The Shapes Of Cross Correlation Interferometers. Daniel Birman 034815654 Boaz Chen 024356560. Aperture Synthesis. In astronomy carried out at radio frequencies it is possible to record both the amplitude and phase from stellar objects.
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Daniel Birman 034815654
Boaz Chen 024356560
In astronomy carried out at radio frequencies it is possible to record both the amplitude and phase from stellar objects.
This enables us to add up different observations after they have been recorded. This is used for high-resolution sub-millimeter and radio astronomy observations.
The farther apart the observations are the better the resolutions can get by Rayleigh condition:
In order to produce a high quality image, a large number of different separations between different telescopes are required in order to get a good quality image. [n*(n-1) baselines are produced from n telescopes]
Most aperture synthesis interferometers use the rotation of the Earth to increase the number of different baselines included in an observation.
Positioning an array of optical sensors (Telescopes) in order to produce the best general propose interferometer using aperture synthesis
While trying to maximize
The best response is the one that provides the most complete sampling of the Fourier space of the image out to the limit of some best spatial resolution
The sampling should be invariant to measuring different directions
This implies that the response function should be circular symmetric confined in the boundaries of the best resolution
If we want to different separations between different telescopes are required in order to get a good quality image. [n*(n-1) baselines are produced from n telescopes]maximize the signal to noise ratio and the accuracy of the measurement the Fourier plane ought to be sampled uniformly.
Signal to noise ratio decreases as we use nonuniform weighting (as result of uneven spread in the Fourier plane as well as using different weights for the measurements)
Uniform sampling will provide images least susceptible to errors arising from the unmeasured Fourier components
constant width (the length
of the original triangle side)
So we understand we should position our sensors on the curve of the Reuleaux triangle
However placing the sensors non-uniformly on that curve as well as small perturbation off that curve might further reduce symmetry and produce a more uniform sampling pattern
Calculating the best perturbation is a hard exponential (by the number of sensors) problem. As the cross correlation function is not invertible and even calculating it takes O(n2)
The problem is analogous to a continuous traveling salesman problem and might be treated with similar tools i.e.:
The results of these algorithms of the Reuleaux triangle are quite good as seen in the picture
We must not forget however that most aperture synthesis interferometers use the rotation of the Earth to increase the number of different baselines included in an observation.
The spiral galaxy M51. The SMA observations reveal gas and dust in the spiral structure and regions of active star formation.
Keto, Eric, 1997, "The Shapes of Cross-Correlation Interferometers",
ApJ 475, p. 843.
Optical Physics. Third Edition. By S. G. Lipson and H. Lipson and D. S. Tannhauser