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The development of the FSR method in electron microscopy began roughly in the 1970s. Over time, generations of scientists contributed to the evolvement of various mathematical variants, numerical implementations, and actual applications of FSR. For this reason, developing an only rudimentarily fair genealogical table of important contributors would simply require too much space. Instead, we name here only one person, who was frequently ignored in the scientific literature and who is barely known: Peter Schiske. He is the guy who invented the FSR principle! Peter Schiske (1924–2012) was an Austrian physicist, mathematician and early computer expert. In the early 1950s he collaborated with the wellknown Austrian physicist and electron optician Walter Glaser, who was a strong proponent of the wave optical view of image formation based on the Schrödinger equation. Not surprisingly, we also made strong use of the wave optical view throughout this chapter. It was finally Peter Schiske who published in 1968 for the first time the idea of focalseries reconstruction in electron microscopy. The original paper was a short conference abstract written in German. Fortunately, due to its fundamental importance, Schiske’s original paper has meanwhile been translated to English and reprinted (see References).
Why is it favorable to have the object wavefunction available compared to a single HRTEM image?
Are you aware of a TEM technique, where the object wavefunction can be obtained without requiring a multitude of images?
State at least two reasons why it is advisable to perform HRTEM experiments in thinobject regions. How many nanometers are roughly considered as ‘thin’?
How is the thickness dependence of a wavefunction related to the atomic charge number?
What kind of artifacts are introduced even by a ‘neutral’ microscope, which just produces a magnified image of the object wavefunction?
What would you expect to see in images of a thin object made with a ‘neutral’ microscope?
If a constantphaseshift microscope was available (Zernike phase plate), how many images would be required to restore the object wavefunction?
How do the projection surfaces in the 3D (Re, Im,
g) space of a constantphaseshift microscope differ from those of a real microscope?
How are the projection surfaces in the 3D (Re, Im,
g) space related to the wellknown contrast transfer function (CTF)?
How large roughly is the minimum contrast delocalization obtainable with a noncorrected field emission microscope? What minimum contrast delocalization can be obtained with a
C
_{ S }corrected version?
By which feature of the projection surfaces in the 3D (Re, Im,
g) space can one observe the function ∇
χ(
g)?
Is there an analytical solution to the linear reconstruction problem? Is there an analytical solution to the nonlinear reconstruction problem?
At which defocus value should one approximately place the midpoint of a focal series?
Is there a substantial difference in the defocus value
Z
_{opt} between an uncorrected microscope and a
C
_{S}corrected microscope? State typical values.
Does the choice of the classical Scherzer defocus instead of
Z
_{opt} make any sense for FSR with an uncorrected field emission microscope?
Which single parameter apart from the wavelength determines the lowest reconstructible frequency
g
_{min}?
Which single parameter apart from the wavelength determines the resonance frequency
g
_{res} in the highfrequency regime?
Which single parameter apart from the wavelength determines the optimum focal step size
δ
_{opt}?
Would it be efficient from a mathematical point of view to decrease the lowest reconstructible frequency
g
_{min} by increasing the number of recorded images? Additionally, what physical effect related to the object hampers such an attempt?
Is it a good idea to try a reconstruction using only a small number of images (e.g., less than five)? What exactly is sacrificed when reducing the number of images?
Is there an advantage of recording an equidistant focal series over recording an irregularly spaced series?
State three reasons why the application of FSR can yield an advantage over taking just one
C
_{S}corrected image at the optimum defocus?
Would it be a good idea to apply FSR to amorphous materials or to nanoparticles lying loosely on a support film?
Who is the third Austrian named in the “People” section at the end of the chapter? Which view in physics/optics do they share?
Derive the fundamental Eq.
9.12, which is one possible definition of the Scherzer defocus
Z
_{ S }, by requiring that
χ(
g
^{*},
Z
_{S}) = −2
π/3, where
g
^{*} is the position of the local minimum of
χ.
The local minimum of the aberration function
g
^{*} can be easily recognized as a dip in the plateau of the Scherzer CTF displayed in Fig.
