Super-resolution wavefront reconstruction

Journal of the Optical Society of America A, 2009

The performances of various estimators for wavefront sensing applications such as adaptive optics (AO) are compared. Analytical expressions for the bias and variance terms in the mean squared error (MSE) are derived for the minimum-norm maximum likelihood (MNML) and the maximum a posteriori (MAP) reconstructors. The MAP estimator is analytically demonstrated to yield an optimal trade-off that reduces the MSE, hence leading to a better Strehl ratio. The implications for AO applications are quantified thanks to simulations on 8-m-and 42-m-class telescopes. We show that the MAP estimator can achieve twice as low MSE as MNML methods do. Large AO systems can thus benefit from the high quality of MAP reconstruction in O͑n͒ operations, thanks to the fast fractal iterative method (FrIM) algorithm (Thiébaut and Tallon, submitted to J. Opt. Soc. Am. A).

Journal of the Optical Society of America A, 2010

Extremely Large Telescopes (ELTs) are very challenging with respect to their adaptive optics (AO) requirements. Their diameters and the specifications required by the astronomical science for which they are being designed imply a huge increment in the number of degrees of freedom in the deformable mirrors. Faster algorithms are needed to implement the real-time reconstruction and control in AO at the required speed. We present the results of a study of the AO correction performance of three different algorithms applied to the case of a 42-m ELT: one considered as a reference, the matrix-vector multiply (MVM) algorithm; and two considered fast, the fractal iterative method (FrIM) and the Fourier transform reconstructor (FTR). The MVM and the FrIM both provide a maximum a posteriori estimation, while the FTR provides a least-squares one. The algorithms are tested on the European Southern Observatory (ESO) end-to-end simulator, OCTOPUS. The performance is compared using a natural guide star single-conjugate adaptive optics configuration. The results demonstrate that the methods have similar performance in a large variety of simulated conditions. However, with respect to system misregistrations, the fast algorithms demonstrate an interesting robustness.

Journal of the Optical Society of America A, 2010

We present a new algorithm, FRiM (FRactal Iterative Method), aiming at the reconstruction of the optical wavefront from measurements provided by a wavefront sensor. As our application is adaptive optics on extremely large telescopes, our algorithm was designed with speed and best quality in mind. The latter is achieved thanks to a regularization which enforces prior statistics. To solve the regularized problem, we use the conjugate gradient method which takes advantage of the sparsity of the wavefront sensor model matrix and avoids the storage and inversion of a huge matrix. The prior covariance matrix is however non-sparse and we derive a fractal approximation to the Karhunen-Loève basis thanks to which the regularization by Kolmogorov statistics can be computed in O(N) operations, N being the number of phase samples to estimate. Finally, we propose an effective preconditioning which also scales as O(N) and yields the solution in 5-10 conjugate gradient iterations for any N. The resulting algorithm is therefore O(N). As an example, for a 128 × 128 Shack-Hartmann wavefront sensor, FRiM appears to be more than 100 times faster than the classical vector-matrix multiplication method.

Proceedings of the International Astronomical Union, 2005

Adaptive Optics (AO) will be essential for accomplishing many, if not most, of the science objectives currently planned for Extremely Large Telescopes including GMT, OWL, and TMT. AO will be needed to support a range of instrumentation, including near infrared (IR) imagers and spectrometers, mid IR imagers and spectrometers, "planet finding" instrumentation and wide-field optical spectrographs. Multiple advanced AO systems, utilizing the full range of concepts currently under development, will need to be combined into an integrated architecture to meet a broad range of requirements for field-of-view, spatial resolution and spectral bandpass. In this paper, we describe several of the possible options for these systems and outline the range of issues, trade studies and component development activities which must be addressed. Some of these challenges include very high-order, large-stroke wavefront correction, tip-tilt sensing with faint natural guide stars to maximize sky coverage, laser guide star wavefront sensing on a very large aperture and achieving extremely high contrast ratios for the detection of extra-solar planet and other faint companions of nearby bright stars.

Optics Letters, 2004

We present a procedure for attaining resolution beyond the diffraction limit in ground-based telescopes. This procedure is based on the use of rotationally symmetric pupil plane filters that can be easily implemented in dynamic optical devices such as a deformable mirror of an adaptive-optics system. We show that a successful application of the technique requires partial compensation for atmospheric distortion by adaptive optics. Consequently, we derive the required level of compensation as a function of the atmospheric conditions. Finally, our results are checked using simulated data.

