The achromatic chessboard, a new concept of a phase shifter for nulling interferometry

II. Theoretical performance assessment

¹ LUTH, Observatoire de Paris, CNRS, Université Paris Diderot, 92190 Meudon, France
e-mail: didier.pelat@obspm.fr
² LESIA, Observatoire de Paris, CNRS, UPMC, Université Paris Diderot, 5 place Jules Janssen, 92190 Meudon, France
e-mail: daniel.rouan@obspm.fr; damien.pickel@obspm.fr

Received: 4 May 2010
Accepted: 11 August 2010

Abstract

Context. Nulling interferometry in the mid-IR using two telescopes (commonly referred to a Bracewell interferometer) is one possible way of directly detecting exoplanets in the habitable zone and their characterisation in terms of possible life signatures. A large wavelength domain is needed to simultaneously detect the infrared spectral features of a set of a bio-tracers. An achromatic phase shift of π is then required, and we previously presented a new concept for such a function that allows a simple design with only one device per beam. It is based on two cellular mirrors, called the chessboards, where each cell has a thickness that introduces, for any given central wavelength, a phase shift of (2k + 1)π or of 2kπ on the fraction of the wave it reflects.

Aims. We explore a more rigorous way to establish the optimum cell pattern design to attain the best theoretical performances for planet detection over a broad wavelength range. Two possible types of interferometres are now considered: on-axis and multi-axis.

Methods. We derived a rather simple iterative scheme for both designs, determining the thickness and XY position of the cells. The method confers to the chessboards a high degree of internal symmetry. Each design can be described as an iterative Bracewell interferometer characterised by an integer order. We demonstrate that their efficiencies increases with the power of that order.

Results. The device acts both spatially and versus wavelengths as an optical differential operator on the 3D light distribution. Its power is best understood in the on-axis case since its effect is topush awaythe stellar light from the centre over a very broad range of wavelengths, leaving space for anout of phase object to appear in the cleaned central region. We explore the theoretical performances for on-axis and multi-axis designs in the parameter space, and we especially compute the rejection factor for starlight and the attenuation factor for planet light and introduce the relative nulling efficiency metric. We show that, even with some realistic piston error added, the performances could meet the Darwin space project specifications for both designs, i.e., cancellation of the starlight by a factor of 10⁵ over a wavelength range of 6–17 μm.