Aperture antenna lab

• Start with Your original preset. Press R × 4 a few times and watch the pattern at R converge onto the dashed far-field pattern as you cross 2D²/λ.
• Choose the 1.2 m dish preset. At R = 20 m you are deep in the near field: the nulls fill in and the main lobe spreads. This is why antenna ranges need long distances or compact-range reflectors.
• Switch the taper from Uniform to Cosine². The first sidelobe drops from −13.3 dB to about −31.5 dB, but the beam gets wider and the gain falls. Find the best compromise for low interference.
• Steer the beam to 40°. The beam broadens roughly as 1/cos θ₀, and the gain drops.
• At R = 20 m on the dish, tick Focus the aperture at distance R. The near-field pattern sharpens again: this is how near-field focusing and microwave imaging work.
• Make D smaller than λ. The pattern becomes almost omnidirectional: small antennas cannot be directive.

The aperture lies along x from −D/2 to D/2, with complex illumination A(x) = a(x)·e^jφ(x). The field at a point P at distance R and angle θ from broadside is the sum of wavelets from every aperture point (the Huygens–Fresnel principle):

This is the exact sum, so it is valid in the near field. In the far field (R ≫ 2D²/λ) the distance can be approximated by r ≈ R − x sin θ and the pattern becomes the Fourier transform of the illumination:

Region boundaries used here: reactive near field below 0.62√(D³/λ), radiating near field (Fresnel) up to 2D²/λ, far field (Fraunhofer) beyond. At R = 2D²/λ the path difference to the aperture edge is λ/16, a phase error of 22.5°.

Steering applies the linear phase φ(x) = −kx sin θ₀. Focusing applies φ(x) = k(√(R² + x²) − R), which cancels the extra path to the aperture edge.

Gain is estimated for a square D × D aperture with the same taper in both directions: G = 4πD²η²/λ² · cos θ₀, where η = |∫a dx|² / (D∫a² dx) is the taper efficiency of one direction. Patterns are normalized to their own peak.