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Comment onA method for the solution of the phase problem in electron microscopy
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TLDR
In this article, the amplitude and phase from the intensity distribution of an electron micrograph is estimated using the relative defocus between micrographs, and the procedure is valid both in bright field and dark field microscopy for any specified coherence of the electron source.Abstract:
A method is given for the evaluation, in transmission electron microscopy, of the amplitude and phase from the intensity distribution of an electron micrograph. The method requires a minimum of two micrographs taken under different defocus conditions. The iterative scheme requires only the relative defocus between micrographs, and the procedure is valid both in bright-field and dark-field microscopy for any specified coherence of the electron source. Assumptions on the scattering properties of the specimen, such as the weak-phase-weak-amplitude object, are not required. For a complete determination of the amplitude-phase distribution for electron transmission through the specimen, the electron micrograph must be corrected for the effect of lens aberrations and defocusing to give the electron wavefunction immediately after transmission; only in the case of a weak-phase object can this wavefunction be directly related to the projected potential distribution in the object. Inelastic electron scattering is explicitly omitted from the analysis presented.read more
Citations
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Journal ArticleDOI
Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm.
TL;DR: An iterative phase retrieval method that uses a series of diffraction patterns, measured only in intensity, to solve for both amplitude and phase of the image wave function over a wide field of view and at wavelength-limited resolution is proposed.
Journal ArticleDOI
Phase Retrieval via Matrix Completion
TL;DR: This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging, and many other applications, and combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements.
Book ChapterDOI
Ptychography and Related Diffractive Imaging Methods
TL;DR: Ptychography as mentioned in this paper is a non-holographic solution of the phase problem, which is a method for calculating the phase relationships among different parts of a scattered wave disturbance in a situation where only the magnitude (intensity or flux) of the wave can be physically measured.
Journal ArticleDOI
Gerchberg–Saxton and Yang–Gu algorithms for phase retrieval in a nonunitary transform system: a comparison
TL;DR: The Yang-Gu algorithm is a generalization of the Gerchberg-Saxton algorithm and is effective in solving the general amplitude-phase-retrieval problem in any linear unitary or nonunitary transform system.
Journal ArticleDOI
Hubble Space Telescope characterized by using phase-retrieval algorithms
TL;DR: The Cramer-Rao lower bounds show that point spread functions taken well out of focus result in smaller errors when aberrations are estimated and that, for those images, photon noise is not a limiting factor.
References
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Journal Article
A practical algorithm for the determination of phase from image and diffraction plane pictures
TL;DR: In this article, an algorithm is presented for the rapid solution of the phase of the complete wave function whose intensity in the diffraction and imaging planes of an imaging system are known.
Journal ArticleDOI
Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm.
TL;DR: An iterative phase retrieval method that uses a series of diffraction patterns, measured only in intensity, to solve for both amplitude and phase of the image wave function over a wide field of view and at wavelength-limited resolution is proposed.
Journal ArticleDOI
Phase Retrieval via Matrix Completion
TL;DR: This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging, and many other applications, and combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements.
Book ChapterDOI
Ptychography and Related Diffractive Imaging Methods
TL;DR: Ptychography as mentioned in this paper is a non-holographic solution of the phase problem, which is a method for calculating the phase relationships among different parts of a scattered wave disturbance in a situation where only the magnitude (intensity or flux) of the wave can be physically measured.
Journal ArticleDOI
Measurement and compensation of defocusing and aberrations by Fourier processing of electron micrographs
Harold P. Erickson,Aaron Klug +1 more
TL;DR: In this paper, the Fourier transform of the image of a thin crystal of catalase, which has discrete diffraction maxima in the resolution range of 10 to 2.5 nm, as a function of defocusing, was determined by finding the relative contributions from phase and amplitude contrast.