limTOD

Time-Ordered Data simulator for single-dish (autocorrelation) radio intensity mapping — with a differentiable pure-JAX port.

limTOD simulates the time-ordered data (TOD) of a single-dish telescope scanning a HEALPix sky with an arbitrary (asymmetric) beam: the beam is rotated to each pointing in spherical-harmonic space and dotted with the sky, then combined with 1/f gain noise and white noise. The package also ships:

• Map-making — HPW_mapmaking (high-pass + Wiener) and GLS_mapmaking (full 1/f + white noise covariance, ported from hydra-tod's iterative GLS);
• limTOD.patchbeam — a MeerKLASS-optimal sky-TOD path that keeps narrow, finely-gridded beams on their native (l, m) grid and integrates disc-restricted sky patches (no harmonic rotation);
• limTOD.uvbeam — adapters for pyuvdata UVBeam objects, feeding measured/simulated beams into either path;
• limtod_jax — a pure-JAX, jit/vmap/grad-safe port of the sky→TOD chain, verified against the numpy implementation to ~1e-12 in float64. It powers the differentiable pipeline of replicant-telescope.

Latest changes: CHANGELOG.

Installation

pip install limTOD

The base install is deliberately lightweight (wheel-only: numpy, healpy, astropy, scipy, tqdm, mpmath — no compiler needed). Heavier dependencies are opt-in extras:

pip install "limTOD[full]"

From source: clone the repository and pip install -e ".[dev,full]" (runs the test suite over both the MPI-present and serial-fallback paths).

Quick start

Simulate multi-frequency TOD for a MeerKAT-like scan (sky model here needs [gdsm]; pass your own sky_func to go without):

from limTOD import TODSim, example_scan

simulator = TODSim(
    ant_latitude_deg=-30.7130, ant_longitude_deg=21.4430, ant_height_m=1054,
    beam_nside=256, sky_nside=256,
)
time_list, azimuth_list = example_scan()
tod, sky_tod, gain_noise = simulator.generate_TOD(
    freq_list=[950, 1000, 1050],          # MHz
    time_list=time_list,
    azimuth_deg_list=azimuth_list,
    elevation_deg=41.5,
)                                          # each (n_freq, n_time)

The same sky→TOD chain, differentiable in JAX ([jax] extra):

import jax; jax.config.update("jax_enable_x64", True)
import jax.numpy as jnp
import limtod_jax as ltj

sky_alm = ltj.map2alm_quad(sky_map, nside=nside, lmax=lmax)
psi, theta, phi = ltj.zyz_of_pointing(lst_deg, lat_deg, az_deg, el_deg, 0.0)
tod = ltj.generate_tod_sky(
    beam_alm, sky_alm, jnp.stack([psi, theta, phi], axis=-1), lmax=lmax,
)
grad = jax.grad(lambda b: ltj.generate_tod_sky(
    b, sky_alm, jnp.stack([psi, theta, phi], axis=-1), lmax=lmax).sum().real
)(beam_alm)                                # d(TOD sum)/d(beam alms)

Documentation

Full documentation: https://limtod.readthedocs.io

Worked notebooks: TOD simulation and map-making. Mathematical derivations: conventions.pdf.

Citation

If you use limTOD in your research, please cite:

@ARTICLE{2026RASTI...5ag024Z,
       author = {{Zhang}, Zheng and {Bull}, Philip and {Santos}, Mario G. and {Nasirudin}, Ainulnabilah},
        title = "{Joint Bayesian calibration and map-making for intensity mapping experiments}",
      journal = {RAS Techniques and Instruments},
     keywords = {Data Methods, methods: data analysis, techniques: spectroscopic, radio lines: general, Instrumentation and Methods for Astrophysics},
         year = 2026,
        month = jan,
       volume = {5},
          eid = {rzag024},
        pages = {rzag024},
          doi = {10.1093/rasti/rzag024},
archivePrefix = {arXiv},
       eprint = {2509.10992},
 primaryClass = {astro-ph.IM},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2026RASTI...5ag024Z},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

License and authorship

MIT License — see LICENSE.

limTOD is developed and maintained by Zheng Zhang (University of Manchester), with help and advice from members of the MeerKLASS and RHINO collaborations — including Phil Bull, Piyanat Kittiwisit, Geoff Murphy, and Mario Santos.