Import standard modules:
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
from IPython.display import HTML
HTML('../style/course.css') #apply general CSS
An interferometric array consists of a collection of individual elements, each pair of elements is cross-correlated to make a baseline measurement. Interferometry is a powerful technique as it enables to indirectly and accurately measure astrometric positions of components of the sky as well as giving information on their spatial structure. Using aperture synthesis, one can perform synthesis imaging from these measurements.
In this chapter, we define the quantities that are measured by an interferometer and how it relates to the derivation of some knowledge of the sky.
The questions we want to address in this chapter are
Before addressing these questions, we will spend some time in $\S$ 4.1 ➞ defining the baseline and its representation in various reference frames, preferably in a convenient frame related to the sky.
The notion of baseline is necessary to address the simple case of a 2-element interferometer in $\S$ 4.2 ➞. This simple interferometer can be seen as a probing tool that samples the visibility function $\S$ 4.3 ➞, associated with the intensity distribution of the sky. Depending on the location of the interferometer on Earth, this function can be probed along $uv$ tracks defined in $\S$ 4.4.1 ➞. In $\S$ 4.4.2 ➞, we investigate how the $uv$ coverage of an interferometric array can be enriched to improve the sampling of the visibility function.
In the final section $\S$ 4.5 ➞, we describe the van Cittert-Zernike theorem, which, using certain approximations, links the intensity distribution of the sky to the interfemetric measurements by a Fourier relationship. Based on this relationship, imaging by aperture synthesis becomes possible.