Atmospheric Wavefront Research Articles

Simulation of a temporally dynamic atmospheric wavefront using the modified von-Kármán spectrum and Zernike-based method

In the simulation of the atmospheric wavefront, the Kolmogorov spectrum facilitates the mathematical treatments, but this model gives inaccurate predictions in cases where the effects of outer- and inner-scale can not be neglected. Therefore, we derive the covariance formula of Zernike coefficients based on the modified von-Kármán turbulence spectrum to improve the Zernike-based method. Further, using the frozen flow hypothesis, the temporal power spectra of Zernike coefficients are derived, and the effects of wind velocity and direction, as well as the outer and inner scales, are also taken into account. Then, we introduce a method for generating the temporally dynamic atmospheric wavefront using the inverse Fourier transform to draw random time-evolving coefficients from the temporal spectra. We evaluate the performance on simulated atmospheric wavefront, and the results confirm that accurate spatial and temporal statistics are obtained.

Demonstration of a photonic lantern focal-plane wavefront sensor: measurement of atmospheric wavefront error modes and low wind effect in the nonlinear regime

Demonstration of a photonic lantern focal-plane wavefront sensor: measurement of atmospheric wavefront error modes and low wind effect in the nonlinear regime

Performance of an iterative wavelet reconstructor for the Multi-conjugate Adaptive Optics RelaY of the Extremely Large Telescope

The Multi-conjugate Adaptive Optics RelaY (MAORY) is one of the key adaptive optics (AO) systems on the European Southern Observatory’s Extremely Large Telescope. MAORY aims to achieve good wavefront correction over a large field of view, which involves a tomographic estimation of the three-dimensional atmospheric wavefront disturbance. Mathematically, the reconstruction of turbulent layers in the atmosphere is severely ill-posed, hence, limits the achievable reconstruction accuracy. Moreover, the reconstruction has to be performed in real time at a few hundred to one thousand hertz frame rates. Huge amounts of data have to be processed and thousands of actuators of the deformable mirrors have to be controlled by elaborated algorithms. Even with extensive parallelization and pipelining, direct solvers, such as the matrix vector multiplication method, are extremely demanding. Thus, research in recent years shifted into the direction of iterative methods. We focus on the iterative finite-element wavelet hybrid algorithm (FEWHA). The key feature of FEWHA is a matrix-free representation of all operators involved, which makes the algorithm fast and enables on-the-fly system updates whenever parameters at the telescope or in the atmosphere change. We provide a performance analysis of the method regarding quality and run-time for the MAORY instrument using the AO software package COMPASS.

Crosstalk in image plane beam combination for optical interferometers

ABSTRACT Image plane beam combination in optical interferometers multiplexes the interference fringes from multiple baselines on to a single detector. The beams of starlight are arranged in a non-redundant pattern at the entrance of the combiner so that the signal from each baseline can be separated from one another in the frequency domain. If the signals from different baselines overlap in the frequency domain, this can give rise to a systematic error in the fringe measurements known as baseline crosstalk. In this paper, we quantify crosstalk arising from the combination of atmospheric seeing and beam propagation over distances of the order of hundreds of metres. We find that in idealized conditions atmospheric wavefront errors and beam propagation do not contribute to crosstalk. However, when aperture stops are included in the optical beam train we observe that wavefront errors can result in squared visibility errors arising from crosstalk as high as ΔV2 = 6.6 × 10−3 under realistic observing conditions.

First on-sky demonstration of spatial Linear Dark Field Control with the vector-Apodizing Phase Plate at Subaru/SCExAO

