 Earth-rotation aperture synthesis

Earth-rotation aperture synthesis uses Earth's changing orientation to vary a fixed ground baseline's projection onto the plane of the sky. In two dimensions, $u$ and $v$ are the components of ${\mathbf{b}}_{\perp }/\lambda$ along two perpendicular sky tangents. Tracking one field traces a curve in this $(u,v)$ plane; changing the physical baseline supplies other curves. A track samples Fourier transform coordinates, rather than the brightness along a track across the sky.

For a horizontal east–west baseline of length $B$, choose the sky-axis signs so thatwhere $H$ is hour angle and $\delta$ is declination. The ellipse follows by projecting the rotating baseline onto sky tangents. At a celestial pole it is a circle; near the celestial equator its minor axis collapses. Thus the same ground layout constrains different sky directions unequally. Rotation improves coverage, but does not fill every spatial frequency, and synthesis across many hours assumes that the source changes negligibly during that interval.