Arbitrary Transform Telescopes: The Generalization of Interferometry

TL;DR

This paper explores the generalization of interferometry by applying arbitrary linear transforms, like the Fractional Fourier Transform, to electric field data, enabling new interpretations for sources near the array and transient signals.

Contribution

It introduces the concept of using arbitrary linear canonical transforms in interferometry, extending beyond the traditional Fourier basis for diverse astrophysical observations.

Findings

Fractional Fourier Transform helps interpret near-field sources.

Any linear canonical transform can model optical systems with thin elements.

Alternative bases are useful for analyzing dispersed transients and quick pulses.

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.