Abstract

With a small double-mirror setup, we used grazing-x-ray interferometry to study nanometric steps. These one-dimensional steps were microfabricated upon the surface of one of the two mirrors; the other mirror provided the reference wave. Two geometries were studied. In the longitudinal case in which the x rays are parallel to the step edges, it is straightforward to determine the step size. In the transverse case, one deals with Fourier holography, and a reconstruction process for a phase object had been demonstrated for the case of a single step.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Polack, D. Joyeux, J. Svatos, D. Phalippou, “Applications of wavefront division interferometers in soft x rays,” Rev. Sci. Instrum. 66, 2180–2183 (1995).
    [CrossRef]
  2. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, “On the possibilities of phase-contrast micro-imaging by coherent high energy synchotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
    [CrossRef]
  3. I. Schelokov, O. Hignette, C. Raven, A. Snigirev, I. Snigireva, A. Souvorov, “X-ray interferometry technique for mirror and multilayer characterization,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2805, 282–291 (1996).
    [CrossRef]
  4. P. Cloetens, J. P. Guigay, C. DeMartino, J. Baruchel, “Fractional Talbot imaging of phase gratings with hard x rays,” Opt. Lett. 22, 1059–1061 (1997).
    [CrossRef] [PubMed]
  5. S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995).
    [CrossRef] [PubMed]
  6. E. Gluskin, I. McNulty, P. J. Viccaro, M. R. Howells, “X-ray intensity interferometry of surfaces with Fresnel mirrors,” Nucl. Instrum. Methods A 319, 213–218 (1992).
    [CrossRef]
  7. Y. Kunimune, Y. Yoda, K. Izumi, M. Yabashi, X.-W. Zhang, T. Harami, M. Ando, S. Kikuta, “Two-photon correlations in x-rays from a synchotron radiation source,” J. Synchroton Radiat. 4, 199–203 (1997).
    [CrossRef]
  8. S. Marchesini, R. Coïsson, “Two-dimensional coherence measurements with Fresnel mirrors,” Opt. Eng. 53, 3597–3601 (1996).
    [CrossRef]
  9. K. Fezzaa, F. Comin, S. Marchesini, R. Coïsson, M. Belakhovsky, “X-ray interferometry at ESRF using two coherent beams from Fresnel mirrors,” J. X-Ray Sci. Technol. 7, 12–23 (1997).
    [CrossRef]

1997

P. Cloetens, J. P. Guigay, C. DeMartino, J. Baruchel, “Fractional Talbot imaging of phase gratings with hard x rays,” Opt. Lett. 22, 1059–1061 (1997).
[CrossRef] [PubMed]

Y. Kunimune, Y. Yoda, K. Izumi, M. Yabashi, X.-W. Zhang, T. Harami, M. Ando, S. Kikuta, “Two-photon correlations in x-rays from a synchotron radiation source,” J. Synchroton Radiat. 4, 199–203 (1997).
[CrossRef]

K. Fezzaa, F. Comin, S. Marchesini, R. Coïsson, M. Belakhovsky, “X-ray interferometry at ESRF using two coherent beams from Fresnel mirrors,” J. X-Ray Sci. Technol. 7, 12–23 (1997).
[CrossRef]

1996

S. Marchesini, R. Coïsson, “Two-dimensional coherence measurements with Fresnel mirrors,” Opt. Eng. 53, 3597–3601 (1996).
[CrossRef]

1995

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995).
[CrossRef] [PubMed]

F. Polack, D. Joyeux, J. Svatos, D. Phalippou, “Applications of wavefront division interferometers in soft x rays,” Rev. Sci. Instrum. 66, 2180–2183 (1995).
[CrossRef]

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, “On the possibilities of phase-contrast micro-imaging by coherent high energy synchotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

1992

E. Gluskin, I. McNulty, P. J. Viccaro, M. R. Howells, “X-ray intensity interferometry of surfaces with Fresnel mirrors,” Nucl. Instrum. Methods A 319, 213–218 (1992).
[CrossRef]

Abernathy, D. L.

