  Reconstruction of the sky brightness measured by radio interferometers is
typically achieved through gridding techniques, or histograms in spatial
Fourier space. For Epoch of Reionisation (EoR) 21 cm power spectrum
measurements, extreme levels of gridding resolution are required to reduce
spectral contamination, as explored in other works. However, the role of the
shape of the Fourier space spreading function, or kernel, also has consequences
in reconstructed power spectra. We decompose the instrumental Murchison
Widefield Array (MWA) beam into a series of Gaussians and simulate the effects
of finite kernel extents and differing shapes in gridding/degridding for
optimal map making analyses. For the MWA, we find that the kernel must extend
out to 0.001--0.0001% of the maximum value in order to measure the EoR using
foreground avoidance. This requirement changes depending on beam shape, with
compact kernels requiring far smaller extents for similar contamination levels
at the cost of less-optimal errors. However, simple calibration using pixelated
degridding results, regardless of shape of the kernel, cannot recover the EoR
due to catastrophic errors caused by the pixel resolution. Including an opaque
horizon with widefield beams also causes significant spectral contamination via
a beam--horizon interaction that creates an infinitely extended kernel in
Fourier space, which cannot be represented well. Thus, our results indicate
that simple calibration via degridded models and optimal map making for extreme
widefield instrumentation are not feasible.
