aperture synthesis

Question 1

what is aperture synthesis

Answer 1

the practical way to make an image with an interferometer

Question 2

preliminaries for aperture synthesis

Answer 2

take an east-west interferometer observing a source at declination delta and hour angle H

Question 3

hour angle=

Answer 3

local siderial time - right ascension

Question 4

interferometer baseline

Answer 4

D=(D,0,0)

Question 5

path compensation

Answer 5

our target is not usually overhead, so we must introduce a physical delay into one arm of the interferometer to compensate

Question 6

path compensation can be done by

Answer 6

switching in physical lengths of real cable or digitally, in memory

Question 7

as the earth spins, the phase of the correlated signal

Answer 7

changes, and we get a fringe rate

Question 8

what is fringe stopping

Answer 8

complex fringe visibility will be rotating at fringe rate in the complex plane and must be constantly rotated backwards to compensate

Question 9

why do we need to path-compensate?

Answer 9

If bandwidth is deltav
⇒ noise signal evolves randomly on timescales of 1/deltav
⇒ must synchronise the two signals (in time) so that the excess path is
≪ c/deltav
This can be done coarsely with path compensation before fine
adjustment with fringe-stopping.

Question 10

can we use more than two antennas?

Answer 10

yes - just take tehm in pairs

Question 11

n antennas, how many baselines

Answer 11

n ways to choose first antenna
(n-1) to choose second
n(n-1) groupings but take away double counting gives
1/2 n(n-1) baseliens

Question 12

multi-element interferometers are an efficient way to

Answer 12

generate many values of complex fringe visibility simultaneously

Question 13

solution to only getting measurements in one direction

Answer 13

space the elements out on the ground in two dimensions

eg the very large array in new mexico:

y-shaped configuration

Question 14

solution 2 for only getting measurements in one direction

Answer 14

let the Earth rotation supply different baseline projected lengths and orientations with respect to the source
“earth rotation aperture synthesis”

Question 15

what is is that always determines resolution

Answer 15

the projection of the baseline perpendicular to the source direction

Question 16

we should measure Γ(u,v) in what spatial plane

Answer 16

plane perpendicular to the source direction:

the (u,v) plane

Question 17

u is parallel to

Answer 17

the right ascension direction

Question 18

v is parallel to

Answer 18

the declination direction

Question 19

because the sky brightness is real, the fourier transform Γ(u,v) is

Answer 19

hermitian conjugate

ie Γ(u,v)= Γ*(-u,-v)

so one half of the (u,v) plane measurements can be deduced form the other half - 12 hours observation needed

Question 20

the synthesised aperture has a synthesised beam defining the

Answer 20

angular resolution of the interferometer

Question 21

for an east-west line interferometer, the resolution in declination is

Answer 21

poor for low-dec sources

Question 22

advantage of y-shaped interferometer

Answer 22

north-south spacings maintain resolution in declination even when dec=0

Question 23

unlike conventional apertures, the synthesised beam of an imaging interferometer can be

Answer 23

very ‘dirty; with lots of strong sidelobes

Question 24

if the (u,v)-plane sampling is sparse, we get a

Answer 24

heavily degraded (‘dirty’) image, missing many spatial frequencies

Question 25

solution to sparse sampling

Answer 25

image reconstruction aka deconvolution

Question 26

image reconstruction

Answer 26

an attempt to remove the effects of the convolving beam patttern

Question 27

image reconstruction: the CLEAN algorithm

Answer 27

Disassemble the dirty image into many, weak, overlapping versions of the synthesised beam, then reconstruct with cleaner beams (e.g., Gaussians).

Question 28

image reconstruction: the maximum entropy method

Answer 28

Determine the ‘least committal’
image consistent with the data. Use the configurational entropy of
any consistent image to quantify its prior probability, and progress
via Bayes Theorem to get the most probable representation of the
source