PurposePropagation and speckle-based techniques allow reconstruction of the phase of an X-ray beam with a simple experimental setup. Furthermore, their implementation is feasible using low-coherence laboratory X-ray sources. We investigate different approaches to include X-ray polychromaticity for sample thickness recovery using such techniques.ApproachSingle-shot Paganin (PT) and Arhatari (AT) propagation-based and speckle-based (ST) techniques are considered. The radiation beam polychromaticity is addressed using three different averaging approaches. The emission-detection process is considered for modulating the X-ray beam spectrum. Reconstructed thickness of three nylon-6 fibers with diameters in the millimeter-range, placed at various object-detector distances are analyzed. In addition, the thickness of an in-house made breast phantom is recovered by using multi-material Paganin’s technique (MPT) and compared with micro-CT data.ResultsThe best quantitative result is obtained for the PT and ST combined with sample thickness averaging (TA) approach that involves individual thickness recovery for each X-ray spectral component and the smallest considered object-detector distance. The error in the recovered fiber diameters for both techniques is <4%, despite the higher noise level in ST images. All cases provide estimates of fiber diameter ratios with an error of 3% with respect to the nominal diameter ratios. The breast phantom thickness difference between MPT-TA and micro-CT is about 10%.ConclusionsWe demonstrate the single-shot PT-TA and ST-TA techniques feasibility for thickness recovery of millimeter-sized samples using polychromatic microfocus X-ray sources. The application of MPT-TA for thicker and multi-material samples is promising.
Juan Soto, Fabio Aguilar Mora, José Rodrigo, Yana Geng, Nshunge Musheshe, Manon Buist-Homan, Frank Lezoualc'h, Xiaodong Cheng, Martina Schmidt, Han Moshage, Tatiana Alieva
Refractive index tomography compatible with conventional microscope is used for analyzing primary rat hepatocytes injury induced by pharmacological treatments. We found that mitochondria malfunctioning is correlated with refractive index variation.
Partially coherent optical diffraction tomography (PC-ODT) is a labelfree quantitative 3D imaging technique based on the refractive index contrast. It provides fast non-interferometric speckle noise-free imaging compatible with conventional wide-field transmission microscopes, but suffers from two principal inconveniences. One of them is the missing cone problem, which is a common drawback for all tomographic modalities with limited-angle inspection, including interferometric coherent ODT. The second one, considered in this paper, is a nonhomogeneous contrast for different spatial frequency regions. Analyzing the microscope 3D optical transfer functions for various illuminations over the condenser aperture we have found that the Gaussian illumination shape is a proper one. Numerical simulations and experimental results support this finding. A future line in the development of post-deconvolution processing is also discussed.
Different applications such as astronomy, remote optical sensing and free space optical communications, among others, require both numerical and laboratory experimental simulations of beam propagation through turbulent atmosphere prior to an outdoor test. While rotating phase plates or hot chambers can be applied to such studies, they do not allow changing the atmospheric conditions and the propagation distance in situ. In contrast, the spatial light modulators (SLMs) are a flexible alternative for experimental turbulence simulation. In this work we consider an experimental setup comprising two SLMs for studying laser beam propagation in weak atmospheric turbulence. The changes of atmospheric conditions and propagation distances are properly achieved by the adjustment of the phase screens and the focal distances of digital lenses implemented in both SLMs. The proposed system can be completely automatized and all its elements are in fixed positions avoiding mechanical misalignment. Its design, propagation distance and atmospheric condition adjustment are provided. The setup performance is verified by numerical simulation of Gaussian beam propagation in the weak turbulence regime. The obtained parameters: scintillation index, beam wander and spreading are compared to their theoretical counterparts for different propagation distances and atmospheric conditions.
Partially coherent light provides attractive benefits for different applications in microscopy, astronomy, telecommunications,
optical lithography, etc. However, design and generation of partially coherent beams with desirable
properties is challenging. Moreover, the experimental characterization of the spatial coherence is a difficult
problem involving second-order statistics represented by four-dimensional functions that cannot be directly measured
and analyzed. We discuss the techniques for design and generation of partially coherent structurally stable
beams and the recently developed phase-space tomography methods supported by simple experimental setups for
practical quantitative characterization of partially coherent light spatial structure, including its local coherence
properties.
We present a novel technique for coherence engineering of the microscope illumination based on a DLP projector providing fast (millisecond range) switchable both temporal and spatial coherence design. Its performance is experimentally demonstrated for speckle-noise free quantitative phase imaging with different spatial coherence states. Strategies for design and control of the light coherence are discussed.
We present a non-iterative holographic technique for efficient and versatile laser beam shaping along arbitrary 3D curves. Light beams with intensity shaped for several 3D curves: Tilted ring, Viviani’s curve, Archimedean spiral, and trefoil-knotted curve have been experimentally generated and applied for optical trapping of micrometer-sized dielectric particles. The high intensity gradients and independent phase control prescribed along the curve make this kind of laser trap attractive for multiple particle manipulation and allow for forward and backward motion to the light source. Indeed, different configurations of tractor beam traps are experimentally demonstrated. This technique can also be applied for laser micro-machining.