9.6d. What property of the respective helical surface of Fig.
9.8a, d changes at the specific frequency
g
^{*}?
Derive the fundamental Eq.
9.16, which defines the optimum defocus
Z
_{opt}, by setting ∇
χ(
g
_{int},
Z
_{opt}) = −∇
χ(
g
_{max},
Z
_{opt}), and by solving the resulting thirdorder equation. Take care with the signs! It might be helpful to use 
Z in combination with compensating signs.
Derive the optimum value of the spherical aberration
C
_{S} and the thereby resulting minimal achievable radius
R
_{min} of the pointspread function for a
C
_{S}corrected microscope by demanding that
Z
_{ S } of Eq.
9.12 equals
Z
_{opt} of Eq.
9.16.
What is the purpose of the first and the second terms in the enumerator of the linear filter function of Eq.
9.30?
What important property is reflected by the denominator of the linear filter function of Eq.
9.30?
Explain why the titanium atom columns produce stronger phase peaks in the image of Fig.
9.15 (righthand side) than the barium atom columns, although titanium is the lighter and therefore also the weaker scattering element.
In the reconstructed phase of Fig.
9.16 it can be observed that the two polygonal structure units stacked above each other are absolutely identical. However, in both input images of Fig.
9.14 one can observe clear differences between the upper and the lower units. How can one and the same image exhibit different contrast for identical object features?
When comparing the number of intensity maxima in the
C
_{S}corrected Scherzer image of Fig.
9.18c with the number phase maxima in Fig.
9.18d one finds that there are many more intensity maxima than phase maxima. Whereas the phase maxima are all located at Ga or As atomic column positions as is expected, some of the intensity maxima are located at empty crystal positions and are thus artifacts. Which mechanism can be responsible for the ‘ghost’ atoms in the
C
_{S}corrected Scherzer image?
Q9.1
Why is it favorable to have the object wavefunction available compared to a single HRTEM image?
Q9.2
Are you aware of a TEM technique, where the object wavefunction can be obtained without requiring a multitude of images?
Q9.3
State at least two reasons why it is advisable to perform HRTEM experiments in thinobject regions. How many nanometers are roughly considered as ‘thin’?
Q9.4
How is the thickness dependence of a wavefunction related to the atomic charge number?
Q9.5
What kind of artifacts are introduced even by a ‘neutral’ microscope, which just produces a magnified image of the object wavefunction?
Q9.6
What would you expect to see in images of a thin object made with a ‘neutral’ microscope?
Q9.7
If a constantphaseshift microscope was available (Zernike phase plate), how many images would be required to restore the object wavefunction?
Q9.8
How do the projection surfaces in the 3D (Re, Im,
g) space of a constantphaseshift microscope differ from those of a real microscope?
Q9.9
How are the projection surfaces in the 3D (Re, Im,
g) space related to the wellknown contrast transfer function (CTF)?
Q9.10
How large roughly is the minimum contrast delocalization obtainable with a noncorrected field emission microscope? What minimum contrast delocalization can be obtained with a
C
_{ S }corrected version?
Q9.11
By which feature of the projection surfaces in the 3D (Re, Im,
g) space can one observe the function ∇
χ(
g)?
Q9.12
Is there an analytical solution to the linear reconstruction problem? Is there an analytical solution to the nonlinear reconstruction problem?
Q9.13
At which defocus value should one approximately place the midpoint of a focal series?
Q9.14
Is there a substantial difference in the defocus value
Z
_{opt} between an uncorrected microscope and a
C
_{S}corrected microscope? State typical values.
Q9.15
Does the choice of the classical Scherzer defocus instead of
Z
_{opt} make any sense for FSR with an uncorrected field emission microscope?
Q9.16
Which single parameter apart from the wavelength determines the lowest reconstructible frequency
g
_{min}?
Q9.17
Which single parameter apart from the wavelength determines the resonance frequency
g
_{res} in the highfrequency regime?
