478 research outputs found
Aberrated dark-field imaging systems
We study generalized dark-field imaging systems. These are a subset of linear
shift-invariant optical imaging systems, that exhibit arbitrary aberrations,
and for which normally-incident plane-wave input yields zero output. We write
down the theory for the forward problem of imaging coherent scalar optical
fields using such arbitrarily-aberrated dark-field systems, and give numerical
examples. The associated images may be viewed as a form of dark-field Gabor
holography, utilizing arbitrary outgoing Green functions as generalized
Huygens-type wavelets, and with the Young-type boundary wave forming the
holographic reference
Phase-and-amplitude recovery from a single phase contrast image using partially spatially coherent X-ray radiation
A simple method of phase-and-amplitude extraction is derived that corrects
for image blurring induced by partially spatially coherent incident
illumination using only a single intensity image as input. The method is based
on Fresnel diffraction theory for the case of high Fresnel number, merged with
the space-frequency description formalism used to quantify partially coherent
fields and assumes the object under study is composed of a single material. A
priori knowledge of the object's complex refractive index and information
obtained by characterizing the spatial coherence of the source is required. The
algorithm was applied to propagation-based phase contrast data measured with a
laboratory-based micro-focus X-ray source. The blurring due to the finite
spatial extent of the source is embedded within the algorithm as a simple
correction term to the so-called Paganin algorithm and is also numerically
stable in the presence of noise
Aberrations in shift-invariant linear optical imaging systems using partially coherent fields
Here the role and influence of aberrations in optical imaging systems
employing partially coherent complex scalar fields is studied. Imaging systems
require aberrations to yield contrast in the output image. For linear
shift-invariant optical systems, we develop an expression for the output
cross-spectral density under the space-frequency formulation of statistically
stationary partially coherentfields. We also develop expressions for the output
cross{spectral density and associated spectral density for weak-phase,
weak-phase-amplitude, and single-material objects in one transverse spatial
dimension
Inferring the time-dependent complex Ginzburg-Landau equation from modulus data
We present a formalism for inferring the equation of evolution of a complex
wave field that is known to obey an otherwise unspecified (2+1)-dimensional
time-dependent complex Ginzburg-Landau equation, given field moduli over three
closely-spaced planes. The phase of the complex wave field is retrieved via a
non-interferometric method, and all terms in the equation of evolution are
determined using only the magnitude of the complex wave field. The formalism is
tested using simulated data for a generalized nonlinear system with a
single-component complex wave field. The method can be generalized to
multi-component complex fields.Comment: 9 pages, 9 figure
X-ray dark-field and phase retrieval without optics, via the Fokker-Planck equation
Emerging methods of x-ray imaging that capture phase and dark-field effects
are equipping medicine with complementary sensitivity to conventional
radiography. These methods are being applied over a wide range of scales, from
virtual histology to clinical chest imaging, and typically require the
introduction of optics such as gratings. Here, we consider extracting x-ray
phase and dark-field signals from bright-field images collected using nothing
more than a coherent x-ray source and detector. Our approach is based on the
Fokker--Planck equation for paraxial imaging, which is the diffusive
generalization of the transport-of-intensity equation. Specifically, we utilize
the Fokker--Planck equation in the context of propagation-based phase-contrast
imaging, where we show that two intensity images are sufficient for successful
retrieval of the projected thickness and dark-field signals associated with the
sample. We show the results of our algorithm using both a simulated dataset and
an experimental dataset. These demonstrate that the x-ray dark-field signal can
be extracted from propagation-based images, and that x-ray phase can be
retrieved with better spatial resolution when dark-field effects are taken into
account. We anticipate the proposed algorithm will be of benefit in biomedical
imaging, industrial settings, and other non-invasive imaging applications.Comment: 16 pages, 8 figure
Phase vortices from a Young's three-pinhole interferometer
An analysis is presented of the phase vortices generated in the far field, by
an arbitrary arrangement of three monochromatic point sources of complex
spherical waves. In contrast with the case of three interfering plane waves, in
which an infinitely-extended vortex lattice is generated, the spherical sources
generate a finite number of phase vortices. Analytical expressions for the
vortex core locations are developed and shown to have a convenient
representation in a discrete parameter space. Our analysis may be mapped onto
the case of a coherently-illuminated Young's interferometer, in which the
screen is punctured by three rather than two pinholes.Comment: 10 pages, 8 figures, REVTeX4, Submitted to Phys. Rev.
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