Fast Fourier Optimization: Sparsity Matters

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier transform} (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursive, it is difficult to embed into a linear optimization problem. In this paper, we explain the main idea behind the fast Fourier transform and show how to adapt it in such a manner as to make it encodable as constraints in an optimization problem. We demonstrate a real-world problem from the field of high-contrast imaging. On this problem, dramatic improvements are translated to an ability to solve problems with a much finer grid of discretized points. As we shall show, in general, the "fast Fourier" version of the optimization constraints produces a larger but sparser constraint matrix and therefore one can think of the fast Fourier transform as a method of sparsifying the constraints in an optimization problem, which is usually a good thing.Comment: 16 pages, 8 figure

Laboratory validation of the dual-zone phase mask coronagraph in broadband light at the high-contrast imaging THD-testbed

Specific high contrast imaging instruments are mandatory to characterize circumstellar disks and exoplanets around nearby stars. Coronagraphs are commonly used in these facilities to reject the diffracted light of an observed star and enable the direct imaging and spectroscopy of its circumstellar environment. One important property of the coronagraph is to be able to work in broadband light. Among several proposed coronagraphs, the dual-zone phase mask coronagraph is a promising solution for starlight rejection in broadband light. In this paper, we perform the first validation of this concept in laboratory. First, we recall the principle of the dual-zone phase mask coronagraph. Then, we describe the high-contrast imaging THD testbed, the manufacturing of the components and the quality-control procedures. Finally, we study the sensitivity of our coronagraph to low-order aberrations (inner working angle and defocus) and estimate its contrast performance. Our experimental broadband light results are compared with numerical simulations to check agreement with the performance predictions. With the manufactured prototype and using a dark hole technique based on the self-coherent camera, we obtain contrast levels down to $2\,10^{-8}$ between 5 and 17$\,\lambda_0/D$ in monochromatic light (640 nm). We also reach contrast levels of $4\,10^{-8}$ between 7 and 17$\lambda_0/D$ in broadband ($\lambda_0=675$ nm, $\Delta\lambda=250$ nm and $\Delta\lambda / \lambda_0 = 40$ %), which demonstrates the excellent chromatic performance of the dual-zone phase mask coronagraph. The performance reached by the dual-zone phase mask coronagraph is promising for future high-contrast imaging instruments that aim at detecting and spectrally characterizing old or light gaseous planets.Comment: 9 pages, 16 figure

Apodized Pupil Lyot Coronagraphs for Arbitrary Telescope Apertures

In the context of high dynamic range imaging, this study presents a breakthrough for the understanding of Apodized Pupil Lyot Coronagraphs, making them available for arbitrary aperture shapes. These new solutions find immediate application in current, ground-based coronagraphic studies (Gemini, VLT) and in existing instruments (AEOS Lyot Project). They also offer the possiblity of a search for an on-axis design for TPF. The unobstructed aperture case has already been solved by Aime et al. (2002) and Soummer et al. (2003). Analytical solutions with identical properties exist in the general case and, in particular, for centrally obscured apertures. Chromatic effects can be mitigated with a numerical optimization. The combination of analytical and numerical solutions enables the study of the complete parameter space (central obstruction, apodization throughput, mask size, bandwidth, and Lyot stop size).Comment: 7 pages 4 figures - ApJL, accepte

Adaptive optics in high-contrast imaging

The development of adaptive optics (AO) played a major role in modern astronomy over the last three decades. By compensating for the atmospheric turbulence, these systems enable to reach the diffraction limit on large telescopes. In this review, we will focus on high contrast applications of adaptive optics, namely, imaging the close vicinity of bright stellar objects and revealing regions otherwise hidden within the turbulent halo of the atmosphere to look for objects with a contrast ratio lower than 10^-4 with respect to the central star. Such high-contrast AO-corrected observations have led to fundamental results in our current understanding of planetary formation and evolution as well as stellar evolution. AO systems equipped three generations of instruments, from the first pioneering experiments in the nineties, to the first wave of instruments on 8m-class telescopes in the years 2000, and finally to the extreme AO systems that have recently started operations. Along with high-contrast techniques, AO enables to reveal the circumstellar environment: massive protoplanetary disks featuring spiral arms, gaps or other asymmetries hinting at on-going planet formation, young giant planets shining in thermal emission, or tenuous debris disks and micron-sized dust leftover from collisions in massive asteroid-belt analogs. After introducing the science case and technical requirements, we will review the architecture of standard and extreme AO systems, before presenting a few selected science highlights obtained with recent AO instruments.Comment: 24 pages, 14 figure

