The Importance of Phase in Nulling Interferometry and a Three‐Telescope Closure‐Phase Nulling Interferometer Concept

Abstract

We discuss the theory of the Bracewell nulling interferometer and explicitly demonstrate that the phase of the "white light" null fringe is the same as the phase of the bright output from an ordinary stellar interferometer. As a consequence a "closure phase" exists for a nulling interferometer with three or more telescopes. We calculate the phase offset as a function of baseline length for an Earth-like planet around the Sun at 10 pc, with a contrast ratio of 10 −6 at 10 µm. The magnitude of the phase due to the planet is ∼ 10 −6 radians, assuming the star is at the phase center of the array. Although this is small, this phase may be observable in a three-telescope nulling interferometer that measures the closure phase. We propose a simple non-redundant three-telescope nulling interferometer that can perform this measurement. This configuration is expected to have improved characteristics compared to other nulling interferometer concepts, such as a relaxation of pathlength tolerances, through the use of the "ratio of wavelengths" technique, a closure phase, and better discrimination between exodiacal dust and planets.

Astrophysics in 2006

“…Danchi et al (2006) provide reassurance that it does. If this enables you to sleep better at night, you may have to switch to some waveband other than optical astronomy that is done by day.…”

Review and scientific prospects of high-contrast optical stellar interferometry

“…New attempts with CHARA/MIRCX and VLTI/GRAVITY are underway. New combiners that measure closure phases using nulled outputs of pairwise combiners could dramatically improve the signal-to-noise of this technique 15,16,42 but this still requires lab development and on-sky testing. Note that if phase referencing or differential phase approaches could work, then more objects could be done since photocenter shifts caused by planets are linear with angular resolution, unlike closure phases which disappear when separation is marginally-resolved.…”

A new interferometer architecture combining nulling with phase closure measurements

“…where E 1 and E 2 are complex phasor representations of light beams such that the instantaneous electric field at some location labeled 1 Note that this optical system must not be mistaken with the concept of phase closure nulling (Duvert et al 2010) or closure-phase nulling Interferometer (Danchi et al 2006). These two papers propose reduction techniques using the closure phase observable on traditional optical setups (a three telescope interferometer on one hand, and a three telescope nuller on the other hand).…”