X-ray microscope for imaging distribution of spiral structures inside materials

Significance 

Wide variety of applications have been developed using structured light due to its flexibility especially in the visible wavelength. For natural user interface, structured light, typically stripes or grids, are illuminated onto objects to derive their three-dimensional shape by analyzing the distorted reflected image. Several different types of the state-of-the-art super resolution microscopes are realized using structured light and have been the key equipment for accelerating the biological cell imaging. The structured light introducing singularity or so-called topological defects in the light waves, such as edges or vortices, helps us to realize the super resolution scheme. Optical vortex is known to host integer number of helical turns on its wavefront, carry discrete orbital angular momentum and provides multiple degree of freedom for communication. Besides, they can be realized in a wide frequency range. To date, numerous methods have been used to diagnose the topological charges or winding numbers of optical vortices, especially in the visible light region. Nevertheless, it has been sparsely characterized in the X-ray region despite the potential practical implications.

To this note, Japanese researchers at RIKEN SPring-8 Center: Professor Yoshiki Kohmura, Professor Kei Sawada, and Professor Tetsuya Ishikawa together with Professor Masaichiro Mizumaki from Japan Synchrotron Radiation Research Institute, and Professor Kenji Ohwada and Tetsu Watanuki from National Institutes for Quantum and Radiological Science and Technology (QST) explored the distribution of topological charges of X-ray orbital angular momentum formed by chiral materials. The main aim was to verify whether a differential radial Hilbert transform (RHT) microscope with reversed spiral phase filter is useful for visualizing topological charges on the X-ray vortices. Their research work is currently published in the journal, Optics Express.

In their approach, the research team characterized the X-ray structured light. A differential Fourier space filtering microscope was adopted to measure the topological charges of the X-ray vertices. The microscope contained a spiral phase filter based on the radial Hilbert transform principle. The radial Hilbert transform is generalization of the Hilbert transform developed for signal processing of complex-valued data, such as calculation of the temporal derivative of radio signals. The RHT microscope visualizes the 2D distribution of the derivative of the “phase and amplitude” of a wave passing through a sample. The feasibility of the differential radial Hilbert transform microscope in visualizing the distribution of topological charges was validated.

Experimental results showed that a single image of X-ray RHT microscope provided edge-enhanced imaging over a wide field of view. On the other hand, the differential RHT microscope with reversed spiral phase filter could visualize the topological charge of orbital angular momentum downstream of the chiral materials, thus confirming the accuracy of the initial theoretical predictions. This was attributed to its high sensitivity to azimuthal derivative of the X-ray wave. Similar to the theoretical calculations, a pair of bright and dark spots were exhibited at the center of the spiral phase plate when two images were differentiated to derive the distribution of the topological charges. Furthermore, the topological charges were theoretically proved to be proportional to the Berry curvature, the rotation of the generalized vector potential on the parameter space.

In summary, the study was the first to experimentally determine the distribution of the topological charges of X-ray orbital angular momentum downstream of chiral materials. This included the visualization of topological charges on the X-ray vortices using a differential RHT microscope with a reversed spiral phase filter. The RHT microscope enabled a high sensitivity necessary to detect the topological defects in the wave-field downstream. In a statement to Advances in Engineering, the authors said the high-performance microscope would be of great significance in the future investigation of the properties and dynamical interactions of dislocations that mainly affect material properties.

X-ray microscope for imaging distribution of spiral structures inside materials - Advances in Engineering
Fig.1. Schematics of the present research. Spiral staircase structure inside model specimen is transferred onto the X-ray wave front and form the distinguished X-ray vortex. Our new X-ray microscope using Spiral Fresnel Zone Plate (SFZP) as the objective lens is used to discriminate the spiral orientations and to derive the two-dimensional map of spiral structures in the model specimen.
X-ray microscope for imaging distribution of spiral structures inside materials - Advances in Engineering
Fig.2. (a) Schematic diagram of experiment. At the object plane, spiral phase plates were set which gave the 2π phase jump to produce X-ray vortices with two inverse orientations as shown at the left. Due to the cancellation of vorticity, bright spots at the center of the spiral phase plates are observed in the microscope image plane only when the winding numbers of the spiral phase plates m and that of the SFZP l are cancelled for (l, m) = (-1, +1), or (+1, -1) [see orange dotted lines]. Otherwise, dark spots are observed at the center [see green dotted lines]. (b)Visible light microscope image of SFZP. The scale bar is 100μm.
X-ray microscope for imaging distribution of spiral structures inside materials - Advances in Engineering
Fig.3. (a) Scanning electron microscope image of sample containing four spiral phase plates on silicon substrate with the thickness decrement in the clockwise and in the anti-clockwise orientations. The values of m= -1, +1 correspond to the winding number of the optical vortex when X-ray transmits through the spiral phase plates. (b) Middle panels show the orientations of the SFZP objective lens, which generates vorticity with the winding number l= -1, +1 to the wave front. The bottom panels show the X-ray Radial Hilbert transform microscope image of sample (a) with the corresponding settings of l= -1, +1. Bright spots were observed at the center of the spiral plates only for the cases of (l, m) = (-1, +1), or (+1, -1).

About the author

Yoshiki Kohmura is currently a Team Leader of Synchrotron Radiation Imaging Instrumentation Team at SPring-8 facility, Japan. He received his PhD in the Department of Physics, Faculty of Science & Graduate School of Science, the University of Tokyo in 1994. He has been working at Harima Institute of RIKEN since 1996.

He is involved in developing various x-ray optical elements and methodologies applicable to synchrotron radiation experiments. One of his research interests is to make best use of the x-ray structured light for x-ray super-resolution microscopes. His microscope technique with super-resolution technique is now utilized in 3D observation project researching cranial nerve networks. In the past ten years, he studied the novel waveguiding phenomenon of x-rays occurring inside slightly deformed crystals and its application to fast switching of x-rays. His interest to transfer the structural properties of various defects inside materials to x-rays resulted in the microscope reported in the article.

Reference

Kohmura, Y., Sawada, K., Mizumaki, M., Ohwada, K., Watanuki, T., & Ishikawa, T. (2020). X-ray microscope for imaging topological charge and orbital angular momentum distribution formed by chiralityOptics Express, 28(16), 24115.

Go To Optics Express

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