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3rd of March 2021
ATNF Colloquium
Geometric Intuition and Image-plane Methods for Measuring Closure Phases in Interferometry
Nithya Thyagarajan (CASS)
Abstract: In interferometric applications, closure phase refers to the phase of the product of spatial coherences obtained around a closed loop of interferometer elements. Its property of invariance to image-plane translation as well as to phase corruption due to the propagation and element-based instrumental effects, has been well-known for several decades. The property that this can be measured robustly even using raw and uncalibrated interferometric data makes it a true measurable physical property of the object being imaged, particularly of the degree of symmetry in the object's morphology. Therefore, it has been a valuable tool in challenging interferometric applications that otherwise require high-accuracy phase calibration. Interesting astronomical applications include the Event Horizon Telescope (EHT) imaging of the supermassive black hole event horizon at the centre of M87 using very long baseline interferometry, an independent approach to statistical detection of redshifted 21 cm power spectrum of neutral Hydrogen during the epoch of reionization, and optical imaging of stellar surfaces.

Until now, the understanding of interferometric closure phase has been limited to a mathematical description that gets applied primarily in the aperture-plane (the Fourier domain of the image-plane). However, a geometrical intuition for this valuable physical quantity has been lacking. I will present the Shape-Orientation-Size (SOS) conservation theorem in the image plane, which forms the foundation for such an insight. Two geometric methods will be described to measure the closure phase directly from images (without requiring a Fourier- or aperture-plane view) – one using the positional offset of one fringe relative to the other two, and the other estimated from the areas of the triangles in the aperture and image planes. I will demonstrate this understanding using real data from the Jansky Very Large Array (VLA) and the EHT. These relationships are further generalized to N-element interferometers.

The geometric understanding provided herein can be potentially valuable to optical interferometry and other interferometric applications. I will outline some of these applications including crystallography, seismic imaging, interferometric synthetic aperture radar (InSAR), synthetic aperture sonar (SAS), gravitational wave detection with LISA, and quantum mechanics and polarized states of light.

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