Ground-layer Adaptive Optics for the 2.5 m Wide-field and High-resolution Solar Telescope

The 2.5 m wide-field and high-resolution solar telescope(WeHoST)is currently under developing for solar observations.WeHoST aims to achieve high-resolution observations over a super-wide field of view(FOV)of5′×5′,and a desired resolution of 0.3″.To meet the scientific requirements of WeHoST,the ground-layer adaptive optics(GLAO)with a specially designed wave front sensing system is as the primary consideration.We introduce the GLAO configuration,particularly the wave front sensing scheme.Utilizing analytic method,we simulate the performance of both classical AO and GLAO systems,optimize the wave front sensing system,and evaluate GLAO performance in terms of PSF uniformity and correction improvement across whole FOV.The results indicate that,the classical AO will achieve diffraction-limited resolution;the suggested GLAO configuration will uniformly improve the seeing across the full 5′×5′FOV,reducing the FWHM across the axis FOV to less than0.3″(λ≥705 nm,r0≥11 cm),which is more than two times improvement.The specially designed wave front sensor schedule offers new potential for WeHoST’s GLAO,particularly the multi-FOV GLAO and the flexibility to select the detected area.These capabilities will significantly enhance the scientific output of the telescope.

Statistical analysis of ocular monochromatic aberrations in Chinese population for adaptive optics ophthalmoscope design

It is necessary to know the distribution of the Chinese eye's aberrations in clinical environment to guide high-resolution retinal imaging system design for large Chinese population application.We collected the monochromatic wave aberration of 332 healthy eyes and 344 diseased eyes in Chinese population across a 6.0-mm pupil.The aberration statistics of Chinese eyes including healthy eyes and diseased eyes were analyzed,and some differences of aberrations between the Chinese and European race were concluded.On this basis,the requirement for adaptive optics(AO)correction of the Chinese eye's monochromatic aberrations was analyzed.The result showed that a stroke of 20μm and ability to correct aberrations up to the 8th Zernike order were needed for reflective wavefront correctors to achieve near difraction-limited imaging in both groups for a reference wavelength of 550 nm and a pupil diameter of 6.0mm.To verify the:analysis mentioned above,an A0 floodillumination system was established,and high-resolution retinal imaging in vivo was achieved for Chinese eye including both healthy and diseased eyes.

A slope-based decoupling algorithm to simultaneously control dual deformable mirrors in a woofer–tweeter adaptive optics system

We propose a slope-based decoupling algorithm to simultaneously control the dual deformable mirrors （DMs） in a woofer-tweeter adaptive optics system. This algorithm can directly use the woofer＇s response matrix measured from a Shack-Hartmann wave-front sensor to construct a slope-based orthogonal basis, and then selectively distribute the large- amplitude low-order aberration to woofer DM and the remaining aberration to tweeter DM through the slope-based orthogonal basis. At the same moment, in order to avoid the two DMs generating opposite compensation, a constraint matrix used to reset tweeter control vector is convenient to be calculated with the slope-based orthogonal basis. Numeral simulation demonstrates that this algorithm has a good performance to control the adaptive optics system with dual DMs simultaneously. Compared with the typical decoupling algorithm, this algorithm can take full use of the compensation ability of woofer DM and release the stroke of tweeter DM to compensate high-order aberration. More importantly, it does not need to measure the accurate shape of tweeter＇s influence function and keeps better performance of restraining the coupling error with the continuous-dynamic aberration.

High-resolution visible imaging with piezoelectric deformable secondary mirror: experimental results at the 1.8-m adaptive telescope

Integrating deformable mirrors within the optical train of an adaptive telescope was one of the major innovations in astronomical observation technology,distinguished by its high optical throughput,reduced optical surfaces,and the incorporation of the deformable mirror.Typically,voice-coil actuators are used,which require additional position sensors,internal control electronics,and cooling systems,leading to a very complex structure.Piezoelectric deformable secondary mirror technologies were proposed to overcome these problems.Recently,a high-order piezoelectric deformable secondary mirror has been developed and installed on the 1.8-m telescope at Lijiang Observatory in China to make it an adaptive telescope.The system consists of a 241-actuator piezoelectric deformable secondary mirror,a 192-sub-aperture Shack-Hartmann wavefront sensor,and a multi-core-based real-time controller.The actuator spacing of the PDSM measures 19.3 mm,equivalent to approximately 12.6 cm when mapped onto the primary mirror,significantly less than the voicecoil-based adaptive telescopes such as LBT,Magellan and VLT.As a result,stellar images with Strehl ratios above 0.49 in the R band have been obtained.To our knowledge,these are the highest R band images captured by an adaptive telescope with deformable secondary mirrors.Here,we report the system description and on-sky performance of this adaptive telescope.

