Arbitrary Transform Telescopes: The Generalization of Interferometry
  The basic principle of astronomical interferometry is to derive the angular
distribution of radiation in the sky from the Fourier transform of the electric
field on the ground. What is so special about the Fourier transform? Nothing,
it turns out. I consider the possibility of performing other transforms on the
electric field with digital technology. The Fractional Fourier Transform (FrFT)
is useful for interpreting observations of sources that are close to the
interferometer (in the atmosphere for radio interferometers). Essentially,
applying the FrFT focuses the array somewhere nearer than infinity. Combined
with the other Linear Canonical Transforms, any homogeneous linear optical
system with thin elements can be instantiated. The time variation of the
electric field can also be decomposed into other bases besides the Fourier
modes, which is especially useful for dispersed transients or quick pulses. I
discuss why the Fourier basis is so commonly used, and suggest it is partly
because most astrophysical sources vary slowly in time.