Q9.18
Which single parameter apart from the wavelength determines the optimum focal step size
δ
_{opt}?
Q9.19
Would it be efficient from a mathematical point of view to decrease the lowest reconstructible frequency
g
_{min} by increasing the number of recorded images? Additionally, what physical effect related to the object hampers such an attempt?
Q9.20
Is it a good idea to try a reconstruction using only a small number of images (e.g., less than five)? What exactly is sacrificed when reducing the number of images?
Q9.21
Is there an advantage of recording an equidistant focal series over recording an irregularly spaced series?
Q9.22
State three reasons why the application of FSR can yield an advantage over taking just one
C
_{S}corrected image at the optimum defocus?
Q9.23
Would it be a good idea to apply FSR to amorphous materials or to nanoparticles lying loosely on a support film?
Q9.24
Who is the third Austrian named in the “People” section at the end of the chapter? Which view in physics/optics do they share?
T9.1
Derive the fundamental Eq.
9.12, which is one possible definition of the Scherzer defocus
Z
_{ S }, by requiring that
χ(
g
^{*},
Z
_{S}) = −2
π/3, where
g
^{*} is the position of the local minimum of
χ.
T9.2
T9.3
Derive the fundamental Eq.
9.16, which defines the optimum defocus
Z
_{opt}, by setting ∇
χ(
g
_{int},
Z
_{opt}) = −∇
χ(
g
_{max},
Z
_{opt}), and by solving the resulting thirdorder equation. Take care with the signs! It might be helpful to use 
Z in combination with compensating signs.
T9.4
T9.5
What is the purpose of the first and the second terms in the enumerator of the linear filter function of Eq.
9.30?
T9.6
What important property is reflected by the denominator of the linear filter function of Eq.
9.30?
T9.7
Explain why the titanium atom columns produce stronger phase peaks in the image of Fig.
9.15 (righthand side) than the barium atom columns, although titanium is the lighter and therefore also the weaker scattering element.
T9.8
In the reconstructed phase of Fig.
9.16 it can be observed that the two polygonal structure units stacked above each other are absolutely identical. However, in both input images of Fig.
9.14 one can observe clear differences between the upper and the lower units. How can one and the same image exhibit different contrast for identical object features?
T9.9
When comparing the number of intensity maxima in the
C
_{S}corrected Scherzer image of Fig.
9.18c with the number phase maxima in Fig.
9.18d one finds that there are many more intensity maxima than phase maxima. Whereas the phase maxima are all located at Ga or As atomic column positions as is expected, some of the intensity maxima are located at empty crystal positions and are thus artifacts. Which mechanism can be responsible for the ‘ghost’ atoms in the
C
_{S}corrected Scherzer image?
Zurück zum Zitat Humphreys CJ (1979) Scattering of fast electrons by crystals. Rep Prog Phys 42:1825 (Useful as background to section 9.2.) CrossRef Humphreys CJ (1979) Scattering of fast electrons by crystals. Rep Prog Phys 42:1825 (Useful as background to section 9.2.)
CrossRef
Zurück zum Zitat Reimer L (1984) Transmission Electron Microscopy. Springer Series in Optical Sciences, vol. 36. Springer, Berlin Heidelberg New York Tokio (Useful as background to section 9.2.) Reimer L (1984) Transmission Electron Microscopy. Springer Series in Optical Sciences, vol. 36. Springer, Berlin Heidelberg New York Tokio (Useful as background to section 9.2.)
