Theoretical Limits on Extrasolar Terrestrial Planet Detection with Coronagraphs

Abstract

Many high-contrast coronagraph designs have recently been proposed. In this paper, their suitability for direct imaging of extrasolar terrestrial planets is reviewed. We also develop a linear algebra based model of coronagraphy that can both explain the behavior of existing coronagraphs and quantify the coronagraphic performance limit imposed by fundamental physics. We find that the maximum theoretical throughput of a coronagraph is equal to 1 minus the nonaberrated noncoronagraphic PSF of the telescope. We describe how a coronagraph reaching this fundamental limit may be designed, and how much improvement over the best existing coronagraph design is still possible. Both the analytical model and numerical simulations of existing designs also show that this theoretical limit rapidly degrades as the source size is increased: the ''highest performance'' coronagraphs, those with the highest throughput and smallest inner working angle (IWA), are the most sensitive to stellar angular diameter. This unfortunately rules out the possibility of using a small IWA (<k/d) coronagraph for a terrestrial planet imaging mission. Finally, a detailed numerical simulation that accurately accounts for stellar angular size, zodiacal and exozodiacal light is used to quantify the efficiency of coronagraph designs for direct imaging of extrasolar terrestrial planets in a possible real observing program. We find that in the photon noiseYlimited regime, a 4 m telescope with a theoretically optimal coronagraph is able to detect Earth-like planets around 50 stars with 1 hr exposure time per target (assuming 25% throughput and exozodi levels similar to our solar system). We also show that at least two existing coronagraph design can approach this level of performance in the ideal monochromatic case considered in this study.

Optical Vectorial Vortex Coronagraphs using Liquid Crystal Polymers: theory, manufacturing and laboratory demonstration

“…The optical vortex coronagraph family is a promising and nearly ideal phase mask solution, proposed almost concurrently by [4] and [5], and confirmed later in [1]. An optical vortex is a phase singularity in an optical field, a point of zero intensity, resulting from a phase screw dislocation of the form e ilθ , with l being the so-called topological charge 1 , and θ the azimuthal coordinate.…”

“…A number of new optimized coronagraph concepts has been considered for dedicated exoplanet-finding projects at both ground-and space-based observatories (see the rather exhaustive survey of [1]). Four groups of coronagraphs can be identified.…”

“…An optical vortex is a phase singularity in an optical field, a point of zero intensity, resulting from a phase screw dislocation of the form e ilθ , with l being the so-called topological charge 1 , and θ the azimuthal coordinate. This anomaly forces the intensity to vanish by a total destructive interference, creating a dark core.…”

Observing Faint Companions Close to Bright Stars

“…In the imaging area, these include extreme adaptive optics wavefront correction, including non-common-path speckle reduction with phase retrieval algorithms , novel coronagraphs with small inner working angles (Guyon et al 2006), and new data reduction methods, such as the locally optimized combination of images (LOCI) algorithm (Lafreniere et al 2007). Regarding interferometry, deeper nulls can be measured by employing fiber optic beam combiners (Haguenauer and Serabyn 2006), and by carrying out a statistical analysis of the measured null depth fluctuations .…”

Adaptive Optics in High-Contrast Imaging

“…The state-of-the-art designs are reviewed in [34] and more recently in [35]. They can be sorted between amplitude masks and phase masks, whether they act on the ampitude or the phase of the wavefront, or between focal and pupil masks, wether they are located in a pupil or in a focal plane.…”