Abstract

A new type of zone plate has been designed for soft x-rays, based on radial modulation of the refractive indices of the material. It is made with two materials; the concentration of one material increases gradually and that of the other decreases with increasing radius in each pair of zones. When such a zone plate is made with titanium and chromium and their concentrations are optimized for use at the wavelength of 2.74 nm, its x-ray focusing efficiency would be 34%. This value is 3.4 and 1.4 times the efficiencies of the Fresnel zone plate and the π-radian phase shifting zone plate, respectively.

© 1990 Optical Society of America

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References

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  1. G. Schmahl, D. Rudolph, Eds., X-Ray Microscopy (Springer-Verlag, Berlin, 1984).
  2. P. C. Cheng, G. J. Jan, Eds., X-Ray Microscopy. Instrumentation and Biological Applications (Springer-Verlag, Berlin, 1987).
  3. J. Kirz, “Phase Zone Plates for X Rays and the Extreme uv,” J. Opt. Soc. Am. 64, 301–309 (1974).
    [CrossRef]
  4. N. M. Ceglio, A. M. Hawryluk, M. Schattenburg, “X-ray Phase Lens Design and Fabrication,” J. Vac. Technol. B 1, 1285–1288 (1983).
    [CrossRef]
  5. H. Fujisaki, “Materials for Phase Zone Plate Fabrication for Use with Soft X-Rays,” Jpn. J. Appl. Phys. 27, 1335–1337 (1988).
    [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 380.
  7. B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-RAY Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
    [CrossRef]
  8. Y. Nagai et al., “Feasibility Study for the Observations of Biological Materials in VUV Wavelength Regions. Using Zone Plates Fabricated by Electron and Ion Beam Lithographies,” X-Ray Microscopy. Instrumentation and Biological Applications, P. C. Cheng, G. J. Jan, Eds. (Springer-Verlag, Berlin, 1987), pp. 263–288.
  9. T. W. Barbee, “Sputtered Layered Synthetic Microstructures (LSM) Dispersion Elements,” AIP Conf. Proc. No. 75, 131–145 (1981).
    [CrossRef]
  10. Y. Suzuki, “Tungsten-Carbon X-ray Multilayered Mirror Prepared by Photo-Chemical Vapor Deposition,” Jpn. J. Appl. Phys. 28, 920–924 (1989).
    [CrossRef]
  11. K. Saitoh, K. Inagawa, K. Kohra, C. Hayashi, A. ida, N. Kato, “Fabrication and Characterization of Multilayer Zone Plate for Hard X-Rays,” Jpn. J. Appl. Phys. 27, L2131–L2133 (1988).
    [CrossRef]

1989

Y. Suzuki, “Tungsten-Carbon X-ray Multilayered Mirror Prepared by Photo-Chemical Vapor Deposition,” Jpn. J. Appl. Phys. 28, 920–924 (1989).
[CrossRef]

1988

K. Saitoh, K. Inagawa, K. Kohra, C. Hayashi, A. ida, N. Kato, “Fabrication and Characterization of Multilayer Zone Plate for Hard X-Rays,” Jpn. J. Appl. Phys. 27, L2131–L2133 (1988).
[CrossRef]

H. Fujisaki, “Materials for Phase Zone Plate Fabrication for Use with Soft X-Rays,” Jpn. J. Appl. Phys. 27, 1335–1337 (1988).
[CrossRef]

1983

N. M. Ceglio, A. M. Hawryluk, M. Schattenburg, “X-ray Phase Lens Design and Fabrication,” J. Vac. Technol. B 1, 1285–1288 (1983).
[CrossRef]

1982

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-RAY Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

1981

T. W. Barbee, “Sputtered Layered Synthetic Microstructures (LSM) Dispersion Elements,” AIP Conf. Proc. No. 75, 131–145 (1981).
[CrossRef]

1974

Barbee, T. W.

T. W. Barbee, “Sputtered Layered Synthetic Microstructures (LSM) Dispersion Elements,” AIP Conf. Proc. No. 75, 131–145 (1981).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 380.

Ceglio, N. M.

