Abstract
Context.The use of interferometric nulling for the direct detection of extrasolar planets is in part limited by the extreme sensitivity of the instrumental response to tiny optical path differences between apertures. The recently proposed kernel-nuller architecture attempts to alleviate this effect with an all-in-one combiner design that enables the production of observables inherently robust to residual optical path differences (≪λ).Aims.To date, a unique kernel-nuller design has been proposed ad hoc for a four-beam combiner. We examine the properties of this original design and generalize them for an arbitrary number of apertures.Methods.We introduce a convenient graphical representation of the complex combiner matrices that model the kernel nuller and highlight the symmetry properties that enable the formation of kernel nulls. The analytical description of the nulled outputs we provide demonstrates the properties of a kernel nuller.Results.Our description helps outline a systematic way to build a kernel nuller for an arbitrary number of apertures. The designs for three- and six-input combiners are presented along with the original four-input concept. The combiner grows in complexity with the square of the number of apertures. While one can mitigate this complexity by multiplexing nullers working independently over a smaller number of sub-apertures, an all-in-one kernel nuller recombining a large number of apertures appears as the most efficient way to characterize a high-contrast complex astrophysical scene.Conclusions.Kernel nullers can be designed for an arbitrary number of apertures that produce observable quantities robust to residual perturbations. The designs we recommend are lossless and take full advantage of all the available interferometric baselines. They are complete, result in as many kernel nulls as the theoretically expected number of closure-phases, and are optimized to require the smallest possible number of outputs.
Highlights
The last 25 years have seen the detection of more than 4000 exoplanets (Schneider et al 2011)
The exploitation of these instruments is still limited by their vulnerability to optical path difference (OPD) errors, and requires sophisticated statistical analysis, like those proposed by Hanot et al (2011) and Defrère et al (2016), and more recently used by Norris et al (2020) to disentangle the off-axis astrophysical signal from the effects of unwanted OPDs
In this work we offer a new description of the kernel-nuller design introduced by Martinache & Ireland (2018). This is done by introducing a new graphical representation of the complex matrix that models the nuller and the transformations it operates on the input electric field
Summary
The last 25 years have seen the detection of more than 4000 exoplanets (Schneider et al 2011). Some combining solutions have been found that optimize the rejection of resolved stars (Angel & Woolf 1997; Guyon et al 2013) The exploitation of these instruments is still limited by their vulnerability to optical path difference (OPD) errors, and requires sophisticated statistical analysis, like those proposed by Hanot et al (2011) and Defrère et al (2016), and more recently used by Norris et al (2020) to disentangle the off-axis astrophysical signal from the effects of unwanted OPDs. Classical long-baseline and Fizeau interferometry make extensive use of the production of robust observables, like closure phases (Jennison 1958), and their generalized form, kernel phases (Martinache 2010), to sidestep the limitations brought by the OPD residuals.
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