Multi-stage four-quadrant phase mask: achromatic coronagraph for space-based and ground-based telescopes

Less than 3% of the known exoplanets were directly imaged for two main reasons. They are angularly very close to their parent star, which is several magnitudes brighter. Direct imaging of exoplanets thus requires a dedicated instrumentation with large telescopes and accurate wavefront control devices for high-angular resolution and coronagraphs for attenuating the stellar light. Coronagraphs are usually chromatic and they cannot perform high-contrast imaging over a wide spectral bandwidth. That chromaticity will be critical for future instruments. Enlarging the coronagraph spectral range is a challenge for future exoplanet imaging instruments on both space-based and ground-based telescopes. We propose the multi-stage four-quadrant phase mask that associates several monochromatic four-quadrant phase mask coronagraphs in series. Monochromatic device performance has already been demonstrated and the manufacturing procedures are well-under control since their development for previous instruments on VLT and JWST. The multi-stage implementation simplicity is thus appealing. We present the instrument principle and we describe the laboratory performance for large spectral bandwidths and for both pupil shapes for space- (off-axis telescope) and ground-based (E-ELT) telescopes. The multi-stage four-quadrant phase mask reduces the stellar flux over a wide spectral range (30%) and it is a very good candidate to be associated with a spectrometer for future exoplanet imaging instruments in ground- and space-based observatories.Comment: 7 pages, 11 figures, 4 tables, accepted in A&

The Solar-System-Scale Disk Around AB Aurigae

The young star AB Aurigae is surrounded by a complex combination of gas-rich and dust dominated structures. The inner disk which has not been studied previously at sufficient resolution and imaging dynamic range seems to contain very little gas inside a radius of least 130 astronomical units (AU) from the star. Using adaptive-optics coronagraphy and polarimetry we have imaged the dust in an annulus between 43 and 302 AU from the star, a region never seen before. An azimuthal gap in an annulus of dust at a radius of 102 AU, along with a clearing at closer radii inside this annulus, suggests the formation of at least one small body at an orbital distance of about 100 AU. This structure seems consistent with crude models of mean motion resonances, or accumulation of material at two of the Lagrange points relative to the putative object and the star. We also report a low significance detection of a point source in this outer annulus of dust. This source may be an overdensity in the disk due to dust accreting onto an unseen companion. An alternate interpretation suggests that the object's mass is between 5 and 37 times the mass of Jupiter. The results have implications for circumstellar disk dynamics and planet formation.Comment: 11 pages, 5 figures, accepted for publication in Astrophysical Journal, V. 680, June 10, 200

The Lyot Project Direct Imaging Survey of Substellar Companions: Statistical Analysis and Information from Nondetections

The Lyot project used an optimized Lyot coronagraph with Extreme Adaptive Optics at the 3.63m Advanced Electro-Optical System telescope (AEOS) to observe 86 stars from 2004 to 2007. In this paper we give an overview of the survey results and a statistical analysis of the observed nondetections around 58 of our targets to place constraints on the population of substellar companions to nearby stars. The observations did not detect any companion in the substellar regime. Since null results can be as important as detections, we analyzed each observation to determine the characteristics of the companions that can be ruled out. For this purpose we use a Monte Carlo approach to produce artificial companions, and determine their detectability by comparison with the sensitivity curve for each star. All the non-detection results are combined using a Bayesian approach and we provide upper limits on the population of giant exoplanets and brown dwarfs for this sample of stars. Our nondetections confirm the rarity of brown dwarfs around solar-like stars and we constrain the frequency of massive substellar companions (M>40Mjup) at orbital separation between and 10 and 50 AU to be <20%.Comment: 32 pages, 11 figures, 2 tables. Published in the Astrophysical Journa