# Optimal gridding and degridding in radio interferometry imaging

## TL;DR

This paper introduces a new family of gridding functions for radio interferometry imaging that significantly reduce aliasing and misfit errors, improving accuracy while maintaining computational efficiency.

## Contribution

The authors propose a parameterised family of least-misfit gridding functions that outperform traditional spheroidal functions in alias suppression and RMS misfit reduction.

## Key findings

- Over 100 times better alias suppression compared to spheroidal functions.
- Achieves near machine precision accuracy with minimal lookup tables.
- Balances accuracy, computational cost, and storage effectively.

## Abstract

In radio interferometry imaging, the gridding procedure of convolving visibilities with a chosen gridding function is necessary to transform visibility values into uniformly sampled grid points. We propose here a parameterised family of "least-misfit gridding functions" which minimise an upper bound on the difference between the DFT and FFT dirty images for a given gridding support width and image cropping ratio. When compared with the widely used spheroidal function with similar parameters, these provide more than 100 times better alias suppression and RMS misfit reduction over the usable dirty map. We discuss how appropriate parameter selection and tabulation of these functions allow for a balance between accuracy, computational cost and storage size. Although it is possible to reduce the errors introduced in the gridding or degridding process to the level of machine precision, accuracy comparable to that achieved by CASA requires only a lookup table with 300 entries and a support width of 3, allowing for a greatly reduced computation cost for a given performance.