Observational Astronomy Astronomical interferometers 1022020 1 Basic principles

Observational Astronomy Astronomical interferometers 10/2/2020 1

Basic principles n n 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 10/2/2020 2

Two point interference Fringes Young two-pinhole experiment 10/2/2020 3

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 nonmonochromatic light • Combined fringes from an object with size > /B show reduced contrast 10/2/2020 4

Visibility function n 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: n n Baseline n Amplitude is the fringe contrast Phase is the shift relative to OPD=0 10/2/2020 Phase 5

Examples of visibility functions 10/2/2020 6

The 10/2/2020 uv-plane 7

Delay lines 10/2/2020 8

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 10/2/2020 9

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 10/2/2020 10

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 10/2/2020 11

VLTI beam combiner Huge pit with a parabolic mirror at the bottom produces spatially modulated signal on the detector (fringes) 10/2/2020 12

Scanning interferometry n n 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 10/2/2020 13

What is measured? n n n 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 V 2 and give up on phase 10/2/2020 14

Spectral dimension n n 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 I 0 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 10/2/2020 15

VLTI MIDI Optical layout 10/2/2020 Dispersed fringes 16

Additional problems n n n 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 10/2/2020 17

Useful links n n n http: //www. sc. eso. org/santiago/science/interf 2 002. 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) 10/2/2020 18