Context.One of the key noise sources that currently limits high-contrast imaging observations for exoplanet detection is quasi-static speckles. Quasi-static speckles originate from slowly evolving non-common path aberrations (NCPA). These NCPA are related to the different optics encountered in the wavefront sensing path and the science path, and they also exhibit a chromatic component due to the difference in the wavelength between the science camera and the main wavefront sensor. These speckles degrade the contrast in the high-contrast region (or dark hole) generated by the coronagraph and make the calibration in post-processing more challenging.Aims.The purpose of this work is to present a proof-of-concept on-sky demonstration of spatial Linear Dark Field Control (LDFC). The ultimate goal of LDFC is to stabilize the point spread function by addressing NCPA using the science image as additional wavefront sensor.Methods.We combined spatial LDFC with the Asymmetric Pupil vector-Apodizing Phase Plate (APvAPP) on the Subaru Coronagraphic Extreme Adaptive Optics system at the Subaru Telescope. To allow for rapid prototyping and easy interfacing with the instrument, LDFC was implemented in Python. This limited the speed of the correction loop to approximately 20 Hz. With the APvAPP, we derive a high-contrast reference image to be utilized by LDFC. LDFC is then deployed on-sky to stabilize the science image and maintain the high-contrast achieved in the reference image.Results.In this paper, we report the results of the first successful proof-of-principle LDFC on-sky tests. We present results from two types of cases: (1) correction of instrumental errors and atmospheric residuals plus artificially induced static aberrations introduced on the deformable mirror and (2) correction of only atmospheric residuals and instrumental aberrations. When introducing artificial static wavefront aberrations on the DM, we find that LDFC can improve the raw contrast by a factor of 3–7 over the dark hole. In these tests, the residual wavefront error decreased by ∼50 nm RMS, from ∼90 nm to ∼40 nm RMS. In the case with only residual atmospheric wavefront errors and instrumental aberrations, we show that LDFC is able to suppress evolving aberrations that have timescales of < 0.1–0.4 Hz. We find that the power at 10−2Hz is reduced by a factor of ∼20, 7, and 4 for spatial frequency bins at 2.5, 5.5, and 8.5λ/D, respectively.Conclusions.We have identified multiplied challenges that have to be overcome before LDFC can become an integral part of science observations. The results presented in this work show that LDFC is a promising technique for enabling the high-contrast imaging goals of the upcoming generation of extremely large telescopes.

High-spatial resolution stacked-actuator deformable mirror for correction of atmospheric wavefront aberrations.

Deformable mirrors are vital components of any adaptive optical system. Considering such a crucial role in compensation of incident wavefront distortions, the main requirements are imposed on these elements that determine performance of the entire system. To correct for phase distortions in high-power laser complexes a stacked-actuator deformable mirror with water cooling was developed. The main characteristics of the mirror, such as the initial surface profile (flatness), response functions of the actuators, maximal stroke, and amplitude-frequency characteristics are presented in this paper. Experimental investigations of the proposed cooling method of the mirror surface through actuators were performed.

Uplink wavefront corrector system: from paper to reality.

The Uplink Wavefront Corrector System (UWCS) is a pathfinder instrument to demonstrate the uplink correction by Adaptive Optics techniques; this novel application can be directly usable in two fields: Free-Space Optical Communications and the generation of Laser Guide Stars. A Rayleigh LGS is propagated to the sky while the atmospheric wavefront aberrations are measured by a Shack-Hartmann WFS with 12 x 12 sub-apertures using a Natural Guide Star as a reference. The laser upwards propagation path is then pre-compensated by a 97-actuator deformable mirror. A scoring camera is attached to the finder telescope, next to the main aperture, in order to show the overall result, which is assessed in terms of beam power concentration. Present paper described the design process of the UWCS and its integration and testing in the Optical Ground Station telescope, at Teide Observatory (Spain).

Diffraction-limited Littrow imaging grating spectrometer for the New Vacuum Solar Telescope

To observe fine structures on the Sun and study the thermodynamic properties of the solar atmosphere with different height distributions, a diffraction-limited imaging grating spectrometer with high spectral resolution is an essential tool. However, its imaging performance will be limited by wavefront aberration caused by atmospheric turbulence and static wavefront aberration. In order to compensate the aberrations and lower the manufacturing precision of the optical element, an aberration correction method for a diffraction-limited Littrow imaging grating spectrometer (DLIGS) based on adaptive optics is proposed. To correctly detect the static aberration, the calibration system is adopted. To validate the method, a prototype for the New Vacuum Solar Telescope is developed. The results demonstrate that the proposed method is feasible, and near diffraction-limited imaging performance is achieved after the adaptive optics correction. The real spectral resolution of the prototype is roughly 6 pm, which is close to the numerical result (5.6 pm).

Neural networks for image-based wavefront sensing for astronomy.

