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An improved programmable grating array based wavefront sensor (GAWS) is proposed which is capable of estimating the incident wavefront more accurately, by generating an array of uniform intensity +1 order spots with negligible contribution from unwanted higher order spots. The duty cycle of each grating element of the proposed sensor is effectively varied in order to independently control the intensity of each +1 order spot. Furthermore, random binarisation technique is implemented on the diffraction grating array to reduce the contribution from undesirable higher order spots by disintegrating them into noise. Proof-of-principle simulation results are presented to demonstrate the working of the proposed GAWS in comparison to the conventional GAWS, for non-uniform intensity of the +1 order spots.

In the ophthalmic Shack-Hartmann wavefront sensor beacon light originates from various depths within the retina. We model the retina of the human and mouse eyes as formed by two backscattering planes, showing that the use of lenslets with low Fresnel number and/or too small search boxes in the centroiding algorithm will produce artifactual aberrations. We evaluate the impact of these errors for four common beacon illumination strategies: full circular, annular, small circular on-axis and small circular off-axis. We find that artifactual aberrations are larger for annular and off-axis beacon illumination, dominated by defocus plus spherical aberration and defocus plus coma, respectively. These artifactual aberrations can be almost completely eliminated by selecting the minimum centroid search box size based on a simple Gaussian optics model and ocular biometry, provided the lenslet Fresnel number is sufficiently large to introduce minimal cross-talk between images of adjacent lenslets.

With the rise of extremely large telescopes such as ELT, TMT, and GMT, the precision of mirror segment alignment will become critical to maintaining the resolution of the full aperture. A Shack-Hartmann wavefront sensor can be used to determine the tip/tilt of individual segments, but since it measures the displacement of a focal spot from the center, it is blind to any piston step (θ) between segments. However, if a lenslet is centered over the gap between two mirror segments, the image results in an interference pattern from those segments. The interference pattern is highly dependent on the piston step between the two segments and is mathematically expressed by a modified sinc function. This leaves three main parameters that can be used to identify θ; the curve shape, the peak intensity, and the primary peak position. Curve fitting and correlation algorithms have previously been used to recover θ from the curve shape. However, they run significantly slower than a centroiding algorithm used for the position measurement of spots in the Shack-Hartmann wavefront sensor. For a system that is stable to segment piston, this is not an issue. But for a system like the GMT, where piston will need to be corrected almost continuously, an algorithm that is of a similar speed to centroiding could enable piston sensing to be integrated into a traditional Shack-Hartmann wavefront sensor (SHWFS). Also, the number of pixels needed to sample the interference spot has been much greater than the number for regular spot sampling in a SHWFS. This paper presents the derivation, simulation results, and an optical bench demonstration of a fast alternative piston-sensing algorithm; called the pixel difference algorithm, that is capable of utilizing a limited number of pixels across the interference spot (nominally 7). The pixel difference algorithm is based on the primary peak intensity parameter and is significantly faster than the curve fitting algorithm; by approximately a factor of 22 both in the simulation and in the optical bench demonstration. The simulation showed this speed comes with a trade-off; the method is more susceptible to noise and has approximately twice the error of the curve fitting algorithm at signal-to-noise ratios (SNR)

In order to measure the altitude profile of the atmospheric turbulence in real-time, we are applying a MASSDIMM method (Multi Aperture Scintillation Sensor and Differential Image Motion Monitor) to the ShackHartmann wavefront sensor data. Tomographic estimation of the atmospheric turbulence is a key technique in new generation of adaptive optics systems with multiple guide stars, and the real-time turbulence profiling provide a useful prior information for the tomography, which is an ill-posed inverse problem. By using the data of a Shack-Hartmann sensor, a turbulence profile in the same direction as the AO correction can be acquired. Moreover, since more information can be used compared with the traditional MASS-DIMM, the resolution in the height direction can be increased. This time, the data of the Shack-Hartmann sensor attached to Tohoku University 50cm telescope was analyzed, and the estimation of the turbulence profile was obtained. Similar profiles were obtained while the elevation of the star and the apparent distance to the turbulence changed in one hour monitoring measurements. The results supported the validity of the method.

