📡 Deployable Parabolic Reflector: Petal Deployment, Gain and Surface Error (2D)

Side section of a segmented radio reflector whose petals unfold from a hub, with rays running from the aperture to the focus. Set the aperture, focal length, deployed fraction, frequency, panel surface error and feed taper, and read off gain, beamwidth and the efficiency lost to surface roughness and illumination. Parabola geometry, the Airy beam and the Ruze loss are computed, with four in-page numerical checks. An antenna-engineering companion to the 3D deployable reflector.