Abstract

We have designed and built a soft-x-ray interferometer to test the possibility of a direct measurement of the refractive index (i.e., the real part of the complex index) of materials in the soft-x-ray range. The interferometer is based on the Fresnel bimirror setup. It works near the zero path difference and requires only little spatial coherence. Plane mirrors at grazing incidence are the only optical elements. Interference fringes have been recorded at 4.8 nm, near the K edge of carbon. An index value could be obtained by measuring the fringe pattern shift between two such records, one without and one with a sample in one optical path. An estimation of the noise-limited accuracy in such an index determination shows that a few parts in 10−6 can be anticipated.

© 1993 Optical Society of America

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References

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  1. B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, At. Data Nucl. Data Tables 27, 1 (1982).
    [CrossRef]
  2. E. Spiller, Appl. Opt. 29, 19 (1990).
    [CrossRef] [PubMed]
  3. D. L. Windt, W. C. Cash, M. Scott, P. Arendt, B. Newnam, R. F. Fisher, A. B. Schwartzlander, Appl. Opt. 27, 246 (1988).
    [CrossRef] [PubMed]
  4. J. Nithianandam, J. C. Rife, Phys. Rev. B 47, 3517 (1993).
    [CrossRef]
  5. A. G. Michette, M. Kiihne, in X-Ray Microscopy III, Vol. 67 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1992), p. 293.
  6. S. Aoki, S. Kikuta, AIP Conf. Proc. 47, 49 (1986).
    [CrossRef]
  7. U. Bonse, H. Lotsch, A. Henning, J. X-Ray Sci. Technol. 1, 107 (1989).
    [CrossRef]
  8. F. Polack, D. Joyeux, in X-Ray Microscopy III, Vol. 67 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1992), p. 301.

1993 (1)

J. Nithianandam, J. C. Rife, Phys. Rev. B 47, 3517 (1993).
[CrossRef]

1992 (2)

A. G. Michette, M. Kiihne, in X-Ray Microscopy III, Vol. 67 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1992), p. 293.

F. Polack, D. Joyeux, in X-Ray Microscopy III, Vol. 67 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1992), p. 301.

1990 (1)

1989 (1)

U. Bonse, H. Lotsch, A. Henning, J. X-Ray Sci. Technol. 1, 107 (1989).
[CrossRef]

1988 (1)

1986 (1)

S. Aoki, S. Kikuta, AIP Conf. Proc. 47, 49 (1986).
[CrossRef]

1982 (1)

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

Aoki, S.

S. Aoki, S. Kikuta, AIP Conf. Proc. 47, 49 (1986).
[CrossRef]

Arendt, P.

Bonse, U.

U. Bonse, H. Lotsch, A. Henning, J. X-Ray Sci. Technol. 1, 107 (1989).
[CrossRef]

Cash, W. C.

Fisher, R. F.

Fujikawa, B. K.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

Henke, B. L.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

Henning, A.

U. Bonse, H. Lotsch, A. Henning, J. X-Ray Sci. Technol. 1, 107 (1989).
[CrossRef]

Joyeux, D.

F. Polack, D. Joyeux, in X-Ray Microscopy III, Vol. 67 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1992), p. 301.

Kiihne, M.

A. G. Michette, M. Kiihne, in X-Ray Microscopy III, Vol. 67 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1992), p. 293.

Kikuta, S.

S. Aoki, S. Kikuta, AIP Conf. Proc. 47, 49 (1986).
[CrossRef]

Lee, P.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

Lotsch, H.

U. Bonse, H. Lotsch, A. Henning, J. X-Ray Sci. Technol. 1, 107 (1989).
[CrossRef]

Michette, A. G.

A. G. Michette, M. Kiihne, in X-Ray Microscopy III, Vol. 67 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1992), p. 293.

Newnam, B.

Nithianandam, J.

J. Nithianandam, J. C. Rife, Phys. Rev. B 47, 3517 (1993).
[CrossRef]

Polack, F.

F. Polack, D. Joyeux, in X-Ray Microscopy III, Vol. 67 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1992), p. 301.

Rife, J. C.

J. Nithianandam, J. C. Rife, Phys. Rev. B 47, 3517 (1993).
[CrossRef]

Schwartzlander, A. B.

Scott, M.

Shimabukuro, R. L.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

Spiller, E.

Tanaka, T. J.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

Windt, D. L.

AIP Conf. Proc. (1)

S. Aoki, S. Kikuta, AIP Conf. Proc. 47, 49 (1986).
[CrossRef]

Appl. Opt. (2)

At. Data Nucl. Data Tables (1)

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

J. X-Ray Sci. Technol. (1)

U. Bonse, H. Lotsch, A. Henning, J. X-Ray Sci. Technol. 1, 107 (1989).
[CrossRef]

Phys. Rev. B (1)

J. Nithianandam, J. C. Rife, Phys. Rev. B 47, 3517 (1993).
[CrossRef]

Springer Series in Optical Sciences (2)

A. G. Michette, M. Kiihne, in X-Ray Microscopy III, Vol. 67 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1992), p. 293.

F. Polack, D. Joyeux, in X-Ray Microscopy III, Vol. 67 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1992), p. 301.

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Figures (5)

Fig. 1
Fig. 1

Fresnel mirror interferometer. The mirror’s tilt θ has been set to 2′14″, and the interference field is observed at a distance L = 120 mm from the mirror ridge. For any pair of interfering rays, the ray separation in the incident beam is ≈2 = 0.16 mm. The detector plane can be tilted to increase the apparent fringe spacing.

Fig. 2
Fig. 2

Photographic recording (negative) of the interferogram. The recorded fringe spacing is 33 μm because of the tilt (6º) of the photographic plate with respect to the axis of the interference field. The fringe field contains approximately 50 fringes.

Fig. 3
Fig. 3

Simulation of the interferogram. The deviations from the ideal sinusoidal form are due to the Fresnel diffraction of the incident plane wave on the ridge of the mirrors. The interferogram was calculated with the numerical values given in the text. The x coordinate is relative to the zero-path-difference point for an untilted detector plane.

Fig. 4
Fig. 4

Fourier spectrum amplitude of one line of the interferogram of Fig. 2. The abscissa is the sample number, from the frequency origin. Amplitudes are normalized to the main peak height. The arrow points to the first harmonic of the main peak. The fringe position (modulo period) X is estimated from the spectrum phase Φ at the peak’s maximum. Scanning parameters were slit width, 2.5 μm; slit height, 50 μm; sample separation, 2 μm. The discrete Fourier transform used 1024 samples; the spectrum sample separation is therefore 0.49 mm−1.

Fig. 5
Fig. 5

Position data obtained from lines 50 to 180 of the interferogram of Fig. 3 and the linear fit (solid line). Position is given in terms of spectrum peak’s phase Φ and equivalent position X. The rms fluctuation is 0.0175 rad or p/57; the origin of the positions is arbitrary. F. T., Fourier transform.

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