An interferometer correlates the signals of a pair of dishes. For a baseline vector b and a source direction s the correlator measures one Fourier component of the sky brightness I(l,m) at the spatial frequency (u,v) = bproj/λ:
V(u,v) = ∫∫ I(l,m) e−2πi(ul + vm) dl dm u = (X sin H + Y cos H)/λ v = (−X sinδ cos H + Y sinδ sin H + Z cosδ)/λ Dirty image = I ∗ Bdirty, Bdirty(l,m) = (1/N) Σ cos[2π(uk l + vk m)], resolution ≈ λ / Bmax(X,Y,Z) is the baseline in the equatorial frame; X = −N sinφ + U cosφ, Y = E, Z = N cosφ + U sinφ for latitude φ. As the Earth turns, the hour angle H sweeps each baseline through an ellipse, filling the uv plane without moving any dish. The page samples every 5 minutes of sky time, adds the conjugate (−u,−v) points, computes the true visibilities of the chosen sky model and accumulates the dirty image and beam exactly.
Checks: constant projected baseline for a polar source, the elliptical uv track of an east–west baseline, recovery of a point source position and flux, and the uv aspect ratio sinδ.
Simplifications: no deconvolution (CLEAN), no primary beam, noise, delay tracking, bandwidth smearing or w-term; a small flat field of view; coordinates are in units of λ/Bmax so the same picture scales to any wavelength and array size.