First make an image, then ask how fine it is
A microscope must map each point of the specimen to its own point in the image, at a scale that can be reproduced. Bending an electron beam with a magnetic field does not yet do that. An intermediate image must also serve as the object for the next stage. These requirements are what turn beam focusing into electron optics.
The electron microscope came out of experimental teamwork. In his Nobel lecture, Ruska places the work in Max Knoll’s cathode-ray oscillograph group and describes testing Hans Busch’s theory of the magnetic lens. The group had to build a lens, measure an image and get a second stage working. The microscope did not follow automatically from the wavelength equation.
Evidence and definitions: E. Ruska, The development of the electron microscope and of electron microscopy (Nobel lecture, 1986)
1929: a magnetic coil had to pass the glass-lens test
Hans Busch had argued that the magnetic field of a short coil acts on an electron beam the way a convex glass lens acts on light, with a definite focal length that the coil current can change. His own check against measurements made sixteen years earlier agreed poorly. In 1929 Ruska tested the idea on a coil. For a glass lens the test is simple. Put an object a distance s in front of the lens, find where its sharp image forms, a distance s′ behind it, and check both against the thin-lens equation below, where f is the focal length. The image is M times the object’s size, and a minus sign means it is upside down.
Ruska’s coil matched the imaging scale better, but still not entirely satisfactorily. He put the gap down to the coil itself: its field spread much too far along the axis, while the simple equation assumes the beam bends in one thin slice. The same work recorded numerous sharp images, at different magnifications, of a 0.3 mm anode aperture lit by electrons. Ruska calls them the first recorded electron-optical images. He also found that an iron casing with a ring-shaped gap gave the same focal length with far fewer ampere-turns, a step toward the short lenses described below.
The thin-lens bench runs the same test with light. Move the lit F or the screen and watch the sharp image land where the equation puts it, upside down. Bring the F inside the focal length and no screen catches an image any more, because the image has become virtual.
Evidence and definitions: E. Ruska, The development of the electron microscope and of electron microscopy (Nobel lecture, 1986)OpenStax, University Physics Volume 3, §2.4 Thin Lenses
1931: two stages were a proof of principle
According to Ruska’s lecture, a two-stage setup imaged a grid in April 1931. The magnification was modest, but it showed that magnetic lenses could enlarge an electron image in successive steps. The grid gave a recognizable object, and the screen and lenses gave defined image planes. A bright focused spot alone would not have shown this.
The total magnification is the product of the stage magnifications, with signs taken in one consistent convention. It tells you where a feature lands and how large it looks, but not the smallest separation the instrument can distinguish. Enlarging a blurred intermediate image enlarges the blur too.
Evidence and definitions: E. Ruska, The development of the electron microscope and of electron microscopy (Nobel lecture, 1986)JEOL, Objective lens — TEM glossary
1933: short focal lengths shifted the goal to finer detail
Once successive magnification worked, the goal became reaching finer detail in the specimen. Ruska describes squeezing the lens field with iron polepieces to get short focal lengths, work tied to his thesis and to Bodo von Borries. He completed a more powerful instrument in late 1933.
Judge the original images together with their specimen, scale and operating conditions. A large final image shows better resolution only if it actually records detail that can be told apart. A short focal length is an engineering means and does not guarantee resolution on its own; illumination, aperture and stability still matter.
Evidence and definitions: E. Ruska, The development of the electron microscope and of electron microscopy (Nobel lecture, 1986)JEOL, Objective lens — TEM glossary
Changing magnification without moving a lens
A glass zoom lens changes its magnification by sliding lens groups along the axis. A magnetic lens needs no sliding: its focal length is set by the current in its coil. Turning a current knob therefore does what a zoom ring does in a camera, and it brings the same problem with it. Change one lens and its image moves off the plane where the next lens expects it.
A 1973 US patent by David Hilditch of Associated Electrical Industries states the difficulty plainly: “Both the focal length of the lens and the rotation imparted by it are functions of the lens excitation current.” In its scheme the magnification is varied by changing the currents in two or more projector lenses, while the objective lens current is changed at the same time “so as to keep the object in focus”. In its first mode that covers about 8,000 to 1.25 million times.
