Joint estimation of atmospheric and instrumental defects using a parsimonious point spread function model

Ground-based near-IR imagers assisted by Multi Conjugate Adaptive Optics (MCAO) systems are the technological frontier to obtain high-quality stellar photometry in crowded fields at the highest possible spatial resolution. The Gemini MCAO System (GeMS) feeding the Gemini South Adaptive Optics Imager (GSAOI) is the only facility of this kind currently available to the Community. We used a set of images obtained in the J and K s bands of the central regions of two Galactic bulge globular clusters (Liller 1 and NGC 6624) with GeMS/GSAOI, under significantly different atmospheric conditions. We characterized the performances of the system in terms of efficiency and uniformity of the Point Spread Function (PSF) over the field of view with varying seeing, airmass and tip-tilt star asterisms. We also compared the PSF performances of GeMS/GSAOI with the HST/ACS ones in the F606W and F814W bands.

The paper deals with with the on-sky performance of the pyramid wavefront sensor-based Adaptive Optics (AO) systems. These wavefront sensors are of great importance, being used in all first light AO systems of the ELTs (E-ELT, GMT, and TMT), currently in design phase. In particular, non-common path aberrations (NCPAs) are a critical issue encountered when using an AO system to produce corrected images in an associated astronomical instrument. The AO wavefront sensor (WFS) and the supported scientific instrument typically use a series of different optical elements, thus experiencing different aberrations. The usual way to correct for such NCPAs is to introduce a static offset in the WFS signals. In this way, when the AO loop is closed the sensor offsets are zeroed and the deformable mirror converges to the shape required to null the NCPA. The method assumes that the WFS operation is linear and completely described by some pre-calibrated interaction matrix. This is not the case for some frequently used wavefront sensors like the Pyramid sensor or a quad-cell Shack-Hartmann sensor. Here we present a method to work in closed-loop with a pyramid wavefront sensor, or more generally a non-linear WFS, introducing a wavefront offset that remains stable when AO correction quality changes due to variations in external conditions like star brightness, seeing, and wind speed. The paper details the methods with analytical and numerical considerations. Then we present results of tests executed at the LBT telescope, in daytime and on sky, using the FLAO system and LUCI2 facility instrument. The on-sky results clearly show the successful operation of the method that completely nulls NCPA, recovering diffraction-limited images with about 70% Strehl ratio in H band in variable seeing conditions. The proposed method is suitable for application to the above-mentioned ELT AO systems.

In preparation of future Multi-Object Spectrographs (MOS) whose one of the major role is to provide an extensive statistical studies of high redshifted galaxies surveyed, the demonstrator Canary has been designed to tackle technical challenges related to open-loop Adaptive-Optics (AO) control with jointed Natural Guide Star (NGS) and Laser Guide Star (LGS) tomography. We have developed a Point Spread Function (PSF)-Reconstruction algorithm dedicated to MOAO systems using system telemetry to estimate the PSF potentially anywhere in the observed field, a prerequisite to post- process AO-corrected observations in Integral Field Spectroscopy (IFS). In this paper we show how to handle off-axis data to estimate the PSF using atmospheric tomography and compare it to a classical approach that uses on-axis residual phase from a truth sensor observing a natural bright source. We have reconstructed over 450 on-sky Canary PSFs and we get bias/1-${\sigma}$ standard-deviation (std) of 1.3/4.8 on the H-band Strehl ratio (SR) with 92.3% of correlation between reconstructed and sky SR. On the Full Width at Half Maximum (FWHM), we get respectively 2.94 mas, 19.9 mas and 88.3% for the bias, std and correlation. The reference method achieves 0.4/3.5/95% on the SR and 2.71 mas/14.9 mas/92.5% on the FWHM for the bias/std/correlation.

