Abstract The use of a high-angle annular detector in a scanning transmission electron microscope is shown to provide incoherent images of crystalline materials with strong compositional sensitivity. How this occurs, even in the presence of strong dynamical diffraction of the low-angle beams, becomes very clear in a Bloch wave description of the imaging, which shows that only tightly bound s-type Bloch states contribute significantly to the image. Interference effects are therefore precluded and the image can be described as a convolution. There are no contrast reversals with thickness or defocus and no Fresnel fringe effects at interfaces. Each atomic column contributes to the image independently of its neighbors until the s-states themselves overlap. With an optimum imaging probe the nature of the convolution can be visualized intuitively to a scale well below the resolution limit. To first order, therefore, each object has only one possible image, and since the same probe is used for all objects, an unknown structure can be interpreted directly. These ideas will be illustrated with images from semiconductors, superconductors, and alloys.