skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Focusing hard x rays beyond the critical angle of total reflection by adiabatically focusing lenses

Abstract

In response to the conjecture that the numerical aperture of x-ray optics is fundamentally limited by the critical angle of total reflection, the concept of adiabatically focusing refractive lenses was proposed to overcome this limit. Here, we present an experimental realization of these optics made of silicon and demonstrate that they indeed focus 20 keV x rays to a 18.4 nm focus with a numerical aperture of 1.73(9) × 10 –3 that clearly exceeds the critical angle of total reflection of 1.55 mrad.

Authors:
 [1];  [1];  [1];  [1];  [1];  [1];  [1];  [1];  [1]; ORCiD logo [1];  [2];  [3];  [2];  [2];  [4]
  1. Technische Univ. Dresden, Dresden (Germany)
  2. Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
  3. Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); SLAC National Accelerator Lab., Menlo Park, CA (United States)
  4. Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Univ. Hamburg, Hamburg (Germany)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1353210
Grant/Contract Number:
AC02-76SF00515
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Applied Physics Letters
Additional Journal Information:
Journal Volume: 110; Journal Issue: 10; Journal ID: ISSN 0003-6951
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats

Patommel, Jens, Klare, Susanne, Hoppe, Robert, Ritter, Stephan, Samberg, Dirk, Wittwer, Felix, Jahn, Andreas, Richter, Karola, Wenzel, Christian, Bartha, Johann W., Scholz, Maria, Seiboth, Frank, Boesenberg, Ulrike, Falkenberg, Gerald, and Schroer, Christian G. Focusing hard x rays beyond the critical angle of total reflection by adiabatically focusing lenses. United States: N. p., 2017. Web. doi:10.1063/1.4977882.
Patommel, Jens, Klare, Susanne, Hoppe, Robert, Ritter, Stephan, Samberg, Dirk, Wittwer, Felix, Jahn, Andreas, Richter, Karola, Wenzel, Christian, Bartha, Johann W., Scholz, Maria, Seiboth, Frank, Boesenberg, Ulrike, Falkenberg, Gerald, & Schroer, Christian G. Focusing hard x rays beyond the critical angle of total reflection by adiabatically focusing lenses. United States. doi:10.1063/1.4977882.
Patommel, Jens, Klare, Susanne, Hoppe, Robert, Ritter, Stephan, Samberg, Dirk, Wittwer, Felix, Jahn, Andreas, Richter, Karola, Wenzel, Christian, Bartha, Johann W., Scholz, Maria, Seiboth, Frank, Boesenberg, Ulrike, Falkenberg, Gerald, and Schroer, Christian G. Mon . "Focusing hard x rays beyond the critical angle of total reflection by adiabatically focusing lenses". United States. doi:10.1063/1.4977882. https://www.osti.gov/servlets/purl/1353210.
@article{osti_1353210,
title = {Focusing hard x rays beyond the critical angle of total reflection by adiabatically focusing lenses},
author = {Patommel, Jens and Klare, Susanne and Hoppe, Robert and Ritter, Stephan and Samberg, Dirk and Wittwer, Felix and Jahn, Andreas and Richter, Karola and Wenzel, Christian and Bartha, Johann W. and Scholz, Maria and Seiboth, Frank and Boesenberg, Ulrike and Falkenberg, Gerald and Schroer, Christian G.},
abstractNote = {In response to the conjecture that the numerical aperture of x-ray optics is fundamentally limited by the critical angle of total reflection, the concept of adiabatically focusing refractive lenses was proposed to overcome this limit. Here, we present an experimental realization of these optics made of silicon and demonstrate that they indeed focus 20 keV x rays to a 18.4 nm focus with a numerical aperture of 1.73(9) × 10–3 that clearly exceeds the critical angle of total reflection of 1.55 mrad.},
doi = {10.1063/1.4977882},
journal = {Applied Physics Letters},
number = 10,
volume = 110,
place = {United States},
year = {Mon Mar 06 00:00:00 EST 2017},
month = {Mon Mar 06 00:00:00 EST 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 5works
Citation information provided by
Web of Science

Save / Share:
  • Nanofocused x rays are indispensable because they can provide high spatial resolution and high sensitivity for x-ray nanoscopy/spectroscopy. A focusing system using total reflection mirrors is one of the most promising methods for producing nanofocused x rays due to its high efficiency and energy-tunable focusing. The authors have developed a fabrication system for hard x-ray mirrors by developing elastic emission machining, microstitching interferometry, and relative angle determinable stitching interferometry. By using an ultraprecisely figured mirror, they realized hard x-ray line focusing with a beam width of 25 nm at 15 keV. The focusing test was performed at the 1-km-long beamlinemore » of SPring-8.« less
  • We have fabricated and tested a compound lens consisting of an array of four kinoform lenses for hard x-ray photons of 11.3 keV. Our data demonstrate that it is possible to exceed the critical angle limit by using multiple lenses, while retaining lens function, and this suggests a route to practical focusing optics for hard x-ray photons with nanometer scale resolution and below.
  • Takano et al. report the focusing of 10-keV X-rays to a size of 14.4 nm using a total-reflection zone plate (TRZP). This focal size is at the diffraction limit for the optic's aperture. This would be a noteworthy result, since the TRZP was fabricated using conventional lithography techniques. Alternative nanofocusing optics require more demanding fabrication methods. However, as I will discuss in this Comment, the intensity distribution presented by Takano et al. (Fig. 4 of ref. 1) is more consistent with the random speckle pattern produced by the scattering of a coherent incident beam by a distorted optic than withmore » a diffraction-limited focus. When interpreted in this manner, the true focal spot size is {approx}70 nm: 5 times the diffraction limit. When a coherent photon beam illuminates an optic containing randomly distributed regions which introduce different phase shifts, the scattered diffraction pattern consists of a speckle pattern. Each speckle will be diffraction-limited: the peak width of a single speckle depends entirely on the source coherence and gives no information about the optic. The envelope of the speckle distribution corresponds to the focal spot which would be observed using incoherent illumination. The width of this envelope is due to the finite size of the coherently-diffracting domains produced by slope and position errors in the optic. The focal intensity distribution in Fig. 4 of ref. 1 indeed contains a diffraction-limited peak, but this peak contains only a fraction of the power in the focused, and forms part of a distribution of sharp peaks with an envelope {approx}70 nm in width, just as expected for a speckle pattern. At the 4mm focal distance, the 70 nm width corresponds to a slope error of 18 {micro}rad. To reach the 14 nm diffraction limit, the slope error must be reduced to 3 {micro}rad. Takano et al. have identified a likely source of this error: warping due to stress as a result of zone deposition. It will be interesting to see whether the use of a more rigid substrate gives improved results.« less
  • A development of the theory of multilayer systems is presented. It shows precisely how to calculate thicknesses and number of layers to get reflectivity close to unity for a given arbitrary critical angle. Application of the proposed approach to real systems is demonstrated.