digital darkfield

Digital darkfield analysis might help you to:

- map the location of interesting periodicities in a specimen field,
- map picometer-scale vector-strains around defects in a crystalline solid,
- identify icosahedral-twinning in a single randomly-oriented nano-particle,
- locate quantum-dots in a layered heterostructure,
- identify screw-dislocations side-on in a lattice image,
- quantify lattice-disorder around nuclear-particle tracks and within ion-implanted layers,
- quantitatively measure wedge-angle at the perforation edge of a crystalline specimen,

and what else?

The poster below, on user interfaces for realtime nanocrystal lattice parameter determination, was presented at the national 2017 Microscopy and Microanalysis meeting in St. Louis:

We now have a growing list of example applications, that we hope to illustrate here in the days ahead.

Digital darkfield decompositions map the distribution of selected spatial-frequencies (proportional to the transverse momentum of diffracted electrons) in a lattice-resolution image, much as analog darkfield images in a transmission electron microscope map the distribution of diffracting objects across the specimen field. The digital analysis involves a type of image decomposition which,

like wavelets, is intermediate between direct and reciprocal (spatial-frequency) space.We usually implement the analysis in either Mathematica, or with plugins that we've developed for ImageJ.

Some related references:

1. Louis-Victor de Broglie (1925) Recherches sur la Théorie des Quanta, Ann. de Phys. 10e série, t. III.
2. P. Hirsch, A. Howie, R. Nicholson, D. W. Pashley and M. J. Whelan (1965/1977) Electron microscopy of thin crystals (Butterworths/Krieger, London/Malabar FL) ISBN 0-88275-376-2.
3. Jack D. Gaskill (1978) Linear systems, Fourier transforms, and optics (John Wiley, NY).
4. P. Fraundorf and G. K. Fraundorf (1989) "Fourier transform 'darkfield' techniques", Proc. 47th Annual Meeting of the Electron Microscope Society of America (San Francisco Press, CA), page 122-123 pdf.
5. P. Fraundorf (1990) "Localizing periodicity in near-field images", Phys. Rev. Lett. 64:9, 1031-1034. (link,eprint)
6. F. G. Meyer and R. R. Coifman (1997) "Brushlets: A tool for directional image analysis and image compression", Applied and Computational Harmonic Analysis 4, 147 abstract.
7. P. Fraundorf (2004) "Digital darkfield decompositions", arXiv:cond-mat/0403017.
8. P. Fraundorf and Lu Fei (2004) "Digital darkfield decompositions" Microscopy and MicroAnalysis 10 Supplement 2, 300-301.
9. P. Fraundorf, Jinfeng Wang, Eric Mandell and Martin Rose (2006) "Digital darkfield tableaus" Microscopy and Microanalysis 12: Supplement 2, 1010-1011 pdf.
10. Martin Rose and P. Fraundorf (2006) "Picometer scale differences of lattice spacing in TEM images" Microscopy and Microanalysis 12: Supplement 2, 1008-1009 pdf.
11. Martin Rose (2006) Spacing measurements of lattice fringes in HRTEM images using digital darkfield decomposition (M. S. Thesis in Physics & Astronomy, UM-StL) pdf.
12. Jinfeng Wang, P. Fraundorf and Yangchuan Xing (2006) "Lattice fringe signatures of epitaxy on nanotubes", arXiv:cond-mat/0603312.
13. Jinfeng Wang and P. Fraundorf (2006) "Lattice fringe signatures of epitaxy on nanotubes", Microscopy and Microanalysis, 12:Supplement 2, 664-665 pdf.
14. P. Fraundorf, J. Liu and E. Mandell (2007) "Digital darkfield analysis of nanoparticle defects" Microscopy and Microanalysis 13: Supplement 2, 992-993 pdf.
15. Jinfeng Wang (2008) Characterization and synthesis of nanoscale materials (Ph.D. Dissertation in Physics and Astronomy, UM-StL and MST-Rolla).
16. P. Fraundorf and Chris Bishop (2013) "Efficient Lattice-Image Detection of Icosahedral Twins", Microscopy and MicroAnalysis 19:s2, 1804-1805 pdf.

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