Invariants in Interferometry: Geometric Insight into Closure Phases
Year: 2020
Type: preprint
Abstract: Closure phase is the phase of a closed-loop product of correlations within a $\ge 3$-element interferometer array. Its invariance to element-based phase corruption makes it invaluable for interferometric applications that otherwise require high-accuracy phase calibration. However, its understanding has remained mainly mathematical and limited to the aperture plane (Fourier dual of image plane). Here, we lay the foundations for a geometrical insight. We develop a shape-orientation-size (SOS) conservation theorem for images made from a closed triad of elements, in which the relative location of the Null Phase Curves (NPCs) of the three interferometer responses (``fringes'') are preserved, even in the presence of large element-based phase errors, besides overall translation of the fringe pattern. We present two geometric methods to measure closure phase directly in the image plane (without an aperture-plane view) with a 3-element array: (i) the closure phase is measurable from the position offset of one fringe NPC from the intersection of the other two fringe NPCs, and (ii) the squared closure phase is proportional to the product of the areas enclosed by the triad of array elements and the three fringe NPCs in the aperture and image planes, respectively. We validate this geometric understanding across a wide range range of interferometric conditions using data from the Very Large Array and the Event Horizon Telescope. We generalize these geometric relationships to an N-element interferometer. This geometric insight can be potentially valuable to other interferometric applications including optical interferometry. Close parallels between interferometric closure phases, structure invariants in crystallography, interferometric synthetic aperture radar and seismic imaging, gravitational wave time-delay interferometry, and phases of Bargmann invariants in quantum mechanics are highlighted.
Source: arXiv (Cornell University)
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3112715136