# Annular dark-field scanning transmission electron microscopy
Annular dark-field scanning transmission electron microscopy (ADF-STEM) is a scanning transmission electron microscopy mode in which an annular detector collects electrons scattered to medium and high angles, producing images whose intensity follows a power law in the atomic number of the material being imaged. Because the detector ring excludes the unscattered beam and the Bragg-diffracted electrons, the image reads as a direct, incoherent map of columnar scattering power rather than an interference pattern, which makes it composition-sensitive and comparatively easy to interpret.[1](https://iopscience.iop.org/article/10.1088/2515-7639/ac1ab8/pdf) • [2](https://link.springer.com/article/10.1186/s40543-018-0142-4) The same angular selection discards most of the signal, so ADF images are intrinsically noisy, and the method's quantitative use depends on careful detector calibration.[3](https://www.nature.com/articles/srep12419)
| Key fact | Value |
|---|---|
| Typical detector geometry | Inner radius 30–100 mrad, outer radius 100–200 mrad; angles above ~80 mrad collect mainly incoherent electrons[4](https://www.globalsino.com/EM/page4788.html) |
| Composition scaling | Intensity follows a power law in atomic number, \( Z^{\alpha} \), with \( \alpha \) between 1 and 2 depending on the collected angular range[5](https://juser.fz-juelich.de/record/860615/files/s7.pdf) |
| Signal fraction | The high-angle signal is typically about 10% of total scattering, so images are shot-noise limited[1](https://iopscience.iop.org/article/10.1088/2515-7639/ac1ab8/pdf) |
| Probe size | Aberration-corrected instruments routinely form probes smaller than 0.1 nm, even below 100 keV; reported resolution reaches 40.5 pm[1](https://iopscience.iop.org/article/10.1088/2515-7639/ac1ab8/pdf) • [6](https://pmc.ncbi.nlm.nih.gov/articles/PMC8958084/) |
| Elemental sensitivity | About \( 10^{5} \) to \( 10^{6} \) times higher than energy-dispersive X-ray spectroscopy[7](https://onlinelibrary.wiley.com/doi/10.1002/jemt.1060170209) |
| Angle convention | Scattering angles scale inversely with beam energy, so detector geometry should be quoted via the scattering parameter \( s \)[1](https://iopscience.iop.org/article/10.1088/2515-7639/ac1ab8/pdf) |
## How it works
In a classical picture, beam electrons passing close to an atomic nucleus are deflected to high angles by Rutherford-type scattering, with a cross section proportional to \( Z^{2} \) when the inner collection angle is large enough.[1](https://iopscience.iop.org/article/10.1088/2515-7639/ac1ab8/pdf) Screening of the nucleus by inner-shell electrons reduces the measured exponent below 2, and thermal diffuse scattering contributes at the largest angles. The result is an incoherent, direct image of columnar scattering power.[2](https://link.springer.com/article/10.1186/s40543-018-0142-4)
Composition sensitivity is real but not a fixed power law. Experiments with size-selected Pd (Z = 46) and Au (Z = 79) clusters measured the exponent in \( I \sim Z^{\alpha} \) varying between 1.2 and 1.8 as the collection angle changed from 14 to 103 mrad.[8](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.84.073408) Careful quantitative studies agree that a power-law description, though useful qualitatively, is not reliable for quantitative work: it can fail even for monolayer materials when the inner angle is too small for pure Rutherford scattering or when multiple scattering occurs even at heavy single atoms.[1](https://iopscience.iop.org/article/10.1088/2515-7639/ac1ab8/pdf) Quantitative experiments on graphene, MoS₂, and WS₂ monolayers at 80 kV showed the deviation becomes evident at small detection angles (\( s_{\mathrm{inner}} \) < 1 Å⁻¹) and for elements with Z > 20, with two causes: the nonmonotonic Z dependence of the atomic radius and the dynamical diffraction of a single atom.[9](https://www.nature.com/articles/s41598-018-30941-5)
Dynamical diffraction also works in the method's favor. Channeling of the probe along atomic columns makes column intensities sensitive to the depth of an impurity atom, because deeper atoms channel a more focused probe and scatter to higher angles; this effect underpins three-dimensional dopant profiling.[3](https://www.nature.com/articles/srep12419)
## How it is done
Optimum high-angle ADF imaging on a TEM/STEM system requires a high maximum diffraction angle, a small minimum camera length, and a descanning facility so the scattered disk stays on the annular detector during scanning.[7](https://onlinelibrary.wiley.com/doi/10.1002/jemt.1060170209) Inner and outer detector angles must be measured precisely for each camera length if the data are to be compared with simulations.[10](https://iopscience.iop.org/article/10.1088/1757-899X/109/1/012008/pdf)
