For ExAO instruments for the Giant Segmented Mirror Telescopes (GSMTs), alternative architectures of WFS are under consideration because there is a tradeoff between detector size, speed, and noise that reduces the performance of GSMT-ExAO wavefront c
ontrol. One option under consideration for a GSMT-ExAO wavefront sensor is a three-sided PWFS (3PWFS). The 3PWFS creates three copies of the telescope pupil for wavefront sensing, compared to the conventional four-sided PWFS (4PWFS) which uses four pupils. The 3PWFS uses fewer detector pixels than the 4PWFS and should therefore be less sensitive to read noise. Here we develop a mathematical formalism based on the diffraction theory description of the Foucault knife edge test that predicts the intensity pattern after the PWFS. Our formalism allows us to calculate the intensity in the pupil images formed by the PWFS in the presence of phase errors corresponding to arbitrary Fourier modes. We then use the Object Oriented MATLAB Adaptive Optics toolbox (OOMAO) to simulate an end-to-end model of an adaptive optics system using a PWFS with modulation and compare the performance of the 3PWFS to the 4PWFS. In the case of a low read noise detector, the Strehl ratios of the 3PWFS and 4PWFS are within 0.01. When we included higher read noise in the simulation, we found a Strehl ratio gain of 0.036 for the 3PWFS using Raw Intensity over the 4PWFS using Slopes Maps at a stellar magnitude of 10. At the same magnitude, the 4PWFS RI also outperformed the 4PWFS SM, but the gain was only 0.012 Strehl. This is significant because 4PWFS using Slopes Maps is how the PWFS is conventionally used for AO wavefront sensing. We have found that the 3PWFS is a viable wavefront sensor that can fully reconstruct a wavefront and produce a stable closed-loop with correction comparable to that of a 4PWFS, with modestly better performance for high read-noise detectors.
We investigate the focal plane wavefront sensing technique, known as Phase Diversity, at the scientific focal plane of a segmented mirror telescope with an adaptive optics (AO) system. We specifically consider an optical system imaging a point source
in the context of (i) an artificial source within the telescope structure and (ii) from AO-corrected images of a bright star. From our simulations, we reliably disentangle segmented telescope phasing errors from non-common path aberrations (NCPA) for both a theoretical source and on-sky, AO-corrected images where we have simulated the Keck/NIRC2 system. This quantification from on-sky images is appealing, as its sensitive to the cumulative wavefront perturbations of the entire optical train; disentanglement of phasing errors and NCPA is therefore critical, where any potential correction to the primary mirror from an estimate must contain minimal NCPA contributions. Our estimates require a one-minute sequence of short-exposure, AO-corrected images; by exploiting a slight modification to the AO-loop, we find that 75 defocused images produces reliable estimates. We demonstrate a correction from our estimates to the primary and deformable mirror results in a wavefront error reduction of up to 67% and 65% for phasing errors and NCPA, respectively. If the segment phasing errors on the Keck primary are on the order of ~130 nm RMS, we show we can improve the H-band Strehl ratio by up to 10% by using our algorithm. We conclude our technique works well to estimate NCPA alone from on-sky images, suggesting it is a promising method for any AO-system.
Predictive wavefront control is an important and rapidly developing field of adaptive optics (AO). Through the prediction of future wavefront effects, the inherent AO system servo-lag caused by the measurement, computation, and application of the wav
efront correction can be significantly mitigated. This lag can impact the final delivered science image, including reduced strehl and contrast, and inhibits our ability to reliably use faint guidestars. We summarize here a novel method for training deep neural networks for predictive control based on an adversarial prior. Unlike previous methods in the literature, which have shown results based on previously generated data or for open-loop systems, we demonstrate our networks performance simulated in closed loop. Our models are able to both reduce effects induced by servo-lag and push the faint end of reliable control with natural guidestars, improving K-band Strehl performance compared to classical methods by over 55% for 16th magnitude guide stars on an 8-meter telescope. We further show that LSTM based approaches may be better suited in high-contrast scenarios where servo-lag error is most pronounced, while traditional feed forward models are better suited for high noise scenarios. Finally, we discuss future strategies for implementing our system in real-time and on astronomical telescope systems.
In this paper, we describe Fourier-based Wave Front Sensors (WFS) as linear integral operators, characterized by their Kernel. In a first part, we derive the dependency of this quantity with respect to the WFSs optical parameters: pupil geometry, fil
tering mask, tip/tilt modulation. In a second part we focus the study on the special case of convolutional Kernels. The assumptions required to be in such a regime are described. We then show that these convolutional kernels allow to drastically simplify the WFSs model by summarizing its behavior in a concise and comprehensive quantity called the WFSs Impulse Response. We explain in particular how it allows to compute the sensors sensitivity with respect to the spatial frequencies. Such an approach therefore provides a fast diagnostic tool to compare and optimize Fourier-based WFSs. In a third part, we develop the impact of the residual phases on the sensors impulse response, and show that the convolutional model remains valid. Finally, a section dedicated to the Pyramid WFS concludes this work, and illustrates how the slopes maps are easily handled by the convolutional model.
