92 research outputs found
Lateral and axial resolution criteria in incoherent and coherent optics and holography, near- and far-field regimes
This work presents an overview of the spatial resolution criteria in
classical optics, digital optics and holography. Although the classical Abbe
and Rayleigh resolution criteria have been thoroughly discussed in the
literature, there are still several issues which still need to be addressed,
for example the axial resolution criterion for coherent and incoherent
radiation, which is a crucial parameter of three-dimensional (3D) imaging, the
resolution criteria in the Fresnel regime, and the lateral and axial resolution
criteria in digital optics and holography. This work discusses these issues and
provides a simple guide for which resolution criteria should be applied in each
particular imaging scheme: coherent/incoherent, far- and near-field, lateral
and axial resolution. Different resolution criteria such as two-point
resolution and the resolution obtained from the image spectrum (diffraction
pattern) are compared and demonstrated with simulated examples. Resolution
criteria for spatial lateral and axial resolution are derived, and their
application in imaging with coherent and incoherent (noncoherent) waves is
considered. It is shown that for coherent light, the classical Abbe and
Rayleigh resolution criteria do not provide an accurate estimation of the
lateral and axial resolution. Lateral and axial resolution criteria based on an
evaluation of the spectrum of the diffracted wave provide a more precise
estimation of the resolution for coherent and incoherent light. It is also
shown that resolution criteria derived in approximation of the far-field
imaging regime can be applied for the near-field (Fresnel) regime
Reconstruction of missing information in diffraction patterns and holograms by iterative phase retrieval
It is demonstrated that an object distribution can be successfully retrieved
from its diffraction pattern or hologram, even if some of the measured
intensity samples are missing. The maximum allowable number of missing values
depends on the linear oversampling ratio s, where the higher the value of s,
the more intensity samples can be missing. For a real-valued object, the ratio
of missing pixels to the total number of pixels should not exceed (1 - 2/s^2)
or (1 - 1/s^2) in the acquired diffraction pattern or hologram, respectively.
For example, even 5% of the measured intensity values at an oversampling ratio
of s = 8 are sufficient to simultaneously retrieve the object distribution and
the missing intensity values. It is important that the missing intensity values
should not be concentrated in the centre, but should be randomly distributed
over the acquired diffraction pattern
Three-dimensional double helical DNA structure directly revealed from its X-ray fiber diffraction pattern by iterative phase retrieval
Coherent diffraction imaging (CDI) allows the retrieval of the structure of
an isolated object, such as a macromolecule, from its diffraction pattern. CDI
requires the fulfilment of two conditions: the imaging radiation must be
coherent and the object must be isolated. We discuss that it is possible to
directly retrieve the molecular structure from its diffraction pattern which
was acquired neither with coherent radiation nor from an individual molecule,
provided the molecule exhibits periodicity in one direction, as in the case of
fiber diffraction. We demonstrate that by applying iterative phase retrieval
methods to a fiber diffraction pattern, the repeating unit, that is, the
molecule structure, can directly be reconstructed without any prior modeling.
As an example, we recover the structure of the DNA double helix in
three-dimensions from its two-dimensional X-ray fiber diffraction pattern,
Photograph 51, acquired in the famous experiment by Raymond Gosling and
Rosalind Franklin, at a resolution of 3.4 Angstrom
Practical algorithms for simulation and reconstruction of digital in-line holograms
Here we present practical methods for simulation and reconstruction of
in-line digital holograms recorded with plane and spherical waves. The
algorithms described here are applicable to holographic imaging of an object
exhibiting absorption as well as phase shifting properties. Optimal parameters,
related to distances, sampling rate, and other factors for successful
simulation and reconstruction of holograms are evaluated and criteria for the
achievable resolution are worked out. Moreover, we show that the numerical
procedures for the reconstruction of holograms recorded with plane and
spherical waves are identical under certain conditions. Experimental examples
of holograms and their reconstructions are also discussed.Comment: including MATLAB code
Spatial coherence of electron beams from field emitters and its effect on the resolution of imaged objects
Sub-nanometer and nanometer-sized tips provide high coherence electron
sources. Conventionally, the effective source size is estimated from the extent
of the experimental biprism interference pattern created on the detector by
applying the van Cittert Zernike theorem. Previously reported experimental
intensity distributions on the detector exhibit Gaussian distribution and our
simulations show that this is an indication that such electron sources must be
at least partially coherent. This, in turn means that strictly speaking the Van
Cittert Zernike theorem cannot be applied, since it assumes an incoherent
source. The approach of applying the van Cittert Zernike theorem is examined in
more detail by performing simulations of interference patterns for the electron
sources of different size and different coherence length, evaluating the
effective source size from the extent of the simulated interference pattern and
comparing the obtained result with the pre-defined value. The intensity
distribution of the source is assumed to be Gaussian distributed, as it is
observed in experiments. The visibility or the contrast in the simulated
holograms is found to be always less than 1 which agrees well with previously
reported experimental results and thus can be explained solely by the Gaussian
intensity distribution of the source. The effective source size estimated from
the extent of the interference pattern turns out to be of about 2-3 times
larger than the pre-defined size, but it is approximately equal to the
intrinsic resolution of the imaging system. A simple formula for estimating the
intrinsic resolution, which could be useful when employing nano-tips in in-line
Gabor holography or point-projection microscopy, is provided
The role of the coherence in the cross-correlation analysis of diffraction patterns from two-dimensional dense mono-disperse systems
The investigation of the static and dynamic structural properties of
colloidal systems relies on techniques capable of atomic resolution in real
space and femtosecond resolution in time. Recently, the cross-correlation
function (CCF) analysis of both X-rays and electron diffraction patterns from
dilute and dense aggregates has demonstrated the ability to retrieve
information on the sample's local order and symmetry. Open questions remain
regarding the role of the beam coherence in the formation of the diffraction
pattern and the properties of the CCF, especially in dense systems. Here, we
simulate the diffraction patterns of dense two-dimensional monodisperse systems
of different symmetries, varying the transverse coherence of the probing wave,
and analyze their CCF. We study samples with different symmetries at different
size scale, as for example, pentamers arranged into a four-fold lattice where
each pentamer is surrounded by triangular lattices, both ordered and
disordered. In such systems, different symmetry modulations are arising in the
CCF at specific scattering vectors. We demonstrate that the amplitude of the
CCF is a fingerprint of the degree of the ordering in the sample and that at
partial transverse coherence, the CCF of a dense sample corresponds to that of
an individual scattering object.Comment: 22 pages, 7 figure
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