Modelling Different Farfield Polarisations

This example uses the frequency domain lyceanem.models.frequency_domain.calculate_farfield() function to predict the farfield pattern for a linearly polarised aperture. This could represent an antenna array without any beamforming weights.

import numpy as np
import open3d as o3d
import copy

Setting Farfield Resolution and Wavelength

LyceanEM uses Elevation and Azimuth to record spherical coordinates, ranging from -180 to 180 degrees in azimuth, and from -90 to 90 degrees in elevation. In order to launch the aperture projection function, the resolution in both azimuth and elevation is required. In order to ensure a fast example, 37 points have been used here for both, giving a total of 1369 farfield points.

The wavelength of interest is also an important variable for antenna array analysis, so we set it now for 10GHz, an X band aperture.

az_res = 37
elev_res = 37
wavelength = 3e8 / 10e9

Generating consistent point source to explore farfield polarisations, and rotating the source

from lyceanem.base_classes import points,structures,antenna_structures

aperture_coords=o3d.geometry.PointCloud()
point1=np.asarray([0.0,0,0]).reshape(1,3)
normal1=np.asarray([0,0,1.0]).reshape(1,3)
aperture_coords.points=o3d.utility.Vector3dVector(point1)
aperture_coords.normals=o3d.utility.Vector3dVector(normal1)
aperture=points([aperture_coords])
blockers=structures([None])
point_antenna=antenna_structures(blockers, aperture)


from lyceanem.models.frequency_domain import calculate_farfield

The first source polarisation is based upon the u-vector of the source point. When the excitation_function method of the antenna structure class is used, it will calculate the appropriate polarisation vectors based upon the local normal vectors.

desired_E_axis = np.zeros((1, 3), dtype=np.complex64)
desired_E_axis[0, 0] = 1.0
Etheta, Ephi = calculate_farfield(
    point_antenna.export_all_points(),
    point_antenna.export_all_structures(),
    point_antenna.excitation_function(desired_e_vector=desired_E_axis),
    az_range=np.linspace(-180, 180, az_res),
    el_range=np.linspace(-90, 90, elev_res),
    wavelength=wavelength,
    farfield_distance=20,
    elements=False,
    project_vectors=False,
)

Antenna Pattern class is used to manipulate and record antenna patterns

from lyceanem.base_classes import antenna_pattern

u_pattern = antenna_pattern(
    azimuth_resolution=az_res, elevation_resolution=elev_res
)
u_pattern.pattern[:, :, 0] = Etheta
u_pattern.pattern[:, :, 1] = Ephi
u_pattern.display_pattern(desired_pattern='Power')

The second source polarisation is based upon the v-vector of the source point.

desired_E_axis = np.zeros((1, 3), dtype=np.complex64)
desired_E_axis[0, 1] = 1.0
Etheta, Ephi = calculate_farfield(
    point_antenna.export_all_points(),
    point_antenna.export_all_structures(),
    point_antenna.excitation_function(desired_e_vector=desired_E_axis),
    az_range=np.linspace(-180, 180, az_res),
    el_range=np.linspace(-90, 90, elev_res),
    wavelength=wavelength,
    farfield_distance=20,
    elements=False,
    project_vectors=False,
)


v_pattern = antenna_pattern(
    azimuth_resolution=az_res, elevation_resolution=elev_res
)
v_pattern.pattern[:, :, 0] = Etheta
v_pattern.pattern[:, :, 1] = Ephi
v_pattern.display_pattern(desired_pattern='Power')

The third source polarisation is based upon the n-vector of the source point. Aligned with the source point normal.

desired_E_axis = np.zeros((1, 3), dtype=np.complex64)
desired_E_axis[0, 2] = 1.0
Etheta, Ephi = calculate_farfield(
    point_antenna.export_all_points(),
    point_antenna.export_all_structures(),
    point_antenna.excitation_function(desired_e_vector=desired_E_axis),
    az_range=np.linspace(-180, 180, az_res),
    el_range=np.linspace(-90, 90, elev_res),
    wavelength=wavelength,
    farfield_distance=20,
    elements=False,
    project_vectors=False,
)

n_pattern = antenna_pattern(
    azimuth_resolution=az_res, elevation_resolution=elev_res
)
n_pattern.pattern[:, :, 0] = Etheta
n_pattern.pattern[:, :, 1] = Ephi
n_pattern.display_pattern(desired_pattern='Power')

The point source can then be rotated, by providing a rotation matrix, and the u,v,n directions are moved with it in a consistent way.

point_antenna.rotate_antenna(o3d.geometry.get_rotation_matrix_from_axis_angle(np.radians(np.asarray([90.0,0.0,0.0]))))

desired_E_axis = np.zeros((1, 3), dtype=np.complex64)
desired_E_axis[0, 0] = 1.0
Etheta, Ephi = calculate_farfield(
    point_antenna.export_all_points(),
    point_antenna.export_all_structures(),
    point_antenna.excitation_function(desired_e_vector=desired_E_axis),
    az_range=np.linspace(-180, 180, az_res),
    el_range=np.linspace(-90, 90, elev_res),
    wavelength=wavelength,
    farfield_distance=20,
    elements=False,
    project_vectors=False,
)
u_pattern.pattern[:, :, 0] = Etheta
u_pattern.pattern[:, :, 1] = Ephi
u_pattern.display_pattern(desired_pattern='Power')


desired_E_axis = np.zeros((1, 3), dtype=np.complex64)
desired_E_axis[0, 1] = 1.0
Etheta, Ephi = calculate_farfield(
    point_antenna.export_all_points(),
    point_antenna.export_all_structures(),
    point_antenna.excitation_function(desired_e_vector=desired_E_axis),
    az_range=np.linspace(-180, 180, az_res),
    el_range=np.linspace(-90, 90, elev_res),
    wavelength=wavelength,
    farfield_distance=20,
    elements=False,
    project_vectors=False,
)
v_pattern.pattern[:, :, 0] = Etheta
v_pattern.pattern[:, :, 1] = Ephi
v_pattern.display_pattern(desired_pattern='Power')


desired_E_axis = np.zeros((1, 3), dtype=np.complex64)
desired_E_axis[0, 2] = 1.0
Etheta, Ephi = calculate_farfield(
    point_antenna.export_all_points(),
    point_antenna.export_all_structures(),
    point_antenna.excitation_function(desired_e_vector=desired_E_axis),
    az_range=np.linspace(-180, 180, az_res),
    el_range=np.linspace(-90, 90, elev_res),
    wavelength=wavelength,
    farfield_distance=20,
    elements=False,
    project_vectors=False,
)
n_pattern.pattern[:, :, 0] = Etheta
n_pattern.pattern[:, :, 1] = Ephi
n_pattern.display_pattern(desired_pattern='Power')