Fast Deterministic Ptychographic Imaging Using X-Rays

Yan, Aimin; D’Alfonso, Adrian J.; Morgan, Andrew J.; Putkunz, Corey T.; Allen, L. J.

doi:10.1017/s1431927614000932

Cited by 3 publications

(6 citation statements)

References 30 publications

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“…As such, this method has been the focus of much recent literature, leading to the development of steepest descent methods [16,24,25], conjugate gradient methods [4,16,26], Gauss-Newton methods [27], and quasi-Newton methods [28]. These algorithms have found application in the far-field ptychographic problem not only to solve for the object alone [24,25,29,30,31,32] but also to additionally solve for the probe [32,33] as well.…”

Section: Introductionmentioning

confidence: 99%

Using automatic differentiation as a general framework for ptychographic reconstruction

Kandel¹,

Maddali²,

Allain³

et al. 2019

Opt. Express

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Coherent diffraction imaging methods enable imaging beyond lens-imposed resolution limits. In these methods, the object can be recovered by minimizing an error metric that quantifies the difference between diffraction patterns as observed, and those calculated from a present guess of the object. Efficient minimization methods require analytical calculation of the derivatives of the error metric, which is not always straightforward. This limits our ability to explore variations of basic imaging approaches. In this paper, we propose to substitute analytical derivative expressions with the automatic differentiation method, whereby we can achieve object reconstruction by specifying only the physics-based experimental forward model. We demonstrate the generality of the proposed method through straightforward object reconstruction for a variety of complex ptychographic experimental models.

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Section: Introductionmentioning

confidence: 99%

Using automatic differentiation as a general framework for ptychographic reconstruction

Kandel¹,

Maddali²,

Allain³

et al. 2019

Opt. Express

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“…The final term, nonlinear with respect to the functionÔ(g), is assumed to be negligible and is ignored in subsequent equations. This is equivalent to making a weak phase approximation, but it is possible to correct for this after an initial solution, without the nonlinear term, has been obtained [22]. With this approximation, and defininĝ…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…We seek to correct for this following the procedure described in Ref. [22]. The values ofÔ(g) obtained from the reconstruction can be used to estimate the nonlinear term in Eq.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Structure retrieval with fast electrons using segmented detectors

et al. 2016

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We introduce an algorithm for the reconstruction of the complex transmission function of a specimen using segmented detectors in scanning transmission electron microscopy geometry. The phase of the transmission function can be related to magnetic and electric fields within the specimen and is sensitive to lighter elements. The technique is demonstrated for simulated data and also using experimental datasets taken from a MoS 2 monolayer and a SrTiO 3 crystal. We present an extension to the algorithm to account for uncertainties in the illuminating probe. The algorithm can be implemented using fast Fourier transforms, and this provides the possibility of reconstructing specimen transmission functions in real time.

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“…is a second order term and can be neglected, at least initially; a correction for its omission can be made subsequently [23]. This means that the cross terms over the whole autocorrelation plane are amenable to analysis in a linear fashion, not just those in the area where r r obj obj…”

Section: Deterministic Phase Retrieval From a Single Diffraction Patternmentioning

confidence: 99%

“…Further improvement in the result shown in figure 4(c) can be obtained by estimating r r obj obj ( ) ( ) y y Ä from the intial solution, subtracting this from the autocorrelation, having already subtracted the autocorrelation of the illumination, and repeating the linear solution [23]. Even when the nonlinear term is significant numerical tests have shown this approach to be successful [23].…”

Section: Deterministic Phase Retrieval Using Electronsmentioning

confidence: 99%

Deterministic approaches to coherent diffractive imaging

Allen

D’Alfonso

Martin

et al. 2015

J. Opt.

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In this review we will consider the retrieval of the wave at the exit surface of an object illuminated by a coherent probe from one or more measured diffraction patterns. These patterns may be taken in the near-field (often referred to as images) or in the far field (the Fraunhofer diffraction pattern, where the wave is the Fourier transform of that at the exit surface). The retrieval of the exit surface wave from such data is an inverse scattering problem. This inverse problem has historically been solved using nonlinear iterative methods, which suffer from convergence and uniqueness issues. Here we review deterministic approaches to obtaining the exit surface wave which ameliorate those problems.

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Fast Deterministic Ptychographic Imaging Using X-Rays

Cited by 3 publications

References 30 publications

Using automatic differentiation as a general framework for ptychographic reconstruction

Using automatic differentiation as a general framework for ptychographic reconstruction

Structure retrieval with fast electrons using segmented detectors

Deterministic approaches to coherent diffractive imaging

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