This paper investigates the performance and optimization of the Geometric Wavefront Sensor (GWFS) in openloop wavefront sensing, along with the Curvature Wavefront Sensor (CWFS) and Shack-Hartmann Wavefront Sensor (SH-WFS). The GWFS uses a ray tracing process to calculate the displacement of intensity fluctuations from two defocused point source images. Various parameters within the GWFS – such as the signal-to-noise ratio (SNR) sensitivity, the number of Radon angles, the virtual propagation distance, and the number of reconstruction modes – are explored on a laboratory test bench. We found that the GWFS wavefront estimate error experiences an inverse relationship to the SNR, a minimum of 5 Radon angles is required to accurately estimate the single Zernike mode wavefronts (Z4 – Z15), the virtual propagation distance is confined by ray crossing and Fresnel diffraction effects, and the number of reconstruction Zernike modes is limited by noise amplification and over-fitting. This paper demonstrates the capabilities of the GWFS, illustrates the resulting wavefront estimates, and confirms the superior performance of the GWFS compared to the CWFS. The optimized GWFS will be utilized at Mt. John University Observatory (MJUO) in New Zealand for satellite and space debris imaging and tracking

ULTIMATE-Subaru Tomography Adaptive optics Research experimenT (ULTIMATE-START) is a laser tomography AO project on the Subaru telescope. The project is planned to achieve high Strehl Ratio AO correction in NIR bands, and moderate AO correction in visible bands above 600nm. An asterism of 4 laser guide stars (LGSs) will be launched from the laser launching telescope behind the secondary mirror. The tomography wavefront sensing unit with four 32$times$32 Shack-Hartmann wavefront sensors will be installed behind the current facility LGS AO system, AO188. The deformable mirror of AO188 will be upgraded to a 64$times$64 element DM. The corrected light will be fed to the optical integral field spectrograph, 3DII, and NIR camera and spectrograph, IRCS, through a beam switching optics for IR-side Nasmyth focus instruments under development. The first light of the laser launching system and wavefront sensing unit is planned in 2021.

The Shack-Hartmann wavefront sensor is widely used to measure aberrations induced by atmospheric turbulence in adaptive optics systems. However if there exists strong atmospheric turbulence or the brightness of guide stars is low, the accuracy of wavefront measurements will be affected. In this paper, we propose a compressive Shack-Hartmann wavefront sensing method. Instead of reconstructing wavefronts with slope measurements of all sub-apertures, our method reconstructs wavefronts with slope measurements of sub-apertures which have spot images with high signal to noise ratio. Besides, we further propose to use a deep neural network to accelerate wavefront reconstruction speed. During the training stage of the deep neural network, we propose to add a drop-out layer to simulate the compressive sensing process, which could increase development speed of our method. After training, the compressive Shack-Hartmann wavefront sensing method can reconstruct wavefronts in high spatial resolution with slope measurements from only a small amount of sub-apertures. We integrate the straightforward compressive Shack-Hartmann wavefront sensing method with image deconvolution algorithm to develop a high-order image restoration method. We use images restored by the high-order image restoration method to test the performance of our the compressive Shack-Hartmann wavefront sensing method. The results show that our method can improve the accuracy of wavefront measurements and is suitable for real-time applications., To appear in the MNRAS and the complete code can be downloaded from: https://nadc.china-vo.org/article/20200722160959?id=101045

The results of resolution enhancement of the stellar imaging system by using a Rayleigh laser guide star are presented. The estimation of residual phase error value of adaptive correction is carried out at various position of a laser guide star.

The dynamical phase correction of laser radiation distorted by atmospheric turbulence in the adaptive optical system (AOS) with Shack-Hartmann wavefront sensor is numerically investigated. The criterions of correction efficiency have been obtained depending on the relation between the bandwidths of AOS and turbulence. The ideal as well as actual adaptive mirrors are considered.

Numerical investigation of laser beam phase correction in the turbulent atmosphere by adaptive optical system with Shack-Hartmann wavefront sensor has been performed. The criterions of correction efficiency depending on the adaptive mirror and wavefront sensor spatial resolution have been determined for various values of Fried parameter.

We presented a new method to measure the topological charge (TC) of the vortex beam (VB) by use a Shack-Hartmann wavefront sensor with sector microlens array (SMLA). The SMLA is circularly symmetric, which perfectly corresponds to helical phase and ring intensity of the VB. On the focal plane, there are spot array with circular distribution due to the special arrangement of the SMLA. In this letter, we also analyzed the error, and concluded that the error of the outer ring is smaller. As a result, we only employed the data of the outermost ring. This method easily can obtain the sign and magnitude of the TC by calculating offset direction and offset of the spots respectively. The simulation results show that our method can determine large TCs and has high accuracy. While this method has a simple structure and can be used in optical communications in the future.

