The theory of optical stellar interferometry

These videos are part of Section 2 of the on-line course “Eagle Eye Astronomy”, initially released on France Université Numérique. These have recently been re-uploaded on youtube and close-captioned, to help better understand the audio track despite the French accent.

Turn the constraint of diffraction into an advantage: the interferometric trick

Understanding interference fringes: an electromagnetic theory of light

Stars are not lasers: a better model for ordinary light sources

Self-coherence and spatial incoherence of astronomical sources

Coherence length

Coherence length and bandwitdh

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?



Bandpass

This tool was developed as a part of the on-line course Eagle Eye Astronomy, hosted on the France Université Numérique website.

uv-coverage

Interferometric arrays and spatial frequencies

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.


?? ??
Resulting uv-coverage

This tool was developed as a part of the on-line course Eagle Eye Astronomy, hosted on the France Université Numérique website.