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The Foucault in-focus method for viewing magnetic domains in a conventional electron microscope has been modified. The main feature of our modification is to introduce an aperture below the intermediate lens and to use it for stopping out one part of the split central spot instead of the objective aperture. This arrangement substantially reduces the axial astigmatism due to the objective aperture and makes it possible to reach the point resolution 5-6nm in both light and dark domains. The image resolution is limited by the small image magnification achieved using the three-stage optical system of a Tesla BS 413 microscope. I N T R O D U C T I O NIn the last two decades an increasing interest has been shown in the magnetic properties of thin ferromagnetic films, especially in magnetic domain walls, their width, inhomogenities and variations of magnetization etc. When using a transmission electron microscope two methods of imaging magnetic domains have been used: (i) the Fresnel method using a defocused image (Hale, Fuller & Rubinstein, 1959) and (ii) the Foucault method using an off-centre objective aperture (Boersch & Raith, 1959). The quantum theory of the magnetic contrasr formation was derived (Wohlleben, 1967; Cohen, 1967) but inadequate attention has been paid to the question of the image resolution. Thus, in many cases thc image resolution has such a low value that structural details are not visible and it is, therefore, impossible to study the interaction between crystallographic defects and magnetic domains. The image resolution depends to a great extent on the proper choice of imaging conditions. This paper tries to solve the question of the optimal arrangement of the transmission electron microscope with a three-stage optical system and an accelerating voltage of about 100 kV using the Foucault method, which is the only method which makes it possible to attain good image resolution. For this purpose the classical theory of the interaction between an electron and a magnetic field is sufficient. The results are derived using a Tesla BS 413 electron microscope.A parallel electron beam passing through a ferromagnetic specimen with antiparallel domains is split into two beams with the angle of 20 given by the relation 2 e 28 = --IB Id

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