Linear systems modeling of adaptive optics in the spatial-frequency domain

Performance evaluation of ground layer adaptive optics based on layer correction efficiency

Ground layer adaptive optics (GLAO) has been widely employed in wide-field observations with ground-based telescopes. However, the present evaluation of GLAO performance lacks a criterion in terms of turbulence layer correction. This deficiency results in a significant gap in understanding the effectiveness of GLAO correction at different heights of the turbulence layer, thereby hindering the optimization of GLAO system performance. To bridge this gap, this Letter introduces a new, to the best of our knowledge, performance criterion for GLAO, termed layer correction efficiency (LCE). This criterion is formulated to quantify the effective compensation of the GLAO system for a specific altitude layer of turbulence, providing support for the further enhancement of GLAO performance. The simulation results indicate that the LCE has high applicability in GLAO performance analysis.

FAST: Fourier domain adaptive optics simulation tool for bidirectional ground-space optical links through atmospheric turbulence

Free space optical links between the ground and space may be severely degraded by atmospheric turbulence. Adaptive Optics, a technique allowing partial correction of this degradation, is beginning to see use in the field with the potential to achieve more robust and higher bandwidth links. Here we present a simulation tool, FAST, which utilises an analytical Fourier domain Adaptive Optics model developed for astronomy. Using the reciprocity principle, the simulation may be applied either to downlink post-compensated or uplink pre-compensated beams. We show that FAST gives similar results to full end-to-end simulations with wave-optical propagation whilst being between 10 and 200 times faster, enabling the characterisation of optical links with complex Adaptive Optics systems in timely fashion.

Spatiotemporal statistics of the turbulent piston-removed phase and Zernike coefficients for two distinct beams

In the context of adaptive optics for astronomy, one can rely on the statistics of the turbulent phase to assess a part of the system's performance. Temporal statistics with one source and spatial statistics with two sources are well known and widely used for classical adaptive optics systems. A more general framework, including both spatial and temporal statistics, can be useful for analysis of the existing systems and to support the design of future ones. In this paper, we propose an expression of the temporal cross power spectral densities of turbulent phases in two distinct beams, which is from two different sources to two different apertures. We consider the phase either as it is, without a piston, or as its decomposition on Zernike modes. The general formulas allow coverage of a wide variety of configurations, from single-aperture to interferometric telescopes equipped with adaptive optics, with the possibility to consider apertures of different sizes and/or sources at a finite distance. The presented approach should lead to similar results with respect to existing methods in the Fourier domain, but it is focused on temporal frequencies rather than spatial ones, which might be convenient for some aspects such as control optimization. To illustrate this framework with a simple application, we demonstrate that the wavefront residual due to the anisoplanatism error in a single-conjugated adaptive optics system is overestimated when it is computed from covariances without taking into account the temporal filtering of the adaptive optics loop. We also show this overestimation in the case of a small-baseline interferometer, for which the two beams are significantly correlated.

Impact of CMOS Pixel and Electronic Circuitry in the Performance of a Hartmann-Shack Wavefront Sensor

This work presents a numerical simulation of a Hartmann-Shack wavefront sensor (WFS) that assesses the impact of integrated electronic circuitry on the sensor performance, by evaluating a full detection chain encompassing wavefront sampling, photodetection, electronic circuitry and wavefront reconstruction. This platform links dedicated C algorithms for WFS to a SPICE circuit simulator for integrated electronics. The complete codes can be easily replaced in order to represent different detection or reconstruction methods, while the circuit simulator employs reliable models of either off-the-shelf circuit components or custom integrated circuit modules. The most relevant role of this platform is to enable the evaluation of the applicability and constraints of the focal plane of a given wavefront sensor prior to the actual fabrication of the detector chip. In this paper, we will present the simulation results for a Hartmann-Shack wavefront sensor with an orthogonal array of quad-cells (QC) integrated along with active-pixel (active-pixel sensor (APS)) circuitry and analog-to-digital converters (ADC) on a “complementary metal oxide semiconductor” (CMOS) process and deploying a modal wavefront reconstructor. This extended simulation capability for wavefront sensors enables the test and verification of different photosensitive and circuitry topologies for position-sensitive detectors combined with the simulation of sampling microlenses and reconstruction algorithms, with the goal of enhancing the accuracy in the prediction of the wavefront-sensor performance before a detector CMOS chip is actually fabricated.

