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

TL;DR

fftvis presents a fast, accurate visibility simulator for 21 cm cosmology by reformulating the RIME with a Type-3 NUFFT implemented via finufft. It achieves large-speedups and reduced memory usage compared to matvis, especially for dense, multi-element arrays, while maintaining near machine-precision fidelity for diffuse sky models and preserving spectral/temporal coherence essential for EoR validation. The framework includes coordinate rotation, beam interpolation, and a configurable precision parameter, with validations against analytic solutions and delay/fringe-rate metrics guiding practical usage. The work positions fftvis as a scalable forward-modeling tool that complements existing simulators, with clear paths for future enhancements such as per-antenna beams and GPU acceleration, to support growing demands of 21 cm pipeline validation and forward modeling.

Abstract

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.

Figures (8)

• Figure 1: Schematic representation of the Flatiron Institute Non-Uniform Fast Fourier Transform (finufft) algorithm as utilized by fftvis. The simulation pipeline consists of five key stages: (Panel A) The user-supplied sky model is weighted by the antenna beam pattern, which is interpolated to each source component's position. (Panel B) The beam-weighted source intensities are projected onto a fine grid through convolution with a compact gridding kernel $\phi$. (Panel C) The gridded sky model undergoes transformation from image-domain to visibility-domain via Fast Fourier Transform (FFT). (Panel D) The visibility-domain grid is corrected for gridding artifacts through deconvolution with the Fourier transform of the gridding kernel, $\hat{\phi}$. (Panel E) Finally, the algorithm interpolates the gridded visibilities to the exact sampling positions in the $uv$-plane determined by the unique baseline vectors derived from the input antenna positions. This process enables efficient computation of visibilities from arbitrary source distributions and antenna positions while maintaining numerical accuracy within user-specified NUFFT tolerance parameters.
• Figure 2: Validation of fftvis against analytic full-sky visibility solutions for diffuse emission patterns from 2022ApJS..259...22L. Each panel shows the magnitude of the visibilities $|V|$ for a different sky models varying in zenith angle (top curves), along with absolute value of the difference $|V_1 - V_2|$ (bottom curves) between fftvis and the analytic result (blue), and between fftvis and matvis (pink). All simulations were performed using discretized sky models generated by the analytic_diffuse package. fftvis matches the analytic solutions to better than $\sim$$10^{-5}$ for most of the range of $u$ values simulated, and agrees with matvis to near machine precision, confirming the accuracy and reliability of the NUFFT-based method for simulating smooth, diffuse sky structure. We note that this sky model error is the result of HEALPix gridding errors, and will decrease with the size of the input sky model.
• Figure 3: Delay spectra (top row) and the corresponding absolute difference between matvis and fftvis (bottom row) are shown for visibilities simulated using an airy beam model and smooth spectrum sky model for four different baselines (14.6m EW, 146.0m EW, 25.3m NS, and 193.9m NS). Here, we compare simulated visibilities from matvis (dashed black), treated here as an exact numerical reference, and fftvis at various NUFFT precision levels (colored lines). For context, the FFT of the squared Blackman-Harris tapering function (dotted black) indicates the dynamic range limit imposed by the spectral windowing itself. In the top row, we show the normalized amplitude of the delay transform for each set of simulated visibilities, while in the bottom row reveals numerical artificats introdcued by the NUFFT approximation in fftvis, computed as the absolute difference relative to the matvis reference. As the NUFFT precision parameter, $\epsilon$, decreases, fftvis converges more closely to matvis across the full range of delays. As $\epsilon$ decreases from $10^{-7}$ to $10^{-13}$, the fftvis solutions demonstrate progressively improved convergence to the reference set of matvis simulations. Even at moderate precision settings, fftvis maintains numerical accuracy compared to matvis exceeding $10^{-6}$ relative to foreground amplitudes. These results validate that the NUFFT-based approach introduces negligible algorithmic artifacts at precision levels appropriate for validating 21 cm analysis pipelines.
• Figure 4: Fringe-rate spectra of simulated visibilities for three baselines with east-west projections of $14.6 \, \rm m$, $292.0 \, \rm m$, and $584.0 \, \rm m$, generated using fftvis (using $\epsilon = 10^{-13}$) and matvis. The top panel shows the normalized amplitude of the fringe-rate transformed visibilities, while the bottom panel presents the absolute residuals between the two simulators. Vertical dotted lines indicate the analytically expected maximum fringe rate, corresponding to the east-west projection associated with each baseline and latitude of the simulated array 2016ApJ...820...51P where the slight bleed outside of this window is caused by extra temporal structure introduced by sources moving through the beam. We find that the residuals between fftvis and matvis are below $10^{-13}$ for all baselines and fringe rates tested. The excellent agreement across all three baselines demonstrates that the use of the NUFFT in fftvis does not introduce significant time-dependent artifacts into the simulated visibilities.
• Figure 5: Here, we demonstrate how execution times (top row) of matvis and fftvis scale with three key simulation parameters: (left column) the number of sources in the sky model, (middle) the number of antennas in a densely packed array, and (right) maximum baseline length in wavelengths. We begin from a fiducial simulation that uses a HEALPix sky model of $N_{\rm side} = 256 \ (\approx 7.8 \times 10^5 \ \rm pixels)$, a densely-packaged hexagonal array of $N_{\rm ants} = 261$, and 32 time integrations at a single frequency channel. In each plot, we vary one parameter while holding the other parameters fixed. In the bottom row, we show the ratio of execution times (matvis/fftvis) for both single-core and 4-core CPU runs. From these panels, we find that fftvis excels when simulating many-element, dense arrays, but struggles when the input array becomes more sparse in $uv$-coordinates, due to an under-utilization of the FFT of the input sky. However, an important exception occurs when antenna positions form a grid. In this scenario, a Type 1 NUFFT enables more efficient visibility simulation, as shown in the right-hand column.