A geometric view of closure phases in interferometry
A geometric view of closure phases in interferometry
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DOI：
10.1017/pasa.2022.6
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发表时间：
2020-12
影响因子：
6.3
通讯作者：
N. Thyagarajan;C. Carilli
中科院分区：
文献类型：
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作者：
N. Thyagarajan;C. Carilli
摘要闭合相位是由3元干涉仪阵列形成的空间相干性闭环乘积的相位。它的不变性相位腐败期间获得的传播和测量过程中，随后的校准，以及其中的错误，个别阵列元素，使其成为一个有价值的工具，否则需要高精度相位校准的干涉测量应用。然而，它的理解仍然主要是数学和限制的光圈平面（傅立叶对偶的图像平面）。在这里，我们提出了一个几何，图像域视图的封闭阶段，这到目前为止一直缺乏。利用干涉仪三元组干涉像中的主三角形，我们证明了封闭相位的性质，特别是它对基于乘性单元的破坏因子的不变性，（甚至是很大的幅度）和平移，都与三角形的保守性质，即它的形状，方向和大小，这在本文中被称为“形状-取向-尺寸（SOS）守恒原理”。在不需要干涉仪阵列的基于元件的振幅校准的情况下（如在光学干涉测量中典型的），由相位未校准的空间相干性形成的任何3元件干涉图像中的主三角形仍然是源对象的形态的真实且未损坏的表示，除了可能的移位。基于三角形SOS守恒原理，我们提出了两种直接从简单的三元干涉图像测量闭合相位的几何方法（不需要孔平面视图）：（i）闭合相可以从三角形的任何一个高度直接测量，以及（ii）平方闭合相位分别与由阵列元件的三元组和孔径平面和像平面中的主三角形包围的面积的乘积成比例。我们验证了几何理解的封闭阶段的图像平面使用的观察与卡尔G。Jansky甚大阵和视界望远镜。这些结果验证了SOS守恒原理在广泛的无线电干涉条件。这种几何洞察力对其他干涉测量应用，如光学干涉测量，可能是有价值的。我们还概括了这些几何关系的N元干涉仪。
Abstract Closure phase is the phase of a closed-loop product of spatial coherences formed by a ${\ge}3$ -element interferometer array. Its invariance to phase corruption attributable to individual array elements acquired during the propagation and the measurement processes, subsequent calibration, and errors therein, makes it a valuable tool in interferometry applications that otherwise require high-accuracy phase calibration. However, its understanding has remained mainly mathematical and limited to the aperture plane (Fourier dual of the image plane). Here, we present a geometrical, image domain view of closure phase, which until now has been lacking. Using the principal triangle in a 3-element interference image formed by a triad of interferometer elements, we show that the properties of closure phase, particularly its invariance to multiplicative element-based corruption factors (even of a large magnitude) and to translation, are intricately related to the conserved properties of the triangle, namely, its shape, orientation, and size, which is referred herein as the ‘shape-orientation-size (SOS) conservation principle’. In the absence of a need for element-based amplitude calibration of the interferometer array (as is typical in optical interferometry), the principal triangle in any 3-element interference image formed from phase-uncalibrated spatial coherences is still a true and uncorrupted representation of the source object’s morphology, except for a possible shift. Based on this knowledge of the triangle SOS conservation principle, we present two geometric methods to measure the closure phase directly from a simple 3-element interference image (without requiring an aperture-plane view): (i) the closure phase is directly measurable from any one of the triangle’s heights, and (ii) the squared closure phase is proportional to the product of the areas enclosed by the triad of array elements and the principal triangle in the aperture and image planes, respectively. We validate the geometric understanding of closure phase in the image plane using observations with the Karl G. Jansky Very Large Array, and the Event Horizon Telescope. These results verify the SOS conservation principle across a wide range of radio interferometric conditions. This geometric insight can be potentially valuable to other interferometric applications, such as optical interferometry. We also generalise these geometric relationships to an N-element interferometer.