A finite spectral bandwidth results in some spectral decorrelation of the electric field emanating from a source: even with a true point source, you will only observe the interference phenomenon (mutual coherence of the field) over a finite range of optical path difference (OPD) that is constrained by the coherence length.
Coherence length: Λ0 = λ²/Δλ
An purely monochromatic and phase-calibrated signal like the one coming out of a very good laser would exhibit an infinite coherence length, represented by the green curve plotted below.
Change the bandpass of the filter (here expressed as 1/R=Δλ/λ) to see its effect on the coherence length (the blue curve).
For a given bandpass (say 0.05 and 0.1), how many fringes can you make out in the fringe packet? How do the two quantities (bandpass, number of fringes) relate to each other?
One of the pillars on which the KERNEL project rests is a data processing pipeline that aims at being as versatile and portable as possible, for general astrophysics purposes as well as for metrology. The maintenance of this tool is one of the tasks listed among the work packages that make up the bulk of the KERNEL project. Since the idea is to make the pipeline available to the community at large, it was decided to host the source code on an open access repository on GitHub. The new package is called XARA, an acronym that stands for eXtreme Angular Resolution Astronomy, and can be downloaded right here. This package is an evolution of a previous incarnation called PYSCO (Python Self-Calibrating Observables), that was hosted on the now defunct Google Code platform. The most notable difference is that it is properly packaged and can be installed, so that its classes and functions can be called from anywhere in your python scripts.
It is accompanied by a convenient simulation package of eXtreme Adaptive Optics (XAO) astutely called XAOSIM and also made available on GitHub. Keep in mind that both are work in progress, that will be regularly updated over the course of the KERNEL project, as features are added and bugs are accounted for, so always check for the latest update of these tools before using them!
This post features a pretty fun simulation tool that will allow you to experience “by hand” the relation between the geometry of an interferometric array (that is the location of the telescopes or apertures making up the array) and the corresponding so called “uv-coverage”, that shows all the spatial frequencies the interferometric array gives access to.
The left-hand side plot shows the arangement of apertures. The user can select from several pre-set configurations (Y-shaped, hexagonal-grid, non-redundant) and modify them by moving, adding or removing individual apertures.
Moving one aperture by hand and observing what simultaneously happens on the right-hand side display is particularly “enlightening”: for one, you develop a more intuitive of the relation between one aperture and the different interferometric baselines it is involved with. In addition, you can also observe that geometries laying on a regular grid pattern sometimes result in overlapping points in the uv-plane. The only pattern that strictly avoids this situation is the non-redundant geometry.
Every good project needs a good logo. KERNEL now therefore has one: it was realized by my brother, Wilfried Martinache, who’s training to become a professional graphic designer. Check out his website: thebigbluebear.net. I think the logo is pretty neat, as it suggests that the stuff that really matters, at the heart of things (ie. the kernel!), may be invisible although it influences everything around it!
Combined with adaptive optics (AO), a kernel-phase data analysis makes it possible to further improve our understanding of astronomical images, and bypass the generally accepted limit of angular resolution, imposed by the theory of diffraction. This is sometimes refered to as “super-resolution”.
Astronomy requires large telescopes to improve the sensitivity and the angular resolution of its observations. Of these qualities, angular resolution is the most difficult to maintain in the optical and near-infrared, since the atmosphere reduces it to that of a 10 cm aperture, regardless of the telescope size. On the one-hand, Adaptive Optics (AO) actively compensates for this effect but the improvement is often partial only. On the other hand, interferometric techniques (most notably sparse aperture masking interferometry) passively allow the extraction of self-calibrating observables, that boost the angular resolution, but severely affect the sensitivity of observations.
The KERNEL project will enable every optical telescope equiped with AO to reach its ultimate angular resolution potential at full sensitivity, using a Fourier-phase framework, with applications ranging from the reinterpretation of archival science data to the development of wavefront control strategies for the giant segmented aperture of large telescopes like the space-borne JWST, or the upcoming generation of ground based extremely large telescope (ELTs).
KERNEL will achieve this objectives thanks to:
a streamlined general use and highly accessible data reduction process relying on a powerful pipeline
a coordinated effort to revisit existing archival ground-based AO (or assimilated) data sets to produce new, exclusive science
a ruggedized Fourier-phase framework that will open new use cases of currently less favorable datasets
the further development of concepts with applications to high-contrast imaging, wide-field imaging and the caracterization of complex sources
the development of prescriptions for powerful wavefront control strategies on existing and future facilities
That will require the combined development of:
an upgraded Fourier-phase extraction/processing software for archival, simulated and laboratory data
an experimental setup that will validate the concepts, strategies and prescriptions developed over the course of the project
the deployment of on-sky experiments on world class telescopes
The consequences of this project will have a major impact on the design and scientific exploitation of future high angular resolution instrumentation on the existing generation of 8-10 meter class telescopes as well as on the upcoming generation of 30-40 meter giants, championned by Europe and its E-ELT.
Astronomy and Instrumentation by Frantz Martinache