wavefront sensor type analysis. We find that the near-infrared regime is the most suitable for METIS. We then analysed the performance of Shack-Hartmann and pyramid wavefront sensors under realistic conditions at the ELT, did a balancing with our scientific requirements, and concluded that a pyramid wavefront sensor is the best choice for METIS. For this choice we additionally examined the impact of non-common path aberrations, of vibrations, and the long-term stability of the SCAO system including high-contrast imaging performance. [ABSTRACT FROM AUTHOR]

We develop a phase reconstruction algorithm for the Shack–Hartmann wavefront sensor (SHWFS) that is tolerant to phase discontinuities, such as the ones imposed by shock waves. In practice, this algorithm identifies SHWFS locations where the resultant tilt information is affected by the shock and improves the tilt information in these locations using the local SHWFS observation-plane irradiance patterns. The algorithm was shown to work well over the range of conditions tested with both simulated and experimental data. In turn, the reconstruction algorithm will enable robust wavefront sensing in transonic, supersonic, and hypersonic environments. [ABSTRACT FROM AUTHOR]

Two methods for identifying branch points from Shack–Hartmann wavefront sensor (SHWFS) measurements were studied: the circulation of phase gradients approach and the beam-spread approach. These approaches were tested using a simple optical-vortex model, with wave-optics simulations, and with experimental data. It was found that these two approaches are synergistic regarding their abilities to detect branch points. Specifically, the beam-spread approach works best when the branch point is located toward the center of the SHWFS's lenslet pupil, whereas the circulation of phase gradients approach works best when the branch point is located toward the edge of the SHWFS's lenslet pupil. These behaviors were observed studying the simple optical-vortex model; however, they were further corroborated with the wave-optics and experimental results. The developments presented support researchers studying high scintillation optical-turbulence environments and inform efforts in developing branch-point tolerant reconstruction algorithms. [ABSTRACT FROM AUTHOR]

Abstract In general, misalignment, surface quality of optical components, thermal and nonlinear properties, doping level and inhomogeneity in the gain material can induce unexpected pulse propagation effects on intnese femtosecond laser pulses. Among them, the thermal lens in a thermally loaded material is more serious since it limits power scaling and degrades maximum achievable intensity at the focus by introducing distortion into the wavefront. Thereby, an understanding of thermally distortion wavefront is of great importance for optimum design of high power laser amplifiers and efficient serving femtosecond lasers in various specific applications. In this paper, we experimentally studied beam quality and wavefront distortion in a longitudinally pumped two-stage chirped pulse high power Ti:sapphire amplifier laser at 1 kHz operation in terms of pump power. The amplifier crystals are cooled thermoelectrically to below −10 °C. A simple formula for coupling the thermal lens in a two-stage amplifier consists of a regenerative amplifier followed by a single-pass amplifier pumped equally by the Nd:YLF laser at 527 nm with maximum average output power of 44 W and 130 ns pulse duration at 1 kHz is presented. The wavefront curvature of the compressed laser pulses with ∼40 fs pulse duration and center wavelength of 800 nm is evaluated directly by Shack-Hartmann Wavefront Sensor (SHWS) with help of the Zernike polynomials. While the beam radius and spatial beam quality M2 factor are estimated by knife-edge testing. Also, the optical wavefront distortion caused by an iris inserted into the beam path of a high power laser for quick spot size adjustment has been presented. When diameter of the iris is about 75% of the laser beam size (corresponding to 67% fraction transmission), laser beam distortion associated with the iris is negligible. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient approach to decrease the computational costs of correlation-based centroiding methods used for point source Shack–Hartmann wavefront sensors. Four typical similarity functions have been compared, i.e. the absolute difference function (ADF), ADF square (ADF 2 ), square difference function (SDF), and cross-correlation function (CCF) using the Gaussian spot model. By combining them with fast search algorithms, such as three-step search (TSS), two-dimensional logarithmic search (TDL), cross search (CS), and orthogonal search (OS), computational costs can be reduced drastically without affecting the accuracy of centroid detection. Specifically, OS reduces calculation consumption by 90%. A comprehensive simulation indicates that CCF exhibits a better performance than other functions under various light-level conditions. Besides, the effectiveness of fast search algorithms has been verified. [ABSTRACT FROM AUTHOR]