Representation of two-dimensional optical signals on the orbital angular Poincaré sphere is useful for beam
analysis, synthesis and comparison. This mapping is based on the measurement of the second-order moments,
which are widely used for beam characterization. It is well known that two second-order moments invariants
allow dividing two-dimensional signals into two classes: isotropic and anisotropic. Using the modified Iwasawa
decomposition of the ray transformationmatrix and bringing the second-order moments matrix to its diagonalized
form, we are able to associate the anisotropic signal with a certain point on the sphere. The latitude of this point
describes the vorticity of the signal, while its longitude corresponds to the orientation of the beam's principal
axes. Apart from that, the beam's scaling and its curvature can be defined. Before beam comparison, it is thus
appropriate to perform first its normalization and mapping on the Poincaré sphere. There are many very different
beams associated with the same point and therefore this procedure makes sense for fine analysis of beams whose
intensity distributions have similar forms. Moreover, every point on the sphere is associated with an orthonormal
set of Hermite-Laguerre-Gaussian modes, which can be used for the corresponding beam decomposition that is
important for its synthesis and analysis. The developed algorithm for the beam mapping is demonstrated on
several examples.
The investigation of the first order Bessel beam diffraction on a binary amplitude diffraction mask with two open zones
has been performed. It has been shown by computer modeling and experimentally that the structure of the beam intensity
distribution along the propagation axis resembles a chain-like beams structure, but a dark hole can be observed along the
propagation axis in the center of the beam. The interference pattern of the beam under investigation and Gauss beam has
demonstrated the phase singularity presence. The transverse intensity distribution of the beam has shown ring structure
with periodically changing intensity.
KEYWORDS: Tomography, Optical tomography, Commercial off the shelf technology, Spatial light modulators, Reconstruction algorithms, Current controlled current source, Charge-coupled devices, Digital video discs, Free space optics, Optical imaging
The application of partially coherent optical beams for imaging, free space communication, random medium analysis requires controlling its mutual intensity. This task can be done using the phase-space tomography method consisting on the reconstruction of the Wigner distribution (WD), and therefore the mutual intensity, from its projections associated with the fractional power spectra. We propose two schemes that apply spatial light modulators (SLMs) for the measurements of the required WD projections in the case of one- and two-dimensional optical signals. The use of the SLMs allows rapid data acquisition and operative change of the projection number. Moreover, the measured intensity distributions do not require further rescaling, which accelerates the WD reconstruction algorithm and improves its efficiency. The developed numerical methods provide different ways for data analysis such as the reconstruction of the WD using the inverse Radon transform and its visualization for the case of one-dimensional signals; the determination of the mutual intensity for two fixed points without previous reconstruction of the entire WD for two-dimensional signals, etc. The validity of the proposed approaches has been verified experimentally for the test signals and the results are in a good agreement with the numerical simulations.
The fractional Fourier transform (FT) is a powerful tool with relevant applications in optical and digital information
processing. Such applications demand a programmable and versatile optical system able to perform the
fractional FT almost at real time. We have recently developed an optical setup satisfying these requirements.
In contrast with other proposed setups, it offers the following advantages: the operation is achieved without
additional scaling and/or phase factors and a minimal number of lenses, located at fixed position, are utilized.1
In this work we present the main design features of the fractional FT processor and discuss its performance for
some relevant applications.
We present an overview of the main properties and the emerging implementations corresponding to a photopolymerizable glass modified with high refractive index species (HRIS) incorporated at molecular level. The study concerns to transmission and reflection holograms in Bragg and Raman-Nath regimens and polarization properties of
gratings with high spatial frequencies are also analyzed demonstrating a strong dependence of the refractive index
modulation with the polarization state of the reading beam. Not limited to the study of the optical properties of the
photopolymerizable glass we propose two applications of the holographic material. The first one is the fabrication of
polarizers elements with high performance at low cost such us holographic polarizers and holographic polarizers beam splitters. The second application concerns to the holographic recording of stables modes exhibiting high diffraction efficiency. Also, we have recently extended our studies to ultrashort pulse lasers in femtosecond regime. The photopolymerizable gratings are good candidates as optic elements to beam manipulation of ultrashort pulse lasers.
KEYWORDS: Holography, Holograms, Digital holography, Diffraction, Digital video discs, Video, Digital recording, Spatial light modulators, Physics, Multimedia
In this work we present a Virtual Holographic Laboratory for educational purposes. This project is edited on DVD support and it has been designed to be interactive: schemes, pictures, videos in order to clarify the theoretical description of the phenomena improving the understanding of its fundamental concepts. We believe that this project is helpful for undergraduate and graduate students in physics and engineering to obtain the solid knowledge about holography and to prepare for practical lessons on holography or partially substitute the lasts in the case of absence of appropriated technical base at a specific university level.
