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Fresnel fringes are produced along the edges of TEM objects when the objects are out of focus under a coherent illumination. For instance, the edge between the carbon film and vacuum, or the aperture edges in the TEM present such fringes. Moreover, the number of Fresnel fringes formed in the TEM image of the holey carbon (C) film is much higher for a microscope with a field-emission filament than for a tungsten (W) thermionic filament due to the difference of the sizes of the electron sources. The effective size of the field-emission source is only ~5 nm so that the emitted electrons are in-phase, and thus the source is coherent (see page1409).

Figure 1963a shows the schematic illustration of the interference of the plane waves of the non-scattered and scattered electrons. Assuming the scattering occurs at the edge　(point A)　of a carbon film, the interference of the waves passing points A and B to point C can be given by the path difference between AC and BC, namely AC-BC. This gives intensity maxima of (nλD)^1/2. Here, n is integral numbers.

Figure 1963a. The schematic illustration of the interference of the plane waves of the non-scattered and scattered electrons.

Figure 1963b shows typical Ronchigrams taken at the edge of an amorphous carbon film. At defoci (defined by z-height), there is a distance between the electron cross-over and the point on the specimen along the optic axis. At large underfocus, electron rays at all angles cross the optic axis after the specimen and it shows a shadow image of the specimen edge. At small underfocus, low-angle rays cross the optic axis after the specimen, while high-angle rays cross before the specimen due to spherical aberration. Therefore, the shadow image changes in magnification as a function of the angle. The low-angle asymmetry indicates the presence of astigmatism. At Gaussian focus, the lowest-angle rays cross the axis at the specimen, while higher-angle rays cross before the specimen due to the spherical aberration. The coma free axis is defined at this focus and all alignment and positioning of detectors and apertures can be performed with respect to the low-angle “disk”. Defocus and spherical aberration can effectively cancel each other at those lowest angles. Axial astigmatism can be accurately corrected by using the stigmator coils, resulting in circularly symmetric Ronchigram features. At overfocus, rays at all angles cross the axis before the specimen.

Figure 1963b. Ronchigrams of a thin amorphous carbon (C) film at: (a) Large underfocus, (b) Small underfocus, (c) Gaussian focus, and (d) Overfocus. [1]

[1] E.M. James, N.D. Browning, Practical aspects of atomic resolution imaging and analysis in STEM, Ultramicroscopy 78 (1999) 125-139.