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Register a new userCharacterizing the Adaptive Optics Off-Axis Point-Spread Function - I: A Semi-Empirical Method for Use in Natural-Guide-Star Observations
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E. Steinbring
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Even though the technology of adaptive optics (AO) is rapidly maturing, calibration of the resulting images remains a major challenge. The AO point-spread function (PSF) changes quickly both in time and position on the sky. In a typical observation the star used for guiding will be separated from the scientific target by 10 to 30. This is sufficient separation to render images of the guide star by themselves nearly useless in characterizing the PSF at the off-axis target position. A semi-empirical technique is described that improves the determination of the AO off-axis PSF. The method uses calibration images of dense star fields to determine the change in PSF with field position. It then uses this information to correct contemporaneous images of the guide star to produce a PSF that is more accurate for both the target position and the time of a scientific observation. We report on tests of the method using natural-guide-star AO systems on the Canada-France-Hawaii Telescope and Lick Observatory Shane Telescope, augmented by simple atmospheric computer simulations. At 25 off-axis, predicting the PSF full width at half maximum using only information about the guide star results in an error of 60%. Using an image of a dense star field lowers this error to 33%, and our method, which also folds in information about the on-axis PSF, further decreases the error to 19%.
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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.]
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.
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.
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.
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.
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