autofocus and astigmatism correction in scanning transmission … · 2013-11-19 · autofocus and...
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Autofocus and Astigmatism Correctionin Scanning Transmission Electron Microscopy
M. Rudnaya, W. Van den Broek, R. DoornbosJ. Maubach, R. Mattheij
CASA-day28.10.2009
Outline• Electron microscopy• Condor project
• Defocus and astigmatism• CASA-day 2008
• Variance as an image quality measure • Variance for STEM• 3-parameter optimization
• STEM Application
Outline• Electron microscopy
- Electrons vs. light- Astigmatism aberration
• Condor project
• Defocus and astigmatism• CASA-day 2008
• Variance as an image quality measure • Will the variance work for STEM?• 3-parameter optimization
• STEM Application
Light Microscopy: Resolution 0.0002 mm = 200 nm - red light: λ ≈ 800 nm - blue light λ ≈ 400 nm
Electron Microscopy
100 kV 300 kV 1 MV 3 MV
λ (pm) 3.70 1.97 0.87 0.36
• h is Planck’s constant,• E is the accelerating voltage• e and m are the electron’s
charge and mass
Electron microscopy: Resolution 0.002 nm
Electron microscopy: Atomic resolution
FEI’s TitanScanning TransmissionElectron Microscope (STEM)
Pictures from the PhD-thesis “Advanced Focus Methods in Electron Microscopy: Tomographic Reconstruction of the EELS Data Cube Autofocus of HAADF-STEM Images”by W. van den Broek
Astigmatism
Pictures from “A Robust Focusing and Astigmatism Correction Method for the Scanning Electron Microscope” by K.H. ONG, J.C.H. PHANG, J.T.L. THONG
Outline• Electron microscopy• Condor project
• Defocus and astigmatism• CASA-day 2008
• Variance as an image quality measure • Will the variance work for STEM?• 3-parameter optimization
• STEM Application
Condor Project
AcknowledgmensThis work has been carried out as a part of the Condor project at FEI company under the responsibilities of the Embedded Systems Institute (ESI). This project is partially supported by the Dutch Ministry of Economic Affairs under the BSIK program.
Outline• Electron microscopy• Condor project
• Defocus and astigmatism- Linear image formation model- Gaussian point spread function- Defocus and astigmatism in STEM
• CASA-day 2008
• Variance as an image quality measure • Will the variance work for STEM?• 3-parameter optimization
• STEM Application
Linear image formation model
Gaussian PSF
=
=
=
*
*
*
Defocus and Astigmatism
Autofocus and astigmatism correction
Outline• Electron microscopy• Condor project
• Defocus and astigmatism• CASA-day 2008
- Our approach- New challenges
• Variance as an image quality measure • Will the variance work for STEM?• 3-parameter optimization
• STEM Application
CASA-day 2008
ChallengeSome real sample’s Fourier transforms are difficult to analyze
Outline• Electron microscopy• Condor project
• Defocus and astigmatism• CASA-day 2008
• Variance as an image quality measure - Definition- Why would it work?
• Will the variance work for STEM?• 3-parameter optimization
• STEM Application
Variance as an image quality measure
Variance definition
Variance as an image quality measure
Variance definitionWhy will it work?
Assumptions
Parseval’s theorem
(A.1)
(A.2) (A.3)
(A.4)
(4)
(5)
(1)
(2)
(3)
(6)
(7)
Outline• Electron microscopy• Condor project
• Defocus and astigmatism• CASA-day 2008
• Variance as an image quality measure• Variance for STEM
- STEM point spread function- Numerical simulation for typical objects
• 3-parameter optimization
• STEM Application
STEM PSF
STEM defocus and astigmatism
d=d0=-45 nm d=-22.5 nm d=0 nmd=-67.5nmd=-90 nm
Ca=-10 nm
Ca=0 nm
Ca=10 nm
Numerical experiment - amorphous
Numerical experiment - crystalline
Outline• Electron microscopy• Condor project
• Defocus and astigmatism• CASA-day 2008
• Variance as an image quality measure • Will the variance work for STEM?• 3-parameter optimization
- Optimization challenges- Nelder-Mead simplex method
• STEM Application
3-parameter optimization• Destructive and time consuming function evaluations• No derivative information available
• (*) Local optima due to the noise• (*) Deviation in the function values for the same parameters
Nelder-Mead simplex method
Image from “Derivative-free optimization” by Andrew Conn
Outline• Electron microscopy• Condor project
• Defocus and astigmatism• CASA-day 2008
• Variance as an image quality measure • Will the variance work for STEM?• 3-parameter optimization
• STEM Application- Cross-section- Golden particle
Application
Evaluations and iterations
Experiment with the gold particle
Concluding remarksA new method for STEM autofocus and astigmatism correction is proposed. It is based on a 3-parameter optimization of the variance image quality measure. Nelder-Mead simplex method is used as optimization technique. The method works for both numerical simulation and a real STEM application.
Plans for the future- Noise robustness- Reduce the number of function evaluations
Questions
?
Window function
Focus Series (Gold-on-Carbon)
Astigmatic Imagesdefocus
AstY
0
1
-1 0 1
Spherical aberration
Lens
Image plane
Modified varianceModel
Real world:
Modified variance