E27 · Electron acquisition / diffraction

TEM Bright Field, Dark Field & SAED

In a TEM, which aperture selects one beam and which selects one region of the specimen? To pick a beam, use the objective aperture: it sits in the back focal plane, where electrons are sorted by scattering angle. To pick a region, use the selected-area aperture: it sits in an image plane, where position matches position on the specimen. The intermediate lens then decides what the detector records: focused on the image plane, an image; on the back focal plane, a diffraction pattern.

The specimen has two grains with different orientations. Move the objective aperture across the back focal plane until one grain lights up in dark field. Then switch the relay lens to diffraction focus and move the selected-area aperture in the first image plane to isolate the diffraction pattern of that grain.

Recorded mode $\text{—}$

Grain A count-derived fraction $0\,\mathrm{\%}$

Grain B count-derived fraction $0\,\mathrm{\%}$

Image grain selectivity $0\,\mathrm{\%}$

More measurements and target

Objective direct-beam acceptance $\text{—}$

Reference area from grain A $0\,\mathrm{\%}$

Reference area from grain B $0\,\mathrm{\%}$

Predicted central-beam fraction $0\,\mathrm{\%}$

Saved detector counts $0\,\mathrm{\mathrm{e}^{-}}$

Exposed source area $0\,\mathrm{nm^2}$

Recorded incident fluence $0\,\mathrm{\mathrm{e}^{-}\,nm^{-2}}$

Counts outside central region $0\,\mathrm{\mathrm{e}^{-}}$

Saturated detector pixels $0\,\mathrm{\mathrm{pixel}}$

Total-count shot-noise estimate $0\,\mathrm{\%}$

Recorded / incident fraction $0\,\mathrm{\%}$

Experiment task $\text{—}$

Simulated examples; each plot identifies its data source.

More examples

Record selected-area diffractionWithdraw the objective aperture, insert the image-plane area selector and focus the relay on the objective back focal plane.Common specimen tilt

\beta

0\,\mathrm{{}^\circ}

Objective center, horizontal

\theta_x

0\,\mathrm{mrad}

Objective center, vertical

\theta_y

0\,\mathrm{mrad}

Objective aperture semiangle

\alpha

2\,\mathrm{mrad}

Advanced settings

Crystal thickness

t

5\,\mathrm{nm}

Selected-area horizontal center

x_s

0\,\mathrm{nm}

Selected-area vertical center

y_s

0\,\mathrm{nm}

Selected-area radius

r_s

95\,\mathrm{nm}

Incident fluence for next exposure

\Phi_e

300\,\mathrm{\mathrm{e}^{-}\,nm^{-2}}

Display gain on saved counts

G

1

Learning goal and model limits

Instrument settings

TEM Bright Field, Dark Field & SAED

First isolate grain A in dark field: block the direct beam and reach at least 90 percent image selectivity. Then isolate grain A in SAED, with more than 95 percent of the selected area coming from that grain. Acquire before you check. The dark-field task also needs at least 100 counts from grain A, and SAED needs at least 25 counts outside the central region. Saturated pixels fail either task. These thresholds are set for teaching; they are not confidence guarantees.

Model assumptions

Tilting changes only how strongly the reflections are excited; the projected layout of the grains stays fixed. The beam is fixed at 200 keV, the lattice is monatomic simple cubic with a 0.4 nm parameter, and the two grain orientations differ by 35 degrees. Intensities use a weak single-scattering approximation for thicknesses of 1–5 nm, and the direct beam loses exactly the modeled diffracted fraction. The grain images add intensities incoherently, so phase interference and dynamical diffraction are left out. Each acquisition saves a seeded electron-count array together with its settings. Images are sampled at 1 nm per pixel, and the selected-area signal scales with the illuminated area and the fluence. The diffraction spot spread is set to 0.35 mrad and each detector pixel holds at most 65535 electrons; saturated pixels are marked orange. Counts are Poisson below a mean of 40 and use a rounded Gaussian approximation above it. Detector efficiency, charge sharing, read noise, beam damage and camera calibration are not modeled. Images are displayed with a gamma of 0.4, and SAED patterns on a log scale. Display gain changes brightness but not counts. Dark field is made by moving the objective aperture, not by tilting the incident beam. Ideal paraxial objective and relay lenses separate the focal and image planes; the drawn ray slopes are enlarged 22 times. In SAED the objective aperture is withdrawn automatically, and changing the selected region changes the recorded diffraction pattern.