We study the possibility of using convolutional neural networks for wavefront sensing from a guide star image in astronomical telescopes. We generated a large number of artificial atmospheric wavefront screens and determined associated best-fit Zernike polynomials. We also generated in-focus and out-of-focus point-spread functions. We trained the well-known "Inception" network using the artificial data sets and found that although the accuracy does not permit diffraction-limited correction, the potential improvement in the residual phase error is promising for a telescope in the 2-4m class.

Fast Coherent Differential Imaging on Ground-based Telescopes Using the Self-coherent Camera

Direct imaging and spectral characterization of exoplanets using extreme adaptive optics (ExAO) is a key science goal of future extremely large telescopes and space observatories. However, quasi-static wavefront errors will limit the sensitivity of this endeavor. Additional limitations for ground-based telescopes arise from residual AO-corrected atmospheric wavefront errors, generating millisecond-lifetime speckles that average into a halo over a long exposure. A solution to both of these problems is to use the science camera of an ExAO system as a wavefront sensor to perform a fast measurement and correction method to minimize these aberrations as soon as they are detected. We develop the framework for one such method based on the self-coherent camera (SCC) to be applied to ground-based telescopes, called Fast Atmospheric SCC Technique (FAST). We show that with the use of a specially designed coronagraph and coherent differential imaging algorithm, recording images every few milliseconds allows for a subtraction of atmospheric and static speckles while maintaining a close to unity algorithmic exoplanet throughput. Detailed simulations reach a contrast close to the photon noise limit after 30 seconds for a 1 % bandpass in H band on both 0$^\text{th}$ and 5$^\text{th}$ magnitude stars. For the 5th magnitude case, this is about 110 times better in raw contrast than what is currently achieved from ExAO instruments if we extrapolate for an hour of observing time, illustrating that sensitivity improvement from this method could play an essential role in the future detection and characterization of lower mass exoplanets.

Effect of uplink atmospheric wavefront distortion on image quality of sheared-beam imaging

Sheared-beam imaging (SBI) is a non-traditional imaging technique in which utilized are three sheared coherent lasers for illumination, and detector array to receive the intensity of speckle pattern reflected from the target. Finally the image of target can be reconstructed by computer algorithm from the data collected before. The SBI has some advantages in high resolution imaging for long-distance space targets. However, the wavefront distortion caused by atmospheric turbulence is a key factor affecting the imaging quality of SBI. Therefore, this paper focuses on the influence of wavefront distortion caused by atmospheric turbulence on the extraction of target spectral information. Theoretical model of the influence of wavefront distortion on imaging is established. The effects of low-order and high-order atmosphere turbulence on SBI imaging quality are analysed respectively. It turns out that low-order atmosphere turbulence does not result in poor image quality nor low-resolution, and just change the position of target on the image plane. But the image quality can be degraded when the wavefront root mean square (RMS) value at the target plane, caused by high-order atmosphere turbulence, exceeds /20. Beam emitted from larger aperture becomes more susceptible to perturbing effect, thus forming lower-quality wavefront. Considering that after passing through the atmosphere, beam also travels a long distance to reach the target surface. Targets at different heights will obtain different wavefront quality due to the diffraction of light. Thus the final wavefront quality is determined by turbulence intensity, aperture size and target height. Multi-layer phase-screen model and Hufnagel-Valley model are used to simulate the influences of near-earth (25 km) atmosphere on wavefront distortion at target plane with different imaging distances. Simulation results show that the wavefront RMS value rises with the increase of transmitting aperture diameter, and decreases with the increase of imaging distance. Transmitting aperture sizes in a range from 0.2 times r0 to twice r0 have been recommended for effective imaging by Hutchin[Hutchin R A 1993 Proc. SPIE 2029 161]. However, we find in our simulations that beams on the order of 2 r0 may cause significant wavefront error at short range target, and under some circumstances the clear image of target cannot be reconstructed. The imaging results of SBI at different laser transmitting apertures and different imaging distances are obtained, and evaluated by Strehl ratio. Imaging results show that choosing appropriate transmitting aperture size can effectively improve the imaging quality. But for the short-range targets, aperture size selection range presented by Hutchin can be too broad to be practicable. This paper suggests some approaches to choosing suitable aperture size for SBI system, and also providing a reference for the difference analysis of imaging quality for targets in different heights.

