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. |