Phasing segmented telescopes via deep learning methods: application to a deployable CubeSat.

Capturing high-resolution imagery of the Earth's surface often calls for a telescope of considerable size, even from low Earth orbits (LEOs). A large aperture often requires large and expensive platforms. For instance, achieving a resolution of 1 m at visible wavelengths from LEO typically requires an aperture diameter of at least 30 cm. Additionally, ensuring high revisit times often prompts the use of multiple satellites. In light of these challenges, a small, segmented, deployable CubeSat telescope was recently proposed creating the additional need of phasing the telescope's mirrors. Phasing methods on compact platforms are constrained by the limited volume and power available, excluding solutions that rely on dedicated hardware or demand substantial computational resources. Neural networks (NNs) are known for their computationally efficient inference and reduced onboard requirements. Therefore, we developed a NN-based method to measure co-phasing errors inherent to a deployable telescope. The proposed technique demonstrates its ability to detect phasing errors at the targeted performance level [typically a wavefront error (WFE) below 15 nm RMS for a visible imager operating at the diffraction limit] using a point source. The robustness of the NN method is verified in presence of high-order aberrations or noise and the results are compared against existing state-of-the-art techniques. The developed NN model ensures its feasibility and provides a realistic pathway towards achieving diffraction-limited images.

Feasibility demonstration of AO pre-compensation for GEO feeder links in a relevant environment.

Optical technologies are extremely competitive candidates to achieve very-high throughput links between ground and GEO satellites; however, their feasibility relies on the ability to mitigate channel impairments due to atmospheric turbulence. For that purpose, Adaptive Optics (AO) has already proved to be highly efficient on the downlink. However, for the uplink, anisoplanatism induced by point-ahead angle (PAA) compromises AO pre-compensation efficiency to an extent that depends on propagation conditions. The ability to properly assess the anisoplanatism impact in a wide variety of conditions is thus critical in designing the optical ground terminals. In this paper, we demonstrate the consistency of experimental coupled flux statistics with results coming from performance and end-to-end models, on an AO pre-compensated 13 km slant path in Tenerife. This validation is demonstrated in a wide variety of turbulence conditions, hence consolidating propagation channel models that are of critical importance for the reliability of future GEO feeder links. We then compare experimental results to theoretical on-sky performance, and discuss to what extent such slant path or horizontal path experiments can be representative of real GEO links.

Kernel formalism applied to Fourier-based wave-front sensing in presence of residual phases.

In this paper, we describe Fourier-based wave-front sensors (WFSs) as linear integral operators, characterized by their kernel. In the first part, we derive the dependency of this quantity with respect to the WFS's optical parameters: pupil geometry, filtering mask, and tip/tilt modulation. In the 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 WFS model by summarizing its behavior in a concise and comprehensive quantity called the WFS impulse response. We explain in particular how it allows to compute the sensor's sensitivity with respect to spatial frequencies. Such an approach therefore provides a fast diagnostic tool to compare and optimize Fourier-based WFSs. In the third part, we develop the impact of the residual phases on the sensor's 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 slope maps are easily handled by the convolutional model.

Terahertz adaptive optics with a deformable mirror.

We report on the wavefront correction of a terahertz (THz) beam using adaptive optics, which requires both a wavefront sensor that is able to sense the optical aberrations, as well as a wavefront corrector. The wavefront sensor relies on a direct 2D electro-optic imaging system composed of a ZnTe crystal and a CMOS camera. By measuring the phase variation of the THz electric field in the crystal, we were able to minimize the geometrical aberrations of the beam, thanks to the action of a deformable mirror. This phase control will open the route to THz adaptive optics in order to optimize the THz beam quality for both practical and fundamental applications.

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.

Iterative wave-front reconstruction in the Fourier domain.

The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40×40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.

Fast-moving features in the debris disk around AU Microscopii.

In the 1980s, excess infrared emission was discovered around main-sequence stars; subsequent direct-imaging observations revealed orbiting disks of cold dust to be the source. These 'debris disks' were thought to be by-products of planet formation because they often exhibited morphological and brightness asymmetries that may result from gravitational perturbation by planets. This was proved to be true for the ß Pictoris system, in which the known planet generates an observable warp in the disk. The nearby, young, unusually active late-type star AU Microscopii hosts a well-studied edge-on debris disk; earlier observations in the visible and near-infrared found asymmetric localized structures in the form of intensity variations along the midplane of the disk beyond a distance of 20 astronomical units. Here we report high-contrast imaging that reveals a series of five large-scale features in the southeast side of the disk, at projected separations of 10-60 astronomical units, persisting over intervals of 1-4 years. All these features appear to move away from the star at projected speeds of 4-10 kilometres per second, suggesting highly eccentric or unbound trajectories if they are associated with physical entities. The origin, localization, morphology and rapid evolution of these features are difficult to reconcile with current theories.

Variation around a pyramid theme: optical recombination and optimal use of photons.

We propose a new type of wave-front sensor (WFS) derived from the pyramid WFS (PWFS). This new WFS, called the flattened pyramid-WFS (FPWFS), has a reduced pyramid angle in order to optically overlap the four pupil images into an unique intensity. This map is then used to derive the phase information. In this Letter, this new WFS is compared to three existing WFSs, namely the PWFS, the modulated PWFS (MPWFS), and the Zernike WFS (ZWFS) following tests about sensitivity, linearity range, and low-photon-flux behavior. The FPWFS turns out to be more linear than a modulated pyramid for the high-spatial order aberrations, but it provides an improved sensitivity compared to the non-modulated pyramid. The noise propagation may even be as low as the ZWFS for some given radial orders. Furthermore, the pixel arrangement being more efficient than for the PWFS, the FPWFS seems particularly well suited for high-contrast applications.

Optimal method for exoplanet detection by angular differential imaging.

We propose a novel method for the efficient direct detection of exoplanets from the ground using angular differential imaging. The method combines images appropriately, then uses the combined images jointly in a maximum-likelihood framework to estimate the position and intensity of potential planets orbiting the observed star. It takes into account the mixture of photon and detector noises and a positivity constraint on the planet's intensity. A reasonable detection criterion is also proposed based on the computation of the noise propagation from the images to the estimated intensity of the potential planet. The implementation of this method is tested on simulated data that take into account static aberrations before and after the coronagraph, residual turbulence after adaptive optics correction, and noise.

Calibration and precompensation of noncommon path aberrations for extreme adaptive optics.

Noncommon path aberrations (NCPAs) are one of the main limitations of an extreme adaptive optics (AO) system. NCPAs prevent extreme AO systems from achieving their ultimate performance. These static aberrations are unseen by the wavefront sensor and therefore are not corrected in closed loop. We present experimental results validating what we believe to be new procedures of measurement and precompensation of the NCPAs on the AO bench at ONERA (Office National d'Etudes et de Recherches Aérospatiales). The measurement procedure is based on refined algorithms of phase diversity. The precompensation procedure makes use of a pseudo-closed-loop scheme to overcome the AO wavefront-sensor-model uncertainties. Strehl ratio obtained in the images reaches 98.7% at 632.8 nm. This result allows us to be confident of achieving the challenging performance required for direct observation of extrasolar planets.