Adaptive optics (AO) enhances astronomical images by correcting perturbations in the optical system, resulting in complex point spread function (PSF) shapes, which provide critical information for optical design, calibration, and diagnostics. This paper presents a parametric model for an AO-corrected long-exposure PSF that adapts to complex shapes and various seeing conditions. A complementary estimation method is also introduced, addressing the inverse problem of estimating the atmospheric PSF or power spectral density (PSD) from observed PSF data. The model, based on Gaussian sum approximation (GSA), was tested using simulated PSF data from the OOMAO toolbox for Fried parameter (r0) values ranging from 0.10 to 0.20 m and on-sky data from the Very Large Telescope’s MUSE instrument. Two approaches were analyzed: (i) direct PSF estimation using GSA, and (ii) PSF estimation derived from atmospheric PSD estimation. Both methods were evaluated using root mean square error (RMSE). While approach (i) provided the best performance, approach (ii) produced more accurate atmospheric PSF estimates compared to the Moffat approximation and the Fetick method. Additionally, approach (ii) enabled the estimation of key physical parameters, such as the Fried parameter (r0) and residual AO variance ($\sigma _{AO}^2$). The proposed methods effectively estimate atmospheric PSF and PSD, even for complex PSF shapes influenced by spiders, central obstructions, or static aberrations.

Solar Adaptive Optics (AO) shares many issues with night-time AO, but it also has its own particularities. The wavefront sensing is performed using correlations to efficiently work on the solar granulation as a reference. The field of view for that measurement usually is around 10". A sensor collecting such a wide field of view averages wavefront information from different sky directions, and the anisoplanatism thus has a peculiar impact on the performance of solar AO and MCAO systems. Since we are entering the era of large solar telescopes (European Solar Telescope, Advanced Technology Solar Telescope) understanding this issue is crucial to evaluate its impact on the performance of future AO systems. In this paper we model the correlating wide field sensor and the way it senses the high altitude turbulence. Thanks to this improved modelling, we present an analysis of the influence of this sensing on the performance of each AO configuration, conventional AO and MCAO. In addition to the analytical study, simulations similar to the case of the EST AO systems with FRiM-3D (the Fractal Iterative Method for Atmospheric tomography) are used in order to highlight the relative influence of design parameters. In particular, results show the performance evolution when increasing the telescope diameter. We analyse the effect of high altitude turbulence correlation showing that increasing the diameter of the telescope does not degrade the performance when correcting on the same spatial and temporal scales.

In this paper we discuss the performance of low order adaptive optics (AO) systems. We present improved calculations of Strehl ratio achievable at various D/r<SUB>o</SUB> ratios for AO systems up to 7<SUP>th</SUP> order. Additionally we present calculations concerning the throughput of low order AO systems used in conjunction with spectrometers. We then show the results of a detailed simulation of the expected interaction of the University of Hawaii prototype AO system with spectrometers through the V,I,J,H,K optical bands. This simulation shows that AO spectroscopy performance should always be acceptable in the near IR (J,H,K), and often in the visible (V,I). We show the results of our initial efforts at deconvolving the AO PSF. These results indicate that deconvolution is likely to be quite widely applicable to AO images. Finally we discuss how it might be possible to extend the applicability and accuracy of deconvolution using the AO drive and wavefront error signals. The following results are for on-axis system, the effects of atmospheric anisoplanitism have not been addressed in this paper.

Accurate astrometry and photometry of saturated and coronagraphic point spread functions (PSFs) are fundamental to both ground- and space-based high contrast imaging projects. For ground-based adaptive optics imaging, differential atmospheric refraction and flexure introduce a small drift of the PSF with time, and seeing and sky transmission variations modify the PSF flux distribution. For space-based imaging, vibrations, thermal fluctuations and pointing jitters can modify the PSF core position and flux. These effects need to be corrected to properly combine the images and obtain optimal signal-to-noise ratios, accurate relative astrometry and photometry of detected objects as well as precise detection limits. Usually, one can easily correct for these effects by using the PSF core, but this is impossible when high dynamic range observing techniques are used, like coronagrahy with a non-transmissive occulting mask, or if the stellar PSF core is saturated. We present a new technique that can solve these issues by using off-axis satellite PSFs produced by a periodic amplitude or phase mask conjugated to a pupil plane. It will be shown that these satellite PSFs track precisely the PSF position, its Strehl ratio and its intensity and can thus be used to register and to flux normalize the PSF. A laboratory experiment is also presented to validate the theory. This approach can be easily implemented in existing adaptive optics instruments and should be considered for future extreme adaptive optics coronagraph instruments and in high-contrast imaging space observatories.

