TEM ray diagrams ‒ LSME ‐ EPFL

This webpage provides optical ray diagrams for different transmission electron microscopy (TEM) and scanning TEM (STEM) modes. The aim is to illustrate schematically the effects and coupling of the different electromagnetic lenses between the electron gun and detector plane, all while utilizing optically correct focal planes and lens conjugations. The notes below provide further details on the ray diagram constructions.

Update 2 November 2025: the C2 condenser aperture has been moved to a more physically realistic position, below the C2 lens. The originally published diagrams with the condenser aperture at the level of the C2 lens can be found here: TEM ray diagrams V1.0.

Update 5 November 2025: slide formatting. An extra resource has been added containing ray diagrams reformatted with larger font sizes, so that the text is legible when using the diagrams in slides. Some minor corrections to text annotations have been applied to all the diagrams.

TEM Ray Diagrams @ 2025 by Duncan T.L. Alexander are licensed under CC-BY 4.0.

Further notes on the diagrams:

Only the primary, toroidal electromagnetic lenses of the TEM instrument are considered. Functionally, the polepiece of such a lens concentrates a strong magnetic field onto the optic axis at its center; further, this magnetic field is radially symmetric around the optic axis.
Each of these electromagnetic lenses is represented by an idealized thin convergent lens. We believe that this is the correct schematic approach to take—rather than using a thick refractive lens representation, which in itself is appropriate only to a convergent lens utilized in light optical microscopy. (Indeed, representation by a thin convergent lens is the connection between electron optics and light optics ray diagrams; physically, the interaction of fast electrons with an electromagnetic lens is entirely different from that of photons with a convex lens made of transparent, refractive material.)
Each convergent lens is indicated with a double-headed arrow. Small horizontal lines on the optic axis are used to indicate the front and back focal planes of each lens in the system. Feint grey lines are used to indicate ray constructions going from effective object plane to image plane for each lens.
As starting point, I take the first cross-over formed by the electron gun. In a field emission gun, this would be the cross-over formed by the electrostatic gun lens. For a thermionic gun, it would be the cross-over formed by the Wehnelt.
A three condenser lens system is illustrated, as used on the typical modern TEM instrument, where the first C1 lens controls “spot size”, the second C2 lens controls “intensity” (i.e., the spread of the illumination), and the third lens is a condenser minilens.
The C1 lens creates the first cross-over in the system. If its strength is increased, the cross-over moves upwards. This decreases the number of electrons that pass through the C2 aperture and, therefore, decreases beam current at the sample level. Moreover, if the condenser lens system is adjusted to make a focused probe on the sample (which corresponds to making an image of the source at the sample level), increasing C1 strength increases the demagnification of the electron source and, therefore, produces a smaller focused probe. (Here ignoring contributions of lens aberrations and aperture effects.)
The beam-forming aperture is shown at the C2 level. When at the microscope, the user has free control of the C2 lens strength; changing its strength adjusts beam diameter and, therefore, beam intensity at the sample level. In the TEM mode diagrams shown here, it is adjusted to give a fully parallel beam at the sample level.
An objective “twin-lens” system is described, where the optical effects of the strong, condensed magnetic field of the full objective lens polepiece is synthesized by a symmetric arrangement of two thin, convergent lenses of equal strength: the objective pre-field and the objective post-field. This is annotated as the “polepiece” because, when we refer to the “polepiece” of a transmission electron microscope, we usually mean the objective lens polepiece.
The objective pre-field and post-field lenses are given a magnification of 2x. This magnification was chosen purely to give clarity and compactness to the global representation. In reality, the objective (post-field) lens is the strongest lens in the system, with a magnification of ~50x.
In TEM mode, the condenser minilens is a strong lens that couples with the objective polepiece to help form a (near) parallel illumination across the sample. This is done by using it to form a cross-over at the front focal plane of the objective lens pre-field (which acts in symmetry with the back focal plane of the objective lens post-field). Here, for illustrative purposes, the condenser minilens is given a 1.5x demagnification.
The coupling of the condenser minilens with the objective pre-field and post-field lenses corresponds well to the lens description and effects of instruments made by the JEOL manufacturer. Two condenser lens instruments from Thermo Fisher Scientific (TFS, the other main commercial manufacturer) instead have a minicondenser lens and objective twin lens design. In terms of exact electron optical functioning, the principles of the TFS system have some specific differences. However, the principles shown in these schematic ray diagrams are sufficiently analogous that they should make a useful starting point for understanding TFS operation.
The condenser lens configuration has been set in such a way that, when the condenser minilens is turned off, the objective pre-field forms a focused probe on the sample, without any modification to the strength of the latter. While this again reflects the ray diagram approach taken by JEOL, it also correlates with a TFS instrument, where we go from a quasi-parallel illumination “microprobe” mode (TEM) with the minicondenser lens “activated” (positive lens current) to a “nanoprobe” mode with a highly converged electron probe (STEM) with the minicondenser lens “deactivated” (reversed polarity with negative lens current, that optically turns off the minicondenser lens via interaction with the objective lens pre-field).
The post objective lens optics are described by just two lenses: an intermediate lens and a projector lens, to give a simple representation of their respective roles. For the intermediate lens, this function is choosing between image mode (where it takes the first image plane of the objective lens as its object plane), and diffraction mode (where it takes the back focal plane of the objective lens as its object plane). The projector lens then takes the “image plane” of the intermediate lens as its object, and magnifies it onto the detector plane. For simplicity, I have set the magnification of the intermediate lens to be 1x in diffraction mode. The projector lens is set with a magnification of 4x.
In reality, a modern TEM instrument has multiple (3–4) intermediate/projector lenses, giving significant flexibility for adjusting both TEM image magnification and “camera length” in diffraction mode. At the same time, careful control of their couplings are used to correct the inherent rotation effect of toroidal electromagnetic lenses, as the amount of “turning” from the Lorentz force changes as lens strength is changed. That is, neither the image nor the diffraction pattern rotate as you change magnification, and a fixed value is set for the rotation between image and diffraction mode.
In the STEM diagrams, the high angle annular dark-field (HAADF) detector is illustrated in the back-focal plane of the objective lens post-field. This is purely representational. The HAADF detector collects electrons scattered to high angles. By placing it in the back-focal plane, the schematically illustrated detector has collection angles which are proportionally correct with respect to the convergence angle of the schematic incident beam on the sample. In reality, the HAADF detector would usually insert in the detector plane, after the projector lens(es). In STEM mode, the post specimen optics are set in diffraction mode. Therefore, the detector plane conjugates with the back-focal plane, such that the STEM detectors collect electrons scattered to certain angles. In this location, there is both the physical space needed for the HAADF detector, and the collection angles on it can be adjusted by changing the camera length (i.e., by adjusting intermediate + projector lens currents). However, for the purposes of these diagrams, putting the HAADF detector here, while achieving proportionally correct collection angles on it, would make the diagram inconveniently wide—hence it is represented in the back-focal plane instead.
Throughout the lens system, all angles are vastly increased compared to a real TEM instrument, in order to make them visually discernible. This ties to the aim of providing a synthetic description of the optical functioning of the system, not to give a fully accurate representation.