http://arxiv.org/abs/2012.05254
Closure phase is the phase of a closed-loop product of spatial coherences formed by a $\ge 3$-element interferometer array. Its invariance to element-based phase corruption acquired during propagation and measurement processes, and phase calibration and errors therein, 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 and demonstrate 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 the closure phase directly in the image plane (without an aperture-plane view) with a 3-element array and its interference pattern: (i) the closure phase is directly measurable from the positional offset of the NPC of one fringe 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 using data observed with the Jansky Very large Array radio telescope. This geometric insight can be potentially valuable to other interferometric applications including optical interferometry. Close parallels exist between interferometric closure phases, structure invariants in crystallography, and phases of Bargmann invariants in quantum mechanics. We generalize these geometric relationships to an N-element interferometer.
N. Thyagarajan and C. Carilli
Fri, 11 Dec 20
12/75
Comments: 22 pages, 10 captioned figures (12 including sufigures), submitted to Physical Review X. Abstract may be slightly abridged compared to the actual manuscript due to length limitations on arXiv. Comments are welcome!