Abstract

Two example ultrahigh-spatial-resolution laser-backlit grazing-incidence x-ray microscope designs for inertial confinement fusion (ICF) research have been described [Appl. Opt. 40, 4570 (2001)]. Here details of fabrication, assembly, and optical surface errors that are characteristic of present state-of-the-art superpolished multilayer-coated spherical mirrors are given. They indicate that good image qualities can be expected; in particular, <0.5-µm spatial resolution at very high x-ray energies (up to 25 keV) appears to be feasible: Existing ICF imaging diagnostics approach ∼2 µm spatial at low (<2 keV) energy. The improvement in resolution compared with that of other grazing-incidence devices is attributed to a fortuitous residual on-axis aberration dependence on short wavelengths; recent advances in mirror fabrication, including a new thin-film deposition technique to correct figure errors precisely in one dimension; and novel design. For even higher resolutions, a means of creating precise aspherical mirrors of spheric-quality microroughness may be possible by use of the same deposition technique.

© 2001 Optical Society of America

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2001

G. R. Bennett, O. L. Landen, R. G. Adams, J. L. Porter, L. E. Ruggles, W. W. Simpson, C. Wakefield, “X-ray imaging techniques on Z using the Z-Beamlet laser,” Rev. Sci. Instrum. 72, 657–662 (2001).
[CrossRef]

G. R. Bennett, “Advanced laser-backlit grazing-incidence x-ray imaging systems for inertial confinement fusion research. I. Design,” Appl. Opt. 40, 4570–4587 (2001).
[CrossRef]

2000

P. L. Thompson, J. E. Harvey, “Systems engineering analysis of aplantic Wolter type I x-ray telescope,” Opt. Eng. 36, 1677–1691 (2000).
[CrossRef]

1998

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “High-resolution monochromatic x-ray imaging system based on spherically bent crystals,” Appl. Opt. 37, 5253–5261 (1998).
[CrossRef]

1996

1995

1993

E. Spiller, D. Stearns, M. Krumrey, “Multilayer x-ray mirrors: interfacial roughness, scattering, and image quality,” J. Appl. Phys. 74, 107–118 (1993).
[CrossRef]

1992

E. Spiller, J. Wilczynski, D. Stearns, L. Golub, G. Nystrom, “Imaging performance of multilayer x-ray mirrors,” Appl. Phys. Lett. 61, 1481–1483 (1992).
[CrossRef]

E. Spiller, J. Wilczynski, D. Stearns, L. Golub, G. Nystrom, “Erratum: imaging performance of multilayer x-ray mirrors [Appl. Phys. Lett. 61, 1481 (1992)],” Appl. Phys. Lett. 61, 3195 (1992).

1988

1982

Adams, R. G.

G. R. Bennett, O. L. Landen, R. G. Adams, J. L. Porter, L. E. Ruggles, W. W. Simpson, C. Wakefield, “X-ray imaging techniques on Z using the Z-Beamlet laser,” Rev. Sci. Instrum. 72, 657–662 (2001).
[CrossRef]

Aglitskiy, Y.

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “High-resolution monochromatic x-ray imaging system based on spherically bent crystals,” Appl. Opt. 37, 5253–5261 (1998).
[CrossRef]

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “The use of spherically bent crystals for the Nike laser plasmas spectral diagnostics and monochromatic imaging,” in Applications of X Rays Generated from Lasers and Other Bright Sources, G. A. Kyrala, J. C. J. Gauthier, eds., Proc. SPIE3157, 104–115 (1997).
[CrossRef]

Babish, R.

A. Slomba, R. Babish, P. Glenn, “Mirror surface metrology and polishing for AXAF/TMA,” in X-Ray Instrumentation in Astronomy, J. L. Culhane, ed., Proc. SPIE597, 40–54 (1985).
[CrossRef]

Bajt, S.

C. Montcalm, S. Bajt, P. B. Mirkarimi, E. Spiller, F. J. Weber, J. A. Folta, “Multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies II, Y. Vladimirsky, ed., Proc. SPIE3331, 42–51 (1998).
[CrossRef]

J. A. Folta, S. Bajt, T. W. Barbee, R. F. Grabner, P. B. Mirkarimi, T. Nguyen, M. A. Schmidt, E. Spiller, C. C. Walton, M. Wedowski, C. Montcalm, “Advances in multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 702–709 (1999).
[CrossRef]

Barbee, T. W.

J. A. Folta, S. Bajt, T. W. Barbee, R. F. Grabner, P. B. Mirkarimi, T. Nguyen, M. A. Schmidt, E. Spiller, C. C. Walton, M. Wedowski, C. Montcalm, “Advances in multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 702–709 (1999).
[CrossRef]

Bennett, G. R.

G. R. Bennett, O. L. Landen, R. G. Adams, J. L. Porter, L. E. Ruggles, W. W. Simpson, C. Wakefield, “X-ray imaging techniques on Z using the Z-Beamlet laser,” Rev. Sci. Instrum. 72, 657–662 (2001).
[CrossRef]

G. R. Bennett, “Advanced laser-backlit grazing-incidence x-ray imaging systems for inertial confinement fusion research. I. Design,” Appl. Opt. 40, 4570–4587 (2001).
[CrossRef]

Bennett, J. M.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, Washington, D.C., 1999).

