 Two-stage electron imaging

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.