Zurück zum Zitat Tillmann K, Thust A, Urban K (2004) Spherical aberration correction in tandem with exitplane wave function reconstruction: interlocking tools for the atomic scale imaging of lattice defects in GaAs. Microsc Microanal 10:185–198 (Example of application) CrossRef Tillmann K, Thust A, Urban K (2004) Spherical aberration correction in tandem with exitplane wave function reconstruction: interlocking tools for the atomic scale imaging of lattice defects in GaAs. Microsc Microanal 10:185–198 (Example of application)
CrossRef
Zurück zum Zitat Bethe H (1928) Theorie der Beugung von Elektronen an Kristallen. Ann Phys 87:55–129 (For the Bethe–Bloch formalism) CrossRef Bethe H (1928) Theorie der Beugung von Elektronen an Kristallen. Ann Phys 87:55–129 (For the Bethe–Bloch formalism)
CrossRef
Zurück zum Zitat Gerchberg RW, Saxton WO (1972) Practical algorithm for determination of phase from image and diffraction plane pictures. Optik 35:237 Gerchberg RW, Saxton WO (1972) Practical algorithm for determination of phase from image and diffraction plane pictures. Optik 35:237
Zurück zum Zitat Kübel C, Thust A (2006) TrueImage – A software package for focalseries reconstruction in HRTEM. NATO Science Series, Series II. Math Phys Chem 211:373–392 Kübel C, Thust A (2006)
TrueImage – A software package for focalseries reconstruction in HRTEM. NATO Science Series, Series II. Math Phys Chem 211:373–392
Zurück zum Zitat Misell DL (1973) Examination of an iterative method for solution of phase problem in optics and electron optics. 1. Test calculations. J Phys D 6:2200–2216 CrossRef Misell DL (1973) Examination of an iterative method for solution of phase problem in optics and electron optics. 1. Test calculations. J Phys D 6:2200–2216
CrossRef
Zurück zum Zitat Schiske P (2002) Image reconstruction by means of focus series. J Microsc 207:154–154 (Reprint of the original 1968 paper) CrossRef Schiske P (2002) Image reconstruction by means of focus series. J Microsc 207:154–154 (Reprint of the original 1968 paper)
CrossRef
Zurück zum Zitat Bethe H (1928) Theorie der Beugung von Elektronen an Kristallen. Ann Phys 87:55–129 (The Bethe–Bloch formalism) CrossRef Bethe H (1928) Theorie der Beugung von Elektronen an Kristallen. Ann Phys 87:55–129 (The Bethe–Bloch formalism)
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Zurück zum Zitat Cowley JM, Moodie AF (1957) The scattering of electrons by atoms and crystals. 1. A new theoretical approach. Acta Cryst 10:609–619 (The Multislice Approach) CrossRef Cowley JM, Moodie AF (1957) The scattering of electrons by atoms and crystals. 1. A new theoretical approach. Acta Cryst 10:609–619 (The Multislice Approach)
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Zurück zum Zitat Goodman P, Moodie AF (1974) Numerical evaluation of nbeam wavefunctions in electronscattering by multislice method. Acta Cryst A30:280–290 (More Multislice) CrossRef Goodman P, Moodie AF (1974) Numerical evaluation of nbeam wavefunctions in electronscattering by multislice method. Acta Cryst A30:280–290 (More Multislice)
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Zurück zum Zitat Haider M, Rose H, Uhlemann S, Schwan E, Kabius B, Urban (1998a) A sphericalaberrationcorrected 200 kV transmission electron microscope. Ultramicroscopy 75:53–60 (Using the corrector in Sect. 9.3.3.) CrossRef Haider M, Rose H, Uhlemann S, Schwan E, Kabius B, Urban (1998a) A sphericalaberrationcorrected 200 kV transmission electron microscope. Ultramicroscopy 75:53–60 (Using the corrector in Sect. 9.3.3.)
CrossRef
Zurück zum Zitat Haider M, Uhlemann S, Schwan E, Rose H, Kabius B, Urban K (1998b) Electron microscopy image enhanced. Nature 392:768–769 (Using the corrector in Sect. 9.3.3.) CrossRef Haider M, Uhlemann S, Schwan E, Rose H, Kabius B, Urban K (1998b) Electron microscopy image enhanced. Nature 392:768–769 (Using the corrector in Sect. 9.3.3.)
