Andreas Obereder

Preprocessed cumulative reconstructor with domain decomposition: a fast wavefront reconstruction method for pyramid wavefront sensor

We present a fast method for the wavefront reconstruction from pyramid wavefront sensor (P-WFS) measurements. The method is based on an analytical relation between pyramid and Shack-Hartmann sensor (SH-WFS) data. The algorithm consists of two steps--a transformation of the P-WFS data to SH data, followed by the application of cumulative reconstructor with domain decomposition, a wavefront reconstructor from SH-WFS measurements. The closed loop simulations confirm that our method provides the same quality as the standard matrix vector multiplication method. A complexity analysis as well as speed tests confirm that the method is very fast. Thus, the method can be used on extremely large telescopes, e.g., for eXtreme adaptive optics systems.

Sensing wavefronts on resolved sources with pyramids on ELTs

Pyramid wavefront sensors (PWFS) have been agreed to provide a superior faint-end performance with respect to Shack-Hartmann systems (SHS) quite some time ago. However, much of the advantage relies on the fact that PWFSs exploit the full resolution limit of the telescope. ELTs will thus confront PWFSs with an unprecedented number of resolved targets. To analyze the behavior of PWFS on extended targets in detail observationally is difficult. We will present the result of simulations representing the Single-Conjugated Adaptive Optics (SCAO) system of METIS on the European ELT (E-ELT).

Fast algorithm for wavefront reconstruction in XAO/SCAO with pyramid wavefront sensor

We present a fast wavefront reconstruction algorithm developed for an extreme adaptive optics system equipped with a pyramid wavefront sensor on a 42m telescope. The method is called the Preprocessed Cumulative Reconstructor with domain decomposition (P-CuReD). The algorithm is based on the theoretical relationship between pyramid and Shack-Hartmann wavefront sensor data. The algorithm consists of two consecutive steps - a data preprocessing, and an application of the CuReD algorithm, which is a fast method for wavefront reconstruction from Shack-Hartmann sensor data. The closed loop simulation results show that the P-CuReD method provides the same reconstruction quality and is significantly faster than an MVM.

Efficient iterative tip/tilt reconstruction for atmospheric tomography

The planned new generation of extremely large telescopes (ELT) requires highly efficient algorithms for its adaptive optics systems. Recently, a new iterative reconstruction approach for multi conjugate adaptive optics (MCAO) and multi object adaptive optics (MOAO) was introduced that computes the mirror corrections without the use of matrix-vector multiplications. The method splits the MCAO/MOAO problem into three subproblems – wavefront reconstruction, atmospheric tomography and mirror deformation – sequently. If an AO system uses laser guide stars, then the reconstruction methods have to be extended in order to consider the cone effect and the tip/tilt indetermination. For the reconstruction of an atmosphere with correct tip/tilt we assume that additional measurements from a tip/tilt sensor are available, and propose two iterative reconstruction methods for the atmosphere. In the first approach, the tip/tilt reconstruction is included into the atmospheric tomography, whereas in the second approach the tip/tilt is reconstructed separately and added to the atmosphere after the atmospheric tomography. Both algorithms are tested numerically. The reconstruction quality of our methods is evaluated for ELT.

Wavefront reconstruction for ELT-sized telescopes with pyramid wavefront sensors

The new generation of ground-based telescopes relies on real-time adaptive optics systems to compensate for atmospheric perturbations arising during the imaging process. Pyramid wavefront sensors are planned to be part of many instruments currently under development for ELT-sized telescopes. The high number of correcting elements to be controlled in real-time and the segmented pupils of the ELTs lead to unprecedented challenges posed to the control algorithms. Based on various (approximate) models, several algorithms were developed in the last decades for linear and non-linear wavefront correction from pyramid sensor data. Among those, we emphasize interaction-matrix-based approaches, Fourier domain methods, iterative algorithms, and algorithms based on the inversion of the Finite Hilbert transform. We briefly present the core ideas of the algorithms and provide the necessary theoretical background like, e.g., the Fourier domain filters, or the direct inversion formulas. We give a detailed comparison of the presented methods with respect to underlying pyramid sensor models, the computational complexities, and reconstruction qualities. The performance of our algorithms is demonstrated in the context of an XAO system on the EPICS instrument and a SCAO system on the METIS instrument on the ELT. In the simulations, realistic features as the ELT spiders and the hexagonal M4 geometry are partially taken into account.

Single conjugate adaptive optics for METIS

METIS is the Mid-infrared Extremely large Telescope Imager and Spectrograph, one of the first generation instruments of ESO’s 39m ELT. All scientific observing modes of METIS require adaptive optics (AO) correction close to the diffraction limit. Demanding constraints are introduced by the foreseen coronagraphy modes, which require highest angular resolution and PSF stability. Further design drivers for METIS and its AO system are imposed by the wavelength regime: observations in the thermal infrared require an elaborate thermal, baffling and masking concept. METIS will be equipped with a Single-Conjugate Adaptive Optics (SCAO) system. An integral part of the instrument is the SCAO module. It will host a pyramid type wavefront sensor, operating in the near-IR and located inside the cryogenic environment of the METIS instrument. The wavefront control loop as well as secondary control tasks will be realized within the AO Control System, as part of the instrument. Its main actuators will be the adaptive quaternary mirror and the field stabilization mirror of the ELT. In this paper we report on the phase B design work for the METIS SCAO system; the opto-mechanical design of the SCAO module as well as the control loop concepts and analyses. Simulations were carried out to address a number of important aspects, such as the impact of the fragmented pupil of the ELT on wavefront reconstruction. The trade-off that led to the decision for a pyramid wavefront sensor will be explained, as well as the additional control tasks such as pupil stabilization and compensation of non-common path aberrations.

