diffraction limit

The diffraction limit is the resolution limit due to diffraction of an electron wave for the optical system with no aberrations. Even in the aberration-free optical system, electron waves exiting from one point on the object do not form an infinitesimal point on the image plane but these electron waves are focused into a finite size spot (airy disk) due to their diffraction phenomenon. The radius r of the airy disk is given by the equation r = 0.6λ/sinα, where λ is the wavelength of the electron and α is the divergence angle of the electron. From the equation, it is seen that the size of the airy disk is small for a large divergence angle of the electron beam. This limitation makes it impossible to produce an infinitesimal point resolution even for ideal lenses.

Figure shows the diffraction limit (vertical axis) r ＝ 0.6λ/sinα for each accelerating voltage as a function of divergence semi-angle α. Since the wavelength of an electron beam is longer for the lower accelerating voltage, the diffraction limit r becomes larger for the lower accelerating voltage even for the same semi-angle α. In the case of an accelerating voltage of 200 kV, a resolution of 0.1 nm expected from the diffraction limit is achieved with a divergence semi-angle of approximately 15 mrad. In the case of 80 kV, however, a larger divergence semi-angle of an approximately 25 mrad is required because of a longer wavelength of the electron beam.