Random sampling can lead to algorithms in which the Fourier reconstruction is almost perfect when the underlying spectrum of the signal is sparse or band-limited. Conversely, regular sampling often hampers the Fourier data recovery methods. However, 2D signals that are band-limited in one spatial dimension can be recovered by designing a regular acquisition grid that minimizes the mixing between the unknown spectrum of the well-sampled signal and aliasing artifacts. This concept can be easily extended to higher dimensions and used to define potential strategies for acquisition-guided Fourier reconstruction. The wavenumber response of various sampling operators is derived and sampling conditions for optimal Fourier reconstruction are investigated using synthetic and real data examples.