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Sandbox Physics

E27 · Electron acquisition / diffraction

TEM Bright Field, Dark Field & SAED

Work with two differently oriented grains. Move the objective aperture across the back focal plane to make a grain bright in dark field. Then switch the relay focus to diffraction and move the selected-area aperture in the first image plane to isolate its diffraction pattern.

Interactive modelTEM Bright Field, Dark Field & SAED
Recorded mode—\text{—}
Grain A recorded fraction0 %0\,\mathrm{\%}
Grain B recorded fraction0 %0\,\mathrm{\%}
Objective direct-beam acceptance—\text{—}
Image grain selectivity0 %0\,\mathrm{\%}
Selected area from grain A0 %0\,\mathrm{\%}
Selected area from grain B0 %0\,\mathrm{\%}
SAED central-beam fraction0 %0\,\mathrm{\%}
Experiment task—\text{—}

Physics tutorial

Do you want to select a beam, or a specimen region?

BackgroundWork with two differently oriented grains. Move the objective aperture across the back focal plane to make a grain bright in dark field. Then switch the relay focus to diffraction and move the selected-area aperture in the first image plane to isolate its diffraction pattern.

Why it mattersMeasure how acquisition or aperture selection changes the data before interpreting the specimen.

Start with the essentials

Focus question
Do you want to select a beam, or a specimen region?
One-sentence intuition
They act at different conjugate planes: the objective aperture accepts angles in the back focal plane; the selected-area aperture accepts specimen positions in the image plane. The relay focus determines whether the detector records an image or diffraction.

Core mathematical model

Focal plane selects angle

yBFP=foθ,yimage=−vuy0,1fo=1u+1vy_{\mathrm{BFP}}=f_o\theta,\quad y_{\mathrm{image}}=-\frac vu y_0,\quad \frac1{f_o}=\frac1u+\frac1v

For the displayed ideal objective, object and image distances are both 90 schematic units and focal length is 45. Position and angle are separated at different planes.

Objective aperture selects waves

IA=P0A(0)+∑gPgA(θg),P0=1−∑gPgI_{A}=P_0A(0)+\sum_g P_gA(\boldsymbol\theta_g),\quad P_0=1-\sum_gP_g

Bright field passes the direct wave; displaced-aperture dark field passes selected diffracted waves. These linear readouts precede the display gamma.

Area aperture selects where

ISAED(θ)=∑j∈{0,A,B}wjIj(θ),∑jwj=1I_{\mathrm{SAED}}(\boldsymbol\theta)=\sum_{j\in\{0,A,B\}}w_jI_j(\boldsymbol\theta),\quad \sum_jw_j=1

Weights come from specimen pixels inside the projected area aperture. In diffraction mode the objective aperture is withdrawn and the relay images the back focal plane with an inverted coordinate orientation.

Common difficulties

Interpretation trap

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

Better mental modelThey act at different conjugate planes: the objective aperture accepts angles in the back focal plane; the selected-area aperture accepts specimen positions in the image plane. The relay focus determines whether the detector records an image or diffraction.

Run the experiment

  1. 01

    Select a wave

    Compare Bright field with Dark field: grain A, then grain B. Watch the aperture move in the back focal plane.

    What to observe: The selected grain becomes bright while the other loses its diffracted intensity. The specimen itself has not changed.
  2. 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.
  3. 03

    Check both tasks

    Verify the grain A dark-field target and the grain A selected-area target. Tilt the specimen away and compare the intensity loss.

    What to observe: The measured target uses linear fractions; visually amplified dark-field contrast is not calibrated electron yield.