N. M. Ceglio, A. M. Hawryluk, M. Schattenburg, “X-ray Phase Lens Design and Fabrication,” J. Vac. Technol. B 1, 1285–1288 (1983).
[CrossRef]

Fujikawa, B. K.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-RAY Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Fujisaki, H.

H. Fujisaki, “Materials for Phase Zone Plate Fabrication for Use with Soft X-Rays,” Jpn. J. Appl. Phys. 27, 1335–1337 (1988).
[CrossRef]

Hawryluk, A. M.

N. M. Ceglio, A. M. Hawryluk, M. Schattenburg, “X-ray Phase Lens Design and Fabrication,” J. Vac. Technol. B 1, 1285–1288 (1983).
[CrossRef]

Hayashi, C.

K. Saitoh, K. Inagawa, K. Kohra, C. Hayashi, A. ida, N. Kato, “Fabrication and Characterization of Multilayer Zone Plate for Hard X-Rays,” Jpn. J. Appl. Phys. 27, L2131–L2133 (1988).
[CrossRef]

Henke, B. L.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-RAY Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

ida, A.

K. Saitoh, K. Inagawa, K. Kohra, C. Hayashi, A. ida, N. Kato, “Fabrication and Characterization of Multilayer Zone Plate for Hard X-Rays,” Jpn. J. Appl. Phys. 27, L2131–L2133 (1988).
[CrossRef]

Inagawa, K.

K. Saitoh, K. Inagawa, K. Kohra, C. Hayashi, A. ida, N. Kato, “Fabrication and Characterization of Multilayer Zone Plate for Hard X-Rays,” Jpn. J. Appl. Phys. 27, L2131–L2133 (1988).
[CrossRef]

Kato, N.

K. Saitoh, K. Inagawa, K. Kohra, C. Hayashi, A. ida, N. Kato, “Fabrication and Characterization of Multilayer Zone Plate for Hard X-Rays,” Jpn. J. Appl. Phys. 27, L2131–L2133 (1988).
[CrossRef]

Kirz, J.

Kohra, K.

K. Saitoh, K. Inagawa, K. Kohra, C. Hayashi, A. ida, N. Kato, “Fabrication and Characterization of Multilayer Zone Plate for Hard X-Rays,” Jpn. J. Appl. Phys. 27, L2131–L2133 (1988).
[CrossRef]

Lee, P.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-RAY Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Nagai, Y.

Y. Nagai et al., “Feasibility Study for the Observations of Biological Materials in VUV Wavelength Regions. Using Zone Plates Fabricated by Electron and Ion Beam Lithographies,” X-Ray Microscopy. Instrumentation and Biological Applications, P. C. Cheng, G. J. Jan, Eds. (Springer-Verlag, Berlin, 1987), pp. 263–288.

Saitoh, K.

K. Saitoh, K. Inagawa, K. Kohra, C. Hayashi, A. ida, N. Kato, “Fabrication and Characterization of Multilayer Zone Plate for Hard X-Rays,” Jpn. J. Appl. Phys. 27, L2131–L2133 (1988).
[CrossRef]

Schattenburg, M.

N. M. Ceglio, A. M. Hawryluk, M. Schattenburg, “X-ray Phase Lens Design and Fabrication,” J. Vac. Technol. B 1, 1285–1288 (1983).
[CrossRef]

Shimabukuro, R. L.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-RAY Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Suzuki, Y.

Y. Suzuki, “Tungsten-Carbon X-ray Multilayered Mirror Prepared by Photo-Chemical Vapor Deposition,” Jpn. J. Appl. Phys. 28, 920–924 (1989).
[CrossRef]

Tanaka, T. J.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-RAY Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 380.

AIP Conf. Proc. No.

T. W. Barbee, “Sputtered Layered Synthetic Microstructures (LSM) Dispersion Elements,” AIP Conf. Proc. No. 75, 131–145 (1981).
[CrossRef]

At. Data Nucl. Data Tables

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-RAY Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

J. Opt. Soc. Am.

J. Vac. Technol. B

N. M. Ceglio, A. M. Hawryluk, M. Schattenburg, “X-ray Phase Lens Design and Fabrication,” J. Vac. Technol. B 1, 1285–1288 (1983).
[CrossRef]

Jpn. J. Appl. Phys.

