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A new transmission electron microscope method of measuring fine scale magnetic flux distributions, and in particular the fields associated with magnetic recording heads, is described. An island structured metallic foil or an amorphous film acts as a diffuse scatterer of transmitted electrons. A magnetic field in the region below the scatterer deflects the electron trajectories and as a result distorts the image of the scatterer. The local shearing of the image is compared to a reference zero field image by a double exposure of a photographic plate. Optical Fraunhofer diffraction by transmission through the developed plate shows Young's fringes which reveal the direction and magnitude of the local image shift which is related to the magnetic field component perpendicular to the electron trajectories. In some applications the method is potentially several orders of magnitude more sensitive than other electron beam methods.