1,312 research outputs found
Phase retrieval by power iterations
I show that the power iteration method applied to the phase retrieval problem
converges under special conditions. One is given the relative phases between
small non-overlapping groups of pixels of a recorded intensity pattern, but no
information on the phase between the groups of pixels. Numerical tests show
that the inverse block iteration recovers the solution in 1 iteration.Comment: 4 pages, 6 figure
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
Shaping Coherent X-rays with Binary Optics
Diffractive lenses fabricated by lithographic methods are one of the most
popular image forming optics in the x-ray regime. Most commonly, binary
diffractive optics, such as Fresnel zone plates are used due to their ability
to focus at high resolution and to manipulate the x-ray wavefront. We report
here a binary zone plate design strategy to form arbitrary illuminations for
coherent multiplexing, structured illumination, and wavefront shaping
experiments. Given a desired illumination, we adjust the duty cycle, harmonic
order, and zone placement to vary both the amplitude and phase of the wavefront
at the lens. This enables the binary lithographic pattern to generate arbitrary
structured illumination optimized for a variety of applications such as
holography, interferometry, ptychography, imaging, and others.Comment: 9 pages, 4 figure
Phase retrieval and saddle-point optimization
Iterative algorithms with feedback are amongst the most powerful and
versatile optimization methods for phase retrieval. Among these, the hybrid
input-output algorithm has demonstrated practical solutions to giga-element
nonlinear phase retrieval problems, escaping local minima and producing images
at resolutions beyond the capabilities of lens-based optical methods. Here, the
input-output iteration is improved by a lower dimensional subspace saddle-point
optimization.Comment: 8 pages, 4 figures, revte
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
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