NIFTy for Optical Interferometry — a tutorial

A hands-on tutorial on Bayesian image reconstruction for optical/infrared long-baseline interferometry with NIFTy8 (Numerical Information Field Theory).

The notebooks build the full pipeline from scratch: reading OIFITS data, writing a NIFTy measurement operator for interferometric visibilities, defining sky priors, constructing likelihoods for the optical observables (squared visibilities |V|² and the bispectrum / closure phases), and running Metric Gaussian Variational Inference (MGVI) to obtain a posterior mean image together with an uncertainty map.

Notebooks

Work through them in order:

#	Notebook	What it covers
01	01_dataload	Read an OIFITS file (OI_VIS, OI_VIS2, OI_T3, OI_WAVELENGTH) into a dictionary; plot the (u,v) coverage
02	02_interferometry_response	InterferometryResponse: a NIFTy LinearOperator mapping image → complex visibilities with the ducc0 wgridder, its adjoint (dirty image) and a dot-product test
03	03_sky_models	Synthetic, flux-normalised sky models: Gaussian, elongated Gaussian, uniform disk, ring
04	04_nufft_check	Sanity check of the Fourier step: finufft type-2 NUFFT vs ducc0 dirty2vis (agree to ~1e-10)
05	05_bayesian_reconstruction	Sky priors,

The model in brief

The forward model is the van Cittert–Zernike relation, evaluated on the non-uniform (u,v) points:

$$V(u,v) = \iint I(\ell,m), e^{-2\pi i (u\ell + vm)}, d\ell, dm$$

Optical interferometers rarely measure V directly because the atmosphere scrambles the phase, so the likelihood is built from phase-robust observables:

• squared visibilities |V_ij|²
• bispectrum B = V₁₂ V₂₃ V₁₃^*, whose phase is the closure phase

The sky is modelled as $I = \exp(A,\xi)$ with $\xi$ white Gaussian noise and $A$ a smoothing operator (or a NIFTy SimpleCorrelatedField), which keeps the image positive. MGVI then approximates the posterior over $\xi$ and returns samples, from which the mean image and the per-pixel standard deviation follow.

Results

Test problem (notebook 05): a synthetic sky made of a uniform disk (radius 2 mas, 70 % of the flux) and a ring (2–3 mas, 30 %), observed on the (u,v) coverage of the demo OIFITS file (1224 baselines, 6120 closure triangles, λ = 1.23 µm). |V|² (σ = 0.001) and the complex bispectrum are simulated with Gaussian noise; the image (128 × 128 px, 30 mas field) is reconstructed from |V|² + bispectrum only — no visibility phases — with 10 MGVI iterations (~1 min on a laptop CPU).

• The disk and the ring are recovered at the correct relative separation (12, −2) mas. Since |V|² and closure phases do not constrain the absolute position, the posterior mean is re-centred on the truth's photocentre for the comparison above.
• The ring is recovered as a fainter, smoothed annulus: the smoothness prior (σ = 6 px) and short run blur the sharp edges of the truth.
• The model reproduces the data: |V|, |V|², bispectrum amplitude, and closure phase on the short and intermediate triangles. At the longest baselines the data closure phases are dominated by noise, because |B| ≈ 0 there.

Sky models (notebook 03)	NUFFT vs ducc0 (notebook 04)

Installation

git clone https://github.com/Chandan0107/nifty-oi-tutorial.git
cd nifty-oi-tutorial
pip install -e .          # installs the small `nifty_oi` helper package + nifty8, ducc0, finufft, astropy
jupyter lab nbs/

Tested with Python 3.12, nifty8 8.5, ducc0 0.35, finufft 2.4. On macOS, if you hit an OMP: Error #15 ... libomp crash, run with KMP_DUPLICATE_LIB_OK=TRUE.

Repository layout

nbs/        tutorial notebooks (source of truth, built with nbdev)
nifty_oi/   Python package exported from the notebooks (nbdev_export)
data/       Gaussian_elong.fits — synthetic OIFITS file (17-telescope demo array, λ = 1.23 µm)
figures/    figures used in this README

The nifty_oi package is generated from the notebooks with nbdev: edit the notebooks, then run nbdev_export.

References

• NIFTy: Edenhofer et al., Re-Envisioning Numerical Information Field Theory (NIFTy.re), JOSS 2024; NIFTy documentation
• MGVI: Knollmüller & Enßlin, Metric Gaussian Variational Inference, arXiv:1901.11033 (2019)
• ducc0 wgridder: Arras et al., Efficient wide-field radio interferometry response, A&A 646, A58 (2021)
• OIFITS: Duvert, Young & Hummel, OIFITS 2: the 2nd version of the data exchange standard for optical interferometry, A&A 597, A8 (2017)

License

Apache 2.0 — see LICENSE.