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Fourier phases contain a vast amount of information about structure in direct space, that most statistical tools never tap into. We address ALMAs ability to detect and recover this information, using the probability distribution function (PDF) of phase increments, and the related concepts of phase entropy and phase structure quantity. We show that ALMA, with its high dynamical range, is definitely needed to achieve significant detection of phase structure, and that it will do so even in the presence of a fair amount of atmospheric phase noise. We also show that ALMA should be able to recover the actual amount of phase structure in the noise-free case, if multiple configurations are used.
Most statistical tools used to characterize the complex structures of the interstellar medium can be related to the power spectrum, and therefore to the Fourier amplitudes of the observed fields. To tap into the vast amount of information contained i
{em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum symmetry. We est
We introduce fusion bialgebras and their duals and systematically study their Fourier analysis. As an application, we discover new efficient analytic obstructions on the unitary categorification of fusion rings. We prove the Hausdorff-Young inequalit
Fourier analysis of ghost imaging (FAGI) is proposed in this paper to analyze the properties of ghost imaging with thermal light sources. This new theory is compatible with the general correlation theory of intensity fluctuation and could explain som
Interferometric phase (InPhase) imaging is an important part of many present-day coherent imaging technologies. Often in such imaging techniques, the acquired images, known as interferograms, suffer from two major degradations: 1) phase wrapping caus