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Ernst Ruska and Max Knoll developed electron optics while improving the writing spot of a cathode-ray oscilloscope.^[ref] A structured object tests image formation more strongly than a single bright spot: each feature must retain its own image position.

On 7 April 1931, a cold cathode source and two short magnetic coils imaged aperture grids at $50\mathrm{kV}$. A platinum grid preceded the first coil; a bronze grid preceded the second. The fluorescent screen showed one-stage grid images and the first grid reimaged through both stages. Comparing these patterns tested successive image formation, not merely beam concentration. Heating could destroy even metal grids. This prototype did not establish resolution beyond an optical microscope.^[ref]

In 1933, Ruska measured $3\mathrm{mm}$ focal lengths at $75\mathrm{kV}$ with a pole-piece lens, then built an instrument giving $12000$-fold magnification.^[ref] TU Berlin dates images surpassing conventional optical microscope resolution to 1933.^[ref]

A fluorescent screen converts the spatial Electron distribution into visible light.^[ref] A collector reporting only total electric current would discard that spatial pattern. In a two-stage image relay, the first lens makes an intermediate real image; the second treats that image as its object. The diagram below illustrates this geometry with invented distances and an ideal beam.

Electron optics studies how electric fields and magnetic fields guide Electrons and form images. The Lorentz force supplies a trajectory description, while the de Broglie wavelength supplies the wave scale needed for diffraction. Both descriptions matter: steering a narrow beam and resolving two nearby specimen features are different achievements.

For a magnetic electron lens,Here $e>0$ is the elementary charge, $\mathbf{v}$ the Electron velocity, and $\mathbf{B}$ the magnetic field. The second equality follows because a cross product is perpendicular to each factor: a static magnetic field bends the trajectory without increasing the kinetic energy. Acceleration instead requires work by an electric field. This distinction lets an electron microscope adjust imaging with magnetic fields while an accelerating voltage sets the Electron momentum.

Ernst Ruska received one half for fundamental work in electron optics and designing the first electron microscope. Gerd Binnig and Heinrich Rohrer received one quarter each for designing the scanning tunneling microscope.^[ref]