Adaptive optics (AO) systems for retinal imaging have a small field of view (FoV) of 1°-2°. To increase the FoV we developed a multi-conjugated AO-system. By choosing different scanning patterns, aberrations introduced by the eye at different locations within the FoV can be measured by a Shack Hartmann wavefront sensor. A second deformable mirror that is conjugated to a plane anterior to the retina corrects for varying aberrations across the field. Retinal imaging using spectral-domain optical coherence tomography is performed with 4o x 4o FoV and imaging data including the visualization of the cone mosaic is presented.

The estimation of atmospheric turbulence parameters is of relevance for: a) site evaluation & characterisation; b) prediction of the point spread function; c) live assessment of error budgets and optimisation of adaptive optics performance; d) optimisation of fringe trackers for long baseline optical interferometry. The ubiquitous deployment of Shack-Hartmann wavefront sensors in large telescopes makes them central for atmospheric turbulence parameter estimation via adaptive optics telemetry. Several methods for the estimation of the Fried parameter and outer scale have been developed, most of which are based on the fitting of Zernike polynomial coefficients variances reconstructed from the telemetry. The non-orthogonality of Zernike polynomial derivatives introduces modal cross coupling, which affects the variances. Furthermore, the finite resolution of the sensor introduces aliasing. In this article the impact of these effects on atmospheric turbulence parameter estimation is addressed with simulations. It is found that cross coupling is the dominant bias. An iterative algorithm to overcome it is presented. Simulations are conducted for typical ranges of the outer scale (4 to 32m), Fried parameter (10 cm) and noise in the variances (signal-to-noise ratio of 10 and above). It is found that, using the algorithm, both parameters are recovered with sub-percent accuracy., Accepted for publication by MNRAS

The results of studies of the optics of the 1-m Zeiss-1000 telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences (SAO RAS) by the Shack–Hartmann (SH) method are presented. Using a Shack–Hartmann wavefront sensor (SH WFS) we have adjusted the telescope optical system by means of shifts and tilts of the secondary mirror. The procedure has significantly reduced the aberrations that appeared during the long-term instrument operation. A new method to investigate the surface quality of the mirrors of the Zeiss-1000 being applied, characteristics close to the diffraction limit are achieved. In general, the entire opto-mechanical telescope system provides an image quality of about 0.5″ at 80%energy level.

The method of the dynamic range expansion of the Shack–Hartmann wavefront sensor is discussed. It is based on the use of nonlinear dual focus holographic lenslet arrays with the aberration precompensation. The data concerning the optical setup and the technique of adaptive lenslet array producing based on nonlinear holographic recording phenomenon are represented. On the example of spherical wavefronts it is shown, that the use of three lenslet arrays with different amount of the aberration precompensation allows expanding approximately in five times the dynamic range of the sensor four times greater with preserving the specified sensitivity in comparison with the corresponding refractive lenslet array.

The paper discusses an application of Shack-Hartmann wavefront sensor with stroboscopic illumination for measurements of the vibration modes at resonance frequencies of a MEMS devices. The wavefront sensor estimates the local slopes of the wavefront by measuring the displacement of light spots created by microlens array on the camera plane. The goal of the work is to investigate the features of the proposed method. Amplitudes of vibration modes of a MEMS square membrane are measured and compared with data obtained from the stroboscopic interferometry realized in Twyman-Green configuration. The difference in PV values of the vibration amplitude is less than 52 nm (λ/12). It confirms the high accuracy of the measurement. Moreover, in this case the Shack-Hartmann wavefront sensor enables to simplify the system configuration and reducing the impact of the environmental conditions on the measurement result.

A high-quality flat wave front is usually used to calibrate the Shach-Hartmann wave-front sensors. The article discusses the possibility of calibrating sensors with spherical wave fronts. Special attention is paid to the consideration of calibration in standard laboratory conditions. The mathematical apparatus and the scheme of the experiment are considered.

