Zusammenfassung
Closure phase is the phase of a closed-loop product of spatial coherences
formed by a $3$-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.
Nutzer