H. Fujisaki, “Materials for Phase Zone Plate Fabrication for Use with Soft X-Rays,” Jpn. J. Appl. Phys. 27, 1335–1337 (1988).
[CrossRef]

Y. Suzuki, “Tungsten-Carbon X-ray Multilayered Mirror Prepared by Photo-Chemical Vapor Deposition,” Jpn. J. Appl. Phys. 28, 920–924 (1989).
[CrossRef]

K. Saitoh, K. Inagawa, K. Kohra, C. Hayashi, A. ida, N. Kato, “Fabrication and Characterization of Multilayer Zone Plate for Hard X-Rays,” Jpn. J. Appl. Phys. 27, L2131–L2133 (1988).
[CrossRef]

Other

G. Schmahl, D. Rudolph, Eds., X-Ray Microscopy (Springer-Verlag, Berlin, 1984).

P. C. Cheng, G. J. Jan, Eds., X-Ray Microscopy. Instrumentation and Biological Applications (Springer-Verlag, Berlin, 1987).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 380.

Y. Nagai et al., “Feasibility Study for the Observations of Biological Materials in VUV Wavelength Regions. Using Zone Plates Fabricated by Electron and Ion Beam Lithographies,” X-Ray Microscopy. Instrumentation and Biological Applications, P. C. Cheng, G. J. Jan, Eds. (Springer-Verlag, Berlin, 1987), pp. 263–288.

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Figures (5)

Fig. 1
Fig. 1

Phases of x-rays at the first-order focal point of the FZP: (A) section of an FZP expressed with r2 as the radial coordinate: from the center to the fourth zone. Opaque zones obstruct the x-rays shown by dotted lines in (B)–(D). (B) Phase difference ϕ of the x-rays at the first-order focal point. (C) cosϕ along r2. The integration along r gives 0. (D) sinϕ along r2. Only shaded areas are effective in calculating intensity I.

Fig. 2
Fig. 2

Phases of x-rays at the first-order focal point of the PZP: (A) Section of a PZP expressed with r2 as the radial coordinate: from the center to the fourth zone. (B) Phase difference ϕ of x-rays at the first-order focal point. Dotted lines show geometrically calculated phase differences, which are π-radian shifted by phase-shifting zones (arrows). (C) cosϕ along r2. The integration along r gives 0. (D) sinϕ along r2. Shaded areas are twice these in Fig. 1(D) and contribute four times the latter to intensity I.

Fig. 3
Fig. 3

Basic GRIPZP up to n = 4 and m = 2. The thick line shows the volume concentration distributions [M1] and [M2] of the materials of which the GRIPZP is made as well as the phase shift Δϕ caused by the GRIPZP. A-B-F and A-B-F′ are light paths discussed in the text. F is the first-order focal point of the GRIPZP.

Fig. 4
Fig. 4

Optimized GRIPZP up to n = 4 and m = 2. Same as in Fig. 3 except that the maximum phase shift is less than 2π radians. Only the μ1 < μ2 case is shown. Dotted lines indicate the difference from the basic GRIPZP.

Fig. 5
Fig. 5

Phases of x-rays at the first-order focal point of the GRIPZP. Dotted lines are geometrically calculated phase differences and their cosine and sine. Shaded areas are effective to calculate intensity I. (A) The phase difference ϕ of x-rays at the first-order focal point. (B) cosϕ along r2. (C) sinϕ along r2.

