How would a Fast Fourier Transform Telescope work without a mirror, dish or lenses? I recently came across a short article mentioning the idea for a telescope built without mirrors or lenses that instead uses an array of antennas and massive computing power to resolve an image. Such a thing will apparently become possible if "Moore's law continues to hold", but doesn't explain how it will work.

Here's a link to the original paper: Tegmark and Zaldarriaga 2009


  We will show that it acts much like a single dish telescope with a
  dramatically larger field of view, yet is potentially much cheaper
  than a standard interferometer with comparable area. If a modern
  all-digital interferometer such as the MWA 1 is scaled up to a very
  large number of antennas N , its price becomes completely dominated by
  the computing hardware cost for performing of order N2 correlations
  between all its antenna pairs. The key idea behind the FFT Telescope
  is that, if the antennas are arranged on a rectangular grid, this cost
  can be cut to scale merely as N log2 N using Fast Fourier Transforms.
  As we will see, this design also eliminates the need for individual
  antennas that are pointable (mechanically or electronically),


Unlike a traditional interferometer, which consists of individual telescopes that focus light (or radio waves) to a point before ultimately combining their images, the antennas don't have a dish that focuses the radio waves from a certain point in the sky. Instead it's just an array of antennas that images the entire sky at once:


  The results above also show that the FFTT can be thought of as a cheap
  maximally compact interferometer with a full-sky primary beam.  To
  convert a state-of- the-art interferometers such as MWA 1, LOFAR
  [2], 12 PAPER[4], 21CMA [3] into an FFTT, one would need to do three
  things:
  
  
  Move all antenna tiles together so that they nearly touch.
  Get rid of any beamformer that “points” tiles to- wards a specific sky direction by adding relative phases to its component antennas, and
  treat each antenna as independent instead, thus allowing the array to
  image all sky directions simultaneously.
  Move the antennas onto a rectangular grid to cut the correlator cost from N2 to N log2 N .
  


Can someone explain how a computer can resolve an image without a lens, dish or mirror to make parallel rays of light converge on a sensor? I thought that a sensor without a lens, dish or mirror will just produce a blurry mess.

Edit: I think I understand it now. Watching this video was massively helpful for me in understanding how Fourier transformations allow you to isolate individual waveforms from a signal containing many different waveforms.
From one perspective, the purpose of a telescope lens, or mirror is to delay the light arriving in the centre of the instrument a bit relative to the light arriving at the edges. A lens is thicker in the middle, and light travels more slowly in glass, the path to the centre of the mirror and back to the detector is longer, because of the curve of the mirror than the one to the edge, and so on. The result is that all the waves which hit any part of the lens or mirror from a point source end up arriving at the detector in phase so they add up, while waves from anywhere else cancel out. 

A phased array antenna (common for short wavelength radio operations) achieves the same delay by capturing the signal at lots of points on the (flat) antenna and then artificially delaying it before combining it with the signals from the other points.

An interferometer (such as the Event Horizon telescope) does the same thing digitally. The full waveform of the signal (more or less) is recorded in multiple places and then they are combined in a large computer with various slightly different delays to separate waves coming from slightly different directions (I am over-simplifying greatly).

What this article proposes is mainly a way to do that for more antennae at less computing cost by placing the antennae in a specific layout and using a bit of clever maths (the FFT) to do all the combining in one go.