Modelling Different Farfield Polarisations for an Aperture

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

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 requried. 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 = 181
elev_res = 73
wavelength = 3e8 / 10e9

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

from lyceanem.base_classes import points,structures,antenna_structures

from lyceanem.geometry.targets import meshedHorn
structure,array_points=meshedHorn(3*wavelength, 1*wavelength, 4*wavelength, 1*wavelength,np.radians(10),wavelength*0.5)


horn_antenna=antenna_structures(structures(solids=[structure]), points(points=[array_points]))

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(
    horn_antenna.export_all_points(),
    horn_antenna,
    horn_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,
    beta=(2*np.pi)/wavelength
)

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.reshape(elev_res,az_res)
u_pattern.pattern[:, :, 1] = Ephi.reshape(elev_res,az_res)
u_pattern.display_pattern(desired_pattern='Power')

C:\Users\lycea\miniconda3\envs\CudaDevelopment\Lib\site-packages\lyceanem\electromagnetics\beamforming.py:1277: RuntimeWarning: divide by zero encountered in log10
  logdata = 10 * np.log10(data)

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(
    horn_antenna.export_all_points(),
    horn_antenna,
    horn_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,
    beta=(2*np.pi)/wavelength
)


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

C:\Users\lycea\miniconda3\envs\CudaDevelopment\Lib\site-packages\lyceanem\electromagnetics\beamforming.py:1277: RuntimeWarning: divide by zero encountered in log10
  logdata = 10 * np.log10(data)

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(
    horn_antenna.export_all_points(),
    horn_antenna,
    horn_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,
    beta=(2*np.pi)/wavelength
)

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

C:\Users\lycea\miniconda3\envs\CudaDevelopment\Lib\site-packages\lyceanem\electromagnetics\beamforming.py:1277: RuntimeWarning: divide by zero encountered in log10
  logdata = 10 * np.log10(data)

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.

from scipy.spatial.transform import Rotation as R

r=R.from_euler('xyz', np.radians(np.asarray([45.0,45.0,0.0])))
horn_antenna.rotate_antenna(r.as_matrix())


desired_E_axis = np.zeros((1, 3), dtype=np.complex64)
desired_E_axis[0, 0] = 1.0
Etheta, Ephi = calculate_farfield(
    horn_antenna.export_all_points(),
    horn_antenna,
    horn_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,
    beta=(2*np.pi)/wavelength
)
u_pattern.pattern[:, :, 0] = Etheta.reshape(elev_res,az_res)
u_pattern.pattern[:, :, 1] = Ephi.reshape(elev_res,az_res)
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(
    horn_antenna.export_all_points(),
    horn_antenna,
    horn_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,
    beta=(2*np.pi)/wavelength
)
v_pattern.pattern[:, :, 0] = Etheta.reshape(elev_res,az_res)
v_pattern.pattern[:, :, 1] = Ephi.reshape(elev_res,az_res)
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(
    horn_antenna.export_all_points(),
    horn_antenna,
    horn_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,
    beta=(2*np.pi)/wavelength
)
n_pattern.pattern[:, :, 0] = Etheta.reshape(elev_res,az_res)
n_pattern.pattern[:, :, 1] = Ephi.reshape(elev_res,az_res)
n_pattern.display_pattern(desired_pattern='Power')

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C:\Users\lycea\miniconda3\envs\CudaDevelopment\Lib\site-packages\lyceanem\electromagnetics\beamforming.py:1277: RuntimeWarning: divide by zero encountered in log10
  logdata = 10 * np.log10(data)
C:\Users\lycea\miniconda3\envs\CudaDevelopment\Lib\site-packages\lyceanem\electromagnetics\beamforming.py:1277: RuntimeWarning: divide by zero encountered in log10
  logdata = 10 * np.log10(data)
C:\Users\lycea\miniconda3\envs\CudaDevelopment\Lib\site-packages\lyceanem\electromagnetics\beamforming.py:1277: RuntimeWarning: divide by zero encountered in log10
  logdata = 10 * np.log10(data)