Bodner, S.

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “High-resolution monochromatic x-ray imaging system based on spherically bent crystals,” Appl. Opt. 37, 5253–5261 (1998).
[CrossRef]

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “The use of spherically bent crystals for the Nike laser plasmas spectral diagnostics and monochromatic imaging,” in Applications of X Rays Generated from Lasers and Other Bright Sources, G. A. Kyrala, J. C. J. Gauthier, eds., Proc. SPIE3157, 104–115 (1997).
[CrossRef]

Breeze, S. P.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Brown, C. M.

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “High-resolution monochromatic x-ray imaging system based on spherically bent crystals,” Appl. Opt. 37, 5253–5261 (1998).
[CrossRef]

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “The use of spherically bent crystals for the Nike laser plasmas spectral diagnostics and monochromatic imaging,” in Applications of X Rays Generated from Lasers and Other Bright Sources, G. A. Kyrala, J. C. J. Gauthier, eds., Proc. SPIE3157, 104–115 (1997).
[CrossRef]

Chandler, G. A.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Deeney, C.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Douglas, M. R.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Fehl, D. L.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Feldman, U.

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “High-resolution monochromatic x-ray imaging system based on spherically bent crystals,” Appl. Opt. 37, 5253–5261 (1998).
[CrossRef]

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “The use of spherically bent crystals for the Nike laser plasmas spectral diagnostics and monochromatic imaging,” in Applications of X Rays Generated from Lasers and Other Bright Sources, G. A. Kyrala, J. C. J. Gauthier, eds., Proc. SPIE3157, 104–115 (1997).
[CrossRef]

Folta, J. A.

C. Montcalm, S. Bajt, P. B. Mirkarimi, E. Spiller, F. J. Weber, J. A. Folta, “Multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies II, Y. Vladimirsky, ed., Proc. SPIE3331, 42–51 (1998).
[CrossRef]

J. A. Folta, S. Bajt, T. W. Barbee, R. F. Grabner, P. B. Mirkarimi, T. Nguyen, M. A. Schmidt, E. Spiller, C. C. Walton, M. Wedowski, C. Montcalm, “Advances in multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 702–709 (1999).
[CrossRef]

C. Montcalm, E. Spiller, M. Wedowski, E. M. Gullikson, J. A. Folta, “Multilayer coating of 10× projection optics for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 710–716 (1999).
[CrossRef]

Gerber, K.

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “High-resolution monochromatic x-ray imaging system based on spherically bent crystals,” Appl. Opt. 37, 5253–5261 (1998).
[CrossRef]

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “The use of spherically bent crystals for the Nike laser plasmas spectral diagnostics and monochromatic imaging,” in Applications of X Rays Generated from Lasers and Other Bright Sources, G. A. Kyrala, J. C. J. Gauthier, eds., Proc. SPIE3157, 104–115 (1997).
[CrossRef]

Gilliland, T. L.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Glenn, P.

T. T. Saha, D. B. Leviton, P. Glenn, “Performance of ion-figured silicon carbide SUMER telescope mirror in the vacuum ultraviolet,” Appl. Opt. 35, 1742–1750 (1996).
[CrossRef] [PubMed]

R. J. Knoll, P. Glenn, “Mirror surface autocovariance functions and their associated visible scattering,” Appl. Opt. 21, 1824–1838 (1982).
[CrossRef]

P. Glenn, “Robust, sub-angstrom level mid spatial frequency profilometry,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 175–182 (1990).
[CrossRef]

P. Glenn, “Robust, angstrom level circularity profilometry,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 230–238 (1990).
[CrossRef]

P. Glenn, “Lambda-over-one-thousand metrology results for steep aspheres using a curvature profiling technique,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. SPIE1531, 54–61 (1992).
[CrossRef]

A. Slomba, R. Babish, P. Glenn, “Mirror surface metrology and polishing for AXAF/TMA,” in X-Ray Instrumentation in Astronomy, J. L. Culhane, ed., Proc. SPIE597, 40–54 (1985).
[CrossRef]

P. Glenn, “Angstrom level profilometry for sub-millimeter to meter scale surface errors,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 326–336 (1990).
[CrossRef]

Glenn, P. E.

P. E. Glenn, Bauer Associates, Inc., Suite 30, 888 Worcester Street, Wellesley, Massachusetts 02482-3717 (personal communications, 1999–2000).

Golub, L.

E. Spiller, J. Wilczynski, D. Stearns, L. Golub, G. Nystrom, “Imaging performance of multilayer x-ray mirrors,” Appl. Phys. Lett. 61, 1481–1483 (1992).
[CrossRef]

E. Spiller, J. Wilczynski, D. Stearns, L. Golub, G. Nystrom, “Erratum: imaging performance of multilayer x-ray mirrors [Appl. Phys. Lett. 61, 1481 (1992)],” Appl. Phys. Lett. 61, 3195 (1992).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Grabner, R. F.

