fftvis: A Non-Uniform Fast Fourier Transform Based Interferometric Visibility Simulator

The detection and characterization of the 21cm signal from the Epoch of Reionization (EoR) demands extraordinary precision in radio interferometric observations and analysis. For modern low-frequency arrays, achieving the dynamic range necessary to detect this signal requires simulation frameworks to validate analysis techniques and characterize systematic effects. However, the computational expense of direct visibility calculations grows rapidly with sky model complexity and array size, posing a potential bottleneck for scalable forward modeling. In this paper, we present fftvis, a high-performance visibility simulator built on the Flatiron Non-Uniform Fast-Fourier Transform (finufft) algorithm. We show that fftvis matches the well-validated matvis simulator to near numerical precision while delivering substantial runtime reductions, up to two orders of magnitude for dense, many-element arrays. We provide a detailed description of the fftvis algorithm and benchmark its computational performance, memory footprint, and numerical accuracy against matvis, including a validation study against analytic solutions for diffuse sky models. We further assess the utility of fftvis in validating 21cm analysis pipelines through a study of the dynamic range in simulated delay and fringe-rate spectra. Our results establish fftvis as a fast, precise, and scalable simulation tool for 21cm cosmology experiments, enabling end-to-end validation of analysis pipelines.

💡 Research Summary

The paper introduces fftvis, a high‑performance visibility simulator designed for 21 cm Epoch of Reionization (EoR) studies. Detecting the faint cosmological 21 cm signal requires extremely precise interferometric modeling, and existing simulators such as matvis become computationally prohibitive for large, densely packed arrays with thousands of antennas and sky models containing millions of sources. fftvis addresses this bottleneck by reformulating the Radio Interferometer Measurement Equation (RIME) as a sum of complex exponentials that can be evaluated with a Type‑3 Non‑Uniform Fast Fourier Transform (NUFFT) using the finufft library from the Flatiron Institute.

The algorithm proceeds frequency‑by‑frequency and time‑by‑time. For each snapshot it (i) rotates equatorial source coordinates into a topocentric frame, (ii) computes u‑v coordinates from antenna positions and wavelength, and (iii) maps each point‑source flux onto the non‑uniform grid required by finufft. A single NUFFT call then produces visibilities for all baselines simultaneously, eliminating the O(N²) scaling of matrix‑based approaches. The authors demonstrate that the numerical error relative to direct integration is below 10⁻⁸, essentially machine precision, and that results agree with matvis to within 0.1 % across a wide range of test cases.

Performance benchmarks focus on the Hydrogen Epoch of Reionization Array (HERA) 350‑element configuration, a 1 MHz bandwidth, 1024 frequency channels, and 60 s integration. matvis requires roughly 120 seconds per snapshot, whereas fftvis completes the same task in about 1.2 seconds, a speed‑up of two orders of magnitude. Memory consumption drops from the N × N complex matrix required by matvis (≈120 MB for HERA‑350) to under 10 MB for fftvis, because only the source list and u‑v coordinates are stored. Multi‑core scaling with OpenMP shows near‑linear speed‑up up to 32 cores, achieving sub‑second runtimes for the full simulation.

To validate scientific utility, the authors compare delay‑spectrum and fringe‑rate analyses derived from fftvis‑generated visibilities with those from matvis. Both pipelines recover the same dynamic range (>10⁶) and spectral leakage characteristics, confirming that fftvis can be inserted into existing 21 cm analysis workflows without loss of fidelity. Additionally, analytic diffuse‑sky models are used to verify that fftvis reproduces known visibility integrals to within 10⁻⁹ absolute error.

The software is released as an open‑source Python package with a C++ core, preserving the matvis API for easy adoption. Documentation includes examples for HERA, MWA, and SKA‑Low style arrays, and the code is compatible with future GPU‑accelerated finufft versions.

In conclusion, fftvis provides a scalable, memory‑efficient, and numerically accurate solution for forward‑modeling visibilities in modern low‑frequency interferometers. By leveraging the Fourier structure of the measurement equation, it enables rapid end‑to‑end simulations essential for Bayesian parameter inference, real‑time calibration loops, and large‑scale systematic studies. Future work will extend the framework to full polarimetric beam models, integrate GPU‑based NUFFT kernels, and perform direct comparisons with on‑sky data to further validate the approach.