: The end-to-end performance achieved by an adaptive optical (AO) imaging system is determined by a combination of the residual time-varying phase distortions associated with atmospheric turbulence, and the quasi-static unsensed and uncorrectable aberrations in the optical system itself. Although the effects of these two errors on the time averaged Strehl ratio and the time averaged optical transfer function (OTF) of the AO system are not formally separable, such an approximation is found to be accurate to within a few per cent for a range of representative residual wave-front errors. In these calculations, we have combined static optical system aberrations and time-varying residual phase distortion characteristic of deformable mirror (DM) fitting error, wave-front sensor (WFS) noise, and anisoplanatism. The static aberrations consist of focus errors of varying magnitudes as well as a combination of unsensed and uncorrectable mirror figure errors derived from modeling by the Gemini beta-meter Telescopes project. The overall Strehl ratios and OTF's due to the combined effect of these error sources are well approximated as products of separate factors for the static and time-varying aberrations, as long as the overall Strehl ratio due to both errors is greater than about 0.1. For lower Strehl ratios the products provide lower bounds on the actual values of the Strehl ratio and OTF. The speckle transfer function (STF) is also well approximated by a product of two functions, but only where AO compensation is sufficiently good that speckle imaging techniques are usually not required.

Aim: The objective of this project was to evaluate high resolution images from an adaptive optics retinal imager through comparisons with standard film-based and standard digital fundus imagers. Methods: A clinical prototype adaptive optics fundus imager (AOFI) was used to collect retinal images from subjects with various forms of retinopathy to determine whether improved visibility into the disease could be provided to the clinician. The AOFI achieves low-order correction of aberrations through a closed-loop wavefront sensor and an adaptive optics system. The remaining high-order aberrations are removed by direct deconvolution using the point spread function (PSF) or by blind deconvolution when the PSF is not available. An ophthalmologist compared the AOFI images with standard fundus images and provided a clinical evaluation of all the modalities and processing techniques. All images were also analyzed using a quantitative image quality index. Results: This system has been tested on three human subjects (one normal and two with retinopathy). In the diabetic patient vascular abnormalities were detected with the AOFI that cannot be resolved with the standard fundus camera. Very small features, such as the fine vascular structures on the optic disc and the individual nerve fiber bundles are easily resolved by the AOFI. Conclusion: This project demonstrated that adaptive optic images have great potential in providing clinically significant detail of anatomical and pathological structures to the ophthalmologist.

The curvature‐wavefront‐based adaptive optics (AO) system with a laser guide star is under commissioning at Subaru Telescope. The AO system has been in use since September 2008 using a natural guide star. The testing of laser projection on the sky resumed on February 13, 2009. We have obtained around 0.55 of Strehl ratio in the K band under seeing conditions of 0.4 arcsecond (at K band) using an 8th‐magnitude single star. The Strehl ratio was about 0.2 in the K band using a faint guide star around 16th magnitude. Even though the seeing condition was 1 arcsecond, we obtained an almost diffraction‐limited image. The total equivalent magnitude of the laser guide star was estimated at 10.7 magnitude. However, the full width half maximum is around 2 arcseconds under the seeing condition of 1 arcsecond in K‐band.

.Significance: A scene-based adaptive-optics (AO) system is developed and a method for investigating its imaging performance is proposed. The system enables derivation of Strehl ratios from observed images via collaboration with computer simulations. The resultant Strehl ratios are comparable with those of other current AO systems.Aim: For versatile and noninvasive AO microscopy, a scene-based wavefront-sensing technique working on a Shack–Hartmann wavefront sensor is developed in a modal control system. The purpose of the research is to clarify the imaging performance of the AO system via the derivation of Strehl ratios from observed images toward applications in microscopy of living cells and tissues.Approach: Two imaging metrics that can be directly measured from observed images (i.e., an energy concentration ratio and unbiased maximum ratio) are defined and related to the Strehl ratio via computer simulations. Experiments are conducted using artificial targets to measure the imaging metrics, which are then converted to Strehl ratios.Results: The resultant Strehl ratios are and 0.5 in the cases of defocus and higher aberrations, respectively. The half-widths at half-maximum of the AO-corrected bead images are favorably comparable to those of on-focus images under simple defocus aberration, and the AO system works both under bright-field illumination and on fluorescent bead images.Conclusions: The proposed scene-based AO system is expected to work with a Strehl ratio of more than 0.5 when applied to high-resolution live imaging of cells and tissues under bright-field and fluorescence microscopies.