CrossRef
Zurück zum Zitat Humphreys CJ (1979) Scattering of fast electrons by crystals. Rep Prog Phys 42:1864 (For Bloch waves) CrossRef Humphreys CJ (1979) Scattering of fast electrons by crystals. Rep Prog Phys 42:1864 (For Bloch waves)
CrossRef
Zurück zum Zitat Jia CL, Lentzen M, Urban K (2003) Atomicresolution imaging of oxygen in perovskite ceramics. Science 299:870–873 (Negative C S) CrossRef Jia CL, Lentzen M, Urban K (2003) Atomicresolution imaging of oxygen in perovskite ceramics. Science 299:870–873 (Negative
C
_{S})
CrossRef
Zurück zum Zitat Jia CL, Lentzen M, Urban K (2004) Highresolution transmission electron microscopy using negative spherical aberration. Microsc Microanal 10(2):174–184 (Negative C S) CrossRef Jia CL, Lentzen M, Urban K (2004) Highresolution transmission electron microscopy using negative spherical aberration. Microsc Microanal 10(2):174–184 (Negative
C
_{S})
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Zurück zum Zitat Lentzen M, Jahnen B, Jia CL, Thust A, Tillmann K, Urban K (2002) Highresolution imaging with an aberrationcorrected transmission electron microscope. Ultramicroscopy 92:233–242 (First applications of C S correction) CrossRef Lentzen M, Jahnen B, Jia CL, Thust A, Tillmann K, Urban K (2002) Highresolution imaging with an aberrationcorrected transmission electron microscope. Ultramicroscopy 92:233–242 (First applications of
C
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Zurück zum Zitat Lichte H (1991) Optimum focus for taking electron holograms. Ultramicroscopy 38(1):13–22 (For his defocus Z opt) CrossRef Lichte H (1991) Optimum focus for taking electron holograms. Ultramicroscopy 38(1):13–22 (For his defocus
Z
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Zurück zum Zitat Reimer L (1984) Transmission Electron Microscopy. Springer Series in Optical Sciences, vol. 36. Springer, Berlin Heidelberg New York Tokio Reimer L (1984) Transmission Electron Microscopy. Springer Series in Optical Sciences, vol. 36. Springer, Berlin Heidelberg New York Tokio
Zurück zum Zitat Rose H (1990) Outline of a spherically corrected semiaplanatic mediumvoltage transmission electronmicroscope. Optik 85:19–24 (Using the corrector in Sect. 9.3.3) Rose H (1990) Outline of a spherically corrected semiaplanatic mediumvoltage transmission electronmicroscope. Optik 85:19–24 (Using the corrector in Sect. 9.3.3)
Zurück zum Zitat Scherzer O (1949) The theoretical resolution limit of the electron microscope. J Appl Phys 20:20–29 (For his defocus) CrossRef Scherzer O (1949) The theoretical resolution limit of the electron microscope. J Appl Phys 20:20–29 (For his defocus)
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Zurück zum Zitat Saxton WO in Advances in Electronics and Electron Physics. (1978). Academic Press, London, Suppl. 10, Ch. 9.7. When you are thinking about Eq. 9.30. Saxton WO in
Advances in Electronics and Electron Physics. (1978). Academic Press, London, Suppl. 10, Ch. 9.7. When you are thinking about Eq. 9.30.
Zurück zum Zitat Saxton WO (1980) Correction of artifacts in linear and nonlinear highresolution electronmicrographs. J Microsc Spectrosc Electron 5:665–674 (When you are thinking about Eq. 9.30) Saxton WO (1980) Correction of artifacts in linear and nonlinear highresolution electronmicrographs. J Microsc Spectrosc Electron 5:665–674 (When you are thinking about Eq. 9.30)
Zurück zum Zitat Saxton WO (1986). Proc. 11th Int. Congr. for Electron Microscopy, Kyoto, post deadline paper 1 (unpublished). When you are thinking about Eq. 9.30. Saxton WO (1986). Proc. 11th Int. Congr. for Electron Microscopy, Kyoto, post deadline paper 1 (unpublished). When you are thinking about Eq. 9.30.
