1. Observational Astronomy
Astronomical interferometers
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2. 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
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3. Two point interference
Young two-pinhole experiment
Fringes
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4. 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
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5. 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
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6. Examples of visibility functions
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7. The uv-plane
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8. Delay lines
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9. 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
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10. 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
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11. 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
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12. VLTI beam combiner
Huge pit with a parabolic mirror at the bottom produces spatially modulated signal on the detector (fringes)
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13. 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
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14. 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
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15. 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
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16. VLTI MIDI
Optical layout
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Dispersed fringes

17. 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
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18. Useful links
(proceedings of ESO Chile Interferometry Week 2002)
(Optical Long Baseline Interferometry News tutorials)
(VLTI general description and tutorials)
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