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Register a new userNew algorithms for adaptive optics point-spread function reconstruction
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Eric Gendron
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Context. The knowledge of the point-spread function compensated by adaptive optics is of prime importance in several image restoration techniques such as deconvolution and astrometric/photometric algorithms. Wavefront-related data from the adaptive optics real-time computer can be used to accurately estimate the point-spread function in adaptive optics observations. The only point-spread function reconstruction algorithm implemented on astronomical adaptive optics system makes use of particular functions, named $U_{ij}$. These $U_{ij}$ functions are derived from the mirror modes, and their number is proportional to the square number of these mirror modes. Aims. We present here two new algorithms for point-spread function reconstruction that aim at suppressing the use of these $U_{ij}$ functions to avoid the storage of a large amount of data and to shorten the computation time of this PSF reconstruction. Methods. Both algorithms take advantage of the eigen decomposition of the residual parallel phase covariance matrix. In the first algorithm, the use of a basis in which the latter matrix is diagonal reduces the number of $U_{ij}$ functions to the number of mirror modes. In the second algorithm, this eigen decomposition is used to compute phase screens that follow the same statistics as the residual parallel phase covariance matrix, and thus suppress the need for these $U_{ij}$ functions. Results. Our algorithms dramatically reduce the number of $U_{ij}$ functions to be computed for the point-spread function reconstruction. Adaptive optics simulations show the good accuracy of both algorithms to reconstruct the point-spread function.
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Here we describe a simple, efficient, and most importantly fully operational point-spread-function(PSF)-reconstruction approach for laser-assisted ground layer adaptive optics (GLAO) in the frame of the Multi Unit Spectroscopic Explorer (MUSE) Wide Field Mode. Based on clear astrophysical requirements derived by the MUSE team and using the functionality of the current ESO Adaptive Optics Facility we aim to develop an operational PSF-reconstruction (PSFR) algorithm and test it both in simulations and using on-sky data. The PSFR approach is based on a Fourier description of the GLAO correction to which the specific instrumental effects of MUSE Wide Field Mode (pixel size, internal aberrations, etc.) have been added. It was first thoroughly validated with full end-to-end simulations. Sensitivity to the main atmospheric and AO system parameters was analysed and the code was re-optimised to account for the sensitivity found. Finally, the optimised algorithm was tested and commissioned using more than one year of on-sky MUSE data. We demonstrate with an on-sky data analysis that our algorithm meets all the requirements imposed by the MUSE scientists, namely an accuracy better than a few percent on the critical PSF parameters including full width at half maximum and global PSF shape through the kurtosis parameter of a Moffat function. The PSFR algorithm is publicly available and is used routinely to assess the MUSE image quality for each observation. It can be included in any post-processing activity which requires knowledge of the PSF.
Modern Giant Segmented Mirror Telescopes (GSMT) like the Extremely Large Telescope (ELT), currently under construction depend heavily on Adaptive Optics (AO) systems to correct for atmospheric turbulence. To be able to correct wider fields of view (FoV), Multi-Conjugate Adaptive Optics (MCAO) systems were introduced, which use multiple guide stars to obtain an almost uniform correction over the FoV. However, a residual blur remains in the astronmical images due to the time delay stemming from the wavefront sensor (WFS) integration time and temporal response of the deformable mirror(s) (DM). This results in a blur which can be mathematically described by a convolution of the true image with the point spread function (PSF). Due to the nature of the atmosphere and its correction, the PSF is spatially varying. In this paper, we present an algorithm for MCAO PSF reconstruction adapted to the needs of GSMTs in a storage efficient way. In particular, the PSF reconstruction algorithm for Single Conjugate Adaptive Optics (SCAO) from [33] is combined with an algorithm for atmospheric tomography from [27] to obtain a direction dependent reconstruction of the post-AO PSF. Results obtained in an end-to-end simulation tool show qualitatively good reconstruction of the PSF compared to the PSF calculated directly from the simulated incoming wavefront. Furthermore, the used algorithm has a reasonable runtime and memory consumption.
Astrometric precision and knowledge of the point spread function are key ingredients for a wide range of astrophysical studies including time-delay cosmography in which strongly lensed quasar systems are used to determine the Hubble constant and other cosmological parameters. Astrometric uncertainty on the positions of the multiply-imaged point sources contributes to the overall uncertainty in inferred distances and therefore the Hubble constant. Similarly, knowledge of the wings of the points spread function (PSF) is necessary to disentangle light from the background sources and the foreground deflector. We analyze adaptive optics (AO) images of the strong lens system J0659+1629 obtained with the W. M. Keck Observatory using the laser guide star AO system. We show that by using a reconstructed point spread function we can i) obtain astrometric precision of $< 1$ milliarcsecond (mas), which is more than sufficient for time-delay cosmography; and ii) subtract all point-like images resulting in residuals consistent with the noise level. The method we have developed is not limited to strong lensing, and is generally applicable to a wide range of scientific cases that have multiple point sources nearby.
An explanation for the origin of asymmetry along the preferential axis of the PSF of an AO system is developed. When phase errors from high altitude turbulence scintillate due to Fresnel propagation, wavefront amplitude errors may be spatially offset from residual phase errors. These correlated errors appear as asymmetry in the image plane under the Fraunhofer condition. In an analytic model with an open-loop AO system, the strength of the asymmetry is calculated for a single mode of phase aberration, which generalizes to two dimensions under a Fourier decomposition of the complex illumination. Other parameters included are the spatial offset of the AO correction, which is the wind velocity in the frozen flow regime multiplied by the effective AO time delay, and propagation distance or altitude of the turbulent layer. In this model, the asymmetry is strongest when the wind is slow and nearest to the coronagraphic mask when the turbulent layer is far away, such as when the telescope is pointing low towards the horizon. A great emphasis is made about the fact that the brighter asymmetric lobe of the PSF points in the opposite direction as the wind, which is consistent analytically with the clarification that the image plane electric field distribution is actually the inverse Fourier transform of the aperture plane. Validation of this understanding is made with observations taken from the Gemini Planet Imager, as well as being reproducible in end-to-end AO simulations.
Most current astronomical adaptive optics (AO) systems rely on the availability of a bright star to measure the distortion of the incoming wavefront. Replacing the guide star with an artificial laser beacon alleviates this dependency on bright stars and therefore increases sky coverage, but it does not eliminate another serious problem for AO observations. This is the issue of PSF variation with time and field position near the guide star. In fact, because a natural guide star is still necessary for correction of the low-order phase error, characterization of laser guide star (LGS) AO PSF spatial variation is more complicated than for a natural guide star alone. We discuss six methods for characterizing LGS AO PSF variation that can potentially improve the determination of the PSF away from the laser spot, that is, off-axis. Calibration images of dense star fields are used to determine the change in PSF variation with field position. This is augmented by AO system telemetry and simple computer simulations to determine a more accurate off-axis PSF. We report on tests of the methods using the laser AO system on the Lick Observatory Shane Telescope. [Abstract truncated.]
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