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995).
[CrossRef] [PubMed]

Als-Nielsen, J.

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995).
[CrossRef] [PubMed]

Ando, M.

Y. Kunimune, Y. Yoda, K. Izumi, M. Yabashi, X.-W. Zhang, T. Harami, M. Ando, S. Kikuta, “Two-photon correlations in x-rays from a synchotron radiation source,” J. Synchroton Radiat. 4, 199–203 (1997).
[CrossRef]

Baruchel, J.

Belakhovsky, M.

K. Fezzaa, F. Comin, S. Marchesini, R. Coïsson, M. Belakhovsky, “X-ray interferometry at ESRF using two coherent beams from Fresnel mirrors,” J. X-Ray Sci. Technol. 7, 12–23 (1997).
[CrossRef]

Brauer, S.

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995).
[CrossRef] [PubMed]

Brüning, R.

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995).
[CrossRef] [PubMed]

Cloetens, P.

Coïsson, R.

K. Fezzaa, F. Comin, S. Marchesini, R. Coïsson, M. Belakhovsky, “X-ray interferometry at ESRF using two coherent beams from Fresnel mirrors,” J. X-Ray Sci. Technol. 7, 12–23 (1997).
[CrossRef]

S. Marchesini, R. Coïsson, “Two-dimensional coherence measurements with Fresnel mirrors,” Opt. Eng. 53, 3597–3601 (1996).
[CrossRef]

Comin, F.

K. Fezzaa, F. Comin, S. Marchesini, R. Coïsson, M. Belakhovsky, “X-ray interferometry at ESRF using two coherent beams from Fresnel mirrors,” J. X-Ray Sci. Technol. 7, 12–23 (1997).
[CrossRef]

DeMartino, C.

Dufresne, E.

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995).
[CrossRef] [PubMed]

Fezzaa, K.

K. Fezzaa, F. Comin, S. Marchesini, R. Coïsson, M. Belakhovsky, “X-ray interferometry at ESRF using two coherent beams from Fresnel mirrors,” J. X-Ray Sci. Technol. 7, 12–23 (1997).
[CrossRef]

Gluskin, E.

E. Gluskin, I. McNulty, P. J. Viccaro, M. R. Howells, “X-ray intensity interferometry of surfaces with Fresnel mirrors,” Nucl. Instrum. Methods A 319, 213–218 (1992).
[CrossRef]

Grübel, G.

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995).
[CrossRef] [PubMed]

Guigay, J. P.

Harami, T.

Y. Kunimune, Y. Yoda, K. Izumi, M. Yabashi, X.-W. Zhang, T. Harami, M. Ando, S. Kikuta, “Two-photon correlations in x-rays from a synchotron radiation source,” J. Synchroton Radiat. 4, 199–203 (1997).
[CrossRef]

Hignette, O.

I. Schelokov, O. Hignette, C. Raven, A. Snigirev, I. Snigireva, A. Souvorov, “X-ray interferometry technique for mirror and multilayer characterization,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2805, 282–291 (1996).
[CrossRef]

Howells, M. R.

E. Gluskin, I. McNulty, P. J. Viccaro, M. R. Howells, “X-ray intensity interferometry of surfaces with Fresnel mirrors,” Nucl. Instrum. Methods A 319, 213–218 (1992).
[CrossRef]

Izumi, K.

Y. Kunimune, Y. Yoda, K. Izumi, M. Yabashi, X.-W. Zhang, T. Harami, M. Ando, S. Kikuta, “Two-photon correlations in x-rays from a synchotron radiation source,” J. Synchroton Radiat. 4, 199–203 (1997).
[CrossRef]

Joyeux, D.

F. Polack, D. Joyeux, J. Svatos, D. Phalippou, “Applications of wavefront division interferometers in soft x rays,” Rev. Sci. Instrum. 66, 2180–2183 (1995).
[CrossRef]

Kikuta, S.