Physics tutorial

In a TEM, which aperture selects one beam and which selects one region of the specimen?

BackgroundThe specimen has two grains with different orientations. You move the objective aperture across the back focal plane until one grain lights up in dark field. Then you switch the relay lens to diffraction focus and move the selected-area aperture in the first image plane to isolate the diffraction pattern of that grain.

Why it mattersBefore you interpret the specimen, you need to know how the acquisition and the choice of aperture change the data.

Start with the essentials

Focus question: In a TEM, which aperture selects one beam and which selects one region of the specimen?
One-sentence intuition: The two apertures sit in different conjugate planes. The objective aperture, in the back focal plane, picks scattering angles; the selected-area aperture, in the image plane, picks positions on the specimen. The relay focus decides whether the detector records an image or a diffraction pattern.

Core mathematical model

Angle and position separate in different planes

y_{\mathrm{BFP}}=f_o\theta,\quad y_{\mathrm{image}}=-\frac vu y_0,\quad \frac1{f_o}=\frac1u+\frac1v

In the ideal objective shown, the object and image distances are both 90 schematic units and the focal length is 45. The back focal plane sorts rays by angle, and the image plane sorts them by position.

Which waves the objective aperture passes

I_{A}=P_0A(0)+\sum_g P_gA(\boldsymbol\theta_g),\quad P_0=1-\sum_gP_g

In bright field the aperture passes the direct wave. In dark field the aperture is moved off axis to pass chosen diffracted waves. The formula predicts the mean intensity. Dividing the counts in an image region by the incident fluence estimates the passed fraction, and sampling noise can push that estimate above the prediction. Display gamma and gain do not affect the count statistics.

The area aperture chooses which region contributes

I_{\mathrm{SAED}}(\boldsymbol\theta)=\sum_{j\in\{0,A,B\}}w_jI_j(\boldsymbol\theta),\quad \sum_jw_j=1

The weights come from the specimen pixels that fall inside the projected area aperture. In diffraction mode the objective aperture is withdrawn, and the relay images the back focal plane with its coordinates inverted.

Area, counts and detector limits

N_{\mathrm{in}}=\Phi_e A_s,\quad N_i\sim\operatorname{Poisson}(\mu_i),\quad C_i=\min(N_i,65535),\quad \frac{\sigma_N}{N}\simeq\frac1{\sqrt N}

At a fixed fluence, a smaller selected area receives fewer electrons. The noise estimate assumes the counts are independent and unsaturated; clipped pixels lose information. The detector spread and capacity are set for teaching and do not describe a real camera.

Common difficulties

Objective aperture versus selected-area aperture

Typical misconceptionThe selected-area aperture and objective aperture are interchangeable.

Better mental modelThe two apertures sit in different conjugate planes. The objective aperture, in the back focal plane, picks scattering angles; the selected-area aperture, in the image plane, picks positions on the specimen. The relay focus decides whether the detector records an image or a diffraction pattern.

Run the experiment

01
Select a wave
Compare Bright field with Dark field: grain A and then Dark field: grain B. Watch the aperture move in the back focal plane.
What to observe: The selected grain turns bright, and the other grain loses its diffracted intensity. The specimen itself has not changed.
02
Select a region
Switch to SAED: grain A, then SAED: both grains. Move the area center toward grain B.
What to observe: The image-plane selector changes which crystal contributes to the recorded diffraction pattern; it does not pick a single diffraction spot.
03
Check both targets
Use Check target on the grain A dark-field task and on the grain A selected-area task. Then tilt the specimen away and compare how much intensity is lost.
What to observe: Acquire at each setting before you check. Grain fractions and noise readouts come from the saved linear counts. The low-count and saturated examples fail even with the apertures in the right place, and raising the display gain fixes neither problem.