Linear controller error budget assessment for classical adaptive optics systems

Understanding limitations of adaptive optics (AO) systems is crucial when designing new systems. In particular, analyzing the potential of different controllers is of great interest for the upcoming AO systems of the very large telescopes (VLTs) and extremely large telescopes (ELTs). This paper thus details a complete error budget assessment formalism, based on analytic formulas involving the disturbance temporal power spectral density (PSD) and the controller transfer function, and is applicable to any linear controller. This formalism is presented here for the special case of classical AO systems, but can be extended to any closed- or open-loop, single- or multi-conjugated AO configuration. Special attention is paid to the "control-dependent" errors, the importance of which is directly related to the type of control used in the AO system. The proposed method is applied to a NAOS/VLT-type single conjugated AO system, using disturbance PSD derived from a simulated turbulence trajectory or estimated from wavefront sensor measurements, enabling the construction of detailed error budgets for an integrator and different linear quadratic Gaussian controllers. Application to ELT-sized systems is discussed in the conclusion.

Modeling astronomical adaptive optics performance with temporally filtered Wiener reconstruction of slope data

We build on a long-standing tradition in astronomical adaptive optics (AO) of specifying performance metrics and error budgets using linear systems modeling in the spatial-frequency domain. Our goal is to provide a comprehensive tool for the calculation of error budgets in terms of residual temporally filtered phase power spectral densities and variances. In addition, the fast simulation of AO-corrected point spread functions (PSFs) provided by this method can be used as inputs for simulations of science observations with next-generation instruments and telescopes, in particular to predict post-coronagraphic contrast improvements for planet finder systems. We extend the previous results presented in Correia and Teixeira [J. Opt. Soc. Am. A31, 2763 (2014)JOAOD60740-323210.1364/JOSAA.31.002763] to the closed-loop case with predictive controllers and generalize the analytical modeling of Rigaut et al. [Proc. SPIE3353, 1038 (1998)PSISDG0277-786X10.1117/12.321649], Flicker [Technical Report (W. M. Keck Observatory, 2007)], and Jolissaint [J. Eur. Opt. Soc.5, 10055 (2010)1990-257310.2971/jeos.2010.10055]. We follow closely the developments of Ellerbroek [J. Opt. Soc. Am. A22, 310 (2005)JOAOD60740-323210.1364/JOSAA.22.000310] and propose the synthesis of a distributed Kalman filter to mitigate both aniso-servo-lag and aliasing errors while minimizing the overall residual variance. We discuss applications to (i) analytic AO-corrected PSF modeling in the spatial-frequency domain, (ii) post-coronagraphic contrast enhancement, (iii) filter optimization for real-time wavefront reconstruction, and (iv) PSF reconstruction from system telemetry. Under perfect knowledge of wind velocities, we show that ∼60  nm rms error reduction can be achieved with the distributed Kalman filter embodying antialiasing reconstructors on 10 m class high-order AO systems, leading to contrast improvement factors of up to three orders of magnitude at few λ/D separations (∼1-5λ/D) for a 0 magnitude star and reaching close to one order of magnitude for a 12 magnitude star.

Anti-aliasing Wiener filtering for wave-front reconstruction in the spatial-frequency domain for high-order astronomical adaptive-optics systems

Computationally efficient wave-front reconstruction techniques for astronomical adaptive-optics (AO) systems have seen great development in the past decade. Algorithms developed in the spatial-frequency (Fourier) domain have gathered much attention, especially for high-contrast imaging systems. In this paper we present the Wiener filter (resulting in the maximization of the Strehl ratio) and further develop formulae for the anti-aliasing (AA) Wiener filter that optimally takes into account high-order wave-front terms folded in-band during the sensing (i.e., discrete sampling) process. We employ a continuous spatial-frequency representation for the forward measurement operators and derive the Wiener filter when aliasing is explicitly taken into account. We further investigate and compare to classical estimates using least-squares filters the reconstructed wave-front, measurement noise, and aliasing propagation coefficients as a function of the system order. Regarding high-contrast systems, we provide achievable performance results as a function of an ensemble of forward models for the Shack-Hartmann wave-front sensor (using sparse and nonsparse representations) and compute point-spread-function raw intensities. We find that for a 32×32 single-conjugated AOs system the aliasing propagation coefficient is roughly 60% of the least-squares filters, whereas the noise propagation is around 80%. Contrast improvements of factors of up to 2 are achievable across the field in the H band. For current and next-generation high-contrast imagers, despite better aliasing mitigation, AA Wiener filtering cannot be used as a standalone method and must therefore be used in combination with optical spatial filters deployed before image formation actually takes place.

