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Lecture 17 - Interferometry 2 (Multiple baselines: (Each pairing of…
Lecture 17 - Interferometry 2
Correlating interferometers
The correlator can be thought of "placing" a co-sinusoidal and sinusoidal (not-shown in diagram) fringe or "spacial coherence" pattern of angular period onto the sky.
Fringe orientation: perpendicular to the baseline vector b
Fringe spacing: set by projected baselines length and the waveength
Fringe phase: known if source/baseline geometry known and propagation delays calibrated
Physical location of baseline does not matter if source is in the far field
Multiple baselines:
Each pairing of antennas is called a baseline
Maths
Effective length of the baseline is the projection perpendicular to the source direcion
Each baseline measures complex Fourier component of the source at any particular instant. More fourier components, more detailed image
Short baselines, low angular resolution, provide coarse structure
Long baselines, higher angular resolution, provide the fine detail
Importance of phase
Filling the uv plane
Aperture synthesis interferometers for radio astronomy use the rotation of the Earth to increase the number of baseline orientations
As the earth rotates the baseline between A and B changes angle with time as viewed from the radio source.
The baseline vector projected in the direction of the source, can be separated into two orthogonal directions, referred to as u and v with units of wavelengths. These define the (u,v) plane
A single baseline provides on sampe of V(u,v) per integration
Build up coverage by
Having lot of antennas
waiting for the earth to rotate to provide changing projecting baselines
physically relocating the antennas between sets of observation (usually not possible)
Some combination of the below
Maths of uv coverage to measured visibilities
Dirty beams, more N, more resolution
Missing spacings
no data beyond umax,
so limit on smallest structure in image
no data within umin, so failure to measure total power, leads to negative (unphysical) features
holes in coverage, "sidelobe" structure from poor sampling
Effect of missing sampes
Missing short baselines results in poor sensitivity to low brightness extended structure
Interferometer beams
The primary beam: the illumination pattern of the antenna on the sky
The synthesised beam: the resoution pattern from the fourier components in the visibility function
The delay beam: the attenuation pattern due to finite frequency bandwidth
Sensitivity of a (correlation) interferometer
Point source: The flux sensitivity of an array is equal to that of a single antenna with equivalent collecting area
Extended source: The brightness temperature sensitivity of an array is equivalent to the radiometer equaton, mulitplied by the filling factor
Maths