This works illustrates the capability of scanning Small-Angle X-ray Scattering (sSAXS) and Ptychographic X-ray nano Tomography (PXCT) to characterize nanoporous composite materials over multiple length scales on a fuel cell catalyst. Results comprise direct images of the nanostructure in a 30µm catalyst pillar at 20 nm resolution in combination with statistically averaged information of the nanostructure between 1-200nm from sSAXS with a spatial resolution of few tens of µm over macroscopic areas. The ex-situ material study is complemented by in-situ dynamic imaging of vapor condensation in 3D at 20nm spatial and temporal resolution of 10minutes.
Significant advances in lithography and chip manufacturing in recent years have resulted in new challenges in metrology of electronic microdevices. Manufacturing process for the 10 nm node is already available and in combination with complex three-dimensional structured interconnections, there is a lack of methods for verification that the final products correspond to the original specifications. X-ray ptycho-tomography is a locally nondestructive imaging method that could potentially help to fill the gap between electron microscopy and conventional X-ray tomography. Quantitativeness of ptycho-tomography provides detailed device geometries and corresponding sensitivity to elemental composition through the complex-valued refractive index. In order to tackle the experimental challenges and improve the imaging quality, new computational methods need to be developed for both ptychography and tomography that can account for a wide range of imperfections such as sample drifts, illumination changes or sample changes during the scan. Here, we will mention the most important of them and possible ways how to deal with them.
Diffractive X-ray optics, like Fresnel zone plate lenses, are widely employed X-ray optics for collimation and focusing. While they are extremely versatile and easy to use optical elements, they generally suffer from limited efficiency due to limitations in fabrication possibilities. Near-field stacking is an established concept for overcoming fabrication limitations, yet its existing implementations suffer from issues regarding complexity and stability. In this work, an alternative stacking concept is explored, by patterning both the front and back sides of a single membrane. Such double-sided zone plates are shown to exchange conventional zone plate stacks in increasing the efficiency or resolution of conventional zone plate optics. In conventional stacking, they achieve 9.9% focusing efficiency at 9 keV with 30 nm smallest half-pitch and diffraction limited optical performance. Following the blazed stacking scheme, they are shown to provide up to 54.7% diffraction efficiency at 6.2 keV. Finally, using the novel concept of interlaced stacking, they demonstrate the feasibility of large aperture X-ray optics for sub-10 nm X-ray nanofocusing.
Ptychography combines elements of scanning probe microscopy with coherent diffractive imaging and provides a robust high-resolution imaging technique. The extension of X-ray ptychography to 3D provides nanoscale maps with quantitative contrast of the sample complex-valued refractive index. We present here progress in reconstruction and post-processing algorithms for ptychographic nanotomography, as well as outline advances in the implementation and development of dedicated instrumentation for fast and precise 3D scanning at the Swiss Light Source. Compared to the first demonstration in 2010, such developments have allowed a dramatic improvement in resolution and measurement speed, with direct impact in the application of the technique for biology and materials science. We showcase the technique by detailing the measurement and reconstruction of a fossilized dispersed spore.
We describe experimental and algorithmic developments of ptychographic X-ray computed tomography, a recently
reported technique that enables three-dimensional, quantitative X-ray microscopy with high sensitivity. The
technique is based on the incorporation of sample rotation and tomographic reconstruction to scanning X-ray
diffraction microscopy (SXDM), a robust technique for two-dimensional X-ray coherent lensless imaging.
Recent advances in the fabrication of diffractive X-ray optics have boosted hard X-ray microscopy into spatial
resolutions of 30 nm and below. Here, we demonstrate the fabrication of zone-doubled Fresnel zone plates for
multi-keV photon energies (4-12 keV) with outermost zone widths down to 20 nm. However, the characterization
of such elements is not straightforward using conventional methods such as knife edge scans on well-characterized
test objects. To overcome this limitation, we have used ptychographic coherent diffractive imaging to characterize
a 20 nm-wide X-ray focus produced by a zone-doubled Fresnel zone plate at a photon energy of 6.2 keV. An
ordinary scanning transmission X-ray microscope was modified to acquire the ptychographic data from a strongly
scattering test object. The ptychographic algorithms allowed for the reconstruction of the image of the test
object as well as for the reconstruction of the focused hard X-ray beam waist, with high spatial resolution and
dynamic range. This method yields a full description of the focusing performance of the Fresnel zone plate
and we demonstrate the usefulness ptychographic coherent diffractive imaging for metrology and alignment of
nanofocusing diffractive X-ray lenses.
Measuring a series of far-field intensity patterns from an object, taken after a transverse translation of the object with respect to a known illumination pattern, has been shown to make the problem of image reconstruction by phase retrieval much more robust. However, previously reported reconstruction algorithms [Phys. Rev. Lett. 93, 023903 (2004)] rely on an accurate knowledge of the translations and illumination pattern for a successful reconstruction. We developed a nonlinear optimization algorithm that allows optimization over the translations and illumination pattern, dramatically improving the reconstructions if the system parameters are inaccurately known [Opt. Express 16, 7264 (2008)]. In this paper we compare reconstructions obtained with these algorithms under realistic experimental scenarios.
We propose a Fourier transform scaling relation to find analytically, numerically and experimentally the spatial frequency spectrum of a two-dimensional Dirac delta curve from the spectrum of the non-scaled curve, after an arbitrary coordinate scaling. An amplitude factor is derived and given explicitly in terms of the scaling factors and the angle of the forward tangent at each point of the curve about the positive x axis. With this formulation we experimentally obtain the spectrum of an elliptic contour in a circular geometry, thus acquiring non-diffracting beam characteristics. Additionally we include the generalization to N-dimensional Dirac delta curves.