Solar tomography adaptive optics

Conventional solar adaptive optics uses one deformable mirror (DM) and one guide star for wave-front sensing, which seriously limits high-resolution imaging over a large field of view (FOV). Recent progress toward multiconjugate adaptive optics indicates that atmosphere turbulence induced wave-front distortion at different altitudes can be reconstructed by using multiple guide stars. To maximize the performance over a large FOV, we propose a solar tomography adaptive optics (TAO) system that uses tomographic wave-front information and uses one DM. We show that by fully taking advantage of the knowledge of three-dimensional wave-front distribution, a classical solar adaptive optics with one DM can provide an extra performance gain for high-resolution imaging over a large FOV in the near infrared. The TAO will allow existing one-deformable-mirror solar adaptive optics to deliver better performance over a large FOV for high-resolution magnetic field investigation, where solar activities occur in a two-dimensional field up to 60'', and where the near infrared is superior to the visible in terms of magnetic field sensitivity.

Tomographic reconstruction for wide-field adaptive optics systems: Fourier domain analysis and fundamental limitations

Several wide-field-of-view adaptive optics (WFAO) concepts such as multi-conjugate AO (MCAO), multi-object AO (MOAO), and ground-layer AO (GLAO) are currently being studied for the next generation of Extremely Large Telescopes (ELTs). All these concepts will use atmospheric tomography to reconstruct the turbulent-phase volume. In this paper, we explore different reconstruction algorithms and their fundamental limitations, conducting this analysis in the Fourier domain. This approach allows us to derive simple analytical formulations for the different configurations and brings a comprehensive view of WFAO limitations. We then investigate model and statistical errors and their effect on the phase reconstruction. Finally, we show some examples of different WFAO systems and their expected performance on a 42 m telescope case.

Adaptive optics sky coverage modeling for extremely large telescopes

A Monte Carlo sky coverage model for laser guide star adaptive optics systems was proposed by Clare and Ellerbroek [J. Opt. Soc. Am. A 23, 418 (2006)]. We refine the model to include (i) natural guide star (NGS) statistics using published star count models, (ii) noise on the NGS measurements, (iii) the effect of telescope wind shake, (iv) a model for how the Strehl and hence NGS wavefront sensor measurement noise varies across the field, (v) the focus error due to imperfectly tracking the range to the sodium layer, (vi) the mechanical bandwidths of the tip-tilt (TT) stage and deformable mirror actuators, and (vii) temporal filtering of the NGS measurements to balance errors due to noise and servo lag. From this model, we are able to generate a TT error budget for the Thirty Meter Telescope facility narrow-field infrared adaptive optics system (NFIRAOS) and perform several design trade studies. With the current NFIRAOS design, the median TT error at the galactic pole with median seeing is calculated to be 65 nm or 1.8 mas rms.

Optimal Fourier control performance and speckle behavior in high-contrast imaging with adaptive optics

High-contrast imaging with adaptive optics (AO) for planet detection requires a sophisticated AO control system to provide the best possible performance. We evaluate the performance improvements in terms of residual error and point-spread function intensity provided by optimal Fourier control using detailed end-to-end simulation. Intensity, however, is not the final measure of system performance. We explore image contrast through analysis and simulation results, showing that speckles caused by atmospheric errors behave very differently in a temporal fashion from speckles caused by wavefront sensor noise errors.

Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography

By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty.

Analytical modeling of adaptive optics: foundations of the phase spatial power spectrum approach

End-to-end simulation of adaptive optics (AO) systems allows high-fidelity modeling of system performance, but at the cost of long computation time. Analytical modeling, on the other hand, can provide much faster first-order performance estimates for a rapid exploration of the AO parameter space. In this paper, we present the foundations of a modeling method for the AO optical transfer function, based on an analytical description of the residual phase spatial power spectrum. The method has been implemented in an IDL-based code, PAOLA, and comparison with end-to-end simulations demonstrates the validity of the analytical approach.