The Big Question
How densely must we sample an image in order to capture its essence?

Since our sampling grid is periodic we can appeal to Fourier analysis for an answer. Fourier analysis states that all periodic signals can be represented as a summation of sinusiodal waves. Thus every image function that we understand as a height field in the spatial domain, has a dual representaion in the frequency domain.

We can transform signals from one domain to the other using the Fourier transform.