Abstract

When an x-ray beam passes through the tip of a triangular prism, i.e., an edge, it undergoes two consecutive refraction processes. This will also happen when the incident beam is not perpendicular to the tip but when the beam progresses at a very small inclination to it. It will be shown that in such a condition, when both interfaces adjacent to the tip have concave surfaces, decoupled focusing in two orthogonal directions can be introduced in the transmitted x-ray beam. The limitations for this application are discussed, and focusing of x rays to spots with diffraction limited sizes of the order of 100 nanometers is found to be feasible. The feasibility of bidimensional focusing by use of such a device was experimentally verified.

© 2014 Optical Society of America

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  1. P. Kirkpatrick and A. Baez, J. Opt. Soc. Am. 38, 766 (1948).
    [CrossRef]
  2. P. Kirkpatrick, J. Opt. Soc. Am. 39, 796 (1949).
    [CrossRef]
  3. B. Lengeler, C. G. Schroer, J. Tuemmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, J. Synchrotron Rad. 6, 1153 (1999).
    [CrossRef]
  4. C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
    [CrossRef]
  5. H. Yan, V. Rose, D. Shu, E. Lima, H. C. Kang, R. Conley, C. Liu, N. Jahedi, A. T. Macrander, G. B. Stephenson, M. Holt, Y. S. Chu, M. Lu, and J. Maser, Opt. Express 19, 15069 (2011).
    [CrossRef]
  6. M. Montel, X-Ray Microscopy and Microradiography (Academic, 1957), pp. 177–185.
  7. M. Sanchez del Rio and L. Alianelli, J. Synchrotron Rad. 19, 366 (2012).
    [CrossRef]
  8. K. Evans-Lutterodt, J. M. Ablett, A. Stein, C.-C. Kao, D. M. Tennant, F. Klemens, A. Taylor, C. Jacobsen, P. L. Gammel, H. Huggins, S. Ustin, G. Bogart, and L. Ocola, Opt. Express 11, 919 (2003).
    [CrossRef]
  9. B. L. Henke, E. M. Gullickson, and J. C. Davis, At. Data Nucl. Data Tables 54, 181 (1993), http://www-cxro.lbl.gov/optical_constants/ .
    [CrossRef]
  10. M. Simon, “Roentgenlinsen mit grosser Apertur (X-ray lenses with large aperture),” Ph.d. thesis (Karlsruher Institut für Technologie, 2010).
  11. L. Rigon, Z. Zhong, F. Arfelli, R.-H. Menk, and A. Pillon, Proc. SPIE 4682, 255 (2002).
    [CrossRef]

2012 (1)

M. Sanchez del Rio and L. Alianelli, J. Synchrotron Rad. 19, 366 (2012).
[CrossRef]

2011 (1)

2005 (1)

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

2003 (1)

2002 (1)

L. Rigon, Z. Zhong, F. Arfelli, R.-H. Menk, and A. Pillon, Proc. SPIE 4682, 255 (2002).
[CrossRef]

1999 (1)

B. Lengeler, C. G. Schroer, J. Tuemmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, J. Synchrotron Rad. 6, 1153 (1999).
[CrossRef]

1993 (1)

B. L. Henke, E. M. Gullickson, and J. C. Davis, At. Data Nucl. Data Tables 54, 181 (1993), http://www-cxro.lbl.gov/optical_constants/ .
[CrossRef]

1949 (1)

1948 (1)

Ablett, J. M.

Alianelli, L.

M. Sanchez del Rio and L. Alianelli, J. Synchrotron Rad. 19, 366 (2012).
[CrossRef]

Arfelli, F.

L. Rigon, Z. Zhong, F. Arfelli, R.-H. Menk, and A. Pillon, Proc. SPIE 4682, 255 (2002).
[CrossRef]

Baez, A.

Benner, B.

B. Lengeler, C. G. Schroer, J. Tuemmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, J. Synchrotron Rad. 6, 1153 (1999).
[CrossRef]

Bogart, G.

Boye, P.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Burghammer, M.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Chu, Y. S.

Conley, R.

Davis, J. C.

B. L. Henke, E. M. Gullickson, and J. C. Davis, At. Data Nucl. Data Tables 54, 181 (1993), http://www-cxro.lbl.gov/optical_constants/ .
[CrossRef]

Drakopoulos, M.

B. Lengeler, C. G. Schroer, J. Tuemmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, J. Synchrotron Rad. 6, 1153 (1999).
[CrossRef]

Evans-Lutterodt, K.

Feldkamp, J.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Gammel, P. L.

Gullickson, E. M.

B. L. Henke, E. M. Gullickson, and J. C. Davis, At. Data Nucl. Data Tables 54, 181 (1993), http://www-cxro.lbl.gov/optical_constants/ .
[CrossRef]

Henke, B. L.

B. L. Henke, E. M. Gullickson, and J. C. Davis, At. Data Nucl. Data Tables 54, 181 (1993), http://www-cxro.lbl.gov/optical_constants/ .
[CrossRef]

Holt, M.

Huggins, H.

Jacobsen, C.

Jahedi, N.

Kang, H. C.

Kao, C.-C.

Kirkpatrick, P.

Klemens, F.

Küchler, M.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Kurapova, O.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Lengeler, B.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

B. Lengeler, C. G. Schroer, J. Tuemmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, J. Synchrotron Rad. 6, 1153 (1999).
[CrossRef]

Lima, E.

Liu, C.

