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hwp.rst

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Half Wave Plate

The rotation of the polarization angle induced by a HWP can be included in the returned pointing information by passing an instance of IdealHWP, a descendant of the class :class:`.HWP`, to the method :meth:`.Simulation.set_hwp`. Here is an example for the simplest case, with an Ideal HWP:

.. testcode::

    import litebird_sim as lbs

    sim = lbs.Simulation(
        start_time=0,
        duration_s=100.0,
        random_seed=12345,
    )

    sim.set_scanning_strategy(
        lbs.SpinningScanningStrategy(
            spin_sun_angle_rad=0.785_398_163_397_448_3,
            precession_rate_hz=8.664_850_513_998_931e-05,
            spin_rate_hz=0.000_833_333_333_333_333_4,
            start_time=sim.start_time,
        ),
        delta_time_s=60,
    )

    sim.set_instrument(
        instrument = lbs.InstrumentInfo(
            boresight_rotangle_rad=0.0,
            spin_boresight_angle_rad=0.872_664_625_997_164_8,
            spin_rotangle_rad=3.141_592_653_589_793,
        )
    )

    sim.set_hwp(
        lbs.IdealHWP(ang_speed_radpsec=4.084_070_449_666_731),
    )

    det = lbs.DetectorInfo(
        name="Boresight_detector",
        sampling_rate_hz=1.0,
        quat=[0.0, 0.0, 0.0, 1.0],
    )
    obs, = sim.create_observations(detectors=[det])

    sim.prepare_pointings()

    pointing, hwp_angle = sim.observations[0].get_pointings()
    print(f"{pointing.shape=}")
    print(f"{hwp_angle.shape=}")


.. testoutput::

    pointing.shape=(1, 100, 3)
    hwp_angle.shape=(100,)

This example uses the :class:`.IdealHWP`, which represents an ideal spinning HWP. The method :func:`.get_pointings` returns both pointing and hwp angle on the fly; the shape of pointing reveals that there is one detector, 100 samples, and three angles (ϑ, φ, ψ).

As shown before a similar syntax allow to precompute the pointing and the hwp angle:

sim.prepare_pointings()
sim.precompute_pointings()

# Now you can access:
# - sim.observations[0].pointing_matrix
# - sim.observations[0].hwp_angle

This fills the fields pointing_matrix and hwp_angle for all the observations in the current simulation.

Defining a non-ideal HWP

Another descendant of the class :class:`.HWP` is the class :class:`.NonIdealHWP`, which allows to define a more realistic HWP object. When defining a non ideal HWP, one can choose it to be described by Mueller or Jones formalism and if the desired representation should include the expansion of the matrix in harmonics of the HWP rotation frequency. Here is an example:

import litebird_sim as lbs

sim = lbs.Simulation(
    start_time=0,
    duration_s=100.0,
    random_seed=12345,
)

sim.set_scanning_strategy(
    lbs.SpinningScanningStrategy(
        spin_sun_angle_rad=0.785_398_163_397_448_3,
        precession_rate_hz=8.664_850_513_998_931e-05,
        spin_rate_hz=0.000_833_333_333_333_333_4,
        start_time=sim.start_time,
    ),
    delta_time_s=60,
)

sim.set_instrument(
    instrument = lbs.InstrumentInfo(
        boresight_rotangle_rad=0.0,
        spin_boresight_angle_rad=0.872_664_625_997_164_8,
        spin_rotangle_rad=3.141_592_653_589_793,
    )
)

sim.set_hwp(
    lbs.NonIdealHWP(
        ang_speed_radpsec=4.084_070_449_666_731,
        harmonic_expansion=True,
        calculus=lbs.HWPFormalism.JONES,
    )
)

det = lbs.DetectorInfo(
    name="Boresight_detector",
    sampling_rate_hz=1.0,
    quat=[0.0, 0.0, 0.0, 1.0],
)
obs, = sim.create_observations(detectors=[det])

sim.prepare_pointings()

pointing, hwp_angle = sim.observations[0].get_pointings()

For knowing how to define the HWP when performing integration in band, please refer to the correspondent section of the HWP Systematics docs page.

API reference

.. automodule:: litebird_sim.hwp
    :members:
    :undoc-members:
    :show-inheritance: