An interferometer pair separated by baseline B measures one Fourier component of the sky brightness, at spatial frequency (u, v) = B/λ in wavelengths. N antennas give N(N−1)/2 baselines; Earth rotation sweeps each one along an ellipse in the uv plane: u = L_x cos H − L_y sin H, v = sin δ (L_x sin H + L_y cos H) (baseline taken in the equatorial plane, H = hour angle, δ = declination).
The dirty image is the sky convolved with the synthesized beam: I_D(l,m) = Σ_k V_k e^{+2πi(u_k l + v_k m)} / N_uv. The beam is the Fourier transform of the uv sampling, its width is roughly θ ≈ λ/B_max. A single dish of diameter D is limited by diffraction at θ ≈ 1.22 λ/D (first Airy null).
Two point sources are separated when their spacing exceeds about one beam width. Gaps in uv coverage produce sidelobes (ghost peaks); more antennas and longer tracks fill the plane.
Simplifications: no deconvolution (CLEAN), no primary-beam attenuation, no atmosphere, ionosphere, receiver gain errors or bandwidth smearing, point-source models, flat-array approximation, noise added directly to the image. Illustrative, not an instrument simulator.