Principles of Interferometry
Hans-Rainer Klöckner
IMPRS Black Board Lectures 2014
acknowledgement
§  Rick Perly NRAO Summer School lectures 2014
§  Mike Garrett lectures
§  Frederic Gueth IRAM school
§  Uli Klein lecture
Lecture 4
§  2- element interferometer
§  visibilities
§  correlator
§  uv-coverage
§  synthesis imaging
Why Interferometry
because there are limits
The old 300-foot transit telescope in Green Bank.
The basic two element interferometer
assume the following system
•  monochromatic
•  stationary reference frame
•  RF throughout (it should be baseband)
Geometric delay τg
τg
b
geometric delay some details
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antenna position coordinate system
XYZ – coordinate system for position on the earth
- based on a model for the earth
- essentially your correlator knows all about it
- careful if the position of the telescope is wrong
set the system fixed to the terrestrial system:
X hour angle 0h and declination 0o
Y hour angle -6h and declination 0o
Z
declination 90o
The baseline separation (Lx, Ly, Lz) to a reference antenna.
Horizontal coordinate system
geographic latitude ϕ, elevation E, azimuth A
baselines in uvw coordinates
eliminate h
UV coverage
visibility shopping list
§  measure a visibility at a specific time towards a source at
declination δ and right ascension α with respect to the phase
centre
§  get the UV coordinates for each measurement (need the
antenna position for this)
observational parameters declination right ascension
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δ = arcsin(m · cosδ0 + sinδ0 ·
α = α0 + arctan(
cosδ0 ·
√
l = cosδ · sin(α − α0 )
1 − l 2 − m2 )
l
)
2
2
1 − l − m − m · sinδ0
m = sinδ · cosδ0 − cosδ0 · sinδ0 · cos(α − α0 )
get the real Fourier transformation
transform 3d to 2d
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Fourier Transformation
12 hours UV coverage δ = 90o
only use uv points and not
the measured values of the
visibility
synthesized beam
UV coverage and synthesised beams
Synthesis Imaging
UV coverage
brightness distribution