Reading the figure
How to read it. Solid rays are the real illumination, traced by the Ray Optics engine from a point source through the VOA. Teal dashed lines are sample images, orange dashed lines are diffraction planes. Both are read off the post-sample transfer matrix [[A,B],[C,D]]: an image plane is where B = 0 and a diffraction plane is where A = 0. Neither depends on the condenser, so both stay correct in TEM and STEM alike. The illumination crossovers listed in the readout are a different thing — images of the source. With a focused probe they land on the sample images; with parallel illumination they land on the diffraction planes instead, which is why they cannot be used to classify planes.
The number under each label is the primary beam radius at that plane.
Lens controls
Lens sliders are logarithmic in focal length, spanning 10000 mm down to the strength limit at about 0.8% per step, with off at the bottom of travel and stronger upwards. The limit is 4 mm for every round lens and 1.5 mm for the objective (which normally runs at 2 mm), and it is what bounds everything else. From the shipped column the EELS solver reaches camera lengths of about 0.002–700 mm and magnifications of about 0.06–20000×, though only L 0.02–100 mm and M 0.5–3000 with three lenses; past that it has to switch PL3 on or use the four-lens stage. The long camera lengths are the hard end because the objective is strong: L = fOL2 M, so with fOL2 = 2 mm every millimetre of camera length has to be bought as projector magnification. It is the lens strength that binds, not the spacing between the projector lenses.
The checkbox at the foot of a lens stack pins that lens, and a solve may not move a pinned lens. EL is pinned on a fresh load, since holding the EELS lens while PL1–PL4 do the work is the common case; nothing else is. Only the eight lenses a solve can actually reach carry one — C1, C2 and C3, which the illumination solve owns, and PL1–PL4 plus EL, which the EELS solve owns. The objective is set by hand only, with one control for both of its halves, so it has none. Pinning narrows the search rather than breaking it: matching both EELS planes at a chosen camera length is three conditions, so it needs at least three free projector lenses, and below that the solve refuses and says which lenses are pinned. The illumination solve has no slack in C2 and C3 — it sets the mode and the convergence angle with exactly those two — so pinning either one stops it outright; pinning C1 only stops it from bringing C1 in.
Radial scale, zoom and specimen height
Radial exaggeration K is cosmetic. It is pure
vertical zoom — the beam is a fraction of a mm across in a 1595 mm column, so it has to be stretched to be
seen. That is exact rather than a cheat: an ideal thin lens is perfectly linear in
(y, dy/dz), so scaling every radial quantity while leaving z and every focal length alone
reproduces the identical diagram, and no reported number moves.
Horizontal zoom (the controls beside copy/save) stretches the z axis only, up to 2000×, so
the 4 mm between OL1 and OL2 can be filled with beam; the radial scale K is not touched, and no
reported number moves. The scroll bar under the figure, dragging the figure, sideways scroll or shift + wheel
move along the column, and Ctrl/Cmd + wheel (or a trackpad pinch) zooms at the cursor. fit K
refits K to the beam inside the current window — zoomed onto the gap a 30 µm beam is only a
couple of pixels tall at the K that fits the whole column — and copy/save export the view as shown.
Sample defocus dz shifts the specimen off the OL1/OL2 midpoint, positive toward OL2, up to
±1 mm — inside the 4 mm gap, and enough to run a confocal depth series. Note that the
diffraction planes do not move when the sample does: a ray leaving the sample parallel to the axis stays
parallel until OL2, so they are set by OL2 and downstream only. The image planes do move.
Reference plane vs specimen. The reference plane at z = 785, midway between OL1 and OL2, is the objective's nominal object plane and never moves — every conjugate, camera length, magnification and solve is referenced to it, just as a real column's projectors are aligned to a fixed height. The specimen sits at 785 + dz and affects only the Bragg cone origin, the beam radius on the specimen, the probe-defocus readout and its own marker. Sweeping dz therefore moves nothing optical; it just takes the probe off the specimen.