A camera zoom lens solves the same problem with a cam. The zoom Lab shows it with glass: slide the zoom group and a second group must follow a curved path, or the image drifts off the film by about a millimetre. In the microscope, the matched lens currents play the part of that path.
Evidence and definitions: D. H. Hilditch (Associated Electrical Industries), Electron microscopes, US patent 3,746,855 (1973)
A short wavelength opens the way to finer detail
Electrons accelerated through a high voltage have a wavelength far shorter than visible light, so their diffraction scale can be much smaller. The formula below uses a positive voltage, the electron rest mass and the elementary charge taken as positive, and it includes the relativistic correction. At one hundred kilovolts it gives about 3.70 picometres.
A wavelength is not the resolution of any particular microscope. Even an ideal aperture blurs the image by diffraction, and real lenses add other errors. A shorter wavelength cannot bring back spatial frequencies the aperture blocked, undo specimen motion or replace missing signal. That is why the linked column model and a wavelength calculator answer different questions.
Detail finer than the wavelength rides on waves that fade within a fraction of a wavelength of the specimen, so a distant lens never receives it. In 2000 John Pendry calculated that a slab with a negative refractive index could make those fading waves grow again on its far side and bring that detail back. Three years later David Smith and colleagues showed the cost: a little absorption in the slab caps the finest detail it can restore, and the cap tightens as the slab gets thicker. Electron microscopes take the other route. With a wavelength of a few picometres, even the spacing between atoms travels as ordinary waves to the lens.
Evidence and definitions: JEOL, Objective lens — TEM glossaryJEOL, Spherical aberration — TEM glossaryJEOL, Wavelength of electron — relativistic wavelength tableJ. B. Pendry (2000), Negative Refraction Makes a Perfect Lens, Physical Review Letters 85, 3966D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna & J. B. Pendry (2003), Limitations on subdiffraction imaging with a negative refractive index slab, Applied Physics Letters 82, 1506
Choosing the aperture is a trade-off
Opening the aperture trades one blur for another. Rays far from the axis generally focus in a different plane from rays near it; this is spherical aberration. Admitting a wider range of angles can reduce diffraction blur but increases this lens blur. Chromatic aberration also makes the image sensitive to the spread of electron energies. An ideal ray diagram leaves out exactly the effects that matter near the resolution limit.
A resolution claim for a real instrument needs the accelerating voltage, the aperture convention, the aberration coefficients and the criterion for calling two features resolved. Drift, vibration and electrical stability need checking too. A bigger screen or more display zoom cannot replace these measurements. Modern aberration-corrected instruments are a separate story, and their performance should not be credited to the first two-coil microscope.
Evidence and definitions: JEOL, Spherical aberration — TEM glossaryJEOL, Objective lens — TEM glossary
An electron image needs interpreting before it shows atoms
No general rule says the darkest point is an atom. The specimen changes the amplitude and phase of the transmitted electrons, and the apertures and lenses transform those changes before detection. Depending on thickness, orientation and imaging conditions, dark and bright regions can come from scattering, phase transfer or mass-thickness contrast.
In weak-phase imaging, changing the defocus can reverse or suppress contrast at some spatial frequencies. A structure read from an image therefore needs an imaging model and independent checks under different conditions. The phase-transfer Lab shows this later idea with a given synthetic specimen. It does not reproduce Ruska’s early observations or solve a unique structure from one image.
Evidence and definitions: JEOL, Phase-contrast transfer function — TEM glossary
The specimen is part of the achievement
A thin specimen has to survive the beam long enough to show anything useful. Heating, radiation damage, contamination and the preparation itself can erase or change the detail being sought. Ruska’s account puts these obstacles next to lens development; they belong in the main history of microscopy, not in a footnote added once the instrument worked.
Try the two linked models in order. First find the object and image planes in the column. Then hold the reference specimen fixed and change the phase transfer. The first model asks whether the optics forms an image; the second asks which details of the specimen survive into it. That difference is the lasting lesson of the step from magnification to microscopy.
Evidence and definitions: E. Ruska, The development of the electron microscope and of electron microscopy (Nobel lecture, 1986)JEOL, Phase-contrast transfer function — TEM glossary