176,843 research outputs found
Deep-tissue large field of view imaging by Fourier conjugate adaptive optics
Light microscopy enables multifunctional imaging of biological specimens at
unprecedented depths and resolutions. However, the performance of all optical
methods degrades with the imaging depth due to sample-induced aberrations.
Methods of adaptive optics (AO) are aimed at pre-compensation of these
distortions but state-of-the-art adaptive optics still provides a limited field
of view and imaging depth. Here I propose a new approach to overcome these
limitations: Fourier image plane conjugate AO. Two possible experimental
designs of the new approach are investigated and an accurate comparison between
proposed and previously used methods of AO is presented. We see that Fourier
conjugate AO provides a significantly larger field of view, which can only be
limited by the angular optical memory effect, as well as it is simpler in
practical realization for large imaging depth and allows the optimal use of
resolution of spatial light modulator.Comment: 4 pages, 3 figure
Novel Fourier-domain constraint for fast phase retrieval in coherent diffraction imaging
Coherent diffraction imaging (CDI) for visualizing objects at atomic
resolution has been realized as a promising tool for imaging single molecules.
Drawbacks of CDI are associated with the difficulty of the numerical phase
retrieval from experimental diffraction patterns; a fact which stimulated
search for better numerical methods and alternative experimental techniques.
Common phase retrieval methods are based on iterative procedures which
propagate the complex-valued wave between object and detector plane.
Constraints in both, the object and the detector plane are applied. While the
constraint in the detector plane employed in most phase retrieval methods
requires the amplitude of the complex wave to be equal to the squared root of
the measured intensity, we propose a novel Fourier-domain constraint, based on
an analogy to holography. Our method allows achieving a low-resolution
reconstruction already in the first step followed by a high-resolution
reconstruction after further steps. In comparison to conventional schemes this
Fourier-domain constraint results in a fast and reliable convergence of the
iterative reconstruction process.Comment: 13 pages, 7 figure
A sparse reconstruction framework for Fourier-based plane wave imaging
International audienceUltrafast imaging based on plane-wave (PW) insonification is an active area of research due to its capability of reaching high frame rates. Among PW imaging methods, Fourier-based approaches have demonstrated to be competitive compared with traditional delay and sum methods. Motivated by the success of compressed sensing techniques in other Fourier imaging modalities, like magnetic resonance imaging, we propose a new sparse regularization framework to reconstruct high-quality ultrasound (US) images. The framework takes advantage of both the ability to formulate the imaging inverse problem in the Fourier domain and the sparsity of US images in a sparsifying domain. We show, by means of simulations, in vitro and in vivo data, that the proposed framework significantly reduces image artifacts, i.e., measurement noise and sidelobes, compared with classical methods, leading to an increase of the image quality
Fourier Optics in the Classroom
Borrowing methods and formulas from Prof. Goodman's classic Introduction to
Fourier Optics textbook [1], I have developed a software package [2] that has
been used in both industrial research and classroom teaching [3]. This paper
briefly describes a few optical system simulations that have been used over the
past 30 years to convey the power and the beauty of Fourier Optics to our
students at the University of Arizona's College of Optical Sciences.Comment: 2 pages, 5 figures, 3 references, Published in the Proceedings of the
Optical Society of America's Imaging & Applied Optics Congress, Orlando,
Florida (June 2018
A Reconstruction Algorithm for Photoacoustic Imaging based on the Nonuniform FFT
Fourier reconstruction algorithms significantly outperform conventional
back-projection algorithms in terms of computation time. In photoacoustic
imaging, these methods require interpolation in the Fourier space domain, which
creates artifacts in reconstructed images. We propose a novel reconstruction
algorithm that applies the one-dimensional nonuniform fast Fourier transform to
photoacoustic imaging. It is shown theoretically and numerically that our
algorithm avoids artifacts while preserving the computational effectiveness of
Fourier reconstruction.Comment: 22 pages, 8 figure
A Laboratory Demonstration of High-Resolution Hard X-ray and Gamma-ray Imaging using Fourier-Transform Techniques
A laboratory imaging system has been developed to study the use of Fourier-transform techniques in high-resolution hard x-ray and γ-ray imaging, with particular emphasis on possible applications to high-energy astronomy. We discuss considerations for the design of a Fourier-transform imager and describe the instrumentation used in the laboratory studies. Several analysis methods for image reconstruction are discussed including the CLEAN algorithm and maximum entropy methods. Images obtained using these methods are presented
Numerical Approaches for Linear Left-invariant Diffusions on SE(2), their Comparison to Exact Solutions, and their Applications in Retinal Imaging
Left-invariant PDE-evolutions on the roto-translation group (and
their resolvent equations) have been widely studied in the fields of cortical
modeling and image analysis. They include hypo-elliptic diffusion (for contour
enhancement) proposed by Citti & Sarti, and Petitot, and they include the
direction process (for contour completion) proposed by Mumford. This paper
presents a thorough study and comparison of the many numerical approaches,
which, remarkably, is missing in the literature. Existing numerical approaches
can be classified into 3 categories: Finite difference methods, Fourier based
methods (equivalent to -Fourier methods), and stochastic methods (Monte
Carlo simulations). There are also 3 types of exact solutions to the
PDE-evolutions that were derived explicitly (in the spatial Fourier domain) in
previous works by Duits and van Almsick in 2005. Here we provide an overview of
these 3 types of exact solutions and explain how they relate to each of the 3
numerical approaches. We compute relative errors of all numerical approaches to
the exact solutions, and the Fourier based methods show us the best performance
with smallest relative errors. We also provide an improvement of Mathematica
algorithms for evaluating Mathieu-functions, crucial in implementations of the
exact solutions. Furthermore, we include an asymptotical analysis of the
singularities within the kernels and we propose a probabilistic extension of
underlying stochastic processes that overcomes the singular behavior in the
origin of time-integrated kernels. Finally, we show retinal imaging
applications of combining left-invariant PDE-evolutions with invertible
orientation scores.Comment: A final and corrected version of the manuscript is Published in
Numerical Mathematics: Theory, Methods and Applications (NM-TMA), vol. (9),
p.1-50, 201
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