An adaptive scanning optical microscope with extended depth of field (ASOM-EDOF) is described. The system is based on the ASOM developed previously*, and uses a custom-built Thorlabs 0.21NA objective with a 75mm pupil diameter that allows scanned imaging over a circular region of 40mm diameter using fast steering mirror. The microscope is configured for fluorescence imaging with epi-illumination. A 140 actuator, 5.5µm stroke DM is conjugated to the pupil of the objective, and is used in conjunction with a Shack Hartmann wavefront sensor in an adaptive optics loop to measure and compensate errors of the objective as a function of nominal scan angle. At a given scan angle, the microscope camera forms an image of a 200µm x 200µm region with resolution of about 1.4µm. Images recorded at different scan angles can be stitched together to form a larger image mosaic. At each scan angle, the DM has been calibrated not only to compensate astatic aberrations, but also to perform an axial focal sweep: changing shape from concave to convex at high speed during a single camera exposure. This type of extended depth of field (EDOF) imaging (without aberration compensation) has been reported previously**. By combining these two techniques (ASOM and EDOF), a single recorded camera frame includes in-focus light from objects at depths from the nominal objective focus to depths +/-250µm from that focus, corresponding to an extension of the depth of focus by a factor of 100x for this microscope. The image also includes out-of-focus light from all depths. After a simple deconvolution, one can recover the in-focus light from all swept layers, condensed into a 2D image. Calibration details and performance metrics are described, along with example images from large volumetric samples. *Potsaid B, Wen JTY, “Adaptive scanning optical microscope: large field of view and high-resolution imaging using a MEMS deformable mirror,” Journal of Micro-Nanolithography Mems and Moems, [7], 10, (2008). **Shain WJ, Vickers NA, Goldberg BB, Bifano T, Mertz J, “Extended depth-of-field microscopy with a high-speed deformable mirror,” Optics Letters, [42], 995-998, (2017).

Shack–Hartmann wavefront sensor (SHWS) is one of the popular zonal wavefront sensor that typically consists of a two-dimensional (2D) array of lenslets and a camera. Another variant of a zonal wavefront sensor is the programmable grating array based wavefront sensor (PGAWS) that replaces the lenslets array of the SHWS with a 2D array of programmable diffraction gratings and a single focusing lens to result in a 2D array of +1 order spots. The ability of a PGAWS to correctly measure the incident wavefront depends on the accuracy with which each +1 order spot centroid position in the camera plane is calculated. However, in practical applications the intensities of the +1 order spots are usually non-uniform and there is presence of higher order spots that lead to erroneous calculation of the centroid position. In the present work, an improved PGAWS is proposed and by exploiting its programmable facility the transmittance function of the grating array is defined to generate an array of uniform intensity +1 order spots with negligible contribution from unwanted higher order spots by breaking them into noise. We present proof-of-concept simulation results that illustrate the generation of uniform intensity +1 order spots and also quantify its uniformity numerically by defining a quality metric. Furthermore, the working of the proposed PGAWS is substantiated through simulation results which demonstrate its accurate wavefront estimation capability in comparison to the conventional PGAWS, in the presence of non-uniform intensity +1 order spots.

Electron multiplying charge-coupled-device (EMCCD) applied in Shack–Hartmann wavefront sensor (S–H WFS) makes the wavefront sensing more efficient for adaptive optics (AO). However when the brightness of the observed target changes in large ranges in a few minutes, a fixed electron multiplying (EM) gain may not be optimum. Thus an auto-gain-control (AGC) method based on the spots image of the S–H WFS is proposed. The designed control value is the average value of the maximum signals of all the light spots in a frame. It has been demonstrated in the experiments that the control value is sensitive to the change of the target brightness, and is stable in the presence of detecting noises and turbulence influence. The goal value for control is predetermined based on the linear relation of the signal with the EM gain and the number of photons collected in sub-apertures. The conditions of the self-protection of the EMCCD are also considered for the goal value. Simulations and experiments indicate that the proposed control method is efficient, and keeps the sensing in a high SNR which reaches the upper SNR limit when sensing with EMCCD. The self-protection of the EMCCD is avoided during the whole sensing process.

The transformation of an intensity distribution from Gaussian to a flattop, doughnut, etc. still is a very interesting and important task. And the necessary result could be obtained with the use of adaptive optics that changes the phase of the beam and modifies the shape of the focal spot in the far-field zone. In this paper, we present the flattop and doughnut beam formation result with the use of a bimorph and stacked-actuator deformable mirrors as well as LC phase modulator. The experimental results are also given.

This paper presents a method for calculating the cross-wind speed at the entrance aperture of an adaptive system from the coordinates of the energy centers of gravity of the focal spots measured by a Shack–Hartmann wavefront sensor. The range of applicability of the method are determined for data obtained in an experiment on an atmospheric path depending on the intensity of turbulent distortions and the optical parameters of the sensor.

