Abstract

The demand for an x-ray microscope has received much attention because of the desire to study living cells at a high resolution and in a hydrated environment. A Wolter type I mirror used for soft-x-ray microscope optics has many advantages. From the mirror fabrication point of view, it is necessary to perform tolerance analysis, particularly with respect to figure errors that considerably degrade the image quality. The figure tolerance of a Wolter type I mirror for a biological application in terms of the image quality and the state-of-the-art fabrication technology is discussed. The figure errors rapidly destroyed the image quality, and the required slope error depended on the detector used in the soft-x-ray microscope.

© 2007 Optical Society of America

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References

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  1. A. G. Michette, Optical System for Soft X Rays (Plenum Press, 1986).
    [CrossRef]
  2. H. Wolter, "Spiegelsysteme streifenden Einfalls als abbildende Optiken für Röntgenstrahlen," Ann. Phys. 10, 94-114 (1952).
    [CrossRef]
  3. N. Ikawa, R. R. Donaldson, R. Komanduri, W. König, T. H. Aachen, P. A. McKeown, T. Moriwaki, and I. F. Stowers, "Ultraprecision metal cutting--the past, the present and the future," CIRP Ann. 40, 587-594 (1991).
    [CrossRef]
  4. K. S. Chon, Y. Namba, and K.-H. Yoon, "Optimization of a Wolter type I mirror for a soft x-ray microscope," Precis. Eng. 30, 223-230 (2006).
    [CrossRef]
  5. R. C. Chase, A. S. Krieger, and J. H. Underwood, "Grazing incidence relay optics," Appl. Opt. 8, 4446-4452 (1969).
  6. J. D. Mangus and J. H. Underwood, "Optical design of a glancing incidence x-ray telescope," Appl. Opt. 8, 95-102 (1969).
    [CrossRef] [PubMed]
  7. D. Attwood, Soft X-Ray and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge U. Press, 2000).
  8. J. W. Foreman, "Computation of rms spot radii by ray tracing," Appl. Opt. 13, 2585-2588 (1974).
    [CrossRef] [PubMed]
  9. K. Sugisaki, S. Takahashi, Y. Yoshidomi, K. Shinada, O. Mitomi, E. Uchishiba, R. Hamada, T. Kato, and S. Aoki, "Influence of fabrication errors on Wolter mirror imaging performance," Appl. Opt. 37, 8057-8066 (1998).
    [CrossRef]
  10. D. Korsch, C. L. Wyman, and L. M. Perry, "Influence of alignment and surface defects on the performance of x-ray telescope," Proc. SPIE 184, 211-222 (1979).
  11. P. Glenn, "Set of orthonormal surface error descriptors for near-cylindrical optics," Opt. Eng. 23, 384-390 (1984).
  12. T. F. Zehnpfenning, "Figure tolerancing study of an axisymmetric x-ray microscope," Proc. SPIE 563, 72-80 (1985).

2006 (1)

K. S. Chon, Y. Namba, and K.-H. Yoon, "Optimization of a Wolter type I mirror for a soft x-ray microscope," Precis. Eng. 30, 223-230 (2006).
[CrossRef]

1998 (1)

1991 (1)

N. Ikawa, R. R. Donaldson, R. Komanduri, W. König, T. H. Aachen, P. A. McKeown, T. Moriwaki, and I. F. Stowers, "Ultraprecision metal cutting--the past, the present and the future," CIRP Ann. 40, 587-594 (1991).
[CrossRef]

1985 (1)

T. F. Zehnpfenning, "Figure tolerancing study of an axisymmetric x-ray microscope," Proc. SPIE 563, 72-80 (1985).

1984 (1)

P. Glenn, "Set of orthonormal surface error descriptors for near-cylindrical optics," Opt. Eng. 23, 384-390 (1984).

1979 (1)

D. Korsch, C. L. Wyman, and L. M. Perry, "Influence of alignment and surface defects on the performance of x-ray telescope," Proc. SPIE 184, 211-222 (1979).

1974 (1)

1969 (2)

J. D. Mangus and J. H. Underwood, "Optical design of a glancing incidence x-ray telescope," Appl. Opt. 8, 95-102 (1969).
[CrossRef] [PubMed]

R. C. Chase, A. S. Krieger, and J. H. Underwood, "Grazing incidence relay optics," Appl. Opt. 8, 4446-4452 (1969).

1952 (1)

H. Wolter, "Spiegelsysteme streifenden Einfalls als abbildende Optiken für Röntgenstrahlen," Ann. Phys. 10, 94-114 (1952).
[CrossRef]

Aachen, T. H.

N. Ikawa, R. R. Donaldson, R. Komanduri, W. König, T. H. Aachen, P. A. McKeown, T. Moriwaki, and I. F. Stowers, "Ultraprecision metal cutting--the past, the present and the future," CIRP Ann. 40, 587-594 (1991).
[CrossRef]

Aoki, S.

Attwood, D.