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Zurück zum Zitat Schiske P (1968). Proc 4th Reg Congr Electron Microscopy, Rome, 1, 145. If you can find it when you are thinking about Eq. 9.30. Schiske P (1968). Proc 4th Reg Congr Electron Microscopy, Rome,
1, 145. If you can find it when you are thinking about Eq. 9.30.
Zurück zum Zitat Schiske P (2002) Image reconstruction by means of focus series. J Microscopy 207:154–154 (When you are thinking about Eq. 9.30. Reprint of Schiske P (1968)) CrossRef Schiske P (2002) Image reconstruction by means of focus series. J Microscopy 207:154–154 (When you are thinking about Eq. 9.30. Reprint of Schiske P (1968))
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Zurück zum Zitat Allen LJ, Oxley MP (2001) Phase retrieval from series of images obtained by defocus variation. Optics Commun 199:65–75 (The transportofintensity formalism) CrossRef Allen LJ, Oxley MP (2001) Phase retrieval from series of images obtained by defocus variation. Optics Commun 199:65–75 (The transportofintensity formalism)
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Zurück zum Zitat Coene WMJ, Thust A, de Beeck MO, Van Dyck D (1996) Maximumlikelihood method for focusvariation image reconstruction in high resolution transmission electron microscopy. Ultramicroscopy 64:109–135 (Using general leastsquares) CrossRef Coene WMJ, Thust A, de Beeck MO, Van Dyck D (1996) Maximumlikelihood method for focusvariation image reconstruction in high resolution transmission electron microscopy. Ultramicroscopy 64:109–135 (Using general leastsquares)
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Zurück zum Zitat Gerchberg RW, Saxton WO (1972) Practical algorithm for determination of phase from image and diffraction plane pictures. Optik 35(2):237 (The GerchbergSaxton algorithm) Gerchberg RW, Saxton WO (1972) Practical algorithm for determination of phase from image and diffraction plane pictures. Optik 35(2):237 (The GerchbergSaxton algorithm)
Zurück zum Zitat Kirkland EJ (1984) Improved highresolution imageprocessing of bright field electronmicrographs. 1. Theory. Ultramicroscopy 15:151–172 (Using general leastsquares) CrossRef Kirkland EJ (1984) Improved highresolution imageprocessing of bright field electronmicrographs. 1. Theory. Ultramicroscopy 15:151–172 (Using general leastsquares)
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Zurück zum Zitat Kirkland EJ, Siegel BM, Uyeda N, Fujiyoshi Y (1985) Improved highresolution imageprocessing of bright field electronmicrographs. 2. Experiment. Ultramicroscopy 17:87–103 (Using general leastsquares) CrossRef Kirkland EJ, Siegel BM, Uyeda N, Fujiyoshi Y (1985) Improved highresolution imageprocessing of bright field electronmicrographs. 2. Experiment. Ultramicroscopy 17:87–103 (Using general leastsquares)
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Zurück zum Zitat Kübel C, Thust A (2006) TrueImage – A software package for focalseries reconstruction in HRTEM. NATO Science Series, Series II. Math Phys Chem 211:373–392 Kübel C, Thust A (2006)
TrueImage – A software package for focalseries reconstruction in HRTEM. NATO Science Series, Series II. Math Phys Chem 211:373–392
Zurück zum Zitat Misell DL (1973) Examination of an iterative method for solution of phase problem in optics and electron optics.1. Test calculations. J Phys D 6:2200–2216 (The Misell algorithm) CrossRef Misell DL (1973) Examination of an iterative method for solution of phase problem in optics and electron optics.1. Test calculations. J Phys D 6:2200–2216 (The Misell algorithm)