2002

High order adaptive optics at high speed (1kHz), high accuracy (10 cm) and high photon efficiency requirements is needed for high contrast imaging in the infrared for exo-planet detection. An AO system with conventional deformable mirrors and reconstruction from slope measurements would be expensive and extremely difficult to produce. In this paper we describe a "reconstructorfree" high order adaptive optics system using a self-referenced Mach-Zehnder wavefront sensor and a liquid crystal phase corrector. Phase measurements are obtained directly from the two outputs the Mach-Zehnder interferometer, with ±λ/4 pathlength difference between its two legs. The intensity difference between corresponding pixels on the two cameras outputs is proportional to phase error, provided this is small, and correction takes place at the pixel level with a liquid crystal phase corrector whose square geometry matches the wavefront sensor camera pixels. In this way high resolution and photon efficiency are achieved in a system with direct, pixel-based estimation, control and correction of phase error. We have achieved in the laboratory wavefront retrieval with very fine scale sampling (128 phase measurements across the aperture) with λ/30 rms accuracy. Although the current electronics lacks dynamic range and speed, these could be readily improved for a real telescope system. Very recent progresses in decreasing the fall time of liquid crystal using the dual frequency method will allow for correction at kHz rates. While limited to correction of small wavefront amplitude errors (≤ 1 wave), such a system could be used very efficiently in tandem with a lower order system of high dynamic range.

Publications of the Astronomical Society of the Pacific, 2000

Adaptive optics (AO) is a technology that corrects in real time for the blurring e †ects of atmospheric turbulence, in principle allowing Earth-bound telescopes to achieve their di †raction limit and to "" see ÏÏ as clearly as if they were in space. The power of AO using natural guide stars has been amply demonstrated in recent years on telescopes up to 3È4 m in diameter. The next breakthrough in astronomical resolution was expected to occur with the implementation of AO on the new generation of large, 8È10 m diameter telescopes. In this paper we report the initial results from the Ðrst of these AO systems, now coming on line on the 10 m diameter Keck II Telescope. The results include the highest angular resolution images ever obtained from a single telescope and at 0.85 and 1.65 km wavelengths, respectively), as well (0A .022 0A .040 as tests of system performance on three astronomical targets.

2016

Aims. We propose the application of multiresolution transforms, such as wavelets (WT) and curvelets (CT), to the reconstruction of images of extended objects that have been acquired with adaptive optics (AO) systems. Such multichannel approaches normally make use of probabilistic tools in order to distinguish significant structures from noise and reconstruction residuals. Therefore, we also test the performance of two different probabilistic masks: one based on local correlation and the other on local standard deviation. Furthermore, we aim to check the historical assumption that image-reconstruction algorithms using static PSFs are not suitable for AO imaging. Methods. We convolve an image of Saturn taken with the Hubble Space Telescope (HST) with AO PSFs from the 5-m Hale telescope at the Palomar Observatory and add both shot and readout noise. Subsequently, we apply different approaches to the blurred and noisy data in order to recover the original object. The approaches include ...

Ground-based and Airborne Instrumentation for Astronomy V, 2014

Lucky Imaging combined with a low order adaptive optics system has given the highest resolution images ever taken in the visible or near infrared of faint astronomical objects. This paper describes a new instrument that has already been deployed on the WHT 4.2m telescope on La Palma, with particular emphasis on the optical design and the predicted system performance. A new design of low order wavefront sensor using photon counting CCD detectors and multi-plane curvature wavefront sensor will allow virtually full sky coverage with faint natural guide stars. With a 2 x 2 array of 1024 x 1024 photon counting EMCCDs, AOLI is the first of the new class of high sensitivity, near diffraction limited imaging systems giving higher resolution in the visible from the ground than hitherto been possible from space.

Adaptive Optics Systems, 2008

We have recently demonstrated diffraction-limited resolution imaging in the visible on the 5m Palomar Hale telescope. The new LAMP instrument is a Lucky Imaging backend camera for the Palomar AO system. Typical resolutions of 35-40 mas with Strehls of 10-20% were achieved at 700nm, and at 500nm the FWHM resolution was as small as 42 milliarcseconds. In this paper we discuss the capabilities and design challenges of such a system used with current and near future AO systems on a variety of telescopes. In particular, we describe the designs of two planned Lucky Imaging + AO instruments: a facility instrument for the Palomar 200" AO system and its PALM3K upgrade, and a visible-light imager for the CAMERA low-cost LGS AO system planned for the Palomar 60" telescope. We introduce a Monte Carlo simulation setup that reproduces the observed PSF variability behind an adaptive optics system, and apply it to predict the performance of 888Cam and CAMERA. CAMERA is predicted to achieve diffraction-limited resolution at wavelengths as short as 350 nm. In addition to on-axis resolution improvements we discuss the results of frame selection with the aim of improving other image parameters such as isoplanatic patch sizes, showing that useful improvements in image quality can be made by Lucky+AO even with very temporally and spatially undersampled data.