Quantitative work additionally requires detector response uniformity, signal linearity with flux, an accurate detector map for normalization, and accounting for post-specimen aberration distortions.[1](https://iopscience.iop.org/article/10.1088/2515-7639/ac1ab8/pdf) Contrast is commonly normalized as \( Q_{\mathrm{ADF}} = I_{\mathrm{ADF}} / I_{0} \), the detector current divided by the incident probe current.[9](https://www.nature.com/articles/s41598-018-30941-5) Because total high-angle scattering is only around 10% of the primary beam, normalization needs a detector sensitivity scan equivalent to the full beam current, using dropped-gain or dropped-current methods.[10](https://iopscience.iop.org/article/10.1088/1757-899X/109/1/012008/pdf) Dose is a trade-off: excessive dose damages the sample, while too little dose degrades precision through shot noise; at fixed dose, integrated cross-sections always carry lower expected error than peak-intensity measurements.[10](https://iopscience.iop.org/article/10.1088/1757-899X/109/1/012008/pdf)
## Origin
A. V. Crewe, J. Wall and L. M. Welter reported a high-resolution scanning transmission electron microscope in 1968,[11](https://doi.org/10.1063/1.1656079) and in 1970 Crewe, Wall, and J. Langmore reported the visibility of single atoms,[12](https://doi.org/10.1126/science.168.3937.1338) work later described as the first demonstration that individual heavy atoms could be distinguished from lighter supports.[5](https://juser.fz-juelich.de/record/860615/files/s7.pdf) In 1978, M. M. J. Treacy, A. Howie and C. J. Wilson published Z-contrast imaging of platinum and palladium catalysts; these early "Z contrast" images were derived from a combination of signals and differ from the ADF images used today.[13](https://doi.org/10.1080/01418617808239255) • [1](https://iopscience.iop.org/article/10.1088/2515-7639/ac1ab8/pdf)
The modern form emerged from [S. J. Pennycook](https://www.edgepedia.org/stephen-j-pennycook)'s group: a new high-angle annular detector design with D. McMullan in 1983,[14](https://doi.org/10.1016/0304-3991%2883%2990012-8) direct dopant imaging in silicon with J. Narayan in 1984,[15](https://doi.org/10.1063/1.95229) elemental mapping with S. D. Berger and R. J. Culbertson in 1986,[16](https://doi.org/10.1111/j.1365-2818.1986.tb02804.x) chemically sensitive structure imaging with L. A. Boatner in 1988,[17](https://doi.org/10.1038/336565a0) and the incoherent imaging theory of crystals with D. Jesson in 1990.[18](https://doi.org/10.1103/physrevlett.64.938) In parallel, R. F. Loane, P. Xu and J. Silcox showed in 1992 that ADF STEM images of zone-axis crystals are incoherent,[19](https://doi.org/10.1016/0304-3991%2892%2990054-n) and Jesson and Pennycook treated incoherent imaging with coherently scattered electrons in 1993.[20](https://doi.org/10.1098/rspa.1993.0060) Treacy published a historical review of Z-contrast techniques in 2011 that distinguishes Crewe's original Z contrast from ADF imaging.[21](https://doi.org/10.1017/s1431927611012074)
## Variants
**HAADF** collects at angles larger than about 80 mrad, where the signal is dominated by incoherent scattering and contrast is strongly Z-dependent.[5](https://juser.fz-juelich.de/record/860615/files/s7.pdf) At lower inner angles the detector collects more coherent contribution, trading some composition sensitivity for signal. **Annular bright-field (ABF)** uses a similar optical geometry but places the annular detector within the illumination cone, in the bright-field region; it markedly improves the visibility of light columns such as oxygen and lithium, which are only weakly visible in HAADF.[1](https://iopscience.iop.org/article/10.1088/2515-7639/ac1ab8/pdf) • [22](https://www.sciencedirect.com/science/article/abs/pii/S0304399110001129) • [2](https://link.springer.com/article/10.1186/s40543-018-0142-4) • [27](https://pubmed.ncbi.nlm.nih.gov/20434265/) Published accounts disagree on ABF's origin: one review states ABF imaging was developed as an alternative to ADF, while another states it became popular in the aberration-corrected era.