5,949 research outputs found
Phase Retrieval with Application to Optical Imaging
This review article provides a contemporary overview of phase retrieval in
optical imaging, linking the relevant optical physics to the information
processing methods and algorithms. Its purpose is to describe the current state
of the art in this area, identify challenges, and suggest vision and areas
where signal processing methods can have a large impact on optical imaging and
on the world of imaging at large, with applications in a variety of fields
ranging from biology and chemistry to physics and engineering
Ab initio compressive phase retrieval
Any object on earth has two fundamental properties: it is finite, and it is
made of atoms. Structural information about an object can be obtained from
diffraction amplitude measurements that account for either one of these traits.
Nyquist-sampling of the Fourier amplitudes is sufficient to image single
particles of finite size at any resolution. Atomic resolution data is routinely
used to image molecules replicated in a crystal structure. Here we report an
algorithm that requires neither information, but uses the fact that an image of
a natural object is compressible. Intended applications include tomographic
diffractive imaging, crystallography, powder diffraction, small angle x-ray
scattering and random Fourier amplitude measurements.Comment: 7 pages, 4 figures, presented at the XXI IUCr Congress, Aug. 2008,
Osaka Japa
Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems
Like many other advanced imaging methods, x-ray phase contrast imaging and
tomography require mathematical inversion of the observed data to obtain
real-space information. While an accurate forward model describing the
generally nonlinear image formation from a given object to the observations is
often available, explicit inversion formulas are typically not known. Moreover,
the measured data might be insufficient for stable image reconstruction, in
which case it has to be complemented by suitable a priori information. In this
work, regularized Newton methods are presented as a general framework for the
solution of such ill-posed nonlinear imaging problems. For a proof of
principle, the approach is applied to x-ray phase contrast imaging in the
near-field propagation regime. Simultaneous recovery of the phase- and
amplitude from a single near-field diffraction pattern without homogeneity
constraints is demonstrated for the first time. The presented methods further
permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval
and tomographic inversion. We demonstrate the potential of this approach by
three-dimensional imaging of a colloidal crystal at 95 nm isotropic resolution.Comment: (C)2016 Optical Society of America. One print or electronic copy may
be made for personal use only. Systematic reproduction and distribution,
duplication of any material in this paper for a fee or for commercial
purposes, or modifications of the content of this paper are prohibite
A unified evaluation of iterative projection algorithms for phase retrieval
Iterative projection algorithms are successfully being used as a substitute
of lenses to recombine, numerically rather than optically, light scattered by
illuminated objects. Images obtained computationally allow aberration-free
diffraction-limited imaging and the possibility of using radiation for which no
lenses exist. The challenge of this imaging technique is transfered from the
lenses to the algorithms. We evaluate these new computational ``instruments''
developed for the phase retrieval problem, and discuss acceleration strategies.Comment: 12 pages, 9 figures, revte
High-Resolution Crystal Truncation Rod Scattering: Application to Ultrathin Layers and Buried Interfaces
In crystalline materials, the presence of surfaces or interfaces gives rise to crystal truncation rods (CTRs) in their X‐ray diffraction patterns. While structural properties related to the bulk of a crystal are contained in the intensity and position of Bragg peaks in X‐ray diffraction, CTRs carry detailed information about the atomic structure at the interface. Developments in synchrotron X‐ray sources, instrumentation, and analysis procedures have made CTR measurements into extremely powerful tools to study atomic reconstructions and relaxations occurring in a wide variety of interfacial systems, with relevance to chemical and electronic functionalities. In this review, an overview of the use of CTRs in the study of atomic structure at interfaces is provided. The basic theory, measurement, and analysis of CTRs are covered and applications from the literature are highlighted. Illustrative examples include studies of complex oxide thin films and multilayers
Accurate, rapid identification of dislocation lines in coherent diffractive imaging via a min-max optimization formulation
Defects such as dislocations impact materials properties and their response
during external stimuli. Defect engineering has emerged as a possible route to
improving the performance of materials over a wide range of applications,
including batteries, solar cells, and semiconductors. Imaging these defects in
their native operating conditions to establish the structure-function
relationship and, ultimately, to improve performance has remained a
considerable challenge for both electron-based and x-ray-based imaging
techniques. However, the advent of Bragg coherent x-ray diffractive imaging
(BCDI) has made possible the 3D imaging of multiple dislocations in
nanoparticles ranging in size from 100 nm to1000 nm. While the imaging process
succeeds in many cases, nuances in identifying the dislocations has left manual
identification as the preferred method. Derivative-based methods are also used,
but they can be inaccurate and are computationally inefficient. Here we
demonstrate a derivative-free method that is both more accurate and more
computationally efficient than either derivative- or human-based methods for
identifying 3D dislocation lines in nanocrystal images produced by BCDI. We
formulate the problem as a min-max optimization problem and show exceptional
accuracy for experimental images. We demonstrate a 260x speedup for a typical
experimental dataset with higher accuracy over current methods. We discuss the
possibility of using this algorithm as part of a sparsity-based phase retrieval
process. We also provide the MATLAB code for use by other researchers
A simple method for the determination of the structure of ultrashort relativistic electron bunches
In this paper we propose a new method for measurements of the longitudinal
profile of 100 femtosecond electron bunches for X-ray Free Electron Lasers
(XFELs). The method is simply the combination of two well-known techniques,
which where not previously combined to our knowledge. We use seed 10-ps 1047 nm
quantum laser to produce exact optical replica of ultrafast electron bunches.
The replica is generated in apparatus which consists of an input undulator
(energy modulator), and the short output undulator (radiator) separated by a
dispersion section. The radiation in the output undulator is excited by the
electron bunch modulated at the optical wavelength and rapidly reaches 100
MW-level peak power. We then use the now-standard method of ultrashort laser
pulse-shape measurement, a tandem combination of autocorrelator and spectrum
(FROG -- frequency resolved optical gating). The FROG trace of the optical
replica of electron bunch gives accurate and rapid electron bunch shape
measurements in a way similar to a femtosecond oscilloscope. Real-time
single-shot measurements of the electron bunch structure could provide
significant information about physical mechanisms responsible for generation
ultrashort electron bunches in bunch compressors. The big advantage of proposed
technique is that it can be used to determine the slice energy spread and
emittance in multishot measurements. It is possible to measure bunch structure
completely, that is to measure peak current, energy spread and transverse
emittance as a function of time. We illustrate with numerical examples the
potential of the proposed method for electron beam diagnostics at the European
X-ray FEL.Comment: 41 pages, 18 figure
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