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Register a new userPhase-Induced Amplitude Apodization of Telescope Pupils for Extrasolar Terrestrial Planet Imaging
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Olivier Guyon
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In this paper, an alternative to the classical pupil apodization techniques (use of an amplitude pupil mask) is proposed. It is shown that an apodized pupil suitable for imaging of Extrasolar planets can be obtained by reflection of an unapodized flat wavefront on 2 mirrors. By carefully choosing the shape of these 2 mirrors, it is possible to obtain a contrast better than 10^{9} at a distance smaller than 2 lambda/d from the optical axis. Because this technique preserves both the angular resolution and light gathering capabilities of the unapodized pupil, it allows efficient detection of terrestrial extrasolar planets with a 1.5m telescope in the visible.
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One of two approaches to implementing NASAs Terrestrial Planet Finder is to build a space telescope that utilizes the techniques of coronagraphy and apodization to suppress diffraction and image exo-planets. We present a method for calculation of a telescopes apodizer which suppresses the side lobes of the image of a star so as to optimally detect an Earth-like planet. Given the shape of a telescopes aperture and given a search region for a detector, we solve an integral equation to determine an amplitude modulation (an apodizer) which suppresses the stars energy in the focal plane search region. The method is quite general and yields as special cases the product apodizer reported by Nisenson and Papaliolios (2001) and the Prolate spheroidal apodizer of Kasdin et al (2002), and Aime et al (2002). We show computer simulations of the apodizers and the corresponding point spread functions for various aperture-detector configurations.
Phase apodization coronagraphs are implemented in a pupil plane to create a dark hole in the science camera focal plane. They are successfully created as Apodizing Phase Plates (APPs) using classical optical manufacturing, and as vector-APPs using liquid-crystal patterning with essentially achromatic performance. This type of coronagraph currently delivers excellent broadband contrast ($sim$10$^{-5}$) at small angular separations (few $lambda/D$) at ground-based telescopes, owing to their insensitivity to tip/tilt errors.
A set of pupil apodization functions for use with a vortex coronagraph on telescopes with obscured apertures is presented. We show analytically that pupil amplitudes given by real-valued Zernike polynomials offer ideal on-axis starlight cancellation when applied to unobscured circular apertures. The charge of the vortex phase element must be a nonzero even integer, greater than the sum of the degree and the absolute value of its azimuthal order of the Zernike polynomial. Zero-valued lines and points of Zernike polynomials, or linear combinations thereof, can be matched to obstructions in the pupils of ground-based telescopes to improve the contrast achieved by a vortex coronagraph. This approach works well in the presence of a central obscuration and radial support structures. We analyze the contrast, off-axis throughput, and post-coronagraph point spread functions of an apodized vortex coronagraph designed for the European Extremely Large Telescope (E-ELT). This technique offers very good performance on apertures with large obscuring support structures similar to those on future 30-40m class ground-based telescopes.
As the performance of coronagraphs improves, the achievable contrast is more and more dependent of the shape of the pupil. The future generation of space and ground based coronagraphic instruments will have to achieve high contrast levels on on-axis and/or segmented telescopes. To correct for the high amplitude aberrations introduced by secondary mirror structures and segmentation of the primary mirror, we explore a two deformable mirror (DM) method. The major difficulty of several DM methods is the non-linear relation linking actuator strokes to the point spread function in the coronagraph focal plane. The Active Compensation of Aperture Discontinuities (ACAD) method is achieving this minimization by solving a non linear differential Monge Ampere equation. Once this open loop method have reached the minimum, a close-loop stroke minimization method can be applied to correct for phase and amplitude aberrations to achieve the ultimate contrast. In this paper, I describe the results of the parametric analysis that that I have undertaken on this method. After recalling the principle of the method, I will described the explored parameter space (deformable mirror set-up, shape of the pupil, bandwidth, coronagraph designs). I will precisely described the way I simulated the Vortex coronagraph for this numerical simulation. Finally I will present the preliminary results of this parametric analysis for space telescope pupils only.
For direct imaging of exoplanets, a stellar coronagraph helps to remove the image of an observed bright star by attenuating the diffraction effects caused by the telescope aperture of diameter D. The Dual Zone Phase Mask (DZPM) coronagraph constitutes a promising concept since it theoretically offers a small inner working angle (IWA sim lambda_0/D), good achromaticity and high starlight rejection, typically reaching a 1e6 contrast at 5 lambda_0/D from the star over a spectral bandwidth Deltalambda/lambda_0 of 25% (similar to H-band). This last value proves to be encouraging for broadband imaging of young and warm Jupiter-like planets. Contrast levels higher than 1e6 are however required for the observation of older and/or less massive companions over a finite spectral bandwidth. An achromatization improvement of the DZPM coronagraph is therefore mandatory to reach such performance. In its design, the DZPM coronagraph uses a grey (or achromatic) apodization. We propose to replace it by a colored apodization to increase the performance of this coronagraphic system over a large spectral range. This innovative concept, called Colored Apodizer Phase Mask (CAPM) coronagraph, is defined with some design parameters optimized to reach the best contrast in the exoplanet search area. Once this done, we study the performance of the CAPM coronagraph in the presence of different errors to evaluate the sensitivity of our concept. A 2.5 mag contrast gain is estimated from the performance provided by the CAPM coronagraph with respect to that of the DZPM coronagraph. A 2.2e-8 intensity level at 5 lambda_0/D separation is then theoretically achieved with the CAPM coronagraph in the presence of a clear circular aperture and a 25% bandwidth. In addition, our studies show that our concept is less sensitive to low than high-order aberrations for a given value of rms wavefront errors.
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