A rapid adaptive system for atmospheric turbulence compensation is considered in the work. It operates with a frequency of 200 Hz. A deformable mirror with 97 piezoactuators as a stacked actuator and a 2-kHz Shack-Hartmann wavefront sensor have been used for the adaptive system design. A dependence of the residual error of a sine signal correction on the speed of system response is also considered.

Shack-Hartmann wavefront sensors using wound fibre bundles are desired for multi-object adaptive optical systems to provide large multiplex positioned by Starbugs. The use of the large-sized wound fibre bundle provides the exibility to use more sub-apertures wavefront sensor for ELTs. These compact wavefront sensors take advantage of large focal surfaces such as the Giant Magellan Telescope. The focus of this paper is to study the wound fibre image bundle structure defects effect on the centroid measurement accuracy of a Shack-Hartmann wavefront sensor. We use the first moment centroid method to estimate the centroid of a focused Gaussian beam sampled by a simulated bundle. Spot estimation accuracy with wound fibre image bundle and its structure impact on wavefront measurement accuracy statistics are addressed. Our results show that when the measurement signal to noise ratio is high, the centroid measurement accuracy is dominated by the wound fibre image bundle structure, e.g. tile angle and gap spacing. For the measurement with low signal to noise ratio, its accuracy is influenced by the read noise of the detector instead of the wound fibre image bundle structure defects. We demonstrate this both with simulation and experimentally. We provide a statistical model of the centroid and wavefront error of a wound fibre image bundle found through experiment., Comment: 14 pages, 19 figures,5 tables This paper has been accepted for publication in PASA

espanolEn este trabajo se describen dos tecnicaspara la caracterizacion del frente de onda en sistemas opticos. Se trata del sensor de frentes de onda Shack-Hartmann y del Interferometro de Difraccion por Punto. El objetivo principal de este trabajo es probar experimentalmente la equivalencia entre ambas tecnicas, dentro del error experimental, en la caracterizacion de sistemas formadores de imagen. El estudio se ha realizado en el caso de distintas lentes convergentes de tipo comercial. Los resultados abren la posibilidad de disenar un sistema dual que integre ambas tecnicas, con potencial aplicacion en Optica Oftalmica. EnglishIn this work, we present a comparative study between two notorious techniques for wavefront characterization: Shack-Hartmann wavefront sensor and the Point-Diffraction Interferometer. The main goal of this work is to experimentally demonstrate the equivalence of results when wavefront characterization measurements are carried out for both techniques, within the experimental error, in the case of imaging systems. The study has been carried out in several commercial convergent lenses obtaining small root-mean-square difference between both techniques. The results aim the possibility to design a dual set-up combining both techniques with potential use in Ophthalmic applications

In order to detect the aberration from a wide field of view (FOV) on the retina with adaptive optics, we present a multiple-object Shack–Hartmann wavefront sensor (MOSHWFS) design. The simulated results indicate that the wavefront from our MOSHWFS can be reconstructed for multiple objects, and the measurement error can be less than λ/7 with an MOSHWFS with an FOV of 6.7°, for maximum eye aberration. The experimental result with two objects indicates that the measurement error can be less than λ/14, with the root mean square of the reference wavefront as 0.798λ and 0.895λ, respectively.

Using center of gravity to estimate the centroid of the spot in a Shack–Hartmann wavefront sensor, the measurement corrupts with photon and detector noise. Parameters, like window size, often require careful optimization to balance the noise error, dynamic range, and linearity of the response coefficient under different photon flux. It also needs to be substituted by the correlation method for extended sources. We propose a centroid estimator based on stream processing, where the center of gravity calculation window floats with the incoming pixel from the detector. In comparison with conventional methods, we show that the proposed estimator simplifies the choice of optimized parameters, provides a unit linear coefficient response, and reduces the influence of background and noise. It is shown that the stream-based centroid estimator also works well for limited size extended sources. A hardware implementation of the proposed estimator is discussed.

Key elements of the fast adaptive optical system (AOS), having correction frequency of 1400 Hz, for atmospheric turbulence compensation, are described in this paper. A water-cooled bimorph deformable mirror with 46 electrodes, as well as stacked actuator deformable mirror with 81 piezoactuators and 2000 Hz Shack-Hartmann wavefront sensor were considered to be used to control the light beam. The parameters of the turbulence at the 1.2 km path of the light propagation were measured and analyzed. The key parameters for such an adaptive system were worked out.