Y. Kunimune, Y. Yoda, K. Izumi, M. Yabashi, X.-W. Zhang, T. Harami, M. Ando, S. Kikuta, “Two-photon correlations in x-rays from a synchotron radiation source,” J. Synchroton Radiat. 4, 199–203 (1997).
[CrossRef]

Kohn, V.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, “On the possibilities of phase-contrast micro-imaging by coherent high energy synchotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

Kunimune, Y.

Y. Kunimune, Y. Yoda, K. Izumi, M. Yabashi, X.-W. Zhang, T. Harami, M. Ando, S. Kikuta, “Two-photon correlations in x-rays from a synchotron radiation source,” J. Synchroton Radiat. 4, 199–203 (1997).
[CrossRef]

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, “On the possibilities of phase-contrast micro-imaging by coherent high energy synchotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

Marchesini, S.

K. Fezzaa, F. Comin, S. Marchesini, R. Coïsson, M. Belakhovsky, “X-ray interferometry at ESRF using two coherent beams from Fresnel mirrors,” J. X-Ray Sci. Technol. 7, 12–23 (1997).
[CrossRef]

S. Marchesini, R. Coïsson, “Two-dimensional coherence measurements with Fresnel mirrors,” Opt. Eng. 53, 3597–3601 (1996).
[CrossRef]

McNulty, I.

E. Gluskin, I. McNulty, P. J. Viccaro, M. R. Howells, “X-ray intensity interferometry of surfaces with Fresnel mirrors,” Nucl. Instrum. Methods A 319, 213–218 (1992).
[CrossRef]

Mochrie, S. G. J.

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995).
[CrossRef] [PubMed]

Phalippou, D.

F. Polack, D. Joyeux, J. Svatos, D. Phalippou, “Applications of wavefront division interferometers in soft x rays,” Rev. Sci. Instrum. 66, 2180–2183 (1995).
[CrossRef]

Polack, F.

F. Polack, D. Joyeux, J. Svatos, D. Phalippou, “Applications of wavefront division interferometers in soft x rays,” Rev. Sci. Instrum. 66, 2180–2183 (1995).
[CrossRef]

Raven, C.

I. Schelokov, O. Hignette, C. Raven, A. Snigirev, I. Snigireva, A. Souvorov, “X-ray interferometry technique for mirror and multilayer characterization,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2805, 282–291 (1996).
[CrossRef]

Schelokov, I.

I. Schelokov, O. Hignette, C. Raven, A. Snigirev, I. Snigireva, A. Souvorov, “X-ray interferometry technique for mirror and multilayer characterization,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2805, 282–291 (1996).
[CrossRef]

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, “On the possibilities of phase-contrast micro-imaging by coherent high energy synchotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

I. Schelokov, O. Hignette, C. Raven, A. Snigirev, I. Snigireva, A. Souvorov, “X-ray interferometry technique for mirror and multilayer characterization,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2805, 282–291 (1996).
[CrossRef]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, “On the possibilities of phase-contrast micro-imaging by coherent high energy synchotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

I. Schelokov, O. Hignette, C. Raven, A. Snigirev, I. Snigireva, A. Souvorov, “X-ray interferometry technique for mirror and multilayer characterization,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2805, 282–291 (1996).
[CrossRef]

Souvorov, A.

I. Schelokov, O. Hignette, C. Raven, A. Snigirev, I. Snigireva, A. Souvorov, “X-ray interferometry technique for mirror and multilayer characterization,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2805, 282–291 (1996).
[CrossRef]

Stephenson, G. B.

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995).
[CrossRef] [PubMed]

Sutton, M.

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995).
[CrossRef] [PubMed]

Svatos, J.

F. Polack, D. Joyeux, J. Svatos, D. Phalippou, “Applications of wavefront division interferometers in soft x rays,” Rev. Sci. Instrum. 66, 2180–2183 (1995).
[CrossRef]

Viccaro, P. J.

E. Gluskin, I. McNulty, P. J. Viccaro, M. R. Howells, “X-ray intensity interferometry of surfaces with Fresnel mirrors,” Nucl. Instrum. Methods A 319, 213–218 (1992).
[CrossRef]

Yabashi, M.

