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An electron microscope forms a spatially enlarged representation of a specimen using Electrons, electron lenses, and a detector. Its appeal is access to structure too fine for an ordinary optical microscope, but a short de Broglie wavelength alone does not guarantee fine electron microscope resolution. Increasing magnification can enlarge an existing blur without revealing any additional structure.

In transmission electron microscopy, an electron gun illuminates a thin specimen; magnetic electron lenses form and enlarge its transmitted image on a fluorescent screen or detector. A vacuum reduces collisions with gas. Lens electric currents control focusing and magnification.^[ref]

Consider two ideal thin electron lenses in successive imaging stages. In each stage choose positive object and image distances $u_i,v_i$ for a real image, measured from its effective lens plane, and neglect the image rotation of a magnetic electron lens. The paraxial approximation givesThe product follows directly by writing $y_1=m_1{y}_0$ and $y_2=m_2{y}_1$. Here $m_i$ is transverse magnification, rather than the enlargement applied later to a photograph. Both inversions cancel in this planar model; actual magnetic electron lenses can additionally rotate the image.

For an original worked example, take $u_1=40\mathrm{mm}$, $v_1=80\mathrm{mm}$, $u_2=50\mathrm{mm}$ and $v_2=150\mathrm{mm}$. ThenA $100\mu \mathrm{m}$ object interval becomes $600\mu \mathrm{m}$ at the screen. The second lens sits $v_1+u_2=130\mathrm{mm}$ after the first. These are calculated distances, not measurements of the 1931 instrument.

To measure magnification, divide a screen interval between corresponding grid features by the independently known object interval. Repeat over several periods to reduce endpoint uncertainty. For a proposed check, record accelerating voltage, lens electric currents, screen position and specimen orientation; compare one-stage and two-stage images, refocusing as necessary. Changing a lens electric current should change focus and scale, while a blank exposure checks detector background. Keep irradiation and recording enlargement controlled, and repeat the original setting to test drift or specimen damage. These are suggested checks, not a claim that every check was performed in 1931. A grid-scale measurement establishes magnification; resolving much finer features requires a separate target and contrast criterion.