Accurate Fourier-space statistics for line intensity mapping: Cartesian grid sampling without aliased power

Estimators for $n$-point clustering statistics in Fourier-space demand that modern surveys of large-scale structure be transformed to Cartesian coordinates to perform Fast Fourier Transforms (FFTs). In this work, we explore this transformation in the context of pixelised line intensity maps (LIM), highlighting potential biasing effects on power spectrum measurements. Current analyses often avoid a complete resampling of the data by approximating survey geometry as rectangular in Cartesian space, an increasingly inaccurate assumption for modern wide-sky surveys. Our simulations of a $20\,{\times}\,20\,\text{deg}^2$ 21cm LIM survey at $0.34\,{<}\,z\,{<}\,0.54$ show this assumption biases power spectrum measurements by ${>}\,20\%$ across all scales. We therefore present a more robust framework for regridding the voxel intensities onto a 3D FFT field by coordinate transforming large numbers of Monte-Carlo sampling particles. Whilst this unbiases power spectrum measurements on large scales, smaller-scale discrepancies remain, caused by structure smoothing and aliasing from separations unresolved by the grid. To correct these effects, we introduce modelling techniques, higher-order particle assignments, and interlaced FFT grids to suppress the aliased power. Using a Piecewise Cubic Spline (PCS) particle assignment and an interlaced FFT field, we achieve sub-percent accuracy up to 80% of the Nyquist frequency for our 21cm LIM simulations. We find a more subtle hierarchical improvement in results for higher-order assignment schemes, relative to the gains made for galaxy surveys, which we attribute to the extra complexity in LIM from additional discretising steps. Python code accompanying this paper is available at github.com/stevecunnington/gridimp.