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Zurück zum Zitat Thust A, Lentzen M, Urban K (1994) Nonlinear reconstruction of the exit planewave function from periodic highresolution electronmicroscopy images. Ultramicroscopy 53:101–120 (Use of stochastic algorithms) CrossRef Thust A, Lentzen M, Urban K (1994) Nonlinear reconstruction of the exit planewave function from periodic highresolution electronmicroscopy images. Ultramicroscopy 53:101–120 (Use of stochastic algorithms)
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Zurück zum Zitat Thust A, Coene WMJ, de Beeck MO, Van Dyck D (1996) Focalseries reconstruction in HRTEM: Simulation studies on nonperiodic objects. Ultramicroscopy 64:211–230 (Using general leastsquares) CrossRef Thust A, Coene WMJ, de Beeck MO, Van Dyck D (1996) Focalseries reconstruction in HRTEM: Simulation studies on nonperiodic objects. Ultramicroscopy 64:211–230 (Using general leastsquares)
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Zurück zum Zitat Thust A, Lentzen M, Urban K (2000) Scanning Microscopy Suppl 1:435 (Use of stochastic algorithms) Thust A, Lentzen M, Urban K (2000) Scanning Microscopy Suppl 1:435 (Use of stochastic algorithms)
Zurück zum Zitat Thust A, Overwijk MHF, Coene WMJ, Lentzen M (1996) Numerical correction of lens aberrations in phaseretrieval HRTEM. Ultramicroscopy 64:249–264 (Numerical aberration correction; dislocation core) CrossRef Thust A, Overwijk MHF, Coene WMJ, Lentzen M (1996) Numerical correction of lens aberrations in phaseretrieval HRTEM. Ultramicroscopy 64:249–264 (Numerical aberration correction; dislocation core)
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Zurück zum Zitat Barthel J, Weirich TE, Cox G, Hibst H, Thust A (2010) Structure of Cs0.5[Nb 2.5W 2.5O 14] analysed by focalseries reconstruction and crystallographic image processing. Acta Mater 58:3764–3772 (Catalyst) CrossRef Barthel J, Weirich TE, Cox G, Hibst H, Thust A (2010) Structure of Cs0.5[Nb
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Zurück zum Zitat Van Dyck D, Jinschek JR, Chen FR (2012) ‘Big Bang’ tomography as a new route to atomicresolution electron tomography. Nature 486:243–246 (and 489, 460. Graphene) CrossRef Van Dyck D, Jinschek JR, Chen FR (2012) ‘Big Bang’ tomography as a new route to atomicresolution electron tomography. Nature 486:243–246 (and
489, 460. Graphene)
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Zurück zum Zitat Houben L, Thust A, Urban K (2006) Atomicprecision determination of the reconstruction of a 90 degrees tilt boundary in YBa 2CU 3O 7delta by aberration corrected HRTEM. Ultramicroscopy 106:200–214 (Nearpicometreprecision) CrossRef Houben L, Thust A, Urban K (2006) Atomicprecision determination of the reconstruction of a 90 degrees tilt boundary in YBa
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Zurück zum Zitat Jia CL, Thust A (1999) Investigation of atomic displacements at a Sigma 3 {111} twin boundary in BaTiO 3 by means of phaseretrieval electron microscopy. Phys Rev Lett 82(25):5052–5055 (Nearpicometreprecision) CrossRef Jia CL, Thust A (1999) Investigation of atomic displacements at a Sigma 3 {111} twin boundary in BaTiO
_{3} by means of phaseretrieval electron microscopy. Phys Rev Lett 82(25):5052–5055 (Nearpicometreprecision)
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Zurück zum Zitat Jia CL, Thust A, Urban K (2005) Atomicscale analysis of the oxygen configuration at a SrTiO 3 dislocation core. Phys Rev Lett 95:article #225506 (Dislocation core) CrossRef Jia CL, Thust A, Urban K (2005) Atomicscale analysis of the oxygen configuration at a SrTiO
_{3} dislocation core. Phys Rev Lett 95:article #225506 (Dislocation core)
