Abstract

We present an analysis of the transmission of x rays through a single monocapillary under the single-reflection regime. Because ray tracing does not provide an explanation for experimental data, we give a qualitative interpretation of the observed behavior within the framework of wave theory.

© 1999 Optical Society of America

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References

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  1. M. A. Kumakhov, F. F. Komarov, “Multiple reflection from surface: x-ray optics,” Phys. Rep. 191(5), 289–350 (1990).
  2. S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron. Radiat. 2, 132–135 (1995).
  3. S. B. Dabagov, “Passage of x-rays through a single monocapillary,” in Hard X-Ray and Gamma-Ray Detector Physics, Optics, and Applications, R. B. Hoover, F. P. Doty, eds., Proc. SPIE3115, 341–347 (1997).
  4. M. A. Kumakhov, “X-ray and neutron polycapillary optics: status and perspectives,” in Hard X-Ray/Gamma-Ray and Neutron Optics, Sensors, and Applications, R. B. Hoover, F. P. Doty, eds., Proc. SPIE2859, 116–122 (1996).
  5. A. V. Vinogradov, Mirror X-Ray Optics (Mashinostroenie Leningrad, Russia, 1989).
  6. E. Spiller, Soft X-Ray Optics, Monograph PM15/HC (SPIE Press, Bellingham, Wash., 1994).

1995 (1)

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron. Radiat. 2, 132–135 (1995).

1990 (1)

M. A. Kumakhov, F. F. Komarov, “Multiple reflection from surface: x-ray optics,” Phys. Rep. 191(5), 289–350 (1990).

Dabagov, S. B.

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron. Radiat. 2, 132–135 (1995).

S. B. Dabagov, “Passage of x-rays through a single monocapillary,” in Hard X-Ray and Gamma-Ray Detector Physics, Optics, and Applications, R. B. Hoover, F. P. Doty, eds., Proc. SPIE3115, 341–347 (1997).

Fedorchuk, R. V.

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron. Radiat. 2, 132–135 (1995).

Komarov, F. F.

M. A. Kumakhov, F. F. Komarov, “Multiple reflection from surface: x-ray optics,” Phys. Rep. 191(5), 289–350 (1990).

Kumakhov, M. A.

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron. Radiat. 2, 132–135 (1995).

M. A. Kumakhov, F. F. Komarov, “Multiple reflection from surface: x-ray optics,” Phys. Rep. 191(5), 289–350 (1990).

M. A. Kumakhov, “X-ray and neutron polycapillary optics: status and perspectives,” in Hard X-Ray/Gamma-Ray and Neutron Optics, Sensors, and Applications, R. B. Hoover, F. P. Doty, eds., Proc. SPIE2859, 116–122 (1996).

Murashova, V. A.

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron. Radiat. 2, 132–135 (1995).

Nikitina, S. V.

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron. Radiat. 2, 132–135 (1995).

Spiller, E.

E. Spiller, Soft X-Ray Optics, Monograph PM15/HC (SPIE Press, Bellingham, Wash., 1994).

Vinogradov, A. V.

A. V. Vinogradov, Mirror X-Ray Optics (Mashinostroenie Leningrad, Russia, 1989).

Yakimenko, M. N.

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron. Radiat. 2, 132–135 (1995).

J. Synchrotron. Radiat. (1)

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron. Radiat. 2, 132–135 (1995).

Phys. Rep. (1)

M. A. Kumakhov, F. F. Komarov, “Multiple reflection from surface: x-ray optics,” Phys. Rep. 191(5), 289–350 (1990).

Other (4)

S. B. Dabagov, “Passage of x-rays through a single monocapillary,” in Hard X-Ray and Gamma-Ray Detector Physics, Optics, and Applications, R. B. Hoover, F. P. Doty, eds., Proc. SPIE3115, 341–347 (1997).

M. A. Kumakhov, “X-ray and neutron polycapillary optics: status and perspectives,” in Hard X-Ray/Gamma-Ray and Neutron Optics, Sensors, and Applications, R. B. Hoover, F. P. Doty, eds., Proc. SPIE2859, 116–122 (1996).

A. V. Vinogradov, Mirror X-Ray Optics (Mashinostroenie Leningrad, Russia, 1989).

E. Spiller, Soft X-Ray Optics, Monograph PM15/HC (SPIE Press, Bellingham, Wash., 1994).

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Figures (7)

Fig. 1
Fig. 1

Focusing properties of a single monocapillary for f 1L: S, x-ray source; L, capillary length; f 1 and f 2, the distances between the source and the monocapillary and between the monocapillary and the film, respectively.

Fig. 2
Fig. 2

Sketch of the x-ray distribution behind a monocapillary of diameter 2r 0. Radii r min and r max correspond to r 1 and r 2 for zone I and to r 2 and r 1 for zone III.

Fig. 3
Fig. 3

Axial distributions of x rays behind the monocapillary. The ring expands when it moves away from the exit of the monocapillary. For zone II the distribution at the focal plane has a maximum intensity spot along the monocapillary axis.

Fig. 4
Fig. 4

X-ray distribution of zone III in the transverse plane behind a single monocapillary (1 chan means that the monocapillary channel is completely open). The beam energy is E γ = 8 keV and the monocapillary channel diameter is d 0 = 0.1 mm.

Fig. 5
Fig. 5

X-ray distributions of zone III in the transverse plane behind a single monocapillary: solid curve, an open (1 chan) capillary entrance; dashed curve, a half-masked (½ chan) capillary entrance. The beam energy is E γ = 8 keV and the monocapillary channel diameter is d 0 = 1 mm.

Fig. 6
Fig. 6

Simulation of an x-ray distribution behind a single monocapillary calculated for region III in the ray approximation (left plot) and in the wave approximation (right plot).

Fig. 7
Fig. 7

Scheme of the interference of x rays that travel into a monocapillary.

Equations (15)

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Iθ=I1+I2,
R0θ2θ-1-1,
Iθ  const+Rθ.
r1=|r0-L+f2θmax|, r2=|r0-f2θmin|,
θmax=r0f1,  θmin=r0f1+L,
r1/r0=|1-L+f2/f1|, r2/r0=|1-f2/L+f1|.
r1=0 at f1=L+f2, r2=0 at f2=L+f1,
Δfsp=2r0+f2θmin at f2f*,
Δfsp=2f2-f1+Lθmax at f2>f*,
Δθ=r0Lf1f1+L,
Δ=hd0/D,
dIidx  1+coskΔ=1+cos2πλhd0D,
Iih  2li+Bπsin2πliBcos2πhB,
B=D/d0λ
Ih= Iih,

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