Adaptive optics system for the Xinglong 2.16 m telescope

Adaptive optics (AO) is one of the essential techniques for the large-diameter astronomical telescopes to overcome the wavefront aberrations caused by atmospheric turbulence and improve their imaging qualities. This paper describes an adaptive optics system developed for the 2.16-m telescope at Xinglong. This AO system mainly consists of a piezoelectric deformable mirror with 109 actuators, a Shack-Hartmann wavefront sensor with 100 subapertures, and a high-speed control platform based on field-programmable gate array (FPGA). Experimental results show that this AO system can reduce the root-mean-square (RMS) of the atmospheric wavefront aberrations to, or even smaller than 0.1 λ , and then the telescope can obtain a near diffraction limited resolution.

The coronagraphic Modal Wavefront Sensor: a hybrid focal-plane sensor for the high-contrast imaging of circumstellar environments

The raw coronagraphic performance of current high-contrast imaging instruments is limited by the presence of a quasi-static speckle (QSS) background, resulting from instrumental non-common path errors (NCPEs). Rapid development of efficient speckle subtraction techniques in data reduction has enabled final contrasts of up to 10-6 to be obtained, however it remains preferable to eliminate the underlying NCPEs at the source. In this work we introduce the coronagraphic Modal Wavefront Sensor (cMWS), a new wavefront sensor suitable for real-time NCPE correction. This pupil-plane optic combines the apodizing phase plate coronagraph with a holographic modal wavefront sensor, to provide simultaneous coronagraphic imaging and focal-plane wavefront sensing using the science point spread function. We first characterise the baseline performance of the cMWS via idealised closed-loop simulations, showing that the sensor successfully recovers diffraction-limited coronagraph performance over an effective dynamic range of +/-2.5 radians root-mean-square (RMS) wavefront error within 2-10 iterations. We then present the results of initial on-sky testing at the William Herschel Telescope, and demonstrate that the sensor is able to retrieve injected wavefront aberrations to an accuracy of 10nm RMS under realistic seeing conditions. We also find that the cMWS is capable of real-time broadband measurement of atmospheric wavefront variance at a cadence of 50Hz across an uncorrected telescope sub-aperture. When combined with a suitable closed-loop adaptive optics system, the cMWS holds the potential to deliver an improvement in raw contrast of up to two orders of magnitude over the uncorrected QSS floor. Such a sensor would be eminently suitable for the direct imaging and spectroscopy of exoplanets with both existing and future instruments, including EPICS and METIS for the E-ELT.

Simulating large atmospheric phase screens using a woofer-tweeter algorithm.

We describe an algorithm for simulating atmospheric wavefront perturbations over ranges of spatial and temporal scales spanning more than 4 orders of magnitude. An open-source implementation of the algorithm written in Python can simulate the evolution of the perturbations more than an order-of-magnitude faster than real time. Testing of the implementation using metrics appropriate to adaptive optics systems and long-baseline interferometers show accuracies at the few percent level or better.

Generation of atmospheric wavefronts using binary micromirror arrays.

To simulate in the laboratory the influence that a turbulent atmosphere has on light beams, we introduce a practical method for generating atmospheric wavefront distortions that considers digital holographic reconstruction using a programmable binary micromirror array. We analyze the efficiency of the approach for different configurations of the micromirror array and experimentally demonstrate the benchtop technique. Though the mirrors on the digital array can only be positioned in one of two states, we show that the holographic technique can be used to devise a wide variety of atmospheric wavefront aberrations in a controllable and predictable way for a fraction of the cost of phase-only spatial light modulators.

Zonal representation–based residual-wavefront reconstruction using multiframe Shack-Hartmann measurements

Atmospheric turbulence-induced wavefront deformation can be only partially corrected by adaptive optics (AO) techniques in astronomical or artificial space object imaging; an accurate estimation of the residual- wavefront phase is still needed to approach the diffraction-limited resolution. The discrete phase gradients mea- sured by Shack-Hartmann wavefront sensors (SHWFS) can help with the estimation. In this study, we build a dynamic average slopes measurement model for SHWFS in short-exposure AO images postprocessing; the proposed model is based on a zonal representation of the wavefront phase using Bernstein basis polynomials instead of the traditional Zernike modal expansion. Further, the turbulence's frozen flow hypothesis is adopted to update the initial model using multiframe SHWFS measurement data to achieve a more accurate reconstruction. Numerical experiments show the reconstruction errors significantly decrease even in poor seeing conditions, and show that our method is less sensitive to different SHWFS measurement noise levels. © 2015 Society of

Linear prediction of atmospheric wave-fronts for tomographic adaptive optics systems: modelling and robustness assessment.