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Zurück zum Zitat Jia CL, Rosenfeld R, Thust A, Urban K (1999) Atomic structure of a Sigma=3, {111} twinboundary junction in a BaTiO 3 thin film. Phil Mag Lett 79(3):99 (Twin arrangement in barium titanate) CrossRef Jia CL, Rosenfeld R, Thust A, Urban K (1999) Atomic structure of a Sigma=3, {111} twinboundary junction in a BaTiO
_{3} thin film. Phil Mag Lett 79(3):99 (Twin arrangement in barium titanate)
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Zurück zum Zitat Jinschek JR, Yucelen E, Calderon H, Freitag B (2011) Quantitative atomic 3D imaging of single/double sheet graphene structure. Carbon 49:556–562 (Graphene) CrossRef Jinschek JR, Yucelen E, Calderon H, Freitag B (2011) Quantitative atomic 3D imaging of single/double sheet graphene structure. Carbon 49:556–562 (Graphene)
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Zurück zum Zitat Kisielowski C, Hetherington CJD, Wang YC, Kilaas R, O’Keefe MA, Thust A (2001) Imaging columns of the light elements carbon, nitrogen and oxygen with sub Angstrom resolution. Ultramicroscopy 89:243–263 (Applications include e.g. the first reconstruction of light atoms) CrossRef Kisielowski C, Hetherington CJD, Wang YC, Kilaas R, O’Keefe MA, Thust A (2001) Imaging columns of the light elements carbon, nitrogen and oxygen with sub Angstrom resolution. Ultramicroscopy 89:243–263 (Applications include e.g. the first reconstruction of light atoms)
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Zurück zum Zitat Mahalingam K, Eyink KG, Brown GJ, Dorsey DL, Kisielowski CF, Thust A (2006) Quantifying stoichiometry of mixedcationanion III–V semiconductor interfaces at atomic resolution. Appl Phys Lett 88(9):article #091904 (Semiconductor heterostructures) CrossRef Mahalingam K, Eyink KG, Brown GJ, Dorsey DL, Kisielowski CF, Thust A (2006) Quantifying stoichiometry of mixedcationanion III–V semiconductor interfaces at atomic resolution. Appl Phys Lett 88(9):article #091904 (Semiconductor heterostructures)
CrossRef
Zurück zum Zitat Mahalingam K, Eyink KG, Brown GJ, Dorsey DL, Kisielowski CF, Thust A (2008) Compositional analysis of mixedcationanion III–V semiconductor interfaces using phase retrieval highresolution transmission electron microscopy. J Microscopy 230:372–381 (Semiconductor heterostructures) CrossRef Mahalingam K, Eyink KG, Brown GJ, Dorsey DL, Kisielowski CF, Thust A (2008) Compositional analysis of mixedcationanion III–V semiconductor interfaces using phase retrieval highresolution transmission electron microscopy. J Microscopy 230:372–381 (Semiconductor heterostructures)
CrossRef
Zurück zum Zitat Thust A, Rosenfeld R (1998) State of the art of focalseries reconstruction in HRTEM Proc ICEM 14, Cancun, Mexico. vol. 1., pp 119–120 (Use N images to reduce noise) Thust A, Rosenfeld R (1998) State of the art of focalseries reconstruction in HRTEM Proc ICEM 14, Cancun, Mexico. vol. 1., pp 119–120 (Use
N images to reduce noise)
Zurück zum Zitat Tillmann A, Thust K, Urban K (2005) Spherical aberration correction in tandem with exitplane wave function reconstruction: interlocking tools for the atomic scale imaging of lattice defects in GaAs. Microsc Microanal 10(2):185–198 (A structural analysis of the stacking fault in GaAs) CrossRef Tillmann A, Thust K, Urban K (2005) Spherical aberration correction in tandem with exitplane wave function reconstruction: interlocking tools for the atomic scale imaging of lattice defects in GaAs. Microsc Microanal 10(2):185–198 (A structural analysis of the stacking fault in GaAs)
CrossRef
 Titel
 FocalSeries Reconstruction
 DOI
 https://doi.org/10.1007/9783319266510_9
 Autor:

Andreas Thust
 Sequenznummer
 9
 Kapitelnummer
 9