Designing the METIS SCAO and LTAO systems

METIS, the Mid-nfrared E-ELT Imager and Spectrometer, will be providing high-sensitivity imaging and high-resolution spectroscopy in the mid-infrared (3-19 micrometer) to the E-ELT. In order to achieve the exceptional performance required by its driving science cases, exoplanets and proto-planetary disks, METIS will be featuring two Adaptive Optics (AO) systems — a first-light Single Conjugate Adaptive Optics (SCAO) system, complemented by a Laser Tomographic Adaptive Optics (LTAO) system, most likely, a few years after first light. METIS, being one of the three first light science instruments on the European Extremely Large Telescope (E-ELT), will be one of the first instruments using the integrated deformable mirror of the E-ELT for its Adaptive Optics (AO) correction. The internal SCAO system designed to maximize the performance for bright targets and has its wavefront sensors (WFSs) build inside the METIS cryostat to minimize the number of warm surfaces towards the science detectors. Although the internal dichroic will reflect all light short wards of 3 micrometers towards the WFS, only the IR light will most likely be used, mainly due to the expected improved performance at longer wavelengths for the WFS. A trade-off has been made between both visible versus infrared wave front sensing as well as Pyramid versus Shack-Hartmann, under various observing conditions and target geometries, taking into account performance, target availability, reliability and technology readiness level. The base line for the SCAO system is to minimize system complexity, thereby ensuring system availability and reliability even under first-light conditions. Since the SCAO system will require a bright guide star near the science target, it can only be used for a limited number of targets. The LTAO system, consisting of up to 6 LGS and up to 3 low-order NGS WFS and located outside the cryostat, is designed to increase the sky coverage on arbitrary targets to >80%. Investigations are ongoing if the internal SCAO system can be used as either a Low-Order WFS or metrology system.

Dealing with spiders on ELTs: using a Pyramid WFS to overcome residual piston effects

In the design of the future generation ELTs the support structures for the secondary mirror (also known as spiders) lead to a piston on each of the pupil segments created by the spiders, known as ”island effect”. In this talk we focus on fast and stable reconstruction methods to cope with the island effect. We present and compare wavefront reconstruction algorithms and highlight their performance in a METIS- like AO system. We focus on FEWHA (Finite Element-Wavelet Hybrid Algorithm), Poke Matrix Inversion using a set of predefined DM influence functions and new methods for a direct segment piston estimation in combination with the P-CuReD (Preprocessed Cumulative Reconstructor with Domain decomposition). The results are backed up by Octopus (the full AO end-to-end simulator from ESO) simulations highlighting stable Strehl ratios for our simulation setting.

Efficient reconstruction method for ground layer adaptive optics with mixed natural and laser guide stars.

The imaging quality of modern ground-based telescopes such as the planned European Extremely Large Telescope is affected by atmospheric turbulence. In consequence, they heavily depend on stable and high-performance adaptive optics (AO) systems. Using measurements of incoming light from guide stars, an AO system compensates for the effects of turbulence by adjusting so-called deformable mirror(s) (DMs) in real time. In this paper, we introduce a novel reconstruction method for ground layer adaptive optics. In the literature, a common approach to this problem is to use Bayesian inference in order to model the specific noise structure appearing due to spot elongation. This approach leads to large coupled systems with high computational effort. Recently, fast solvers of linear order, i.e., with computational complexity O(n), where n is the number of DM actuators, have emerged. However, the quality of such methods typically degrades in low flux conditions. Our key contribution is to achieve the high quality of the standard Bayesian approach while at the same time maintaining the linear order speed of the recent solvers. Our method is based on performing a separate preprocessing step before applying the cumulative reconstructor (CuReD). The efficiency and performance of the new reconstructor are demonstrated using the OCTOPUS, the official end-to-end simulation environment of the ESO for extremely large telescopes. For more specific simulations we also use the MOST toolbox.

Effects of reconstruction layer profiles on atmospheric tomography in E-ELT AO systems

In this paper, we will present new compression algorithms to determine optimal layer heights and turbulenceweights for the tomographic reconstruction in wide field AO systems. Among other approaches, a new compressionmethod based on discrete optimization of collecting atmospheric layers to subgroups is discussed. Furthermore,studies of the influence of layer heights and c2n-profiles on the reconstruction quality for differentreconstruction algorithms and atmospheric profiles will be shown. Our comparison suggests that reconstructionson fewer atmospheric layers yield comparable quality with lower computational effort, if an appropriatecompression algorithm is used. The numerical results were obtained on the ESO end-to-end simulation toolOCTOPUS.