# Colab Setup (Run this first)

!pip install litebird_sim rich

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[notice] A new release of pip is available: 26.1.2 -> 26.2.1
[notice] To update, run: pip install --upgrade pip

Simulation with an explicit HWP harmonics expansion#

To run this notebook, you have several options:

If you are running this under Binder, you should already be set!
If you are running this under Google Colab, be sure to run the cell with !pip install… that is right above the title.
If you are running this locally, you should first create and activate a new virtual environment with the commands
```
python -m venv ./my_venv
source ./my_venv/bin/activate
```
(you can use Conda environments, if you prefer) and install Jupyter and litebird_sim in it:
```
pip install jupyter litebird_sim
```
If you have a local copy of the litebird_sim repository cloned from litebird/litebird_sim (e.g., because you’re part of the Simulation Team!), you can use a development install instead:
```
cd /my/local/copy/litebird_sim
pip install -e .
```

Import Modules#

import healpy as hp
import matplotlib.pyplot as plt
import numpy as np

import litebird_sim as lbs

Define Parameters#

start_time = 0
time_span_s = 100 * 24 * 3600
nside = 64
imo_location = "schema.json"
imo = lbs.Imo(flatfile_location=lbs.PTEP_IMO_LOCATION)
imo_version = "vPTEP"

Create Simulation#

sim = lbs.Simulation(
    start_time=start_time, duration_s=time_span_s, random_seed=0, imo=imo
)

comm = sim.mpi_comm

[2026-09-03 17:22:17,231 WARNING MPI#0000] MPI layer is already initialized. Reinitializing the entire RNG hierarchy.
[2026-09-03 17:22:17,231 WARNING MPI#0000] MPI layer is already initialized. Reinitializing the entire RNG hierarchy.

Define Frequency Channel#

telescope = "MFT"
channel = "M2-119"

channelinfo = lbs.FreqChannelInfo.from_imo(
    url=f"/releases/{imo_version}/satellite/{telescope}/{channel}/channel_info",
    imo=imo,
)

Define Scanning Strategy#

sim.set_scanning_strategy(
    imo_url=f"/releases/{imo_version}/satellite/scanning_parameters/",
)

Define Instrument#

instrument_info = lbs.InstrumentInfo.from_imo(
    imo,
    url=f"/releases/{imo_version}/satellite/{telescope}/instrument_info",
)

sim.set_instrument(instrument_info)

hwp_radpsec = instrument_info.hwp_rpm * 2 * np.pi / 60

Set HWP#

# if Mueller formalism
#
# sim.set_hwp(
#    lbs.NonIdealHWP(hwp_radpsec, harmonic_expansion=True, calculus=lbs.HWPFormalism.MUELLER)
# )

# if Jones formalism
sim.set_hwp(
    lbs.NonIdealHWP(
        hwp_radpsec, harmonic_expansion=True, calculus=lbs.HWPFormalism.MUELLER
    )
)

Define Detectors#

det = lbs.DetectorInfo.from_imo(
    url=f"/releases/{imo_version}/satellite/{telescope}/{channel}/{channelinfo.detector_names[0]}/detector_info",
    imo=imo,
)

# This is usually not needed. PTEP IMo has no pointing_theta_phi_psi_deg value, so we're setting some values in here so that the code does not break.
det.pointing_theta_phi_psi_deg = [0, 0, 0]
det.pol_angle_rad = 0
# We're also reducing the sampling rate so that the simulation goes faster.
det.sampling_rate_hz = 1

# if Mueller
det.mueller_hwp = {
    "0f": np.array([[1, 0, 0], [0, 0, 0], [0, 0, 0]], dtype=np.float64),
    "2f": np.array([[0, 0, 0], [0, 0, 0], [0, 0, 0]], dtype=np.float64),
    "4f": np.array(
        [
            [0, 0, 0],
            [3.5e-5, 1, 1],
            [3.5e-5, 1, 1],
        ],
        dtype=np.float64,
    ),
}


mueller_phases = {
    "2f": np.zeros((3, 3)),
    "4f": np.array(
        [
            [0, 0, 0],
            [0, 0, -np.pi / 2],
            [0, -np.pi / 2, np.pi],
        ],
        dtype=np.float64,
    ),
}


# if Jones
# det.jones_hwp = {
#    "0f": np.array([[1, 0], [0, -1]], dtype=np.complex128,
#    ),
#    "2f": np.array(
#        [
#            [
#                9.67e-01 * np.exp(1j * np.deg2rad(5.51e01)),
#                6.16e-02 * np.exp(1j * np.deg2rad(1.26e02)),
#            ],
#            [
#                6.18e-02 * np.exp(1j * np.deg2rad(1.25e02)),
#                9.85e-01 * np.exp(1j * np.deg2rad(-1.46e02)),
#            ],
#        ],
#        dtype=np.complex128,),
# }

Create Observations and Prepare Pointings#

(obs,) = sim.create_observations(
    detectors=[det],
)

sim.prepare_pointings(append_to_report=False)
sim.precompute_pointings()

Generate Input Sky Maps#

sky_params = lbs.SkyGenerationParams(
    make_cmb=True,
    make_dipole=True,
    make_fg=True,
    fg_models=["s1", "d1"],
    seed_cmb=1,  # set this seed if you want to fix the CMB realization
    apply_beam=True,  # if True, smooths the input map by the beam of the channel
    bandpass_integration=False,  # if True, integrates over the top-hat bandpass of the channel
    units="K_CMB",
    output_type="map",
    nside=nside,
)

sky = sim.get_sky(
    parameters=sky_params,
    channels=channelinfo,
)

