4D-STEM

Note

These documents cover 4D-STEM techniques and algorithms. They are living documents and are updated over time. Please refer to the Literature page to view all citations related to these techniques.

4D-STEM (4-Dimensional Scanning Transmission Electron Microscopy) is a powerful technique that records a complete diffraction pattern at every scan position in a STEM experiment. Unlike traditional STEM which only records single intensity values, 4D-STEM captures rich information about how electrons interact with the sample at each point.

Contents

• Phase contrast physics
  • Understanding electron wave phase
  • How phase is lost
  • Why we need phase
  • Mathematical foundations
  • The measurement challenge
  • How phase shifts occur
  • Derivation of interaction constant
  • Full derivation
  • Phase gradient derivation
  • Time evolution derivation
• Phase retrieval methods
  • Three approaches
  • Differential Phase Contrast (DPC)
  • Ptychography
  • Beam-tilt corrected bright-field STEM (tcBF-STEM)
• Diffraction peak detection
  • Understanding Bragg diffraction
  • Importance of accurate detection
  • Locating diffraction peaks
  • Drift and pattern evolution
• Strain measurement and analysis
  • Understanding strain and its effects
  • Mathematical framework
• Orientation mapping
  • Understanding crystal orientation
  • Simulating diffraction patterns
• Phase contrast transfer function
  • Why we need PCTF
  • The basic idea
  • Moving to Fourier space
  • Computing the PCTF
  • What it tells you
  • Example PCTF curves
  • Applications
• Single sideband imaging
  • High-level overview
  • Why SSB?
  • Physical setup and approximations
  • Sideband formation in reciprocal space
  • Phase extraction from single sideband
  • Probe specification and aberration measurement
  • Parameters that cannot be reliably estimated
  • Practical guide for using SSB
  • Advantages and limitations
  • Implementation in quantem
  • SSB transfer function
  • Reconstruction workflow
  • Optimizing probe parameters
  • Code organization
  • Transfer function computation
  • Probe evaluation
  • Reconstruction pipeline
  • Usage examples
  • References
• Precession electron diffraction
• In-situ 4D-STEM