According to Shannon Sampling Theory, Fourier interpolation is the optimal way to reach subpixel accuracy from a properly-sampled digital image. However, for most images this interpolation tends to produce an artifact called ringing, that consists in undesirable oscillations near objects contours. In this work, we propose a way to detect this ringing artifact. Using Euler zigzag numbers, we compute the probability that neighboring gray-levels form an alternating sequence by chance, and characterize these undesirable ringing blocks as structures that would be very unlikely in a random image. We then show two applications where the associated algorithm is used to test or enforce the compliance of an image with Fourier interpolation.