What this page is
The interface is the thin-lens ray trace's, and the solvers (illumination, EELS planes, pins, no-target mode) behave the same way. What changes is the physics underneath: every round lens is a magnetic field of finite width, and the rays are the exact paraxial trajectories through those fields, so they curve inside each lens. Zoom in on the objective to see the beam bend through the gap. For the controls themselves, zoom, pins and the two EELS coupling modes, see the thin-lens help; everything there applies here unless it is listed below.
The lens model
Each lens is a Glaser bell field, B(z) = B0/(1 + ((z−zc)/a)2), the standard closed-form model of a round magnetic lens. The paraxial equation in the frame that rotates with the electron has an exact solution for it, so the ray matrix between any two planes, inside a field or across it, is closed-form; nothing is integrated numerically. The glyph drawn for each lens is its own field profile B(z). Lens strength is still quoted as a focal length, and the excitation behind it is found by inverting that focal length exactly. No lens currents are modelled yet.
Widths are fixed defaults, not measured. They are set so that each lens reaches exactly its strongest allowed setting: 4 mm for every round lens (a ≈ 2.74–2.75 mm) and 2 mm for the objective, which has a = 2.013 mm and a field width of about 4.03 mm, the pole-piece gap. Round lenses quote the projective focal length; the objective quotes the focal length of one half of its field, the published pre-field = post-field value. OL1 and OL2 are the two halves of one lens, driven together. The true pole-piece shapes are not known here, so treat the field shapes as a reasonable stand-in rather than the real thing.
What really differs from thin lenses
Thick-lens planes. A strong field lens acts at principal planes that are not at its centre. At the strongest round-lens setting they are crossed, each about 2.9 mm past the other's side, so a column solved with thin lenses puts its crossovers and conjugate planes in slightly wrong places: the page re-solves everything on the exact fields, and the difference is typically one to a few per cent in the projector lenses.
The specimen sits inside the objective field. The reference plane is z = 784.994 mm, where the
strongest objective focuses a parallel beam, about 6 µm above the centre of its field. That is how the real column
is run (Dellby et al., 2011: the crossover is “a few µm above the center of the objective”). Conjugate
planes, camera length and magnification are referenced to it, and moving the specimen by dz moves the exact
in-field matrices with it, unlike the thin-lens page.
Larmor rotation. Electrons spiral in a magnetic field, so an image or a diffraction pattern is rotated relative to the specimen. The readout shows the rotation from specimen to the EELS aperture, and the wave images below are rotated by it. The polarity of each lens is unknown, so all lenses are taken with the same polarity; the absolute angle is therefore indicative, and what is reliable is that it depends on the lens settings.
What does not change. At a fixed focal length, paraxial trajectories do not depend on the accelerating voltage. HT sets the wavelength (λ = 4.176 pm at 80 kV, the default; 30 and 200 kV are selectable) and so the wave images, and will matter for the focal-length-to-current calibration once currents are modelled. Third-order geometric aberrations of the lenses are not computed.
Compared with the thin-lens page
Both pages are solved to the same two targets: 15 mrad focused on the specimen and a 28.2 mm camera length with the EELS aperture on a diffraction plane and the EELS focal plane on an image. So those numbers agree. What the fields change is how the column gets there:
Lens strengths (focal length, mm, thin → field): C2 21.82 → 21.92, C3 36.00 → 36.15, PL1 56.08 → 57.14 (+1.9%), PL2 13.58 → 13.15 (−3.2%), PL4 14.03 → 14.31 (+2.0%), EL pinned at 105. Sample images (mm): 966 / 1047 / 1166 / 1595 → 955.6 / 1045.7 / 1166.3 / 1595. Diffraction planes: 789 / 1015 / 1142 / 1550 → 787.0 / 1015.4 / 1141.8 / 1550. The big shifts are in the first image and first diffraction plane, nearest the objective, where the thick field matters most. Larmor rotation from specimen to EELS aperture is about 331° with all lenses the same polarity, and zero on the thin-lens page.
Illumination
The α slider spans 0.05–50 mrad and sets the convergence semi-angle exactly as on the thin-lens page: α is the slope of the marginal ray at the reference plane, and under parallel illumination it is the angle the objective focuses the beam to. From the bare point source, C2 + C3 alone reach 2.04–138 mrad focused and 0.0030–0.57 mrad parallel. Outside that the solve brings C1 in and says so. With C1 free the focused floor is 0.041 mrad: the low-angle end (below about 0.7 mrad) needs C2 almost at its strongest with C1 near 59 mm and C3 doing the work, a narrow family of exact solutions that the page follows. Parallel illumination reaches the whole slider range. The 15 mrad default needs no C1.
Wave images
The two images under the column are computed, not drawn: a probe at the specimen (or the specimen phase), and the pattern at a chosen plane downstream, by propagating the wave through the exact ray matrices (a Collins integral, done as a Fresnel transform near image planes and a Fourier transform near diffraction planes), then rotating by the Larmor angle. The Wave images panel sets the aberrations (Krivanek notation; Nion residuals loads about 2 nm first order, 20 nm second and 200 nm third, in both the a and b component of each non-axial term, and higher orders are ignored), the specimen (crystal lattice, amorphous carbon or vacuum), the grid and the display. The overlay marks the beam edge and Bragg positions from the ray trace as a check: the direct disc at the aperture has radius L α, and the ±1 discs sit 2 L λ/d apart. The downstream image is never wider than 15 mm: a longer camera length or a larger angle computes a wider window, and only its central 15 mm is shown. Log scale is on by default for both images. Specimens are thin phase objects: no thickness, no inelastic scattering, no EELS spectrum or detector model.
Specimen off the crossover (dz ≠ 0). A probe focused on the reference plane is a disc of radius dz α on a specimen dz away, so computing the wave on the specimen would need a grid that grows with dz (hundreds of thousands of pixels at 50 µm). The page never does that. A thin periodic specimen is a sum of Bragg beams, and through any ray-transfer system a beam g only shifts the output by λBsg and adds a known phase, so the pattern is a handful of copies of the focused probe's own output, displaced and added with their exact relative phases. It agrees with the direct calculation to 0.1% where that is still valid. What you see follows directly: at a diffraction-like plane the copies are discs (radius Lα) that overlap and interfere, with fringes finer than a pixel averaged out; at an image-like plane they are spots — the focused probe is imaged there whatever dz is, and each Bragg beam lands displaced by λBsg = A dz θg. So the image-coupled aperture shows a spot array and the diffraction-coupled one overlapping discs, at any dz. Spots are drawn larger than the 1.4 nm probe so they are visible. For an amorphous film the strongest 250 Fourier beams are added incoherently, so speckle is not modelled away from dz = 0.
What the model leaves out
Paraxial rays only; no spherical or chromatic aberration of the lenses (the probe aberrations above are a separate input), no space charge, no lens bore limits. Positive focal lengths only, none stronger than 4 mm (2 mm for the objective). Element positions are fixed. The aberration corrector and the quadrupole module are not modelled — C3 to the objective is a plain drift — and EL stands in for the coupling module before the spectrometer. Lens fields are truncated at the midpoint between neighbours, which changes a lens's focal length by under about 1% and is absorbed into its definition.