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X-Ray Optics


Development of Novel Approaches in X-Ray Optics and X-Ray Methods to Study Matter

Tech Area / Field

  • MAN-MPS/Manufacturing, Planning, Processing and Control/Manufacturing Technology
  • PHY-OPL/Optics and Lasers/Physics
  • PHY-SSP/Solid State Physics/Physics

8 Project completed

Registration date

Completion date

Senior Project Manager
Malakhov Yu I

Leading Institute
Russian Academy of Sciences / Institute of Crystallography, Russia, Moscow

Supporting institutes

  • VNIITF, Russia, Chelyabinsk reg., Snezhinsk


  • FOM Institute for Plasma Physics Rijnhuizen, The Netherlands, Nieuwegein\nConsiglio Nazionale delle Ricerche / IFN-CNR, Italy, Rome\nEuropean Synchrotron Radiation Facility, France, Grenoble

Project summary

X-ray radiation is one of the main instruments for a matter study and is widely used in science, medicine, industry and modern technology. Therefore, improvement of existing and development of novel approaches in x-ray methods of a matter study as well as development of x-ray optical elements of new generation extending the range of applicability of x-ray methods and techniques are of extreme interest.
The participants of the Project are experts in fields of x-ray, soft x-ray and EUV optics, and in x-ray methods and techniques as applied to a matter study. They published more than 200 research papers related to these fields of physics, which are well-known and widely cited.
The goals of the Project are the followings:
1. Development of a novel approach to the inverse problem of x-ray reflectometry (XRR) consisting in a reconstruction of the depth-distribution of the dielectric permeability of a matter with an angstrom resolution basing on the measurements of x-ray reflectivity curve.
The main problem in practical use of XRR technique is an ambiguity of the inverse problem solution. In contrast to the most-used approaches consisting in approximation of the dielectric constant distribution by one or another model function, the key feature of our approach consists in the modeling of amplitude reflectivity in the whole range of the incidence angle. Such a consideration proved to permit the reconstruction of the dielectric constant distribution with use of very general model of a reflecting media: it is enough to know the points of discontinuity, where the dielectric permeability itself or its nth derivative undergoes step-like variation. In turn, information about points of discontinuity can be extracted from the measured part of the reflectivity curve.
Mathematical and computational aspects of the XRR inverse problem will be analyzed in framework of the project. First of all, the necessary conditions guarantying the uniqueness of the XRR inverse problem solution will be deduced. The approach will be improved to reconstruct the depth-distribution of atomic concentration of materials composed a studied sample and not only the dielectric constant distribution. The approach will be refined to take into account the effect of the surface and interfacial roughness. Finally, the approach will be extended to the study of periodic multilayer structures.
2. X-ray study of a microstructure of near surface layers and interfaces between neighboring materials as applied to material sciences and currently existing technologies of thin films and multilayer structures deposition.
A set of different objects will be studied with the use of x-ray reflectivity and scattering methods. Among them: interface between two different materials used widely for fabrication of short-period x-ray and EUV multilayer mirrors (W/B4C, W/Si, Mo/Si and others), near surface layer (adhered and oxidized) of solids, near surface and subsurface layers of liquids, and interface between two liquids. Analysis of the effects of interdiffusion, chemical reactions, etc. on the microstructure of interfaces with time will be performed. The effect of depth-distribution of the dielectric constant on accuracy of extraction of the PSD function of the surface and interface roughness will be studied.
3. Development and optimization of depth-graded and laterally graded multilayer mirrors design for synchrotron radiation beamlines including mirrors with the constant reflectivity in a wide spectral band and, in contrast, with an ultimately high spectral resolution.
The use of multilayers as x-ray optical elements at third generation synchrotron radiation facilities has been well established, and a variety of useful applications have been realized in recent years. Periodic x-ray multilayer mirrors yield typically a spectral resolution . At the same time, for a number of applications multilayer mirrors with a spectral band of reflection as wide as possible or, in contrast, with much higher spectral resolution are of particular interest.
We developed new approach to the inverse problem in theory of multilayer mirror, which consists in inferring the depth profile of a multilayer structure providing the given spectral or angular dependence of the reflectivity. Basing on the developed approach, a set of multilayers with the constant reflectivity in a wide angular or spectral interval was fabricated and studied. However, oscillations on the reflectivity plateau of about 10% relative amplitude were observed in experiments, which are totally impermissible for a number of applications (for example, in EXAFS experiments). There are several factors influencing the optical quality of depth-graded multilayer mirrors: interfacial roughness, gradual variation of the dielectric permeability nearby interfaces, random fluctuations of layers thickness arising during deposition, inaccuracy in optical constants and density of thin films used under optimization, etc.
