Why is beam efficiency important for radiometry?

In microwave radiometry, the antenna measures the brightness temperature of a scene by integrating the thermal emission weighted by the antenna pattern. If the antenna has low beam efficiency, sidelobes pick up thermal emission from the ground, sun, or other hot sources outside the main beam, contaminating the measurement. The measured antenna temperature is T_A = eta_B times T_main_beam plus (1 minus eta_B) times T_sidelobe. For Earth-observing radiometers, the main beam looks at the ocean (T approximately 100 to 200 K) while sidelobes may see the warm Earth limb (T approximately 300 K) or cold space (T approximately 3 K). A 10 percent sidelobe contribution from warm Earth can bias the ocean temperature measurement by 10 to 30 K, which is catastrophic for climate science requiring 0.1 K accuracy. This is why radiometer antennas demand beam efficiencies exceeding 95 percent.

How is beam efficiency measured?

Beam efficiency is measured from the antenna's far-field radiation pattern. The pattern is measured over the full sphere (4 pi steradians) using an antenna range (far-field, compact, or near-field). The main beam solid angle is determined by integrating the normalized pattern from boresight out to the first null (or a specified angle such as the first sidelobe minimum). The total beam solid angle is the integral over the full sphere. Beam efficiency equals the main beam solid angle divided by the total beam solid angle. In practice, the integration is performed numerically from sampled pattern data. For electrically large antennas, the near-field measurement is faster and provides full 3D pattern data. The accuracy of beam efficiency measurement depends on the dynamic range of the pattern measurement: sidelobes 40 dB down contribute only 0.01 percent to the total power but require measurement accuracy better than 40 dB to resolve.

What affects beam efficiency?

Aperture illumination taper: a uniform illumination gives maximum directivity but highest sidelobes (first sidelobe at minus 13 dB for uniform circular aperture). Tapering the illumination toward the edges reduces sidelobes (improving beam efficiency) at the cost of slightly wider beamwidth and lower peak directivity. A minus 10 dB edge taper reduces the first sidelobe to approximately minus 23 dB. Spillover: in reflector antennas, feed radiation that misses the reflector creates wide-angle sidelobes, reducing beam efficiency. Surface accuracy: reflector surface errors (RMS) scatter energy from the main beam into sidelobes per the Ruze equation: gain loss = exp(minus (4 pi sigma over lambda) squared). Blockage: struts and sub-reflector in center-fed designs block part of the aperture, creating diffraction sidelobes. Edge diffraction: sharp reflector edges create sidelobes; rolled edges or serrated edges reduce this.

Antenna Performance

Beam Efficiency

/beem eh-fish-en-see/ — η_B

η_B = Ω_MB/Ω_A = main beam solid angle / total beam solid angle. Fraction of radiated power in main beam. Horn: 95-99%. Parabolic: 85-95%. Patch array: 80-90%. Dipole: 75-85%. Critical for radiometry (T_A = η_BT_MB + (1−η_B)T_SL). Improved by illumination taper, edge treatment, low spillover.

Horn: 95-99%

Dish: 85-95%

Critical: Radiometry

Understanding Beam Efficiency

Every antenna radiates some power into sidelobes, but the fraction matters enormously depending on the application. For a communication link, sidelobes waste power and create interference. For a radiometer measuring ocean temperature to 0.1 K accuracy, sidelobes that pick up the warm Earth can introduce 10-30 K bias, making the measurement useless.

Beam efficiency separates "useful" radiation (main beam) from "wasted" radiation (sidelobes, back lobes). A corrugated horn can achieve 99% beam efficiency by suppressing all sidelobes below -35 dB, while a simple dipole puts 20-25% of its power into its broad sidelobes.

Beam Efficiency Equations

Definition:
η_B = Ω_MB/Ω_A
= ∫_MB U(θ,φ)sinθ dθdφ / ∫_4π U(θ,φ)sinθ dθdφ

Radiometer antenna temperature:
T_A = η_B·T_MB + (1−η_B)·T_SL
η_B=90%, T_MB=150K, T_SL=300K:
T_A = 135+30 = 165K (15K error!)

Ruze surface error:
G/G₀ = exp[−(4πσ/λ)²]
Scattered power → sidelobes

Antenna Beam Efficiency Comparison

Antenna Type	η_B	1st SLL	Illumination	Application
Corrugated horn	98-99%	−35 dB	Gaussian	Radiometer feed
Smooth horn	95-97%	−25 dB	TE11	Reflector feed
Offset parabolic	90-95%	−25 dB	Tapered	SATCOM
Patch array	80-90%	−13 to −25	Weighted	5G, radar
Dipole	75-85%	−10 dB	N/A	Omni comm

Common Questions

Frequently Asked Questions

Why radiometry?

T_A = η_B×T_MB + (1−η_B)×T_SL. 10% sidelobes seeing 300K Earth: 30K error on ocean (150K). Climate requires 0.1K accuracy. Corrugated horn: 99% η_B, <0.3K sidelobe contribution. Every percent of beam efficiency matters for science instruments.

Measurement?

Full-sphere far-field pattern (antenna range or near-field scan). Integrate main beam to first null. Divide by full-sphere integral. Accuracy needs pattern dynamic range >40 dB to resolve low sidelobes. Near-field faster for large antennas. Numerical integration from sampled data.

What affects it?

Illumination taper: uniform=−13dB SLL, −10dB taper=−23dB SLL. Spillover: feed radiation missing reflector. Surface error: Ruze scattering to sidelobes. Blockage: struts/sub-reflector diffraction. Edge diffraction: rolled/serrated edges help. All reduce main beam power fraction.

Related Terms

← Beam Divergence Beam Failure →

Antenna Engineering

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