[1](https://iopscience.iop.org/article/10.1088/2515-7639/ac1ab8/pdf) • [2](https://link.springer.com/article/10.1186/s40543-018-0142-4)
**Variable-angle HAADF** acquires images at two detector angular ranges (for example 60–390 and 47–306 mrad) and combines them statistically. A 2024 analysis formally connects ADF to 4D-STEM: by reciprocity the ADF detector is equivalent to incoherent illumination over a wide range of illumination angles, ADF imaging and ptychographic reconstruction show similar transfer functions at higher spatial frequencies, and the integrated center-of-mass technique's coherent transfer function is identical to the ADF optical transfer function.[3](https://www.nature.com/articles/srep12419) • [23](https://www.cpsjournals.cn/en/article/doi/10.1088/1674-1056/ad8554?viewType=HTML)
## Applications
ADF-STEM has been used for catalyst studies since the technique's infancy, because Z-contrast allowed individual heavy atoms to be differentiated from lighter, even crystalline, supports well before atomic resolution was possible.[5](https://juser.fz-juelich.de/record/860615/files/s7.pdf) Small metallic nanoparticles for PEMFC catalysts remain a key application where quantitative ADF-STEM and EDX must overcome minute size and irradiation-damage limits.[5](https://juser.fz-juelich.de/record/860615/files/s7.pdf) Dopant imaging is another core use: variable-angle HAADF with two detector ranges raised the probability of determining the correct number of Gd dopants in SrTiO₃ to above 63% for all sixteen configurations, against 56% for a single detector, with depth positions about 17% more likely correct.[3](https://www.nature.com/articles/srep12419) The method also serves tomography, depth sectioning, defect analysis, and interfaces.[1](https://iopscience.iop.org/article/10.1088/2515-7639/ac1ab8/pdf)
Recent developments extend these uses. Atom counting from a combination of two ADF STEM images reveals the number of atoms at each column and can build a three-dimensional atomic model from a single 2D image.[24](https://www.sciencedirect.com/science/article/abs/pii/S0304399123001766) Aberration correction allows atomic-sized probes even at 40 kV, minimizing knock-on damage in beam-sensitive materials.[2](https://link.springer.com/article/10.1186/s40543-018-0142-4)
## Limitations and alternatives
**Thickness and channeling.** Column intensity is not simply linear with sample thickness or detector angle range.[6](https://pmc.ncbi.nlm.nih.gov/articles/PMC8958084/) Multislice simulations including phonon scattering show no contrast reversals with thickness, unlike coherent TEM imaging, but the relationship is nonlinear.[25](https://link.springer.com/article/10.1557/PROC-332-361) In heavy atomic columns, channeling saturates the ADF intensity within a few nanometers of thickness, so the signal comes predominantly from atoms near the probe's focal plane.[1](https://iopscience.iop.org/article/10.1088/2515-7639/ac1ab8/pdf)
**Tilt and contamination.** Sample tilts up to 15 mrad can still yield atomic-resolution images but cause ADF intensity losses of 25% or more. A tilt plateau, with cross-section nearly invariant to mis-tilt up to one probe convergence angle, can be designed through inner-angle choice.[10](https://iopscience.iop.org/article/10.1088/1757-899X/109/1/012008/pdf) Depth identification is further limited by detector noise, sample instability under the beam, contamination, and surface amorphous layers.[3](https://www.nature.com/articles/srep12419)
**Compared with alternatives.** Coherent high-resolution TEM phase contrast is sensitive to light atoms but shows thickness contrast reversals that ADF avoids.[25](https://link.springer.com/article/10.1557/PROC-332-361) EDX and EELS identify elements directly but are far less efficient: HAADF sensitivity exceeds EDX by about \( 10^{5} \) to \( 10^{6} \) times.[7](https://onlinelibrary.wiley.com/doi/10.1002/jemt.1060170209) Low-voltage "gentle" STEM with ADF imaging and EELS at low primary energies extends the method to beam-sensitive materials.[26](https://doi.org/10.1016/j.ultramic.2010.02.007) Depth (optical) sectioning resolution increases quadratically with probe convergence angle while lateral resolution increases linearly; optical sectioning has not achieved atomic resolution.[2](https://link.springer.com/article/10.1186/s40543-018-0142-4)
## References
1. [Quantitative annular dark-field imaging in the scanning transmission electron microscope, a review](https://iopscience.iop.org/article/10.1088/2515-7639/ac1ab8/pdf)
2. [Material structure, properties, and dynamics through scanning transmission electron microscopy (Journal of Analytical Science and Technology, 2018)](https://link.springer.com/article/10.1186/s40543-018-0142-4)