Adaptive optics based on machine learning: a review

Adaptive optics techniques have been developed over the past half century and routinely used in large ground-based telescopes for more than 30 years.Although this technique has already been used in various applications,the basic setup and methods have not changed over the past 40 years.In recent years,with the rapid development of artificial in-telligence,adaptive optics will be boosted dramatically.In this paper,the recent advances on almost all aspects of adapt-ive optics based on machine learning are summarized.The state-of-the-art performance of intelligent adaptive optics are reviewed.The potential advantages and deficiencies of intelligent adaptive optics are also discussed.

Experimental demonstration of single-mode fiber coupling using adaptive fiber coupler

Coupling plane wave into a single-mode fiber （SMF） with high and steady coupling efficiency is crucial for fiber- based free-space laser systems, where random angular jitters are the main influencing factors of fiber coupling. In this paper, we verified a new adaptive-optic device named adaptive fiber coupler （AFC） which could compensate angular jitters and improve the SMF coupling efficiency in some degree. Experiments of SMF coupling under the angular jitter situation using AFC have been achieved. Stochastic parallel gradient descent （SPGD） algorithm is employed as the control strategy, of which the iteration rate is 625 Hz. In closed loop, the coupling efficiency keeps above 65% when angular errors are below 80/3tad. The compensation bandwidth is 35 Hz at sine-jitter of 15 ~rad amplitude with average coupling efficiency of above 60%. Also, experiments with simulated turbulence have been studied. The average coupling efficiency increases from 31.97% in open loop to 61.33% in closed loop, and mean square error （MSE） of coupling efficiency drops from 7.43% to 1.75%.

EAST-Educational Adaptive-optics Solar Telescope

For the public having a better understanding of solar activities,the Educational Adaptive-optics Solar Telescope(EAST)was built in July 2021 and is located at the Shanghai Astronomy Museum.The EAST consists of a 65 cm aperture solar telescope with a 177-element adaptive optics system and two-channel high resolution imaging system at the Hαand TiO bands,in addition to three full disk solar telescopes at CaK,Hαand TiO bands equipped on the tube of the main telescope.In this paper,the configuration of the EAST is described.Its performance and on-sky observational results are presented.The EAST,to our knowledge,is the most advanced solar telescope for the popularization of science in the world.Due to its excellent performance,the data acquired by the EAST can also be used for research on solar physics and space weather prediction.

Comparison between iterative wavefront control algorithm and direct gradient wavefront control algorithm for adaptive optics system

Among all kinds of wavefront control algorithms in adaptive optics systems, the direct gradient wavefront control algorithm is the most widespread and common method. This control algorithm obtains the actuator voltages directly from wavefront slopes through pre-measuring the relational matrix between deformable mirror actuators and Hartmann wavefront sensor with perfect real-time characteristic and stability. However, with increasing the number of sub-apertures in wavefront sensor and deformable mirror actuators of adaptive optics systems, the matrix operation in direct gradient algorithm takes too much time, which becomes a major factor influencing control effect of adaptive optics systems. In this paper we apply an iterative wavefront control algorithm to high-resolution adaptive optics systems, in which the voltages of each actuator are obtained through iteration arithmetic, which gains great advantage in calculation and storage. For AO system with thousands of actuators, the computational complexity estimate is about O(n2) ～ O(n3) in direct gradient wavefront control algorithm, while the computational complexity estimate in iterative wavefront control algorithm is about O(n) ～(O(n)3/2), in which n is the number of actuators of AO system. And the more the numbers of sub-apertures and deformable mirror actuators, the more significant advantage the iterative wavefront control algorithm exhibits.

First generation solar adaptive optics system for 1-m New Vacuum Solar Telescope at Fuxian Solar Observatory

The first generation solar adaptive optics （AO） system, which consists of a fine tracking loop with a tip-tilt mirror （TTM） and a correlation tracker, and a high-order correction loop with a 37-element deformable mirror （DM）, a correlating Shack-Hartmann （SH） wavefront sensor （WFS） based on the ab- solute difference algorithm and a real time controller （RTC）, has been developed and installed at the 1-m New Vacuum Solar Telescope （NVST） that is part of Fuxian Solar Observatory （FSO）. Compared with the 37-element solar AO system developed for the 26-cm Solar Fine Structure Telescope, administered by Yunnan Astronomical Observatories, this AO system has two updates： one is the subaperture arrangement of the WFS changed from square to hexagon; the other is the high speed camera of the WFS and the corre- sponding real time controller. The WFS can be operated at a frame rate of 2100 Hz and the error correction bandwidth can exceed 100 Hz. After AO correction, the averaged residual image motion and the averaged RMS wavefront error are reduced to 0.06＂ and 45 nm, respectively. The results of on-sky testing obser- vations demonstrate better contrast and finer structures of the images taken with AO than those without AO.

