On hysteresis in magnetic lenses of electron microscopes

This paper deals with an experimental procedure to illustrate the problems introduced by ferromagnetic hysteresis present in magnetic lenses of electron microscopes. The magnetic flux density is not available as a measurable quantity. Hysteresis expresses itself in the relation between the input current applied to the lens-coil and the level of sharpness (defocus) of the resulting images. The familiar hysteresis loops are not available, instead we measure hysteresis in the so-called butterfly representation. The input-profiles are non-periodic and illustrate the difficulties with reproducibility in microscopy applications. Image based feedback control is impossible since 99% of the input range yield unusable images. Analysis of the experiments is carried out using a qualitative model consisting of an interconnection of hysteresis representing the magnetic lens and a nonlinear function representing electron optics. Because this model introduces the intermediate magnetic field variable, it is possible to reconstruct and explain the results observed in the experiments.