Theorem for high-resolution high-contrast image synthesis

We show that a band-limited function that has zeros at a prescribed finite number of points within an interval of finite extent can always be found, regardless of how small the bandwidth is. This means that a one-dimensional image that crosses a given level at a number of prescribed points can always be constructed at the output of a diffraction-limited system, regardless of how close the points are, i.e., superresolution in image construction is feasible.