72 research outputs found
Blind Ptychographic Phase Retrieval via Convergent Alternating Direction Method of Multipliers
Ptychography has risen as a reference X-ray imaging technique: it achieves
resolutions of one billionth of a meter, macroscopic field of view, or the
capability to retrieve chemical or magnetic contrast, among other features. A
ptychographyic reconstruction is normally formulated as a blind phase retrieval
problem, where both the image (sample) and the probe (illumination) have to be
recovered from phaseless measured data. In this article we address a nonlinear
least squares model for the blind ptychography problem with constraints on the
image and the probe by maximum likelihood estimation of the Poisson noise
model. We formulate a variant model that incorporates the information of
phaseless measurements of the probe to eliminate possible artifacts. Next, we
propose a generalized alternating direction method of multipliers designed for
the proposed nonconvex models with convergence guarantee under mild conditions,
where their subproblems can be solved by fast element-wise operations.
Numerically, the proposed algorithm outperforms state-of-the-art algorithms in
both speed and image quality.Comment: 23 page
Partially Coherent Ptychography by Gradient Decomposition of the Probe
Coherent ptychographic imaging experiments often discard over 99.9 % of the
flux from a light source to define the coherence of an illumination. Even when
coherent flux is sufficient, the stability required during an exposure is
another important limiting factor. Partial coherence analysis can considerably
reduce these limitations. A partially coherent illumination can often be
written as the superposition of a single coherent illumination convolved with a
separable translational kernel. In this paper we propose the Gradient
Decomposition of the Probe (GDP), a model that exploits translational kernel
separability, coupling the variances of the kernel with the transverse
coherence. We describe an efficient first-order splitting algorithm GDP-ADMM to
solve the proposed nonlinear optimization problem. Numerical experiments
demonstrate the effectiveness of the proposed method with Gaussian and binary
kernel functions in fly-scan measurements. Remarkably, GDP-ADMM produces
satisfactory results even when the ratio between kernel width and beam size is
more than one, or when the distance between successive acquisitions is twice as
large as the beam width.Comment: 11 pages, 9 figure
Iterative Joint Ptychography-Tomography with Total Variation Regularization
In order to determine the 3D structure of a thick sample, researchers have
recently combined ptychography (for high resolution) and tomography (for 3D
imaging) in a single experiment. 2-step methods are usually adopted for
reconstruction, where the ptychography and tomography problems are often solved
independently. In this paper, we provide a novel model and ADMM-based algorithm
to jointly solve the ptychography-tomography problem iteratively, also
employing total variation regularization. The proposed method permits large
scan stepsizes for the ptychography experiment, requiring less measurements and
being more robust to noise with respect to other strategies, while achieving
higher reconstruction quality results.Comment: 5 pages, 5 figure
Analyzer Free Linear Dichroic Ptychography
Linear-dichroism is an important tool to characterize the transmission matrix
and determine the crystal or orbital orientation in a material. In order to
gain high resolution mapping of the transmission properties of such materials,
we introduce the linear-dichroism scattering model in ptychographic imaging,
and then develop an efficient two-stage reconstruction algorithm. Using
proposed algorithm, the dichroic transmission matrix without an analyzer can be
recovered by using ptychography measurements with as few as three different
polarization angles, with the help of an empty region to remove phase
ambiguities.Comment: 12 pages, 7 figure
Iterative X-ray Spectroscopic Ptychography
Spectroscopic ptychography is a powerful technique to determine the chemical
composition of a sample with high spatial resolution. In spectro-ptychography,
a sample is rastered through a focused x-ray beam with varying photon energy so
that a series of phaseless diffraction data are recorded. Each chemical
component in the material under investigation has a characteristic absorption
and phase contrast as a function of photon energy. Using a dictionary formed by
the set of contrast functions of each energy for each chemical component, it is
possible to obtain the chemical composition of the material from high
resolution multi-spectral images. This paper presents SPA (Spectroscopic
Ptychography with ADMM), a novel algorithm to iteratively solve the
spectroscopic blind ptychography problem. We design first a nonlinear
spectro-ptychography model based on Poisson maximum likelihood, and construct
then the proposed method based on fast iterative splitting operators. SPA can
be used to retrieve spectral contrast when considering both a known or an
incomplete (partially known) dictionary of reference spectra. By coupling the
redundancy across different spectral measurements, the proposed algorithm can
achieve higher reconstruction quality when compared to standard
state-of-the-art two-step methods. We demonstrate how SPA can recover accurate
chemical maps from Poisson-noised measurements, and also show its enhanced
robustness when reconstructing reduced redundancy ptychography data using large
scanning stepsizes
Advanced Denoising for X-ray Ptychography
The success of ptychographic imaging experiments strongly depends on
achieving high signal-to-noise ratio. This is particularly important in
nanoscale imaging experiments when diffraction signals are very weak and the
experiments are accompanied by significant parasitic scattering (background),
outliers or correlated noise sources. It is also critical when rare events such
as cosmic rays, or bad frames caused by electronic glitches or shutter timing
malfunction take place.
In this paper, we propose a novel iterative algorithm with rigorous analysis
that exploits the direct forward model for parasitic noise and sample
smoothness to achieve a thorough characterization and removal of structured and
random noise. We present a formal description of the proposed algorithm and
prove its convergence under mild conditions. Numerical experiments from
simulations and real data (both soft and hard X-ray beamlines) demonstrate that
the proposed algorithms produce better results when compared to
state-of-the-art methods.Comment: 24 pages, 9 figure
Negative flat band magnetism in a spin-orbit coupled correlated kagome magnet
It has long been speculated that electronic flat band systems can be a
fertile ground for hosting novel emergent phenomena including unconventional
magnetism and superconductivity. Although flat bands are known to exist in a
few systems such as heavy fermion materials and twisted bilayer graphene, their
microscopic roles and underlying mechanisms in generating emergent behavior
remain elusive. Here we use scanning tunneling microscopy to elucidate the
atomically resolved electronic states and their magnetic response in the kagome
magnet Co3Sn2S2. We observe a pronounced peak at the Fermi level, which is
identified to arise from the kinetically frustrated kagome flat band.
Increasing magnetic field up to +-8T, this state exhibits an anomalous
magnetization-polarized Zeeman shift, dominated by an orbital moment in
opposite to the field direction. Such negative magnetism can be understood as
spin-orbit coupling induced quantum phase effects tied to non-trivial flat band
systems. We image the flat band peak, resolve the associated negative
magnetism, and provide its connection to the Berry curvature field, showing
that Co3Sn2S2 is a rare example of kagome magnet where the low energy physics
can be dominated by the spin-orbit coupled flat band. Our methodology of
probing band-resolved ordering phenomena such as spin-orbit magnetism can also
be applied in future experiments to elucidate other exotic phenomena including
flat band superconductivity and anomalous quantum transport.Comment: Nature Physics onlin
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