Antenna Technology

Cylindrical Near-Field

Q: When should I choose cylindrical near-field over planar or spherical scanning?

Cylindrical scanning is the natural choice for antennas with a fan-beam or sectoral pattern, such as base station panels, airport surveillance radar arrays, and broadcast antennas, where the pattern is broad in azimuth but narrow in elevation. The cylinder captures the full 360 degrees of azimuth while limiting the vertical scan to the angular sector that contains significant energy. Planar near-field is better for high-gain pencil-beam apertures that radiate into a forward half-space, because it only covers a limited angular cone. Spherical near-field gives complete pattern coverage including back radiation but requires the most measurement points and the most complex positioner. For a fan-beam antenna, cylindrical scanning typically needs far fewer points than spherical while still recovering the full azimuth pattern, so it is faster and the positioner is mechanically simpler.

Q: How fine must the cylindrical near-field sampling be to avoid aliasing?

The vertical sample spacing along the cylinder axis must satisfy the Nyquist criterion for plane waves, so delta-z must be less than or equal to lambda/2. The angular sample spacing in azimuth is set by the maximum cylindrical mode index N, where N is approximately equal to k times the cylinder radius r0 plus a margin of about 10 modes. The number of azimuth samples must be at least 2N+1, which corresponds to an angular step delta-phi less than or equal to 180 degrees divided by N. At 10 GHz with a 0.5 m cylinder radius, k times r0 is about 105, so roughly 230 azimuth points and a vertical step of 15 mm are required. Undersampling either coordinate folds high-order modes back into the visible region and corrupts the computed far-field sidelobes.

Q: Why does cylindrical near-field measurement require probe correction?

The probe is not an ideal point sensor; it has its own directive pattern and polarization response, and it couples to the antenna under test over a finite solid angle. In the cylindrical formulation the measured signal is the convolution of the true field with the probe pattern expressed in cylindrical modes. Probe correction divides the measured mode coefficients by the probe receiving coefficients so that the recovered far field reflects only the test antenna. An open-ended waveguide probe is commonly used because its smooth, well-characterized pattern is easy to deconvolve. Skipping probe correction can introduce gain errors of several tenths of a dB and degrade sidelobe and cross-polarization accuracy, especially toward the edges of the scan where the test antenna is seen at wide angles.

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Among the three canonical near-field antenna measurement geometries, the cylindrical method samples the tangential electric field on a cylinder that surrounds the antenna under test, capturing the full 360° of azimuth while scanning only the elevation sector that holds appreciable energy. The complex amplitude and phase collected on this surface are expanded into cylindrical wave modes (Hankel and harmonic functions) and transformed into the complete far-field pattern without ever moving the probe to the far zone. This geometry is ideally matched to fan-beam and sectoral radiators (base station panels, surveillance radar arrays, broadcast antennas) that are broad in azimuth and narrow in elevation, where it needs far fewer measurement points than a full spherical scan.

Category: Antenna Technology

Scan surface: Cylinder (φ, z)

Vertical sampling: ≤ λ/2

How Cylindrical Scanning Reconstructs the Pattern

In a cylindrical near-field range the antenna under test rotates about a vertical axis while a stationary probe travels up and down a vertical rail. At each azimuth angle φ and each height z the receiver records both amplitude and phase of the two tangential field components. The result is a two-dimensional data matrix sampled on the surface of an imaginary cylinder of radius r₀. Because the measurement plane is a regular grid in φ and z, the data can be processed with a one-dimensional discrete Fourier transform in azimuth and a continuous-spectrum integral in the axial wavenumber, making the computation efficient even for electrically large apertures.

The physics rests on cylindrical mode expansion. Any source-free field outside the smallest cylinder enclosing the antenna can be written as a sum of outward-traveling cylindrical waves indexed by an integer azimuthal order n and a continuous axial wavenumber γ. Hankel functions of the second kind, H_n⁽²⁾(κρ), describe the radial dependence. Measuring the field on one cylinder fixes the mode coefficients, and the far field follows directly because each cylindrical mode maps to a known angular contribution as the radial coordinate goes to infinity. The asymptotic form of the Hankel function supplies the stationary-phase result that turns the mode sum into the radiation pattern.

The number of significant azimuthal modes is governed by the cylinder radius. Modes with n much larger than k·r₀ are evanescent and carry negligible energy, so the series truncates at N ≈ k·r₀ plus a small safety margin. This truncation, combined with the λ/2 axial Nyquist limit, fixes the required sampling density and total measurement time.

Governing Mode Expansion and Sampling

Cylindrical wave expansion (field outside r₀):
E(ρ,φ,z) = ∑_n ∫ a_n(γ) H_n⁽²⁾(κρ) e^jnφ e^jγz dγ, κ² = k² − γ²

Maximum azimuthal mode index:
N ≈ k × r₀ + 10, with k = 2π / λ

Sampling criteria (no aliasing):
Δz ≤ λ/2 and Δφ ≤ 180° / N (so azimuth points ≥ 2N + 1)

Example: f = 10 GHz (λ ≈ 30 mm), r₀ = 0.5 m → k×r₀ ≈ 105, N ≈ 115, so ≈ 231 azimuth samples and Δz ≤ 15 mm. Far-field gain accuracy after probe correction is typically ±0.3 dB.

Near-Field Geometry Comparison

Geometry	Scan surface	Pattern coverage	Positioner	Relative point count	Best-fit antenna
Cylindrical	Cylinder (φ, z)	Full azimuth, limited elevation	Rotation + vertical linear	Medium	Fan-beam, sectoral, broadcast
Planar	Flat plane (x, y)	Forward cone only (no back)	2-axis linear scanner	Low to medium	High-gain pencil-beam apertures
Spherical	Sphere (θ, φ)	Complete 4π including back lobes	Two rotation stages	High	Low-gain, broad-beam, full 3D
Far-field range	Direct (R > 2D²/λ)	Direct pattern, no transform	Single rotation	Low	Small antennas, validation

Common Questions

Frequently Asked Questions

When should I choose cylindrical near-field over planar or spherical scanning?

Cylindrical scanning suits fan-beam and sectoral antennas (base station panels, surveillance radar arrays, broadcast antennas) that are broad in azimuth and narrow in elevation. The cylinder captures the full 360° of azimuth while limiting the vertical scan to the energy-bearing elevation sector. Planar near-field fits forward-radiating pencil-beam apertures, while spherical near-field gives complete 4π coverage at the cost of far more points and a two-axis rotation positioner.

How fine must the cylindrical near-field sampling be to avoid aliasing?

The axial spacing must satisfy Δz ≤ λ/2, and the azimuth spacing follows the maximum mode index N ≈ k·r₀ + 10, giving Δφ ≤ 180°/N and at least 2N+1 azimuth points. At 10 GHz with r₀ = 0.5 m, k·r₀ ≈ 105, so roughly 231 azimuth points and a 15 mm vertical step are needed. Undersampling either coordinate folds high-order modes into the visible region and corrupts the computed sidelobes.

Why does cylindrical near-field measurement require probe correction?

The probe has its own directive pattern and polarization response, so the measured signal is the convolution of the true field with the probe pattern in cylindrical modes. Probe correction divides the measured mode coefficients by the probe receiving coefficients to recover only the test antenna. An open-ended waveguide probe is favored for its smooth, easily deconvolved pattern. Skipping correction adds gain errors of several tenths of a dB and degrades sidelobe and cross-polarization accuracy.

Related Terms

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