OSKAR telescope: point response

This file explains in a step-by-step manner how to compute the beam response for an OSKAR station. The complete code is shown at the bottom of this page.

It all starts with importing the everybeam python module, along with any other libraries that are needed for your project.

import everybeam as eb
import numpy as np

In order to evaluate the beam response, we need to specify which Measurement Set will be used, whether or not to apply the differential beam and which element response model should be used. The element response should be eihter one of ["hamaker", "lobes", "oskar_dipole", "skala40_wave"]. Even more important, the element response model needs to be chosen such that it is consistent with the provided telescope. So for an OSKAR Measurement Set, the element response model should be either "oskar_dipole" or "skala40_wave". In this demo we opt for "skala40_wave" - which is the element response model that is currently used in OSKAR simulations:

# Set path to (OSKAR) MS
ms_path = "../../test_data/OSKAR_MOCK.ms"

# Use differential beam?
use_differential_beam = False

# Set element response model
element_response_model = "skala40_wave"

Given the Measurement Set and the options, we can now load the telescope. Given your Measurement Set, EveryBeam sorts out which telescope should be returned. In this example we obviously expect to get an OSKAR telescope back.

# Load the telescope
telescope = eb.load_telescope(
    ms_path,
    use_differential_beam=use_differential_beam,
    element_response_model=element_response_model,
)

# Is this an OSKAR telescope?
assert type(telescope) == eb.OSKAR

In order to evaluate the beam, we need to set some additional (observation related) variables, such as the time, the station index, the frequency, and the point of interest (in ITRF-coordinates)

::

# Set properties for the beam evaluation time = 4.45353e09 station_id = 0 freq = 5.0e07

# Point of interest (given in ITRF coordinates) dir_itrf = np.array([-0.203137, 0.841818, -0.500078])

Now we are in principle all set to compute the beam response. For instance, computing the array factor can be done as:

array_factor_phase_centre = telescope.array_factor(
    time, station_id, freq, dir_itrf, dir_itrf
)

In this specific example, the point of interest and the delay direction are chosen identical. As a result, we expect that a unity (2x2) matrix is returned:

np.testing.assert_allclose(
    array_factor_phase_centre, np.eye(2, dtype=np.complex64), rtol=1e-8
)

To make the example a bit less trivial, we adapt the delay direction so that it doesn’t coincide with the point of interest, e.g.:

delay_dir_itrf = dir_itrf + np.array([-0.1, 0.5, 0.025])

We now can calculate the array factor, element response and the full response for a non trivial delay direction and check that the full response matches the matrix-product of the array factor and the element response:

array_factor = telescope.array_factor(time, station_id, freq, dir_itrf, delay_dir_itrf)

# Element beam for station 0
element_response = telescope.element_response(time, station_id, freq, dir_itrf)

# Full beam for station 0
response = telescope.station_response(time, station_id, freq, dir_itrf, delay_dir_itrf)

# Full beam should match product of array_factor and element_response
np.testing.assert_allclose(
    np.matmul(array_factor, element_response), response, rtol=1e-6
)

A complete overview of the code is shown below:

#!/usr/bin/env python3
# Copyright (C) 2021 ASTRON (Netherlands Institute for Radio Astronomy)
# SPDX-License-Identifier: GPL-3.0-or-later

import everybeam as eb
import numpy as np
import os

"""
Demo script illustrating how the EveryBeam Python
bindings can be used to compute beam responses.

Script requires an OSKAR Measurement Set in order to run.
A minimal OSKAR MSet can be downloaded here:
https://support.astron.nl/software/ci_data/EveryBeam/OSKAR-single-timeslot.tar.bz2
"""

# Set path to (OSKAR) MS
ms_path = os.path.join(os.environ["DATA_DIR"], "OSKAR_MOCK.ms")

# Use differential beam?
use_differential_beam = False

# Set element response model
element_response_model = "skala40_wave"

# Load the telescope
telescope = eb.load_telescope(
    ms_path,
    use_differential_beam=use_differential_beam,
    element_response_model=element_response_model,
)

# Is this an OSKAR telescope?
assert type(telescope) == eb.OSKAR

# Set properties for the beam evaluation
time = 4.45353e09
station_id = 0
freq = 5.0e07

# Point of interest (given in ITRF coordinates)
dir_itrf = np.array([-0.203137, 0.841818, -0.500078])

# Array factor for station 0, since we are evaluating at the phase centre (delay direction and
# direction of interest coincide), a unity matrix should be returned
array_factor_phase_centre = telescope.array_factor(
    time, station_id, freq, dir_itrf, dir_itrf
)
np.testing.assert_allclose(
    array_factor_phase_centre, np.eye(2, dtype=np.complex64), rtol=1e-8
)

# Just a rather arbitrarily chosen delay direction
delay_dir_itrf = dir_itrf + np.array([-0.1, 0.5, 0.025])
array_factor = telescope.array_factor(
    time, station_id, freq, dir_itrf, delay_dir_itrf
)

# Element beam for station 0
element_response = telescope.element_response(time, station_id, freq, dir_itrf)

# Full beam for station 0
response = telescope.station_response(
    time, station_id, freq, dir_itrf, delay_dir_itrf
)

# Full beam should match product of array_factor and element_response
np.testing.assert_allclose(
    np.matmul(array_factor, element_response), response, rtol=1e-6
)