First light for the sodium laser guide star adaptive optics system on the Lijiang 1.8 m telescope

A first generation sodium Laser Guide Star Adaptive Optics System （LGS-AOS） was developed and integrated into the Lijiang 1.8 m telescope in 2013. The LGS-AOS has three sub-systems： （1） a 20W long pulsed sodium laser, （2） a 300-millimeter-diameter laser launch telescope, and （3） a 37-element com- pact adaptive optics system. On 2014 January 25, we obtained high resolution images of an my 8.18 star, HIP 43963, during the first light of the LGS-AOS. In this paper, the sodium laser, the laser launch telescope, the compact adaptive optics system and the first light results will be presented.

CHES: A Space-borne Astrometric Mission for the Detection of Habitable Planets of the Nearby Solar-type Stars

The Closeby Habitable Exoplanet Survey(CHES) mission is proposed to discover habitable-zone Earth-like planets of nearby solar-type stars(~10 pc away from our solar system) via microarcsecond relative astrometry.The major scientific objectives of CHES are:to search for Earth Twins or terrestrial planets in habitable zones orbiting100 FGK nearby stars;further to conduct a comprehensive survey and extensively characterize nearby planetary systems.The primary payload is a high-quality,low-distortion,high-stability telescope.The optical subsystem is a coaxial three-mirror anastigmat(TMA) with a 1.2 m-aperture,0°.44 × 0°.44 field of view and 500 nm-900 nm working wave band.The camera focal plane is composed of a mosaic of 81 scientific CMOS detectors each with4 k × 4 k pixels.The heterodyne laser interferometric calibration technology is employed to ensure microarcsecond level(1 μas) relative astrometry precision to meet the requirements for detection of Earth-like planets.The CHES satellite operates at the Sun-Earth L2 point and observes all the target stars for 5 yr.CHES will offer the first direct measurements of true masses and inclinations of Earth Twins and super-Earths orbiting our neighbor stars based on microarcsecond astrometry from space.This will definitely enhance our understanding of the formation of diverse nearby planetary systems and the emergence of other worlds for solar-type stars,and finally provide insights to the evolution of our own solar system.

Error analysis of the piston estimation method in dispersed fringe sensor

Dispersed fringe sensor （DFS） is an important phasing sensor of next-generation optical astronomical telescopes. The measurement errors induced by the measurement noise of three piston estimation methods for the DFS including leastsquared fitting （LSF） method, frequency peak location （FPL） method and main peak position （MPP） method, are analyzed theoretically and validated experimentally in this paper. The experimental results coincide well with the theoretical analyses. The MPP, FPL, LSF are used respectively when the DFS operates with broadband light （central wavelength： 706 nm, bandwidth： 23 nm）. The corresponding root mean square （RMS） value of estimated piston error can be achieved to be 1 nm, 3 nm, 26 nm, respectively. Additionally, the range of DFS with the FPL can be more than 100 μm at the same time. The FPL method can work well both in coarse and fine phasing stages with acceptable accuracy, compared with LSF method and MPP method.

Simultaneous quantification of longitudinal and transverse ocular chromatic aberrations with Hartmann-Shack wavefront sensor

A simple method to objectively and simultaneously measure eye's longitudinal and transverse chromatic aberrations was proposed.A dual-wavelength wavefront measurement system using two Hartmann-Shack wavefront sensors was developed.The wavefronts of the red(639.1 nm)and near-infrared(786.0 nm)lights were measured simultaneously for different positions in the model eye.The chromatic wavefronts were converted into Zernike polynomials.The Zernike tilt cofficient(irst term)was used to calculate the transverse chromatic aberration along the ax-direction,while the Zernike defocus coefficient(fourth term)was used to calculate the longi-tudinal chromatic aberration.The measurement and simulation data were consistent.

Data point selection for weighted least square fitting of cavity decay time constant

For the accurate extraction of cavity decay time, a selection of data points is supplemented to the weighted least square method. We derive the expected precision, accuracy and computation cost of this improved method, and examine these performances by simulation. By comparing this method with the nonlinear least square fitting （NLSF） method and the linear regression of the sum （LRS） method in derivations and simulations, we find that this method can achieve the same or even better precision, comparable accuracy, and lower computation cost. We test this method by experimental decay signals. The results are in agreement with the ones obtained from the nonlinear least square fitting method.

