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Register a new userFourier phase analysis in radio-interferometry
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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 in the Fourier phases, one may consider the probability distribution function (PDF) of phase increments, and the related concepts of phase entropy and phase structure quantity. We use these ideas here with the purpose of assessing the ability of radio-interferometers to detect and recover this information. By comparing current arrays such as the VLA and Plateau de Bure to the future ALMA instrument, we show that the latter 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 fluctuations. We also show that ALMA will be able to recover the actual amount of phase structure in the noise-free case, if multiple configurations are used.
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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.
Astronomers usually need the highest angular resolution possible, but the blurring effect of diffraction imposes a fundamental limit on the image quality from any single telescope. Interferometry allows light collected at widely-separated telescopes to be combined in order to synthesize an aperture much larger than an individual telescope thereby improving angular resolution by orders of magnitude. Radio and millimeter wave astronomers depend on interferometry to achieve image quality on par with conventional visible and infrared telescopes. Interferometers at visible and infrared wavelengths extend angular resolution below the milli-arcsecond level to open up unique research areas in imaging stellar surfaces and circumstellar environments. In this chapter the basic principles of interferometry are reviewed with an emphasis on the common features for radio and optical observing. While many techniques are common to interferometers of all wavelengths, crucial differences are identified that will help new practitioners avoid unnecessary confusion and common pitfalls. Concepts essential for writing observing proposals and for planning observations are described, depending on the science wavelength, angular resolution, and field of view required. Atmospheric and ionospheric turbulence degrades the longest-baseline observations by significantly reducing the stability of interference fringes. Such instabilities represent a persistent challenge, and the basic techniques of phase-referencing and phase closure have been developed to deal with them. Synthesis imaging with large observing datasets has become a routine and straightforward process at radio observatories, but remains challenging for optical facilities. In this context the commonly-used image reconstruction algorithms CLEAN and MEM are presented. Lastly, a concise overview of current facilities is included as an appendix.
{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 establish bounds on the quantum Fourier transform $FS$, as a map between suitably defined $L^{p}$ spaces, leading to a new uncertainty principle for relative entropy. We cite several applications of the quantum Fourier analysis in subfactor theory, in category theory, and in quantum information. We suggest a new topological inequality, and we outline several open problems.
This is the third installment in a series of papers in which we investigate calibration artefacts. Calibration artefacts (also known as ghosts or spurious sources) are created when we calibrate with an incomplete model. In the first two papers of this series we developed a mathematical framework which enabled us to study the ghosting mechanism itself. An interesting concomitant of the second paper was that ghosts appear in symmetrical pairs. This could possibly account for spurious symmetrization. Spurious symmetrization refers to the appearance of a spurious source (the anti-ghost) symmetrically opposite an unmodelled source around a modelled source. The analysis in the first two papers indicates that the anti-ghost is usually very faint, in particular when a large number of antennas are used. This suggests that spurious symmetrization will mainly occur at an almost undetectable flux level. In this paper, we show that phase-only calibration produces an anti-ghost that is $N$-times (where $N$ denotes the number of antennas in the array) as bright as the one produced by phase and amplitude calibration and that this already bright ghost can be further amplified by the primary beam correction.
This paper presents a detailed analysis of the applicability and benefits of baseline dependent averaging (BDA) in modern radio interferometers and in particular the Square Kilometre Array (SKA). We demonstrate that BDA does not affect the information content of the data other than a well-defined decorrelation loss for which closed form expressions are readily available. We verify these theoretical findings using simulations. We therefore conclude that BDA can be used reliably in modern radio interferometry allowing a reduction of visibility data volume (and hence processing costs for handling visibility data) by more than 80%.
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