Math behind a uv plot in interferometry?
Rick Perley gives a lecture about interferometry to a biannual NRAO Synthesis Imaging Workshop.
Part 2 of his 2016 talk discusses u,v plane coverage.
The 2016 IRAM Millimeter Interferometry School lectures by J. Pety and F. Gueth may also help.

Let $\hat{u}, \hat{v}, \hat{w}$ be orthogonal unit vectors with $\hat{w}$ pointing from Earth to the radio source, $\hat{v}$ oriented northward, and $\hat{u}$ oriented eastward.
Let $B_{ij}$ be the baseline vector between antennas $i$ and $j$ in the array.
Then $(B_{ij} \cdot \hat{u}, B_{ij} \cdot \hat{v})$
and $(-B_{ij} \cdot \hat{u}, -B_{ij} \cdot \hat{v})$
are points in the u,v plot, and
$B_{ij} \cdot \hat{w} / c$ is a time offset between the signals at $i$ and $j$.

If both antennas observe the source for several hours, $B_{ij}$ rotates with the Earth, and the two points in the u,v plot grow into elliptical arcs.
The shape of those ellipses depends on the declination of the source, so
the same array will have different u,v coverage for sources at different declinations.

The interfering signals from the array are combined in a visibility function $V(u, v)$.
The image of the source is an inverse Fourier transform of $V$, typically deconvolved using an algorithm called CLEAN.
To minimize image artifacts, a diverse set of baseline lengths and orientations, without large gaps in u,v coverage, is desirable.