3. [Variable-angle high-angle annular dark-field imaging: application to three-dimensional dopant atom profiling (Scientific Reports, 2015)](https://www.nature.com/articles/srep12419)
4. [Incoherence/Rutherford (Elastic) Scattering/Thermal Diffuse (Quasi-Elastically) Scattering (TDS)/Z-Contrast in HAADF-STEM](https://www.globalsino.com/EM/page4788.html)
5. [The Use of Annular Dark-Field Scanning Transmission Electron Microscopy for Quantitative Catalyst Characterisation](https://juser.fz-juelich.de/record/860615/files/s7.pdf)
6. [Effects of Electron Microscope Parameters and Sample Thickness on High Angle Annular Dark Field Imaging](https://pmc.ncbi.nlm.nih.gov/articles/PMC8958084/)
7. [High-Angle annular dark-field imaging on a TEM/STEM system (Otten, 1991)](https://onlinelibrary.wiley.com/doi/10.1002/jemt.1060170209)
8. [Quantitative Z-contrast imaging in the scanning transmission electron microscope with size-selected clusters (Phys. Rev. B 84, 073408, 2011)](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.84.073408)
9. [Atomic number dependence of Z contrast in scanning transmission electron microscopy (Scientific Reports, 2018)](https://www.nature.com/articles/s41598-018-30941-5)
10. [Quantitative ADF STEM: acquisition, analysis and interpretation (IOP Conf. Ser.)](https://iopscience.iop.org/article/10.1088/1757-899X/109/1/012008/pdf)
11. [A. V. Crewe, J. Wall, L. M. Welter (1968). A High-Resolution Scanning Transmission Electron Microscope. Journal of Applied Physics.](https://doi.org/10.1063/1.1656079)
12. [A. V. Crewe, J. Wall, J. Langmore (1970). Visibility of Single Atoms. Science.](https://doi.org/10.1126/science.168.3937.1338)
13. [M. M. J. Treacy, A Howie, C. J. Wilson (1978). Z contrast of platinum and palladium catalysts. Philosophical magazine. A/Philosophical magazine. A. Physics of condensed matter. Structure, defects and mechanical properties.](https://doi.org/10.1080/01418617808239255)
14. [A new high-angle annular detector for stem (Ultramicroscopy, 1983)](https://doi.org/10.1016/0304-3991%2883%2990012-8)
15. [S. J. Pennycook, J. Narayan (1984). Direct imaging of dopant distributions in silicon by scanning transmission electron microscopy. Applied Physics Letters.](https://doi.org/10.1063/1.95229)
16. [S. J. Pennycook, S. D. Berger, R. J. Culbertson (1986). Elemental mapping with elastically scattered electrons. Journal of Microscopy.](https://doi.org/10.1111/j.1365-2818.1986.tb02804.x)
17. [S. J. Pennycook, L. A. Boatner (1988). Chemically sensitive structure-imaging with a scanning transmission electron microscope. Nature.](https://doi.org/10.1038/336565a0)
18. [S. Pennycook, D. Jesson (1990). High-resolution incoherent imaging of crystals. Physical Review Letters.](https://doi.org/10.1103/physrevlett.64.938)
19. [Incoherent imaging of zone axis crystals with ADF STEM (Ultramicroscopy, 1992)](https://doi.org/10.1016/0304-3991%2892%2990054-n)
20. [D. E. Jesson, S. J. Pennycook (1993). Incoherent imaging of thin specimens using coherently scattered electrons. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences.](https://doi.org/10.1098/rspa.1993.0060)
21. [Michael M.J. Treacy (2011). ZDependence of Electron Scattering by Single Atoms into Annular Dark-Field Detectors. Microscopy and Microanalysis.](https://doi.org/10.1017/s1431927611012074)
22. [Dynamics of annular bright field imaging in scanning transmission electron microscopy (Ultramicroscopy)](https://www.sciencedirect.com/science/article/abs/pii/S0304399110001129)
23. [Making the link between ADF and 4D STEM: Resolution, transfer and coherence (Chinese Physics B, 2024)](https://www.cpsjournals.cn/en/article/doi/10.1088/1674-1056/ad8554?viewType=HTML)
24. [Atom counting from a combination of two ADF STEM images (Ultramicroscopy, 2023/2024)](https://www.sciencedirect.com/science/article/abs/pii/S0304399123001766)
25. [Annular Dark Field Imaging in STEM (Hillyard & Silcox, MRS Proceedings, 1994)](https://link.springer.com/article/10.1557/PROC-332-361)
26. [Ondrej L. Krivanek and colleagues (2010). Gentle STEM: ADF imaging and EELS at low primary energies. Ultramicroscopy.](https://doi.org/10.1016/j.ultramic.2010.02.007)
27. [pubmed.ncbi.nlm.nih.gov](https://pubmed.ncbi.nlm.nih.gov/20434265/)
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*Topic: Encyclopedia › Physical world and mathematics › Physics › Physics methods, practice, and community › Electron microscopy methods*
*Initially written Sep 29, 2026 · Edited: Oct 15, 2026; Oct 21, 2026; Oct 25, 2026*
*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*
License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license