Optimizing calculation of phase screen distribution with minimum condition along an inhomogeneous turbulent path

When building an experimental platform for light propagation along an inhomogeneous turbulent path,it is very essential to set up the reasonable distribution of phase screen.Based on multi-layered model of phase screen,an iterative optimization algorithm of phase screen position is given in this paper.Thereafter,the optimal position of phase screens is calculated under the Hufnagel-Valley5/7 and Hefei-day turbulence profile.The results show that the positions of phase screen calculated by the iterative algorithm can fit well with the turbulence profile rather than mechanically placed phase screens at equal distance.Compared with the uniform distribution of phase screens position,the residual phase error of the iterative algorithm decreases very significantly.The similarity degree between them is minimal when number of layers is equal to two.

Acceleration of optical coherence tomography signal processing by multi-graphics processing units

A multi-GPU system designed for high-speed,real-time signal processing of optical coherencetomography(OCT)is described herein.For the OCT data sampled in linear wave numbers,themaximum procesing rates reached 2.95 MHz for 1024-OCT and 1.96 MHz for 2048-OCT.Data sampled using linear wavelengths were re-sampled using a time-domain interpolation method and zero-padding interpolation method to improve image quality.The maximum processing rates for1024-OCT reached 2.16 MHz for the time-domain method and 1.26 MHz for the zero-paddingmethod.The maximum processing rates for 2048-0CT reached_1.58 MHz,and 0.68 MHz,respectively.This method is capable of high-speed,real-time processing for O CT systems.

Ground-layer adaptive optics for the New Vacuum Solar Telescope:Instrument description and first results

Ground-layer adaptive optics(GLAO)has shown its potential for use in solar observation owing to its wide field-of-view(FOV)correction.A high-order GLAO system that consists of a multiple direction Shack-Hartmann wavefront sensor(WFS),a realtime controller with a multi-CPU processor,and a 151-element deformable mirror was developed for the 1-m New Vacuum Solar Telescope at Yunnan Observatories,Chinese Academy of Sciences.A hexagonal microlens with 9×8 subapertures is employed in the WFS.The detection FOV is 42′′×37′′,in which 9(3×3)guide regions are extracted for multiple direction wavefront sensing with a frame rate of up to 2200 Hz.To our knowledge,this is the first professional solar GLAO system used as a regularly operating instrument for scientific observations.Its installation and adjustment were performed in the summer of 2021.In this article,a detailed account of the GLAO system and its first light results and a comprehensive analysis of the performance of the GLAO system are provided.The results show that this system can effectively improve the imaging quality after compensating for the wavefront aberration due to ground-layer turbulence.

First light of solar multi-conjugate adaptive optics at the 1-m new vacuum solar telescope

Observations play a leading role in any branches of astronomy, including solar physics. In order to solve fundamental problems, such as solar dynamo [1], coronal heating [2] and the triggering of major solar eruptions [3], solar observations with spatial resolution better than 0.1 arcsec are required. Such a goal cannot be achieved without the help of adaptive optics （AO）, which eliminates the wavefront distortion caused by atmosphere turbulence [4,5]. However, solar observations are performed over an extended field of view （FoV）. Flare trigger mechanisms operate rapidly and on the smallest spatial scales and their location within the FoV is difficult to predict.

Co-focus experiment of segmented mirror

In this paper, an active optics and co-focus experimental system of segmented mirror is built. Firstly, a support structure of segmented mirror is designed and it is verified by simulation to meet the requirement for the experimental system of segmented mirror. In this system, the large de-focus and tilt/tip errors of the segmented mirror are adjusted by observing the density and contrast of interference fringes based on isoclinic interference theory until the defocus and tilt/tip errors are in the detective range of the Shack–Hartmann. Then, the Shack–Hartmann is used to measure them and they are adjusted by actuators. The actuators are controlled by active optics to realize the closed-loop adjustment and maintenance for fine co-focus of segmented mirror. And the interference fringes are utilized to verify the detective precision of Shack–Hartmann. After the co-focus fine-tuning of the segmented mirror, the tilt/tip residual surface error is better than 0.01λ RMS; the defocus residual surface error is better than 0.01λ RMS.

A modified phase diversity wavefront sensor with a diffraction grating

The phase diversity wavefront sensor is one of the tools used to estimate wavefront aberration, and it is often used as a wavefront sensor in adaptive optics systems. However, the performance of the traditional phase diversity wavefront sensor is limited by the accuracy and dynamic ranges of the intensity distribution at the focus and defocus positions of the CCD camera. In this paper, a modified phase diversity wavefront sensor based on a diffraction grating is proposed to improve the ability to measure the wavefront aberration with larger amplitude and higher spatial frequency. The basic principle and the optics construction of the proposed method are also described in detail. The noise propagation property of the proposed method is also analysed by using the numerical simulation method, and comparison between the diffraction grating phase diversity wavefront sensor and the traditional phase diversity wavefront sensor is also made. The simulation results show that the diffraction grating phase diversity wavefront sensor can obviously improve the ability to measure the wavefront aberration, especially the wavefront aberration with larger amplitude and higher spatial frequency.