We report an innovative simple alignment method for a VNIR spectrometer in the wavelength region of 400–900 nm; this device is later combined with fore-optics (a telescope) to form a f/2.5 hyperspectral imaging spectrometer with a field of view of ±7.68°. The detector at the final image plane is a 640×480 charge-coupled device with a 24 μm pixel size. We first assembled the fore-optics and the spectrometer separately and then combined them via a slit co-located on the image plane of the fore-optics and the object plane of the spectrometer. The spectrometer was assembled in three steps. In the initial step, the optics was simply assembled with an optical axis guiding He-Ne laser. In the second step, we located a pin-hole on the slit plane and a Shack-Hartmann sensor on the detector plane. The wavefront errors over the full field were scanned simply by moving the point source along the slit direction while the Shack-Hartmann sensor was constantly conjugated to the pin-hole position by a motorized stage. Optimal alignment was then performed based on the reverse sensitivity method. In the final stage, the pin-hole and the Shack-Hartmann sensor were exchanged with an equispaced 10 pin-hole slit called a field identifier and a detector. The light source was also changed from the laser (single wavelength source) to a krypton lamp (discrete multi-wavelength source). We were then easily able to calculate the distortion and keystone on the detector plane without any scanning or moving optical components; rather, we merely calculated the spectral centroids of the 10 pin-holes on the detector. We then tuned the clocking angles of the convex grating and the detector to minimize the distortion and keystone. The final assembly was tested and found to have an RMS WFE < 90 nm over the entire field of view, a keystone of 0.08 pixels, a smile of 1.13 pixels and a spectral resolution of 4.32 nm.

In this work we present the design and manufacture of a compact Shack-Hartmann wavefront sensor using a Raspberry Pi and a microlens array. The main goal of this sensor is to recover the wavefront of a laser beam and to characterize its spatial phase using a simple and compact Raspberry Pi and the Raspberry Pi embedded camera. The recovery algorithm is based on a modified version of the Southwell method and was written in Python as well as its user interface. Experimental results and reconstructed wavefronts are presented.

We introduce a simple wavefront sensing scheme for aberration measurement of pulsed laser beams in near-infrared wavelengths (

We present a simple and flexible method of generating various vectorial vortex beams (VVBs) based on the scheme of double modulations from a single liquid crystal spatial light modulator (SLM). In this configuration, a half-wave plate (HWP) placed in front of the SLM is first used to control the weights of linear polarization components of incident light. Then, we respectively encode two orbital angular momentum (OAM) eigenstates displayed on each half of the SLM onto each of the linear components of light. This yields the generation of VVB fields spanned by a pair of linearly polarized OAM eigenstates. In order to convert polarization bases from the linear pair into another orthogonal pair, a quarter-wave plate (QWP) placed behind the SLM is used. This enables us to generate VVBs spanned by any pair of orthogonally polarized OAM eigenstates. Generally, the light states of polarization (SOP) can be presented as a geodesic path located on the plane perpendicular to the axis connecting the pair of bases used on the Poincare sphere. The light property is adjustable depending on both slow axes of HWP and QWP, as well as via computer generated holograms. To validate generated beams, two measurement procedures are subsequently applied. First, Stokes polarimetry is used to measure the light SOP over the transverse plane. Next, a Shack–Hartmann wavefront sensor is used to measure the OAM charge. Both the simulated and experimental results are shown to be in a good qualitative agreement. In addition, both polarization patterns and OAM charges can be controlled independently using the proposed method.

Stabilization techniques for a wavefront correction system using a Shack-Hartmann wavefront sensor and a membrane deformable mirror (DM) for robust image acquisition were investigated in this research. Though stability of a closed-loop wavefront correction system is essential in practical fields, stability is decreased when the system spends voltage resources to correct non-meaningful residual distortions. In this research, adaptive limit control techniques were devised to ensure the long-term stability of a wavefront correction system. An adaptive deformation technique for the outer non-active actuators of a membrane deformable mirror was adopted to improve the correction efficiency of the wavefront correction system. The experimental results corrected for wavefront distortions by using a configured wavefront correction system were described in this research.