Starting from Hermite-Gaussian beams, we generate a general class of rotationally symmetric beams. These beams are Laguerre-Gaussian beams, parameterized by two parameters h and g, representing the curvature and the width of the beam, respectively. The Wigner distribution of each member of this class is readily derived from
the Wigner distribution of the Hermite-Gaussian beam from which it is generated. If these Laguerre-Gaussian beams propagate through an isotropic abcd-system, they remain in their class, while the propagation of the complex beam parameter h ± ig satisfies the well-known abcd-law.
Wide application of the laser beams in science, technology and biomedicine demands the generation of the beams with desirable structure. In particular for optical trapping the beams with high transversal gradient of intensity distribution or doughnut like structures which carried out the orbital angular momentum are designed. In the recent study of the diffraction on the fractal Cantor zone plates [1-5] the possibility to generate the beams with capsule like structure (closed cylinder with the axis along the direction of beam propagation) for a certain distances has been discovered [5]. This peculiar form of the beam can be used for three dimensional particle trapping. Nevertheless the fractal zone plates are not unique gratings that generate this type of structures.
The orthonormal set of Hermite-Gaussian modes maps into another orthonormal set after propagation through a first-order optical system. A compact expression for these modes is derived. The introduction of a novel class of orthonormal modes is useful for non-interferometric phase recovery techniques and simplifies the design of mode converters and information processing systems.
Based on the common Hermite-Gaussian modes, a general class of orthonormal Hermite-Gaussian-type modes is introduced. Such modes can most easily be defined by means of their generating function. A propagation law for the generating function is formulated, when these modes propagate through first-order optical systems.
The transformation of the vortex part of the orbital angular momentum of linearly polarized, partially coherent beams during their propagation through separable first-order optical systems is analyzed. We obtain that the evolution of the vortex part depends only upon the parameters ax, ay, bx, and by of the ray transformation matrix. Isotropic systems with the same ratio b/a produce the same change of the vortex part of the orbital angular momentum.
We study experimentally and by numerical simulation the Fresnel diffraction on the recently introduced fractal zone plates (ZPs) associated with Cantor sets. The focusing properties of these ZPs and the evolution of the intensity patterns at the plane transversal to the propagation direction are discussed. As it follows from numerical simulation the series of conventional and doughnut-like secondary focuses are observed around the principal focus. The position, depth and the size of these focuses depends on the type of Cantor set and the level of the fractal, which are directly related to the number of the corresponding Fresnel zones. The results obtained by numerical simulations are verified in the experiments. The fractal Cantor ZPs of different levels are implemented with a liquid crystal display and with the diapositives. The experimental results obtained by both types of the dispositives are in good agreement with the theory and numerical simulations.
We present a short overview on the application of fractional cyclic and linear canonical transformations to optical signal processing and dedicate some of the discussions to the particular features found in the fractional Fourier transform domain.
The application of optoelectronic techniques, based on Fourier transform, bilinear distributions, fractional transformations, for biomedical information processing: filtering, segmentation and classification of biomedical images, characterization of optical manipulators, recovering of statistical tissue properties, is discussed.
The main properties of n-th order power filtering in the fractional Fourier domain and its relationship to the differentiation operation are considered. The application of power filtering for solving the phase retrieval problem is proposed.
It is shown how all global Wigner distribution moments of arbitrary order can be measured as intensity moments in the output plane of an appropriate number of fractional Fourier transform systems (generally anamorphic ones). The minimum number of (anamorphic) fractional power spectra that are needed for the determination of these moments is derived.
The Fresnel and Fraunhofer diffraction on the regular structures generated by the multiplicative iterative procedures is considered. It is proved that the iterative procedure of field construction is preserved during Fresnel diffraction, meanwhile the initiator of the structure in the Fresnel region is the Fresnel transform of the original one. The theoretical results are proved experimentally.
The parameters of the transfer matrix describing a first- order optical system that is a cascade of k identical subsystems defined by the transfer matrix M, are determined from considering the subsystem's eigenfunctions. A condition for the cascade to be cyclic is derived. Particular examples of cyclic first-order optical systems are presented.
The structure and main properties of coherent and partially coherent optical fields that are self-reproducible under propagation through a first-order optical system are investigated. A phase space description of self-imaging in first-order optical systems is presented.
The Radon-Wigner transform, associated with the intensity distribution in the fractional Fourier transform system, is used for the analysis of complex structures of coherent as well as partially coherent optical fields. The application of the Radon-Wigner transform to the analysis of fractal fields is presented.
KEYWORDS: Fourier transforms, Fractional fourier transform, Image processing, Image filtering, Radio optics, Optical filters, Signal generators, Systems modeling, Near field diffraction, Optical components
Optical signal decomposition on the set of M orthogonal self-fractional Fourier functions, reproducing themselves under the fractional Fourier transform is considered. The image decomposition on the self-Fourier functions (M equals 4) is demonstrated.
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