The segmentation of the telescope pupil (by spiders & the segmented M4) create areas of phase isolated by the width of the spiders on the wavefront sensor (WFS), breaking the spatial continuity of the wavefront. The poor sensitivity of the Pyramid WF
S (PWFS) to differential piston leads to badly seen and therefore uncontrollable differential pistons. In close loop operation, differential pistons between segments will settle around integer values of the average sensing wavelength. The differential pistons typically range from one to ten times the sensing wavelength and vary rapidly over time, leading to extremely poor performance. In addition, aberrations created by atmospheric turbulence will contain large amounts of differential piston between the segments. Removing piston contribution over each of the DM segments leads to poor performance. In an attempt to reduce the impact of unwanted differential pistons that are injected by the AO correction, we compare three different approaches. We first limit ourselves to only use the information measured by the PWFS, in particular by reducing the modulation. We show that using this information sensibly is important but will not be sufficient. We discuss possible ways of improvement by using prior information. A second approach is based on phase closure of the DM commands and assumes the continuity of the correction wavefront over the entire unsegmented pupil. The last approach is based on the pair-wise slaving of edge actuators and shows the best results. We compare the performance of these methods using realistic end-to-end simulations. We find that pair-wise slaving leads to a small increase of the total wavefront error, only adding between 20-45 nm RMS in quadrature for seeing conditions between 0.45-0.85 arcsec. Finally, we discuss the possibility of combining the different proposed solutions to increase robustness.
Tomographic wave-front reconstruction is the main computational bottleneck to realize real-time correction for turbulence-induced wave-front aberrations in future laser-assisted tomographic adaptive-optics (AO) systems for ground-based Giant Segmente
d Mirror Telescopes (GSMT), because of its unprecedented number of degrees of freedom, $N$, i.e. the number of measurements from wave-front sensors (WFS). In this paper, we provide an efficient implementation of the minimum-mean-square error (MMSE) tomographic wave-front reconstruction mainly useful for some classes of AO systems not requiring a multi-conjugation, such as laser-tomographic AO (LTAO), multi-object AO (MOAO) and ground-layer AO (GLAO) systems, but also applicable to multi-conjugate AO (MCAO) systems. This work expands that by R. Conan [ProcSPIE, 9148, 91480R (2014)] to the multi-wave-front, tomographic case using natural and laser guide stars. The new implementation exploits the Toeplitz structure of covariance matrices used in a MMSE reconstructor, which leads to an overall $O(Nlog N)$ real-time complexity compared to $O(N^2)$ of the original implementation using straight vector-matrix multiplication. We show that the Toeplitz-based algorithm leads to 60,nm rms wave-front error improvement for the European Extremely Large Telescope Laser-Tomography AO system over a well-known sparse-based tomographic reconstruction, but the number of iterations required for suitable performance is still beyond what a real-time system can accommodate to keep up with the time-varying turbulence
We propose and apply two methods to estimate pupil plane phase discontinuities for two realistic scenarios on VLT and Keck. The methods use both Phase Diversity and a form of image sharpening. For the case of VLT, we simulate the `low wind effect (LW
E) which is responsible for focal plane errors in the SPHERE system in low wind and good seeing conditions. We successfully estimate the simulated LWE using both methods, and show that they are complimentary to one another. We also demonstrate that single image Phase Diversity (also known as Phase Retrieval with diversity) is also capable of estimating the simulated LWE when using the natural de-focus on the SPHERE/DTTS imager. We demonstrate that Phase Diversity can estimate the LWE to within 30 nm RMS WFE, which is within the allowable tolerances to achieve a target SPHERE contrast of 10$^{-6}$. Finally, we simulate 153 nm RMS of piston errors on the mirror segments of Keck and produce NIRC2 images subject to these effects. We show that a single, diverse image with 1.5 waves (PV) of focus can be used to estimate this error to within 29 nm RMS WFE, and a perfect correction of our estimation would increase the Strehl ratio of a NIRC2 image by 12%
We use a theoretical frame-work to analytically assess temporal prediction error functions on von-Karman turbulence when a zonal representation of wave-fronts is assumed. Linear prediction models analysed include auto-regressive of order up to three,
bilinear interpolation functions and a minimum mean square error predictor. This is an extension of the authors previously published work (see ref. 2) in which the efficacy of various temporal prediction models was established. Here we examine the tolerance of these algorithms to specific forms of model errors, thus defining the expected change in behaviour of the previous results under less ideal conditions. Results show that +/- 100pc wind-speed error and +/- 50 deg are tolerable before the best linear predictor delivers poorer performance than the no-prediction case.