An adaptive optics (AO) system has advantages of avoiding waffle modes and ease to assemble, when the lenslets of the Shack-Hartmann wavefront sensor (SH-WFS) and the actuators of the deformable mirror (DM) are configured according to the Southwell geometry. However, an AO system which follows the Southwell geometry suffers from the calibration difficulty and from the poor control stability. In this paper, an AO system based on the Southwell configuration is built up and experimentally demonstrated. The calibration problem is solved by adopting a DM which has an appropriate inter-actuator coupling, so that the movement of an actuator can be measured by the neighboring lenslets. The control stability is evaluated by the error propagators, and then, the control stability can be improved by filtering out smaller singular values of the response matrix. It is also shown that a tradeoff between the bandwidth error and the fitting error of an AO system can be made according to the error propagator. Finally, the performance measurement experiments indicate the reasonable ranges for the number of reserved singular values of the response matrix and the integrator gain, i.e. from 81 to 89, and from 0.2 to 0.5, respectively. [ABSTRACT FROM AUTHOR]

Lens characterization is a key challenge for reliable optical and imaging techniques. Shack–Hartmann wavefront sensor (SHWFS) is frequently used as an efficient tool for characterizing optical elements. However, the aberrations arising from the incident wavefront, utilized for the characterization process, cause imprecision in the spherical power measurement. Accordingly, the aim of the present study is to construct an experimental configuration that consists of SHWFS incorporated with a deformable mirror (DM) to provide a correction for the incident wavefront aberrations which yields an ideal plane wave. Different types of thick lenses with a wide range of focal lengths and three single-vision contact lenses were tested before and after aberrations compensation and compared to the reference-based method. The comparison was based on measuring the spherical powers for the tested lenses. The results indicate that the accuracy of measurements is influenced by the incident wavefront aberrations, which has been improved by the proposed compensation system. Finally, the limitations are investigated and it was concluded that the system in its current configuration failed to accurately measure some thick lenses. This issue was solved by suggesting a compound lens correction methodology that extended the measurement range of spherical powers beyond the designated measurable range of the system. • An experimental configuration based on an adaptive Shack–Hartmann wavefront sensor (SHWFS) for accurately characterizing thick and contact lenses is proposed. • In contrast to the standard SHWFS, the proposed system benefits from the utilized deformable mirror (DM) which is used as an active adaptive element. • To extend the dynamic range of measurements by the proposed adaptive sensor, the idea of the compound lenses is utilized. • The proposed system is capable of accurately measuring a wide range of thick and eye contact lenses with an accuracy of measurement ≤ 1%. [ABSTRACT FROM AUTHOR]

The wavefront aberration introduced by both rhomb and square pixel Digital Micromirror Devices (DMDs) to the reconstructed images from the holograms displayed on them is visualized with a color phase map obtained from a Shack-Hartmann wavefront sensor. The aberration causes blurring and distortions in the reconstructed images. The map informs that the aberration is induced by the virtual shrinkage of pixels introduced by their rotation because 1) the aberration is appearing along the DMDs' pixel rotation directions and 2) the DMD with a bigger size pixel introduces more aberration than that with a smaller size pixel. It is also shown that the aberration can be minimized with use of a white beam. The white beam is a reflected beam from the no image loaded On-state DMDs' surfaces when a collimated illumination beam is normally incident to them. Nevertheless, when the phase maps are compensated by the white beam, the reconstructed images become more distinguished and identified for both DMDs. [ABSTRACT FROM AUTHOR]