  Interferometers, such as the Event Horizon Telescope (EHT), do not directly
observe the images of sources but rather measure their Fourier components at
discrete spatial frequencies up to a maximum value set by the longest baseline
in the array. Construction of images from the Fourier components or analysis of
them with high-resolution models requires careful treatment of fine source
structure nominally beyond the array resolution. The primary EHT targets, Sgr
A* and M87, are expected to have black-hole shadows with sharp edges and
strongly filamentary emission from the surrounding plasma on scales much
smaller than those probed by the currently largest baselines. We show that for
aliasing not to affect images reconstructed with regularized maximum likelihood
methods and model images that are directly compared to the data, the sampling
of these images (i.e., their pixel spacing) needs to be significantly finer
than the scale probed by the largest baseline in the array. Using GRMHD
simulations of black-hole images, we estimate the maximum allowable pixel
spacing to be approximately equal to (1/8)GM/c^2; for both of the primary EHT
targets, this corresponds to an angular pixel size of <0.5 microarcseconds.
With aliasing under control, we then advocate use of the second-order
Butterworth filter with a cut-off scale equal to the maximum array baseline as
optimal for visualizing the reconstructed images. In contrast to the
traditional Gaussian filters, this Butterworth filter retains most of the power
at the scales probed by the array while suppressing the fine image details for
which no data exist.
