TEM bright field imaging of thick specimens: nodes in Thon ring patterns

The thickness of an object will, at some point, exceed the depth of field of a transmission electron microscope; the value at which this occurs, depends on the resolution and the wavelength considered. An image is then no longer a true projection of the 3D structure. This effect will be expressed in the power spectrum. Here, we first demonstrate this phenomenon experimentally, using carbon foils of different thicknesses and working at 40, 60, 80 and 300 kV. Since we determined the thicknesses of the foils by tomography, we are also able to confirm experimentally that in the case of a thick object, the Thon ring pattern can be described as the sum of the power spectra originating from thin, independently scattering slices. Thus, a sinc function envelope is observed that attenuates the Thon rings' amplitudes, yielding "nodes" in the pattern at which the amplitudes are zero. These nodes move to lower spatial frequencies with decreasing acceleration voltages and increasing thicknesses. Conversely, the object thickness can be directly derived from node positions at a particular acceleration voltage. We validate our approach by applying it to frozen-hydrated bacteria with experimentally determined thicknesses. Our model will contribute to more reliably determining the defocus to be used with contrast transfer function correction for thicker objects and at lower acceleration voltages.