Therefore, in the framework of the present project the optimization procedure will be improved to take into consideration all the factors resulting in deformation of the reflectivity plateau. Single bi-layers and periodic multilayer structures will be studied to obtain information about thin films density, the depth-distribution of dielectric constants nearby interfaces, and parameters of interfacial roughness, which will be extracted in frame of linear model of a film growth. The optimization procedure will be improved to design multilayer mirror with the highest stability of the reflectivity plateau in respect of random layer fluctuations. Wideband multilayer mirror with the period gradient both into the depth of a structure and along a mirror surface will be designed and optimized as applied to the problem of concentrators fabrication intended for the microspectroscopy of materials. Computational procedure will be developed to design multilayer mirror with the highest spectral resolution at a fixed number of bi-layers. Different factors influencing the optical quality of narrowband multilayer mirrors will be analyzed. Narrowband multilayer mirrors will be designed and optimized taking into consideration all the factors resulting in decreasing spectral resolution. Wideband and narrowband multilayer mirrors operating in the hard x-ray spectral region will be fabricated and studied.
4. Development, fabrication and experimental study of axially symmetrical x-ray collimators and concentrators as applied to steering of synchrotron radiation beam and point source radiation.
Solution of this problem is extremely important for further progress in x-ray methods for a matter study and will allow one to overcome the main problems of their applications (especially with the use of x-ray tube as a radiation source): too small radiation flux density on a sample surface, too small intensity of the detected fluorescent radiation, too large diameter of x-ray probe beam.
Physical basis of x-rays collimating and concentrating will be developed, namely, the theory of x-ray diffraction by a figured surface in geometrical optics approximation as well as computer code to model a real experiment on collimating and concentrating x-rays will be elaborated. The code will take into account the x-ray scattering by the surface roughness and deviation of a form of a reflecting surface from an ideal one. The ultimate possibilities of x-ray concentrating optics limiting by fundamental factors (small polarizability and large absorptivity of any material in x-ray and soft x-ray regions, the pergence of an incident beam, the finite size of a radiation source, etc.) and technological factors (inaccuracy in the form of reflecting surface, the effect of the surface roughness, limitations imposed by existing technology on the form and the size of x-ray concentrators and collimators, etc.) will be analyzed. Parameters of collimators and concentrators will be optimized as applied to different practical problems: increasing productivity of proximity x-ray lithography with a point source; focusing point source radiation into spot of a small size; focusing of a collimating x-ray beam into spot of a small size; increasing sensitivity of XRF methods of a matter study.
The method of thermoplastic deformation will be used for fabrication of axially symmetrical x-ray collimators and concentrators. Methods for deposition of a reflecting coating onto internal surface of concentrators and collimators will be developed. X-ray concentrators and collimators of different types will be fabricated and studied experimentally. The following parameters will be measured: efficiency, size of the focused beam spot, pergence of outgoing beam, increasing flux density on a sample, distribution of the flux along a sample surface, etc.
Within the time of implementation of the present project there will be developed and produced:
- A novel approach to the inverse problem of x-ray reflectometry including theory, experimental methods and techniques, and software for experimental data processing and analysis.
- Improved approaches to designing of x-ray multilayer mirrors with the desired optical properties including wideband and narrowband multilayers for synchrotron radiation beamlines, mirrors for microspectroscopy, multilayers with the highest stability in respect of random fluctuations of layer thickness, and so on. The approaches will include theory, software for design optimization, improved experimental methods for the study of depth-graded and laterally graded multilayers, and software for experimental data processing and analysis.
- Improved technological facility and techniques for fabrication of axially symmetrical x-ray concentrators and collimators, experimental methods and techniques for investigations of their parameters as well as software for concentrator and collimator design optimization, and experimental data processing and analysis.
- A set of working x-ray concentrators and collimators intended for different practical needs.
During the Project execution the main goals of ISTC will be realized:
- The former weapon specialists previously engaged in the development and testing of nuclear weapons will be engaged in civil activity.
- The results of the project will have high potentialities for their practical applications and commercialization.
- The project participants will work in a close cooperation with foreign collaborators. Notice, the foreign collaborators took active part in the proposal preparation and an essential part of the tasks considered in the project was formulated basing on their scientific interest.


The International Science and Technology Center (ISTC) is an intergovernmental organization connecting scientists from Kazakhstan, Armenia, Tajikistan, Kyrgyzstan, and Georgia with their peers and research organizations in the EU, Japan, Republic of Korea, Norway and the United States.


ISTC facilitates international science projects and assists the global scientific and business community to source and engage with CIS and Georgian institutes that develop or possess an excellence of scientific know-how.

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