A novel paraxial propagation scheme for two-dimensional optical field wave-fronts is proposed, in Cartesian and cylindrical coordinate systems. This is achieved by extending the method originally proposed by Ladouceur [Opt. Lett. 21, 4 (1996)], for boundary-less one-dimensional beam propagation, to two-dimensional optical wave-fronts. With this formulation the arbitrary choice of physical window size is avoided by mapping the infinite transverse dimensions into a finite-size domain with an appropriate change of variables, thus avoiding the energy loss through the artificial physical boundary that is usually required for the absorbing or the transparent boundary approach. Comparison of analytical solution of propagating wave-fronts and those obtained with the proposed algorithm is given, a discussion of the method advantages and limitations is also provided.
We report the generation of Bessel-Gauss beams using a CO2 laser resonator. The cavity is composed by a plane output mirror and a total reflective axicon, this configuration had been studied previously by Gutierrez-Vega et al [J.Opt.Soc.Am.A 20, 2113-22 (2003)]. Bessel-Gauss beams are produced directly from the cavity. The use of a reflective axicon instead of a refractive one results in reduction of surface-induced aberrations, minimizing absorption and increasing the non-diffracting distance. This results in a higher power non-diffracting laser beam with potential scientific and industrial applications. In order to characterize the resonator, we have obtained its output transverse intensity distribution. Additionally, we have numerically and experimentally studied the
effects of mirror tilt on the output transverse mode structure. We have made numerical simulations of the misaligned resonator modes based on Bowers’s method [Appl. Opt. 31, 1185-98 (1992)]. Direct comparison of numerical and experimental results allow us to estimate the diffractive losses of the modes on the misaligned cavity and their dependence on the aligned bare cavity eigenmodes, thus providing valuable information of the output power dependence on mirror misalignment. Relevant experimental parameters and numerical procedure are fully described.
The transverse output profile and mode competition in CO2
lasers are significantly affected by the discharge current, as was
reported by Witteman [IEEE J. Quantum Electron. QE-4,
786-8 (1968)]. He found that in a sealed laser, with a stable
resonator, a spatial mode switching is observed upon increasing
the current; due to a modification in the radial profile of the
small signal gain. Through an atypical gain profile the
lowest-loss bare cavity mode, usually dominant in laser dynamics,
may have lower net cavity gain than a mode with higher diffraction
losses. Through this work a dynamic differential equation for the
homogeneously saturating gain is included in the original dynamic
coupled modes method [Appl. Opt. 29, 3905-15 (1990)] and
applied to a CO2 unstable resonator, with suitable high
current small signal gain profiles. By expanding the gain loaded
cavity field into the bare cavity oscillation eigenstates, this
new model provides a realistic temporal evolution of mode
competition, output power and gain saturation within the
resonator. We have found that although unstable resonators have
excellent transverse mode discrimination the spatial mode
switching may also occur, resulting in a significant modification
in the output intensity profile. Thus, under certain design
parameters, the common assumption of the small signal gain to be
constant through the lasing medium may incur in serious
inaccuracies for determining the transverse intensity profile and
output power. The application of the method is fully described,
and the results and their connection to relevant physical
properties of gas lasers are discussed.
An image processing algorithm, mainly based on morphological enhancement and segmentation, is developed and applied to optical microscope images of transverse cuts of fabric filaments, to retrieve useful shape characteristics. Adaptive filtering and non-linear fitting algorithms are also applied. Computer generated noisy images are used to estimate the algorithm accuracy with excellent results. This algorithm is a significant improvement over the current human-based inspection method for filament shape analysis, and its development and application will improve quality control in textile industry. The complete procedure is outlined in the present work, showing relevant results and pointing out pertinent restrictions.
The dynamic coupled modes (DCM) method has been applied to study the transverse mode competition in optical resonators. In this work a differential equation for the homogeneously saturating dynamic gain is included in the original dynamic coupled modes method, thus increasing its physical resemblance and allowing the retrieval of gain temporal evolution at every point within the lasing medium. This new model provides a realistic temporal evolution of the mode competition and gain saturation within the resonator, which can give further information of spatial coherence properties. The temporal information becomes particularly valuable when the laser transient is a matter of interest or when a continuous wave steady output is never reached, as occurs in pulsed lasers. Additionally, transverse spatial hole burning and inhomogeneous line broadening is straightforwardly included in the gain model. The application of the method to a typical CO2 unstable confocal resonator is fully described, results and their connection to relevant physical properties of gas lasers, such as spiking and relaxation oscillations are discussed. Results of the numerical implementation of the DCM method with dynamic gain are in very good agreement with experimental measurements reported previously.
A numerical method for computing integer order Hankel transforms using a Fourier-Bessel expansion is presented. The method satisfies the discrete form of the Parseval theorem assuring energy conservation, this makes the formulation particularly useful for field propagation. Some relevant properties of the transformation matrix are discussed. Additionally, a numerical comparison with other typical methods is performed, the advantages and disadvantages of the method are discussed. To verify its accuracy to propagate an optical field, the method is used to obtain higher azimuthal order modes in an optical resonator using the iterative Fox & Li approach, resulting in a reduction of memory requirements and processing time, the results are compared to the traditional two-dimensional Fourier transform approach.
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