Y. Kunimune, Y. Yoda, K. Izumi, M. Yabashi, X.-W. Zhang, T. Harami, M. Ando, S. Kikuta, “Two-photon correlations in x-rays from a synchotron radiation source,” J. Synchroton Radiat. 4, 199–203 (1997).
[CrossRef]

Yoda, Y.

Y. Kunimune, Y. Yoda, K. Izumi, M. Yabashi, X.-W. Zhang, T. Harami, M. Ando, S. Kikuta, “Two-photon correlations in x-rays from a synchotron radiation source,” J. Synchroton Radiat. 4, 199–203 (1997).
[CrossRef]

Zhang, X.-W.

Y. Kunimune, Y. Yoda, K. Izumi, M. Yabashi, X.-W. Zhang, T. Harami, M. Ando, S. Kikuta, “Two-photon correlations in x-rays from a synchotron radiation source,” J. Synchroton Radiat. 4, 199–203 (1997).
[CrossRef]

J. Synchroton Radiat.

Y. Kunimune, Y. Yoda, K. Izumi, M. Yabashi, X.-W. Zhang, T. Harami, M. Ando, S. Kikuta, “Two-photon correlations in x-rays from a synchotron radiation source,” J. Synchroton Radiat. 4, 199–203 (1997).
[CrossRef]

J. X-Ray Sci. Technol.

K. Fezzaa, F. Comin, S. Marchesini, R. Coïsson, M. Belakhovsky, “X-ray interferometry at ESRF using two coherent beams from Fresnel mirrors,” J. X-Ray Sci. Technol. 7, 12–23 (1997).
[CrossRef]

Nucl. Instrum. Methods A

E. Gluskin, I. McNulty, P. J. Viccaro, M. R. Howells, “X-ray intensity interferometry of surfaces with Fresnel mirrors,” Nucl. Instrum. Methods A 319, 213–218 (1992).
[CrossRef]

Opt. Eng.

S. Marchesini, R. Coïsson, “Two-dimensional coherence measurements with Fresnel mirrors,” Opt. Eng. 53, 3597–3601 (1996).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

F. Polack, D. Joyeux, J. Svatos, D. Phalippou, “Applications of wavefront division interferometers in soft x rays,” Rev. Sci. Instrum. 66, 2180–2183 (1995).
[CrossRef]

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, “On the possibilities of phase-contrast micro-imaging by coherent high energy synchotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

Other

I. Schelokov, O. Hignette, C. Raven, A. Snigirev, I. Snigireva, A. Souvorov, “X-ray interferometry technique for mirror and multilayer characterization,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2805, 282–291 (1996).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

(a) Experimental setup. At the right one of the mirrors is elevated an amount h. (b) Horizontal tilt.

Fig. 2
Fig. 2

Interference pattern produced by the two mirrors at 10.4 keV recorded by a CCD: (a) parallel mirrors, (b) tilt of one mirror, (c) relative distance from the detector decreased by elevation of one mirror.

Fig. 3
Fig. 3

(a) Stepped mirror used for the experiment. Step heights are indicated. (b) Hologram of the stepped mirror in longitudinal geometry at 10.4 keV, θ = 0.44 mrad.

Fig. 4
Fig. 4

(a) Hologram of the mirror in transverse geometry (E = 10.4 keV, θ = 0.8 mrad, D = 20 mm). (b) Spectrogram. The original signal in (a) is divided into parts, and each part is Fourier transformed. The picture shows the signal in phase space of frequency space.

Fig. 5
Fig. 5

(a) Hologram and (b) spectrogram corrected for the inclination effect {I′(z) = I[ z(θ + z/ L)]}.

Fig. 6
Fig. 6

Intensities of the two beams separated by application of Eq. (1) to the data.

Fig. 7
Fig. 7

Reconstruction of the stepped mirror. A phase step corresponds to the phase shift produced by the step.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

Iz=Ir+Io+2IrIo sinkφz+δφz,
Ir,o=12Il±Il2-4IlIo1/2.

Metrics