Antenna Array Radio Telescope

Question

I've learnt that a setup of radio antennas could possibly be used as a radio telescope:

"A linear array of 10 radio antennae is set up as a radio telescope to view the sky at a wavelength of λ = 21 cm. Each antenna receives radiation uniformly from all directions towards the sky. Adjacent antennae are a distance d apart and feed signals to the same receiver via a mixer and identical cables of equal length."

My task is to: "assume the Fraunhofer approximation, obtain an expression for the angular distribution of the intensity, I(θ), received from a distant source of radiation whose line of sight is perpendicular to the array, where θ is an angle measured with respect to the normal to the array from its centre."

While this is from a homework problem, the trouble I am having here is understanding the concepts and description behind this problem. It would be great it someone could explain to me:

• How can this setup of radio antennae be used as a radio telescope?
• What exactly does the problem mean when they say "line of sight is perpendicular to the array"? (Wouldn't this automatically mean θ=0?)

Answer 1

Imagine you have three antennas $A,\, B$ and $C$ with separation $d$.

I think that the arrangement described in the question is as shown in the diagram below.

The electronics associated with the array combine the signals from the antenna without any change of phase (feed signals to the same receiver via a mixer and identical cables of equal length).
However you will note that the signals from each antenna are not in phase with one another except when $\theta = 0$.
This means that the size of the combined signal from each antenna depends on the angle $\theta$.

---

It might help you if you look at the "opposite" arrangement of the interference pattern produced by a number of parallel slits?