Lu, M.

Macrander, A. T.

Maser, J.

Menk, R.-H.

L. Rigon, Z. Zhong, F. Arfelli, R.-H. Menk, and A. Pillon, Proc. SPIE 4682, 255 (2002).
[CrossRef]

Montel, M.

M. Montel, X-Ray Microscopy and Microradiography (Academic, 1957), pp. 177–185.

Ocola, L.

Patommel, J.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Pillon, A.

L. Rigon, Z. Zhong, F. Arfelli, R.-H. Menk, and A. Pillon, Proc. SPIE 4682, 255 (2002).
[CrossRef]

Richwin, M.

B. Lengeler, C. G. Schroer, J. Tuemmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, J. Synchrotron Rad. 6, 1153 (1999).
[CrossRef]

Riekel, C.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Rigon, L.

L. Rigon, Z. Zhong, F. Arfelli, R.-H. Menk, and A. Pillon, Proc. SPIE 4682, 255 (2002).
[CrossRef]

Rose, V.

Sanchez del Rio, M.

M. Sanchez del Rio and L. Alianelli, J. Synchrotron Rad. 19, 366 (2012).
[CrossRef]

Schroer, C. G.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

B. Lengeler, C. G. Schroer, J. Tuemmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, J. Synchrotron Rad. 6, 1153 (1999).
[CrossRef]

Shu, D.

Simon, M.

M. Simon, “Roentgenlinsen mit grosser Apertur (X-ray lenses with large aperture),” Ph.d. thesis (Karlsruher Institut für Technologie, 2010).

Snigirev, A.

B. Lengeler, C. G. Schroer, J. Tuemmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, J. Synchrotron Rad. 6, 1153 (1999).
[CrossRef]

Snigireva, I.

B. Lengeler, C. G. Schroer, J. Tuemmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, J. Synchrotron Rad. 6, 1153 (1999).
[CrossRef]

Stein, A.

Stephenson, G. B.

Taylor, A.

Tennant, D. M.

Tuemmler, J.

B. Lengeler, C. G. Schroer, J. Tuemmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, J. Synchrotron Rad. 6, 1153 (1999).
[CrossRef]

Ustin, S.

van der Hart, A.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Vincze, L.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Yan, H.

Zhong, Z.

L. Rigon, Z. Zhong, F. Arfelli, R.-H. Menk, and A. Pillon, Proc. SPIE 4682, 255 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

At. Data Nucl. Data Tables (1)

B. L. Henke, E. M. Gullickson, and J. C. Davis, At. Data Nucl. Data Tables 54, 181 (1993), http://www-cxro.lbl.gov/optical_constants/ .
[CrossRef]

J. Opt. Soc. Am. (2)

J. Synchrotron Rad. (2)

B. Lengeler, C. G. Schroer, J. Tuemmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, J. Synchrotron Rad. 6, 1153 (1999).
[CrossRef]

M. Sanchez del Rio and L. Alianelli, J. Synchrotron Rad. 19, 366 (2012).
[CrossRef]

Opt. Express (2)

Proc. SPIE (1)

L. Rigon, Z. Zhong, F. Arfelli, R.-H. Menk, and A. Pillon, Proc. SPIE 4682, 255 (2002).
[CrossRef]

Other (2)

M. Simon, “Roentgenlinsen mit grosser Apertur (X-ray lenses with large aperture),” Ph.d. thesis (Karlsruher Institut für Technologie, 2010).

M. Montel, X-Ray Microscopy and Microradiography (Academic, 1957), pp. 177–185.

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Figures (6)

Fig. 1.
Fig. 1.

Schematical illustration of an x-ray beam path following the arrow through an edge, in which the beam is subject to two consecutive refraction processes in orthogonal directions, i.e., upward and toward the reader. The drawing is not made to scale, and the angles are drawn exaggeratedly steep.

Fig. 2.
Fig. 2.

Intersection line between a vertically orientated hyperbolic cylinder with focal length fh, which opens toward the left (decreasing x), and a horizontally lying elliptical cylinder (focal length fe), which opens to the right (increasing x), where its second vertex will be found. The double curved edge is positioned in the octant with x>0, y>0, and z<0.

Fig. 3.
Fig. 3.

Schematical illustration of the curvature of the two consecutively refracting interfaces (in white) in two independent devices with the refracting interfaces oriented as in Fig. 2. Both vertices are at x=0.

Fig. 4.
Fig. 4.

Schematical illustration of the refracting edge, i.e., the right sample border, as an observer at the detector position would see it in a scan of the angle θe, which is increasing from the left to the right. In the three figures to the left, those areas are superimposed as lighter gray lines, in which refracted intensities will be registered at the detector position for an edge with optimum curvature. In the center image, the beam is focused in both directions. In the figure to the right it is assumed that the edge is incorrectly shaped with spherical curvature.

Fig. 5.
Fig. 5.

Registered shadow images and refracted intensities at 1.6 m downstream from a curved edge for three different positions in angle of grazing incidence θe, in a scan, as shown in Fig. 4. Each single picture covers at the detector 0.56mm×0.9mm (125pixels×200pixels).

Fig. 6.
Fig. 6.

Detached and connected assemblies of four curved edges in a symmetric configuration, which will provide fourfold increased geometrical aperture to the incident x rays.

Equations (4)

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yh=2δxhfh.
ze=2δxefe
Azz=z=0exp(zθeAL)dz=θeAL
Ay=θhL.

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