Arbitrary Transform Telescopes: The Generalization of Interferometry

Abstract: 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.