Practical Electron Microscopy and Database

In EMs, the control of the lens currents must be very accurate and must remain stable once set. However, the resolution of electron microscopes (EMs) is partially limited by:
         i) The electrical stability of the EM systems, e.g. the stabilities of the high voltage and the lens currents;
         ii) External disturbances e.g. mechanical vibration, contamination, charging, fluctuation of stray magnetic fields, and the nonuniform magnetic properties of the pole-piece material used.

In STEM, the fluctuations in accelerating voltage or the current flow in the probe-forming electromagnetic lenses contributes to the chromatic aberration that leads a cutoff to the highest spatial frequency. In HRTEM, the cut-off frequency corresponds to the information limit. In STEM, the effect of the fluctuations induces additional contribution to the probe size [1],

         ------------- [4255]

where,
        C_c -- The chromatic coefficient,
        E₀ -- The energy of the electron beam,
        I -- The current in the probe-forming lens,
        ΔE -- The spread in energy of the beam,
        ΔE₀ -- The fluctuation in the accelerating voltage,
        ΔI -- The fluctuation of the lens current.

The high-tension power supply and beam-current in modern electron microscopes can achieve 10^-7 stability so that the main source of the chromatic aberration is due to energy spread of the electrons within the probe.

Note that the instability of lens currents also limits the phase contrast transfer function (CTF) in TEMs. For instance, in EMs (especially in TEMs), the temporal coherency effects comes from the small instabilities in the accelerating voltage and electron gun emission over time, which will give the illumination a small energy spread, and from variations in the lens currents, which induces focus variation with time. Therefore, most of the CTF damping is caused by the fluctuations of the lens currents or the high voltage of the microscope, which affects the information limit (see page1436).

[1] Spence JCH. High resolution electron microscopy. 3rd ed. Oxford: Clarendon Press; 2003.