High-resolution Transmission Electron Microscopy - Image Contrast and Interpretation

Image Contrast and Interpretation

As opposed to conventional microscopy, HRTEM does not use amplitudes, i.e. absorption by the sample, for image formation. Instead, contrast arises from the interference in the image plane of the electron wave with itself. Due to our inability to record the phase of these waves, we generally measure the amplitude resulting from this interference, however the phase of the electron wave still carries the information about the sample and generates contrast in the image, thus the name phase-contrast imaging. This, however is true only if the sample is thin enough so that amplitude variations only slightly affect the image (the so-called weak phase object approximation, WPOA).

The interaction of the electron wave with the crystallographic structure of the sample is not entirely understood yet, but a qualitative idea of the interaction can readily be obtained. Each imaging electron interacts independently with the sample. Above the sample, the wave of an electron can be approximated as a plane wave incident on the sample surface. As it penetrates the sample, it is attracted by the positive atomic potentials of the atom cores, and channels along the atom columns of the crystallographic lattice (s-state model). At the same time, the interaction between the electron wave in different atom columns leads to Bragg diffraction. The exact description of dynamical scattering of electrons in a sample not satisfying the WPOA (almost all real samples) still remains the holy grail of electron microscopy. However, the physics of electron scattering and electron microscope image formation are sufficiently well known to allow accurate simulation of electron microscope images.

As a result of the interaction with the sample, the electron exit wave right below the sample φ_e(x,u) as a function of the spatial coordinate x is a superposition of a plane wave and a multitude of diffracted beams with different in plane spatial frequencies u (high spatial frequencies correspond to large distances from the optical axis). The phase change of φ_e(x,u) compared to the incident wave peaks at the location of the atom columns. The exit wave now passes through the imaging system of the microscope where it undergoes further phase change and interferes as the image wave in the imaging plane (photo plate or CCD). It is important to realize, that the recorded image is NOT a direct representation of the samples crystallographic structure. For instance, high intensity might or might not indicate the presence of an atom column in that precise location (see simulation). The relationship between the exit wave and the image wave is a highly nonlinear one and is a function of the aberrations of the microscope. It is described by the contrast transfer function.