E35 · Energy-filtered imaging

EFTEM: Energy Windows & Elemental Maps

Does a bright energy-filtered pixel mean more carbon? Not necessarily. An image taken just above the carbon edge also contains background from other energy losses. The three-window method uses two images below the edge to estimate that background pixel by pixel, then subtracts it. Even so, the map depends on noise, where the windows sit, how well the images line up, specimen thickness and the background model.

Slide an energy slit across the spectrum of the transmitted electrons. Record two images below the carbon edge and one above it, fit a power-law background at every pixel, and compare the signed net map with a jump-ratio map and a separately recorded relative-thickness map. Then correct a drifting acquisition from its recorded frames, without swapping in the known specimen.

Net map / blurred known amount correlation $\text{—}$

Valid fitted overlap $0\,\mathrm{\%}$

Assumed spatial blur · standard deviation $0\,\mathrm{nm}$

Five-image protocol dose $\text{—}$

More measurements and target

Background window geometry $\text{—}$

Processed output $\text{—}$

Experiment target $\text{—}$

Simulated examples; each plot identifies its data source.

Align using the known frame translationsResamples the acquired images using the known shifts, so the common coverage shrinks. The drift is not estimated from the image content.Live slit energy loss

E_s

300\,\mathrm{eV}

Slit / mapping window full width

\Delta E

16\,\mathrm{eV}

Translation between protocol frames

\delta x

4\,\mathrm{nm}

Advanced settings

Maximum wedge thickness

t_{\max}

30\,\mathrm{nm}

Exposure per image

\tau

1\,\mathrm{s}

Second background-window center

E_2

265\,\mathrm{eV}

Output: 0 net · 1 ratio · 2 thickness

0

Learning goal and model limits

Fit recorded windows, then inspect the residual

Recover the projected carbon signal

First predict why drift creates false edges. Keep the two background windows apart and both below the carbon edge in energy loss. Recover a net-map correlation of at least 0.95 with at least 75 percent valid coverage, then check the target. Then compare the jump ratio and the zero-loss thickness to see why neither one is a concentration map.

Model assumptions

The synthetic field of view is 100 nm wide and sampled on a 40 by 40 grid, with the beam fixed at 200 kV. The spectrum assumes a thin specimen with single core scattering. The nominal carbon edge is at 284 eV; yields, composition and thickness are teaching inputs. The two-window fit integrates the power law exactly over each window instead of taking ratios of center values. The core map leaves out plural scattering, chemical fine structure and absolute quantification from cross sections. Thickness comes from a separate pair of zero-loss and all-loss counts, with an assumed 100 nm mean free path and the same collection for both. Each core frame has the same exposure, with a uniform 100000 incident electrons per pixel per second. The dose readout covers the five-image analysis protocol; the live slit preview is a separate single exposure. Every view recomputes the exposure plan, and animation never adds dose. An assumed Gaussian spatial blur grows with slit width; it is not an instrument specification. Alignment with the known drift resamples the recorded images and masks regions that no longer overlap. Negative net values from noise are kept, and invalid fits are shown in gray. The jump ratio is not elemental concentration. The ideal magnetic filter and relay optics separate the energy and image planes only schematically; their fields and aberrations are not solved.

Start with the essentials

Focus question: Does a bright energy-filtered pixel mean more carbon?
One-sentence intuition: The three-window method fits and subtracts the background at every pixel, so what remains depends on noise, window placement, image alignment and the background model.

Core mathematical model

The slit integrates the spectrum at each pixel

C_k(\mathbf r)=N_{\mathrm{inc}}\int_{E_k-\Delta E/2}^{E_k+\Delta E/2}S(\mathbf r,E)\,\mathrm dE

Counts are drawn from this integral after the stated spatial blur and frame shift are applied. The live slit preview is an exposure separate from the three-image mapping protocol.

Fit the whole window, not its center value

\begin{aligned}B(E)&=A(E/284\,\mathrm{eV})^{-r}\\W_k(r)&=\int_{E_k-\Delta E/2}^{E_k+\Delta E/2}(E/284\,\mathrm{eV})^{-r}\,\mathrm dE\\C_1/C_2&=W_1(r)/W_2(r)\end{aligned}

At each pixel the fit finds the exponent and amplitude from the recorded pre-edge counts. A fit is marked invalid if the exponent falls outside the assumed range from zero up to eight. Edge signal leaking into a pre-edge window breaks the background assumption.

Subtract the background and keep the sign of the residual

C_{\mathrm{net}}=C_{\mathrm{post}}-A W_{\mathrm{post}}(r),\qquad R_{\mathrm{jump}}=\frac{C_{\mathrm{post}}}{C_2}

The net signal and the jump ratio mean different things, and neither gives atomic concentration by itself: cross sections, thickness and plural scattering all matter. Negative residuals are kept instead of being clipped to make the image look cleaner.

Thickness from a separate pair of low-loss counts

\mu_{\mathrm{app}}(\mathbf r)=\ln\frac{C_0(\mathbf r)+C_{\mathrm{loss}}(\mathbf r)}{C_0(\mathbf r)}

The zero-loss and all-loss counts are assumed to have the same collection efficiency. Spatial blur and counting noise prevent an exact pixel-by-pixel result. This relative-thickness image is separate from the carbon map.

Common difficulties

A jump ratio is not concentration

Typical misconceptionA brighter pixel in the ratio map always has a larger atomic fraction.

Better mental modelThe denominator also depends on background and thickness. Quantitative analysis calibrated with cross sections is beyond this model.

Run the experiment

01
Move the slit
Compare losses near zero, 16 eV and 300 eV. Watch which representative paths pass the slit and how the detector changes.
What to observe: The detector always shows the energy window you selected. The three-window mapping protocol uses its own fixed window above the edge.
02
Break a background assumption
Choose Pre-edge contamination, then restore a safe second window. Widen the slit and inspect both boundaries.
What to observe: The check rejects windows that overlap or include the carbon edge. A map that looks plausible is not enough.
03
Correct the drifting frames
Choose Uncorrected drift, then enable known-frame alignment. Compare the raw frames, net profile, correlation and coverage.
What to observe: The raw images do not change. Processing resamples them and masks the edges that no longer overlap; the counting noise stays.
04
Compare the outputs and finish
Try the jump-ratio and relative-thickness presets, then obtain a valid signed map with correlation at least 0.95 and coverage at least 75 percent.
What to observe: More exposure improves counting precision but raises the dose of the protocol. The thickness and ratio maps cannot replace background subtraction for the element.

Core mathematical model

The slit integrates the spectrum at each pixel

Fit the whole window, not its center value

Subtract the background and keep the sign of the residual

Thickness from a separate pair of low-loss counts

Common difficulties

A jump ratio is not concentration

Run the experiment

Move the slit

Break a background assumption

Correct the drifting frames

Compare the outputs and finish