[2026-09-03 17:22:19,073 INFO MPI#0000] Generating CMB...
[2026-09-03 17:22:19,097 INFO MPI#0000] Generating Foregrounds...
[2026-09-03 17:22:19,098 INFO MPI#0000] Retrieve data for pysm_2/synch_t_new.fits (if not cached already)
[2026-09-03 17:22:19,099 INFO MPI#0000] NSIDE = 512
[2026-09-03 17:22:19,099 INFO MPI#0000] ORDERING = RING in fits file
[2026-09-03 17:22:19,099 INFO MPI#0000] INDXSCHM = IMPLICIT
[2026-09-03 17:22:19,133 INFO MPI#0000] Retrieve data for pysm_2/synch_q_new.fits (if not cached already)
[2026-09-03 17:22:19,135 INFO MPI#0000] NSIDE = 512
[2026-09-03 17:22:19,135 INFO MPI#0000] ORDERING = RING in fits file
[2026-09-03 17:22:19,135 INFO MPI#0000] INDXSCHM = IMPLICIT
[2026-09-03 17:22:19,162 INFO MPI#0000] Retrieve data for pysm_2/synch_u_new.fits (if not cached already)
[2026-09-03 17:22:19,163 INFO MPI#0000] NSIDE = 512
[2026-09-03 17:22:19,163 INFO MPI#0000] ORDERING = RING in fits file
[2026-09-03 17:22:19,164 INFO MPI#0000] INDXSCHM = IMPLICIT
[2026-09-03 17:22:19,190 INFO MPI#0000] Retrieve data for pysm_2/synch_beta.fits (if not cached already)
[2026-09-03 17:22:19,191 INFO MPI#0000] NSIDE = 512
[2026-09-03 17:22:19,192 INFO MPI#0000] ORDERING = RING in fits file
[2026-09-03 17:22:19,192 INFO MPI#0000] INDXSCHM = IMPLICIT
[2026-09-03 17:22:19,218 INFO MPI#0000] Retrieve data for pysm_2/dust_t_new.fits (if not cached already)
[2026-09-03 17:22:19,219 INFO MPI#0000] NSIDE = 512
[2026-09-03 17:22:19,219 INFO MPI#0000] ORDERING = RING in fits file
[2026-09-03 17:22:19,219 INFO MPI#0000] INDXSCHM = IMPLICIT
[2026-09-03 17:22:19,245 INFO MPI#0000] Retrieve data for pysm_2/dust_q_new.fits (if not cached already)
[2026-09-03 17:22:19,246 INFO MPI#0000] NSIDE = 512
[2026-09-03 17:22:19,247 INFO MPI#0000] ORDERING = RING in fits file
[2026-09-03 17:22:19,247 INFO MPI#0000] INDXSCHM = IMPLICIT
[2026-09-03 17:22:19,273 INFO MPI#0000] Retrieve data for pysm_2/dust_u_new.fits (if not cached already)
[2026-09-03 17:22:19,274 INFO MPI#0000] NSIDE = 512
[2026-09-03 17:22:19,275 INFO MPI#0000] ORDERING = RING in fits file
[2026-09-03 17:22:19,275 INFO MPI#0000] INDXSCHM = IMPLICIT
[2026-09-03 17:22:19,300 INFO MPI#0000] Retrieve data for pysm_2/dust_beta.fits (if not cached already)
[2026-09-03 17:22:19,302 INFO MPI#0000] NSIDE = 512
[2026-09-03 17:22:19,302 INFO MPI#0000] ORDERING = RING in fits file
[2026-09-03 17:22:19,302 INFO MPI#0000] INDXSCHM = IMPLICIT
[2026-09-03 17:22:19,328 INFO MPI#0000] Retrieve data for pysm_2/dust_temp.fits (if not cached already)
[2026-09-03 17:22:19,329 INFO MPI#0000] NSIDE = 512
[2026-09-03 17:22:19,329 INFO MPI#0000] ORDERING = RING in fits file
[2026-09-03 17:22:19,329 INFO MPI#0000] INDXSCHM = IMPLICIT
[2026-09-03 17:22:20,776 INFO MPI#0000] Generating Dipole...
[2026-09-03 17:22:20,777 INFO MPI#0000] Summing components...

Fill TOD#

lbs.scan_map_in_observations(
    observations=[obs], maps=sky, mueller_phases=mueller_phases
)

output_maps = sim.make_binned_map(nside=nside).binned_map
input_maps = sky["M2-119"].values

Show Output Maps#

plt.figure(figsize=(32, 10))
stokes_parameters = ["T", "Q", "U"]
diff = output_maps - input_maps
for i in range(3):
    hp.mollview(
        input_maps[i] * 1e6,
        cmap="jet",
        sub=(3, 3, i + 1),
        title="Input " + stokes_parameters[i],
    )
    hp.mollview(
        output_maps[i] * 1e6,
        min=np.min(input_maps[i] * 1e6),
        max=np.max(input_maps[i] * 1e6),
        cmap="jet",
        sub=(3, 3, i + 4),
        title="Output " + stokes_parameters[i],
    )
    hp.mollview(
        diff[i] * 1e6,
        min=-0.05,
        max=0.05,
        cmap="jet",
        sub=(3, 3, i + 7),
        title="Output " + stokes_parameters[i],
    )

../_images/5d9b5e85a51ddbc80878639af7eda6c1dd82e90d66e5100b78fa47ecbcd5b57c.png