Spherical Field Samplings

If the antenna field is sampled on a (concentric) spherical surface, the situation is best described with a SphericalFieldSampling. It allows to sample the antenna field at relatively regularly distributed sampling points on a spherical surface. The sampling points on the sphere are defined by a SphereSamplingStrategy. For each sampling point, the antenna field is sampled with two polarizations, i.e., the probe antenna samples the field in the $\chi=0$ and the $\chi=90^°$ configuration.

In general, SphericalFieldSamplings can be used with arbitrary probes but the most efficient algorithms arise from so-called first-order probes.

Note

Very efficient algorithms - e.g., for the transmission - arise when a SphericalFieldSampling is paired with a SphericalWaveExpansion.

Constructors of `SphericalFieldSampling`

To construct a SphericalFieldSampling, the user can specify

a SphereSamplingStrategy to define the number and location of the sampling points on the sphere
the spherical coefficients $\alpha_{s\ell m}^{(1)}$ characterizing the field incident on the antenna under test generated by a radiating probe antenna at the measurement starting position $\vartheta =0, \varphi = 0, \chi =0$.

This is accomplished by using the constructor

SphericalFieldSampling(
    samplingstrategy::SphereSamplingStrategy,
    incidentcoefficients::AbstractSphericalCoefficients,
)

Alternatively, the user can specify

a SphereSamplingStrategy to define the number and location of the sampling points on the sphere
the location and orientation of the probe antenna at the measurement starting position $\vartheta =0, \varphi = 0, \chi =0$
a ProbeAntenna object characerizing the utilized probe antenna
(a flag to indicate if the probe should be treated as a first-order probe)

This is accomplished by using the constructor

SphericalFieldSampling(
    samplingstrategy::SphereSamplingStrategy,
    initialposition::AbstractVector,
    eulerangles::Tuple{<:Real, <:Real, <:Real},
    probe::ProbeAntenna;
    firstorder::Bool=false
)

Using the latter constructor, the incident probe field coefficients are calculatated for the probe configuration and fed into the former constructor to generate the SphereSamplingStrategy.

Spherical Sampling Strategies

At the moment, AntennaFieldRepresentations.jl supports two different kinds of SpheresamplingStrategys:

Spherical Coefficients of the Incident Probe Field

The incident probe field coefficients are represented by a vector of AbstractSphericalCoefficients type. The user must identify the spherical coefficients of the incident probe field (relative to an AUT-centered coordinate system) in a pre-processing step.

The vector for the incident field coefficients must be of type SphericalCoefficients if it contains non-zero entries for some coefficients with $m \neq \pm 1$ or of type FirstOrderSphericalCoefficients if all coefficients with $m \neq \pm 1$ can be ignored.

To create a vector of type AbstractSphericalCoefficients, use one of the following constructors:

SphericalCoefficients(x::AbstractVector)

FirstOrderSphericalCoefficients(x::AbstractVector)

Note

Since a vector of type SphericalCoefficients is itself a subtype of AbstractVector, we can easily convert a vector of SphericalCoefficients into a vector of first-order spherical coefficients via

FirstorderSphericalCoefficients(x::SphericalCoefficients)

Converting a an arbitrary AbstractVector into a FirstOrderSphericalCoefficients-vector drops all entries which correspond to non-first-order modes.

Far Field Sampling

The far-field of the antenna under test is equivalently calculated as the received signal by the AuT when illuminated by an incident plane wave. The spherical coefficients of an incident plane wave are analytically known. They can be conveniently collected up to mode order $L$ via the method

αinc_planewave(L::Integer)

returning a vector of type FirstOrderSphericalCoefficients because all coefficients with $m \neq \pm 1$ are zero for the incident plane wave.