D. Attwood, Soft X-Ray and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge U. Press, 2000).

Chase, R. C.

R. C. Chase, A. S. Krieger, and J. H. Underwood, "Grazing incidence relay optics," Appl. Opt. 8, 4446-4452 (1969).

Chon, K. S.

K. S. Chon, Y. Namba, and K.-H. Yoon, "Optimization of a Wolter type I mirror for a soft x-ray microscope," Precis. Eng. 30, 223-230 (2006).
[CrossRef]

Donaldson, R. R.

N. Ikawa, R. R. Donaldson, R. Komanduri, W. König, T. H. Aachen, P. A. McKeown, T. Moriwaki, and I. F. Stowers, "Ultraprecision metal cutting--the past, the present and the future," CIRP Ann. 40, 587-594 (1991).
[CrossRef]

Foreman, J. W.

Glenn, P.

P. Glenn, "Set of orthonormal surface error descriptors for near-cylindrical optics," Opt. Eng. 23, 384-390 (1984).

Hamada, R.

Ikawa, N.

N. Ikawa, R. R. Donaldson, R. Komanduri, W. König, T. H. Aachen, P. A. McKeown, T. Moriwaki, and I. F. Stowers, "Ultraprecision metal cutting--the past, the present and the future," CIRP Ann. 40, 587-594 (1991).
[CrossRef]

Kato, T.

Komanduri, R.

N. Ikawa, R. R. Donaldson, R. Komanduri, W. König, T. H. Aachen, P. A. McKeown, T. Moriwaki, and I. F. Stowers, "Ultraprecision metal cutting--the past, the present and the future," CIRP Ann. 40, 587-594 (1991).
[CrossRef]

König, W.

N. Ikawa, R. R. Donaldson, R. Komanduri, W. König, T. H. Aachen, P. A. McKeown, T. Moriwaki, and I. F. Stowers, "Ultraprecision metal cutting--the past, the present and the future," CIRP Ann. 40, 587-594 (1991).
[CrossRef]

Korsch, D.

D. Korsch, C. L. Wyman, and L. M. Perry, "Influence of alignment and surface defects on the performance of x-ray telescope," Proc. SPIE 184, 211-222 (1979).

Krieger, A. S.

R. C. Chase, A. S. Krieger, and J. H. Underwood, "Grazing incidence relay optics," Appl. Opt. 8, 4446-4452 (1969).

Mangus, J. D.

McKeown, P. A.

N. Ikawa, R. R. Donaldson, R. Komanduri, W. König, T. H. Aachen, P. A. McKeown, T. Moriwaki, and I. F. Stowers, "Ultraprecision metal cutting--the past, the present and the future," CIRP Ann. 40, 587-594 (1991).
[CrossRef]

Michette, A. G.

A. G. Michette, Optical System for Soft X Rays (Plenum Press, 1986).
[CrossRef]

Mitomi, O.

Moriwaki, T.

N. Ikawa, R. R. Donaldson, R. Komanduri, W. König, T. H. Aachen, P. A. McKeown, T. Moriwaki, and I. F. Stowers, "Ultraprecision metal cutting--the past, the present and the future," CIRP Ann. 40, 587-594 (1991).
[CrossRef]

Namba, Y.

K. S. Chon, Y. Namba, and K.-H. Yoon, "Optimization of a Wolter type I mirror for a soft x-ray microscope," Precis. Eng. 30, 223-230 (2006).
[CrossRef]

Perry, L. M.

D. Korsch, C. L. Wyman, and L. M. Perry, "Influence of alignment and surface defects on the performance of x-ray telescope," Proc. SPIE 184, 211-222 (1979).

Shinada, K.

Stowers, I. F.

N. Ikawa, R. R. Donaldson, R. Komanduri, W. König, T. H. Aachen, P. A. McKeown, T. Moriwaki, and I. F. Stowers, "Ultraprecision metal cutting--the past, the present and the future," CIRP Ann. 40, 587-594 (1991).
[CrossRef]

Sugisaki, K.

Takahashi, S.

Uchishiba, E.

Underwood, J. H.

R. C. Chase, A. S. Krieger, and J. H. Underwood, "Grazing incidence relay optics," Appl. Opt. 8, 4446-4452 (1969).

J. D. Mangus and J. H. Underwood, "Optical design of a glancing incidence x-ray telescope," Appl. Opt. 8, 95-102 (1969).
[CrossRef] [PubMed]

Wolter, H.

H. Wolter, "Spiegelsysteme streifenden Einfalls als abbildende Optiken für Röntgenstrahlen," Ann. Phys. 10, 94-114 (1952).
[CrossRef]

Wyman, C. L.

D. Korsch, C. L. Wyman, and L. M. Perry, "Influence of alignment and surface defects on the performance of x-ray telescope," Proc. SPIE 184, 211-222 (1979).

Yoon, K.-H.

