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

Context. Direct detection of a planet around a star and its characterisation for identification of bio-tracers in the mid-IR requires a nulling interferometer. Such an instrument must be efficient in a large wavelength domain in order to have the capability of simultaneously detecting the infrared spectral features of several bio-tracers: CO2, O3, and H2O. Aims. A broad wavelength range can be effective provided that an achromatic phase shift of π can be implemented, with good enough accuracy to achieve a deep nulling at all considered wavelengths. A new design concept for such an achromatic phase shifter is presented here. The major interest of this solution is that it allows a simple design with only one device per beam. Methods. The heart of the system consists in two cellular mirrors where each cell has a thickness that introduces, for a given central wavelength, a phase shift of $(2k + 1)\pi$ or of $2k \pi$ on the fraction of the wave it reflects. Each mirror is put in one of the collimated beams of the interferometer. Because of the odd/even distribution, a destructive interference is produced on axis for the central wavelength when recombining the two beams. If the number of cells of a given thickness follows a rather simple law based on the Pascal's triangle, we then show that the nulling is also efficient for a wavelength that is not too far from the central wavelength. Results. The effect of achromatization is more efficient the more cells there are. For instance, with two mirrors of $64 \times 64$ cells, where the cells' phase shift ranges between -6π and +6π, one reaches a nulling of 10-6 on a wavelength range $[0.6 \lambda_{0}, 1.25\lambda_{0}]$, i.e. on more than one complete octave. This is why we claim that this device produces a quasi-achromatic phase shift ; especially, it could satisfy the specifications of a space mission as DARWIN. In a second step, we study the optimum way to distribute the cells in the plane of the pupil. The most important criterion is the isolation of the planet image from the residual image of the star. Several algorithms and their nulling performances are presented