Breaking ambiguities in mixed state ptychography

Li, Peng; Edo, T. B.; Batey, Darren; Rodenburg, J. M.; Maiden, Andrew

doi:10.1364/oe.24.009038

Cited by 50 publications

(41 citation statements)

References 27 publications

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“…We form the K×K covariance matrix of the modes, and then find its eigenvalues and eigenvectors. The K orthogonalised modes are then obtained by projecting the original modes onto the eigenvectors of the covariance matrix [26]. Figure 5 shows the first six components of the four partially coherent electron wavefields.…”

Section: Methodsmentioning

confidence: 99%

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Modal decomposition of a propagating matter wave via electron ptychography

Cao

Kok

et al. 2016

Phys. Rev. A

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2 Abstract:We employ ptychography, a phase-retrieval imaging technique, to show experimentally for the first time that a partially coherent high-energy matter (electron) wave emanating from an extended source can be decomposed into a set of mutually independent modes of minimal rank. Partial coherence significantly determines the optical transfer properties of an electron microscope and so there has been much work on this subject. However, previous studies have employed forms of interferometry to determine spatial coherence between discrete points in the wavefield. Here we use the density matrix to derive a formal quantum mechanical description of electron ptychography and use it to measure a full description of the spatial coherence of a propagating matter wavefield, at least to the within the fundamental uncertainties of the measurements we can obtain.

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Section: Methodsmentioning

confidence: 99%

“…The modified Fourier constraint gives us K modes, where K is the number of illumination modes we have chosen to include in the reconstruction. There is an infinite combination of modes that can satisfy the overall intensity constraint, because they can be made up of any linear combination of each other [26].…”

Section: Theorymentioning

confidence: 99%

Modal decomposition of a propagating matter wave via electron ptychography

Cao

Kok

et al. 2016

Phys. Rev. A

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“…This work also opened up the exciting possibilities of information multiplexing [8] and dynamical systems imaging [9] with ptychography. Following results by Thibault, Menzel et al and Batey et al [7,8], Li et al [10] has recently demonstrated the feasibility of recovery of multiple sample modes by applying extra constraints into the iterative algorithms, and they discovered the inability of recovery of individual sample modes due to the mathematical equivalence in mixing the initial sample modes in multi-modal ptychography. Individual sample mode could be recovered when additional constraints on sample were applied [10].…”

Section: Introductionmentioning

confidence: 99%

“…The vibration frequency is selected to be 1 Hz with exposure of 6 seconds per position. Li et al [10] recently successfully performed multi-modal experiments with visible lights on complex test objects with partially coherent illuminations with several orthogonal modes. Their results demonstrate the feasibility of inversion of complex wavefunctions of both object and illumination using multi-modal approach without a priori information to start with.…”

Section: Introductionmentioning

confidence: 99%

Multi-Modal Ptychography: Recent Developments and Applications

et al. 2018

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Utilisation of partially coherent X-rays in Coherent X-ray Diffraction Imaging (CDI) and X-ray ptychography have brought intense research and developments for the past few years. Generally, data reconstructions convergence can be achieved by considering to incorporate partially coherent X-rays in ptychographic iterative reconstructions algorithms. Recently, exploration of both X-ray probe and sample modes have been studied and it was suggested that sufficient constraints are required to achieve accurate data reconstructions due to the mathematical inseparability of multiple sample modes that are superimposed into a single set of ptychographic intensity patterns. Here we review the multi-modal ptychography that can be used as a new emerging technique to investigate dynamical sample systems with partially coherent X-rays by recent experimental and simulated demonstrations.

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“…Further it has been shown, that the reconstruction of states can reveal more information about a specimen [117]. The symmetry of the operations in the ptychographic reconstruction algorithm can also lead to ambiguities in the reconstructed states and additional constraints are required in some cases to break these ambiguities [118].…”

Section: Introductionmentioning

confidence: 99%

X-Ray Near-Field Holography: Beyond Idealized Assumptions of the Probe

Hagemann¹

2017

Göttingen Series in X-Ray Physics

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Breaking ambiguities in mixed state ptychography

Cited by 50 publications

References 27 publications

Modal decomposition of a propagating matter wave via electron ptychography

Modal decomposition of a propagating matter wave via electron ptychography

Multi-Modal Ptychography: Recent Developments and Applications

X-Ray Near-Field Holography: Beyond Idealized Assumptions of the Probe

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