K. S. Chon, Y. Namba, and K.-H. Yoon, "Optimization of a Wolter type I mirror for a soft x-ray microscope," Precis. Eng. 30, 223-230 (2006).
[CrossRef]

Yoshidomi, Y.

Zehnpfenning, T. F.

T. F. Zehnpfenning, "Figure tolerancing study of an axisymmetric x-ray microscope," Proc. SPIE 563, 72-80 (1985).

Ann. Phys. (1)

H. Wolter, "Spiegelsysteme streifenden Einfalls als abbildende Optiken für Röntgenstrahlen," Ann. Phys. 10, 94-114 (1952).
[CrossRef]

Appl. Opt. (4)

CIRP Ann. (1)

N. Ikawa, R. R. Donaldson, R. Komanduri, W. König, T. H. Aachen, P. A. McKeown, T. Moriwaki, and I. F. Stowers, "Ultraprecision metal cutting--the past, the present and the future," CIRP Ann. 40, 587-594 (1991).
[CrossRef]

Opt. Eng. (1)

P. Glenn, "Set of orthonormal surface error descriptors for near-cylindrical optics," Opt. Eng. 23, 384-390 (1984).

Precis. Eng. (1)

K. S. Chon, Y. Namba, and K.-H. Yoon, "Optimization of a Wolter type I mirror for a soft x-ray microscope," Precis. Eng. 30, 223-230 (2006).
[CrossRef]

Proc. SPIE (2)

T. F. Zehnpfenning, "Figure tolerancing study of an axisymmetric x-ray microscope," Proc. SPIE 563, 72-80 (1985).

D. Korsch, C. L. Wyman, and L. M. Perry, "Influence of alignment and surface defects on the performance of x-ray telescope," Proc. SPIE 184, 211-222 (1979).

Other (2)

A. G. Michette, Optical System for Soft X Rays (Plenum Press, 1986).
[CrossRef]

D. Attwood, Soft X-Ray and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge U. Press, 2000).

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Figures (11)

Fig. 1
Fig. 1

Geometry of Wolter type I microscope mirror.

Fig. 2
Fig. 2

X-ray reflectivity of gold as a function of surface roughness for an incidence angle of 28 .8   mrad and a wavelength of 2 .3   nm .

Fig. 3
Fig. 3

rms blur circle radius of the Wolter type I microscope mirror (D32).

Fig. 4
Fig. 4

Spot diagrams of the designed D32 mirror at a Gaussian focal plane for rays starting from half-field heights (Hs) of 5 and 30   μm .

Fig. 5
Fig. 5

Schematic shapes of a mirror with various surface deformations.

Fig. 6
Fig. 6

rms blur circle radius of the designed D32 mirror with surface deformations at an on-axis field. (a) Fixed radial deformations of s h 1 = 20   nm and s e 1 = 20   nm with n h 1 = 2 , n e 1 = 2 , ω h 1 = 0 , ω h 2 = 0 , ω e 1 = 0 , and ω e 2 = 0 . (b) Constant axial deformations of s h 2 = 5   nm and s e 2 = 5   nm with n h 2 = 1 and n e 2 = 1 , ω h 1 = 0 , ω h 2 = 0 , ω e 1 = 0 , and ω e 2 = 0 .

Fig. 7
Fig. 7

rms blur circle radius for changing phase of surface deformations. (a) Fixed ω e 2 = π / 12 and ω e 2 = 13 π / 12 , and ω h 2 is changed from zero to 2π. (b) Plotted at ω h 1 = 0 and ω e 1 = 0 2 π .

Fig. 8
Fig. 8

Spot diagrams of the designed D32 mirror with surface deformations at an on-axis and a half-field height (H) of 5   μm : all phase factors are zero and s h 1 = 10   nm , s h 2 = 5   nm , s e 1 = 10   nm , and s e 2 = 5   nm .

Fig. 9
Fig. 9

rms blur circle radius for defocus at an on-axis field: deformation amplitudes of axial direction are 5   nm for both ellipsoidal and hyperboloidal parts of the designed D32 mirror.

Fig. 10
Fig. 10

Relationship between defocus and half-field height for different deformation amplitudes in the axial direction.

Fig. 11
Fig. 11

Relationship between resolution and half-field height for slope errors ( δ a s ) . Both (a) D32 and (b) D350 mirrors have surface deformations of n h 1 = 2 , n h 2 = 1 , n e 1 = 2 , n e 2 = 1 , ω h 1 = 0 , ω h 2 = 0 , ω e 1 = 0 , and ω e 2 = 0 . Amplitudes of the radial deformation are a constant of 20   nm .

Tables (1)

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Table 1 Design Examples for Wolter Type I Microscope Mirrors

Equations (2)

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R = R 0 ( θ ) e ( 4 π σ sin θ λ ) 2 ,
ρ i + s i 1 sin ( n i 1 ϕ + ω i 1 ) + s i 2 sin ( α i n i 2 ( ρ i ρ c ) + ω i 2 ) .

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