We use a theoretical framework to analytically assess temporal prediction error functions on von-Kármán turbulence when a zonal representation of wavefronts is assumed. The linear prediction models analyzed include auto-regressive of an order up to three, bilinear interpolation functions, and a minimum mean square error predictor. This is an extension of the authors' previously published work Correia etal. [J. Opt. Soc. Am. A31, 101 (2014)JOAOD61084-752910.1364/JOSAA.31.000101], in which the efficacy of various temporal prediction models was established. Here we examine the tolerance of these algorithms to specific forms of model errors, thus defining the expected change in behavior of the previous results under less ideal conditions. Results show that ±100% wind speed error and ±50 deg are tolerable before the best linear predictor delivers poorer performance than the no-prediction case.

Experimental research on focusing anisoplanatism of sodium guide star via synchronous pulse detection

No reports of measuring the focusing anisoplanatism of laser guide star were mentioned before because the guide star instantaneous wavefront measurement technique by using sodium is not mature. As directly verifying the confidence of artificial sodium guide star which takes the place of the natural star to become the reference of atmosphere adaptive optic correction, in this paper a new method is put forward that the focusing anisoplanatic error of sodium guide star can be measured via synchronous pulse detection if the atmosphere Greenwood time is constant. Results of correlation analysis show that it is feasible to establish an experimental system for the measurement. A high-precision wavelength and linewidth sodium guide star laser and a 1.3 m caliber telescope underly the experimental system for the technology research on the focus anisoplanatism. Experiment of detecting sodium guide star has been carried out. And synchronous detection about the returning light matrix of visible light of sodium and the natural star is achieved when both are in a coincident imaging path. In the experiment, the recovered single frame wavefront of sodium guide star is acquired, and experimental data analysis is carried out in several aspects: contrasting the coherence of the two types of wavefront images, comparing the Zernike coefficients, and simulating the imaging calibration. Results show that the imaging contrast in the light matrix of the plused sodium guide star is poor because of the limited experimental condition so that the precision of the recovered wavefront is restricted, but the two groups of wavefronts the sodium guide star wavefront and the natural star wavefront always keep nice comparability, which we can see from the recoverd synchronous wavefront images. And the Zernike coefficients of both are close in the first 36 orders, which we deduce from the Zernike anisoplanatic error curves. Simulation result shows that the acquired sodium wavefront data would contribute to calibrate the far-field images of natural star in astronomical observation activities. And the measured results, below 0.1 rad2, while wiping off the wavefront recovering error are close to the theoretical result. Result shows also that the low SNR of sub aperture imaging restricts the wavefront recovery precision to some extent, but the effective atmospheric wavefront distorted information has been obtained by sodium guide star experiment and it can help to correct the natural star images.

Simulation of Atmospheric Wave-Fronts with Turbulence Intermittency

A new extendable method for the simulation of atmospheric wave-fronts with turbulence intermittency is reported. The purpose is to generate simulations consistent with the distributions observed for the turbulence parameters and the seeing, not available with standard methods. The intermittency is included by entering log-normal distributed arrays for the Fried parameter and the spatial coherence outer scale length into an extended form of the phase spectrum. The method is tested on large samples of simulated long-exposure point-source images. The tests show the agreement of the simulations with literature data. The simulations show that the intermittency affects negligibly the long-term median image size but breaks the symmetry of the wave-front phase spectrum, scatters the phase structure function and changes the image profile.

Performance of a satellite-to-ground downlink coherent lasercom system with random tracking error of receiver

We analyze the performance of a satellite-to-ground downlink coherent lasercom system taking into account the combined effects of atmospheric wavefront aberration and tracking error of the receiver. We revise the wavefront phase variance in the case where the tracking error of the receiver terminal is present. We consider the example of the BPSK modulation scheme and show that the tracking error of the receiver terminal greatly increases the bit error probability of the coherent system. We show the optimum aperture diameter of the receiver. This study can benefit the satellite-to-ground downlink coherent lasercom system design.