Observational Astronomy Astronomical interferometers 13 January 2019

Directions of propagation Basic principles All unresolved sources on the sky produce coherent wavefronts. Why? Two telescope beams combined will produce an interference if the optical path lengths are the same Wavefront Directions of propagation 13 January 2019

Two point interference Young two-pinhole experiment Fringes 13 January 2019

Michelson interferometer Angular size of a target Fringe amplitude drops: the envelope is the diffraction curve of individual telescope An additional drop comes from using non- monochromatic light Combined fringes from an object with size >/B show reduced contrast 13 January 2019

Visibility function What is registered with an interferometer is the Fourier transform of a patch on the sky In the Young experiment: V is the visibility function Visibility function is complex: Amplitude is the fringe contrast Phase is the shift relative to OPD=0 Baseline Phase 13 January 2019

Examples of visibility functions 13 January 2019

The uv-plane 13 January 2019

Delay lines 13 January 2019

Single mirror telescope is an interferometer! The imaging process in a single telescope is the superposition of fringe patterns from all combinations of baselines in the telescope pupil • Masking the pupil, one can select one particular baseline • Every star in the field of view produces fringes 13 January 2019

Michelson interferometer • Image at position 0 (if D’ = D) • Left beam with delay 0 B Right beam with delay 0 B’ OPD = 0 B - 0 B’ ≠ 0 at image position 0 13 January 2019

Fizeau interferometer • If D’ ≠ D the image position is 0’ = 0 D/D’ • If D/D’ = B/B’ one finds: OPD = 0’·B’ = 0 D/D’·B’ = = 0 B/B’·B’ = 0·B • This kind of re-imaging of the telescope pupils is called homothetic mapping 13 January 2019

VLTI beam combiner Huge pit with a parabolic mirror at the bottom produces spatially modulated signal on the detector (fringes) 13 January 2019

Scanning interferometry When the two or more beams are combined co-axially the modulation is temporal (like in a classical Michelson interferometer) Modulation is achieved by scanning the OPD 13 January 2019

What is measured? Complex visibility: where are the components of the projected baseline Visibility is a single Fourier component. Imaging requires good coverage of the u,v plane Visibility is hard to measure. It is easier to measure time-average V2 and give up on phase 13 January 2019

Spectral dimension Dispersing interferogram with e.g. a prism allows having fringes at all wavelengths at the same time It decreases the number of photons but increases fringe contrast Ideally one would get: where I0 is the spectral distribution of the original source while we measure I - the fringe amplitude. Assuming that the phase and the visibility are not a very strong functions of the wavelength one gets the spectrum of the source and the visibility in one scan 13 January 2019

VLTI MIDI Optical layout 13 January 2019 Dispersed fringes

Additional problems Atmospheric turbulence Wavelength dependence of the atmospheric refraction and absorption In the IR, sky background Stability of an optical interferometer Long times needed to find and scan fringes 13 January 2019

Useful links http://www.sc.eso.org/santiago/science/interf2002.html (proceedings of ESO Chile Interferometry Week 2002) http://olbin.jpl.nasa.gov/intro/index.html (Optical Long Baseline Interferometry News tutorials) http://www.eso.org/projects/vlti/general (VLTI general description and tutorials) 13 January 2019