Illumination
The two illumination modes are set by the condenser. The objective's thin lenses sit on the pole faces, 2 mm either side of the specimen, so with f = 2 mm the specimen is exactly on OL1's back focal plane: a focused probe is a parallel beam into OL1, and parallel illumination needs the condenser crossover on OL1's front focal plane at 781 instead. α is the marginal ray's slope inside the objective gap — the ordinary convergence semi-angle, equal to the beam radius at OL1 over fOL1. Under parallel illumination that slope is zero, so there α means the angle OL2 focuses the beam to, and the illuminated radius is exactly r = α fOL2. A condenser beam that is not quite parallel moves the probe crossover off the specimen by f2/x, for a condenser crossover a distance x from OL1's front focal plane — about 8 µm for one near C3 — which is the scale of the few-micron offset the real column is run with. The α slider spans 0.05–50 mrad and applies live, keeping whichever mode you last chose; the VOA stays fixed. C2 and C3 set both the mode and the angle, in closed form. From the bare point source they reach 0.714–137.5 mrad focused — the column's 39 mrad working point needs no C1 — and 0.0030–0.57 mrad parallel; outside that the solve brings C1 in — it scans C1, solves C2 + C3 exactly at every step, keeps the gentlest setting, and says so in the banner. With C1 free the focused floor is 0.043 mrad and every slider position solves in both modes. A C1 that is already on stays where it is whenever C2 + C3 can follow. The 15 mrad default is C2 = 240/11 with C3 = 36 mm, C1 off: C3 collimates the crossover C2 makes at 264.
EELS coupling
The two EELS coupling modes are exact mirrors of one another, and mutually exclusive: diffraction-coupled puts the diffraction pattern on the entrance aperture and the sample image on the EELS focal plane; image-coupled swaps them. Either pairing uses up two degrees of freedom, so a two-lens solve would leave the third quantity as whatever fell out — a third projector lens buys it back. In diffraction coupling the knob is camera length L and Mag = 45/L follows; in image coupling the knob is magnification M and L = 45/M at the focal plane follows (45 mm being the gap between the two EELS planes). Because both conditions live entirely in the post-sample matrix, matching works identically under focused and parallel illumination — the same projector solve either way.
The checkbox beside that value decides whether it is an input at all. Checked, it is a target and the solve has three conditions to meet, so it needs three free projector lenses. Clear it and the target stops being a condition: the solve matches the two planes on their own with two lenses — every pair, in both role orders, gentlest wins — and whatever camera length falls out is written back to the slider, so the control becomes a readout. Whether a given pair has a solution depends on where the lenses you did not free are sitting: from the shipped column five of the six PL pairs solve, spanning L = 0.68 to 28.2 mm, and PL3 + PL4 does not; with the other two projectors switched off a different three do — PL1 + PL4, PL2 + PL4 and PL3 + PL4.
Where A and B come from. Write the ray-transfer matrix from the reference plane to whichever plane you care about as [[A, B], [C, D]]. A ray leaving the reference plane with height y and slope θ arrives at height Ay + Bθ. At a diffraction plane A = 0, so it arrives at Bθ — position depends only on angle — and that B is the camera length L in r = L θ. At an image plane B = 0, so it arrives at Ay, and that A is the magnification. Both are shown at both EELS planes and greyed out wherever the plane is not of the matching kind, because that is the only place each means what it is called.
Camera length defined this way is the same number as the textbook L = fOL2 M — OL2's back focal plane at z = 789 is conjugate to the aperture at M = −14.1, so 2 × 14.1 = 28.2 mm — the two definitions are the same number, always, whenever the aperture really is a diffraction plane. It is perfectly meaningful in STEM: it is what decides which scattering angles get inside the aperture. Note that the beam radius the figure prints at the aperture is exactly L α, so it says nothing about the element spacings — at the shipped 28.2 mm camera length a focused 39 mrad probe puts it at 1.10 mm, which is the measurement the projector defaults are set from.
Bragg cones and camera-length calibration
Bragg cones are a construction: the illumination re-emitted at ±θB, amber for +1 and violet for −1. Each cone ray leaves from its own primary ray's position on the sample, so a focused probe gives cones from a point and parallel illumination gives cones across the whole illuminated width. They merge at every image plane and spread into separated discs at every diffraction plane, which is what a CBED pattern shows — but the exact plane positions come from the paraxial solver, not from the cones.
The ±1 Bragg spacing in the readout is the centre-to-centre distance between those two discs at
the EELS aperture, and it is exactly 2 L θB: every cone ray is its own
primary ray displaced by L θB, so the separation does not care how wide the direct beam
is, whether the illumination is focused or parallel, or where the specimen sits along dz. That
makes it a camera-length calibration: photograph a known d-spacing, measure the distance between the
±g spots, and L = spacing / (2 θB). Mind the factor of
two at each end — θB here is the deflection angle of the scattered beam,
λ/d, which is twice the Bragg angle; and the direct beam to a single spot is half the number shown.
What the model leaves out
Ideal thin lenses only; no spherical or chromatic aberration, no space charge, no lens bore limits. Positive focal lengths only, none stronger than 4 mm (1.5 mm for the objective). Element positions are fixed. The aberration corrector and the quadrupole module that couples it into the objective are not modelled — C3 to OL1 is a plain drift — and EL stands in, as a round lens, for the quadrupole–octupole coupling module in front of the spectrometer.