For performance evaluation of an adaptive optics (AO) system, the probability of the system residual wavefront variance can provide more information than the wavefront variance average. By studying the Zernike coefficients of an AO system residual wavefront, we derived the exact expressions for the probability density functions of the wavefront variance and the Strehl ratio, for instantaneous and long-term exposures owing to the insufficient control loop bandwidth of the AO system. Our calculations agree with the residual wavefront data of a closed loop AO system. Using these functions, we investigated the relationship between the AO system bandwidth and the distribution of the residual wavefront variance. Additionally, we analyzed the availability of an AO system for evaluating the AO performance. These results will assist in designing and probabilistic analysis of AO systems.

The three-dimensional (3D) imaging performance of a cone-beam computed tomography (CBCT) system can be quantitatively characterized by its 3D point spread function (PSF). To avoid the pitfalls associated with 3D PSF measurement through the use of a micro point phantom, we adopt an edge-based technique, which iteratively blurs a step edge into a spread edge with a Gaussian blurring kernel. In experiment, a small Teflon solid ball (diameter ~6mm) is used to provide step edges along the scanlines across the ball center, in terms of x-ray linear attenuation coefficient. Correspondingly, the spread edge profiles are extracted from the digital volume ball reconstructed by a CBCT system. From a spread edge profile, a step edge can be established by a rectification procedure (essentially an edge identification). A 1D PSF along a scanline is modeled as a Gaussian distribution, which is determined by iterative edge-blurring technique. The 1D PSFs on a cross section of the ball constitute a 2D PSF, and the 2D PSFs at three orthogonal cross sections are used to represent the 3D PSF at the position of the ball. By repositioning the ball phantom and repeating the procedure, we measured the 3D PSFs at 126 positions over half of the support space. Experiment shows that a CBCT system is of spatial variance and anisotropy in terms of FWHMs (full width at half maximum) of the blurring kernel. Both numerical and graphical presentations of PSF results are provided. As a result, the FWHM of the 3D PSF in our CBCT system varies in the range between 0.66 mm and 1.39 mm.

For a non-cooperative target, a laser beacon is created by illuminating the target with a beacon beam. When a beacon beam propagates though deep turbulence, turbulence spreads the beam. A conventional phase conjugate adaptive optics (AO) system is not efficient in the presence of Beacon Anisoplanatism when the beacon beam spot size at the target includes many isoplanatic patch sizes. We introduce a concept of the wavefront-based stochastic parallel gradient decent (WSPGD) AO system, which uses an off-axis wavefront sensor to provide feedback for the beam control algorithm. This concept is based on the finding that the phase aberrations of laser return from the target contain information about beam spot size at the target, and that correction of a limited number of low-order Zernike modes increases on-axis intensity and power in the bucket at the target. We evaluated the WSPGD AO system performance in simulation for two tactical engagement scenarios in the presence of strong turbulence. We found that that the WSPGD AO system can efficiently compensate the effects of strong turbulence including Beacon Anisoplanatism, even when the beam spot size at the target includes up to 20 isoplanatic patch sizes and the isoplanatic angle is by a factor of 2.6 less than the diffraction limit. The Strehl ratio gain for this scenario is 1.6 - 2.5, and the maximum Strehl ratio is achieved after 15-20 iterations. A laboratory demonstration performed under a separate program confirmed our theoretical predictions.

Improved Adaptive Optics (AO) systems continue to revolutionize ground-based astronomy. Key to understanding a new AO systems capability is a quantitative measurement of performance, such as the Strehl Ratio (SR). At the Large Binocular Telescope (LBT) we have undertaken a program to monitor the performance of our AO system in regular use for science operations. Input to our analysis includes data taken specifically for this purpose during twilight and on engineering nights. We report our findings thus far and in particular discuss the challenges of collecting consistent data sets in twilight, the methods we used to overcome those challenges, and preliminary results from data collected so far.