As a wavefront sensor, the Shack–Hartmann wavefront sensor plays an important role in the wavefront measurement of human eyes. However, the low measurement accuracy and the small dynamic range of Shack–Hartmann wavefront sensor limit its application. In this paper, we present a matched-filter algorithm to improve the measurement accuracy by more than an order of magnitude. Moreover, we also introduce a new algorithm to extend the dynamic range of Shack–Hartmann wavefront sensor. With this method, the recorded spots of Shack–Hartmann wavefront sensor are not constrained to stay in the corresponding pixel area of the microlens. The result shows that the dynamic range can be extended from 57.1 to 160% for the first 24 items of Zernike wavefronts, respectively. The improvement by our methods makes the Shack–Hartmann more suitable for the measurement of highly aberrated eyes.

著者人数: 13名, Accepted: 2013-12-19, 資料番号: SA1140049000

The Shack–Hartmann wavefront sensor samples a beam of light using an array of lenslets, each of which creates an image onto a pixelated sensor. These images translate from their nominal position by a distance proportional to the average wavefront slope over the corresponding lenslet. This principle fails in partially and/or non-uniformly illuminated lenslets when the lenslet array is focused to maximize peak intensity, leading to image centroid bias. Here, we show that this bias is due to the low Fresnel number of the lenslets, which shifts the diffraction focus away from the geometrical focus. We then demonstrate how the geometrical focus can be empirically found by minimizing the bias in partially illuminated lenslets.

Determining topological charge (TC) of optical vortex (OV) beams is important for many applications, such as optical measurement and information transmission through long-distance propagation. In this application, the OV beams usually have an annular intensity profile at the receiving end and are inevitably distorted by aberrations during propagation. In this paper, we propose a simple, direct, and aberration-resistible method to determine the TC value of this annular-shaped OV beam with a Shack-Hartmann wavefront sensor (SH-WFS). Our approach involves finding a closed-path along the annular intensity distribution ridge, and then determining the TC value by a discrete circulation calculation with only the phase-slope vectors along the closed-path. Verification experiments were performed using a phase-only spatial light modulator to generate OV beams and aberrations, while SH-WFS to measure the intensity profile and phase-slopes. The results show that our method can determine the TC value of up to ± 20. The robustness against wavefront aberration and simulated atmospheric turbulence was evaluated. We also verified the proposed closed-path’s superiority to other circular closed-paths for TC determination.

The efficiency of adaptive correction of turbulent distortions of optical radiation depends on corrector control using information obtained by a wavefront sensor. A wavefront reconstruction algorithm based on analyzing the spatial transformations of the wavefront during passage of the light field through a Shack-Hartmann wavefront sensor and controlling the operation of the system is proposed.

Modal cross coupling between basis functions in modal wavefront reconstruction is discussed. Eigenfunctions of Laplacian are proposed in modal approach for wavefront reconstruction. As the gradients of the eigenfunctions are orthogonal to each other, the modal cross coupling can be avoided theoretically. Wavefront reconstructions by use of Zernike polynomials and eigenfunctions of Laplacian with different sampling densities are compared. The results show that modal cross coupling between eigenfunctions of Laplacian is much smaller than that between Zernike polynomials.

In typical adaptive optics applications, the atmospheric residual turbulence affects the wavefront sensor response decreasing its sensitivity. On the other hand, wavefront sensors are generally calibrated in diffraction limited condition, and, so, the interaction matrix sensitivity differs from the closed loop one. The ratio between the two sensitivities, that we will call the sensitivity loss factor, has to be estimated to retrieve a well-calibrated measurement. The spots size measurement could give a good estimation, but it is limited to systems with spots well sampled and uniform across the pupil. We present an algorithm to estimate sensitivity loss factor from closed loop data, based on the known parameters of the closed loop transfer functions. Here we preferred for simplicity the Shack-Hartmann WFS, but the algorithm we propose can be extended to other WFSs., 5 pages, 4 figures, fifth Adaptive Optics for Extremely Large Telescopes conference, Tenerife, Canary Islands, Spain, June 25-30, 2017

Wavefront analysis of an aberrated Laguerre-Gaussian beam generated using LC-SLM and after passing through a a Pseudo Random Phase Plate(PRPP) is carried out using Shack Hartmann wavefront sensor. The Zernike polynomials coefficient are calculated and compared with and without the L-G beam passing through a PRPP (mimicking atmospheric turbulence). It is found that the aberrations like piston and tilt have a greater value under the influence of turbulence.