Aperture Synthesis: Earth-Rotation u-v Coverage & Dirty Beam (2D)

Every real interferometer array — the VLA, ALMA, the EVN — builds its image not from a single snapshot but from thousands of (u,v) samples accumulated as Earth's rotation sweeps each baseline through a different projection onto the sky. This 2D companion makes that accumulation explicit: choose a Y-shaped, circular or randomly scattered antenna layout, set the source's declination and how many hours either side of transit you observe for, and watch each baseline trace its own ellipse through the Fourier (u,v) plane while a direct-Fourier dirty-beam image — complete with the real negative sidelobes a genuine synthesis image carries — sharpens from a broad, ringing blob into a clean central peak as the "Animate Earth rotation" pass fills in more of the plane, the same trade-off between integration time and image fidelity that governs every real synthesis-imaging observation.