Tables (1)

Tables Icon

Table I Best Three Combinations of Materials for the GRIPZP and the Best Two Materials for the PZP at each Wavelength of 0.6–11.4 nm

Equations (34)

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r n = n r 1 ,
f = r 1 2 / λ .
Δ l = f 2 + r 2 - f r 2 / 2 f ,
ϕ = ( 2 π / λ ) · Δ l π r 2 / r 1 2 .
u = m = 1 N / 2 ( - i u 0 ) r 2 m - 2 r 2 m - 1 exp [ i ( 2 π / λ ) · Δ l ] λ f 2 + r 2 2 π r d r ,
u = - i N u 0 2 ( 2 m - 2 ) π ( 2 m - 1 ) π ( cos ϕ + i sin ϕ ) d ϕ = N u 0 .
I = u 2 = N 2 I 0 ,
u = - i N u 0 2 { ( 2 m - 2 ) π ( 2 m - 1 ) π ( cos ϕ + i sin ϕ ) d ϕ + ( 2 m - 1 ) π 2 m π T [ cos ( ϕ - π ) + i sin ( ϕ - π ) ] d ϕ } = N u 0 ( 1 + T ) ,
I = N 2 I 0 ( 1 + T ) 2 ,
2 π λ [ optical length ( A - B - F ) ] - 2 π λ [ optical length ( A - B - F ) ] = 2 ( m - 1 ) π             ( m = 1 , 2 , ) .
2 π λ { [ ( 1 - c ) ( 1 - δ 1 ) + c ( 1 - δ 2 ) ] w + f 2 + r 2 } - 2 π λ [ ( 1 - δ 1 ) w + f ] = 2 ( m - 1 ) π ,
w = λ δ 2 - δ 1 .
c = r 2 2 r 1 2 - ( m - 1 ) .
T = exp { - [ μ 1 ( 1 - c ) w + μ 2 c w ] / 2 } ,
u = m = 1 N / 2 ( - i u 0 r 1 2 ) r 2 ( m - 1 ) r 2 m T ( cos ϕ + i sin ϕ ) · 2 π r d r .
u = m = 1 N / 2 ( - i u 0 r 1 2 ) 2 ( m - 1 ) r 2 m T · 2 π r d r .
u = - 2 i N π u 0 ( μ 2 - μ 1 ) w exp ( - μ 1 w 2 ) [ 1 - exp - ( μ 2 - μ 1 ) w 2 ] .
I = u 2 = N 2 π 2 I 0 E ,
E = [ 2 ( μ 2 - μ 1 ) w ] 2 exp ( - μ 1 w ) [ 1 - exp - ( μ 2 - μ 1 ) w 2 ] 2 .
r x m 2 = r 2 ( m - 1 ) 2 + k r 1 2             ( 0 < k < 2 ) .
2 π λ { [ ( 1 - c ) ( 1 - δ 1 ) + c ( 1 - δ 2 ) ] w x + f 2 + r 2 } - 2 π λ [ ( 1 - δ 1 ) w x + f ] = 2 ( m - 1 ) π
w x = k λ 2 ( δ 2 - δ 1 ) ,
c = { r 2 k r 1 2 - 2 ( m - 1 ) k , r 2 ( m - 1 ) 2 < r 2 < r x m 2 , 0 or 1 , r x m 2 < r 2 < r 2 m 2 .
T = { T 1 T c , r 2 ( m - 1 ) 2 < r 2 < r x m 2 , T x , r x m 2 < r 2 < r 2 m 2 ,
T x = { T 1 , μ 1 > μ 2 , T 2 , μ 1 < μ 2 ,
T 1 = exp ( - μ 1 w x / 2 ) ,
T 2 = exp ( - μ 2 w x / 2 ) ,
T c = exp [ - ( μ 2 - μ 1 ) w x r 2 - 2 ( m - 1 ) r 1 2 2 k r 1 2 ] .
u = m = 1 N / 2 ( - i u 0 r 1 2 ) [ r 2 ( m - 1 ) r x m T 1 T c · 2 π r d r + r 2 ( m - 1 ) r 2 m T x ( cos ϕ + i sin ϕ ) · 2 π r d r ] .
I = N 2 π 2 I 0 E ,
E = [ ( T 1 A + T x B ) 2 + ( T x C ) 2 ] / 4 π 2 ,
A = 2 k π ( μ 2 - μ 1 ) w x [ 1 - exp - ( μ 2 - μ 1 ) w x 2 ] ,
B = - sin ( k π ) ,
C = cos ( k π ) - 1.

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