J. A. Folta, S. Bajt, T. W. Barbee, R. F. Grabner, P. B. Mirkarimi, T. Nguyen, M. A. Schmidt, E. Spiller, C. C. Walton, M. Wedowski, C. Montcalm, “Advances in multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 702–709 (1999).
[CrossRef]

Gullikson, E. M.

C. Montcalm, E. Spiller, M. Wedowski, E. M. Gullikson, J. A. Folta, “Multilayer coating of 10× projection optics for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 710–716 (1999).
[CrossRef]

Harvey, J. E.

Holland, G.

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “High-resolution monochromatic x-ray imaging system based on spherically bent crystals,” Appl. Opt. 37, 5253–5261 (1998).
[CrossRef]

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “The use of spherically bent crystals for the Nike laser plasmas spectral diagnostics and monochromatic imaging,” in Applications of X Rays Generated from Lasers and Other Bright Sources, G. A. Kyrala, J. C. J. Gauthier, eds., Proc. SPIE3157, 104–115 (1997).
[CrossRef]

Jobe, D. O.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Knoll, R. J.

Kotha, A.

Krumrey, M.

E. Spiller, D. Stearns, M. Krumrey, “Multilayer x-ray mirrors: interfacial roughness, scattering, and image quality,” J. Appl. Phys. 74, 107–118 (1993).
[CrossRef]

Landen, O. L.

G. R. Bennett, O. L. Landen, R. G. Adams, J. L. Porter, L. E. Ruggles, W. W. Simpson, C. Wakefield, “X-ray imaging techniques on Z using the Z-Beamlet laser,” Rev. Sci. Instrum. 72, 657–662 (2001).
[CrossRef]

Lauer, M.

M. Lauer, Research Electro-Optics, Inc., 1855 South 57th Court, Boulder, Colorado 80301 (personal communications, 1997–2000).

Lehecka, T.

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “High-resolution monochromatic x-ray imaging system based on spherically bent crystals,” Appl. Opt. 37, 5253–5261 (1998).
[CrossRef]

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “The use of spherically bent crystals for the Nike laser plasmas spectral diagnostics and monochromatic imaging,” in Applications of X Rays Generated from Lasers and Other Bright Sources, G. A. Kyrala, J. C. J. Gauthier, eds., Proc. SPIE3157, 104–115 (1997).
[CrossRef]

Leviton, D. B.

Lewotsky, K. L.

Mattsson, L.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, Washington, D.C., 1999).

Matzen, M. K.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

McDaniel, D. H.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

McGurn, J. S.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

McKenney, J. L.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Mirkarimi, P. B.

C. Montcalm, S. Bajt, P. B. Mirkarimi, E. Spiller, F. J. Weber, J. A. Folta, “Multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies II, Y. Vladimirsky, ed., Proc. SPIE3331, 42–51 (1998).
[CrossRef]

J. A. Folta, S. Bajt, T. W. Barbee, R. F. Grabner, P. B. Mirkarimi, T. Nguyen, M. A. Schmidt, E. Spiller, C. C. Walton, M. Wedowski, C. Montcalm, “Advances in multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 702–709 (1999).
[CrossRef]

Mock, R. C.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Montcalm, C.

C. Montcalm, S. Bajt, P. B. Mirkarimi, E. Spiller, F. J. Weber, J. A. Folta, “Multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies II, Y. Vladimirsky, ed., Proc. SPIE3331, 42–51 (1998).
[CrossRef]

J. A. Folta, S. Bajt, T. W. Barbee, R. F. Grabner, P. B. Mirkarimi, T. Nguyen, M. A. Schmidt, E. Spiller, C. C. Walton, M. Wedowski, C. Montcalm, “Advances in multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 702–709 (1999).
[CrossRef]

C. Montcalm, E. Spiller, M. Wedowski, E. M. Gullikson, J. A. Folta, “Multilayer coating of 10× projection optics for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 710–716 (1999).
[CrossRef]

Moran, E. C.

Nash, T. J.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Nguyen, T.

J. A. Folta, S. Bajt, T. W. Barbee, R. F. Grabner, P. B. Mirkarimi, T. Nguyen, M. A. Schmidt, E. Spiller, C. C. Walton, M. Wedowski, C. Montcalm, “Advances in multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 702–709 (1999).
[CrossRef]

Nystrom, G.

E. Spiller, J. Wilczynski, D. Stearns, L. Golub, G. Nystrom, “Imaging performance of multilayer x-ray mirrors,” Appl. Phys. Lett. 61, 1481–1483 (1992).
[CrossRef]

E. Spiller, J. Wilczynski, D. Stearns, L. Golub, G. Nystrom, “Erratum: imaging performance of multilayer x-ray mirrors [Appl. Phys. Lett. 61, 1481 (1992)],” Appl. Phys. Lett. 61, 3195 (1992).

Obenschain, S.

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “High-resolution monochromatic x-ray imaging system based on spherically bent crystals,” Appl. Opt. 37, 5253–5261 (1998).
[CrossRef]

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “The use of spherically bent crystals for the Nike laser plasmas spectral diagnostics and monochromatic imaging,” in Applications of X Rays Generated from Lasers and Other Bright Sources, G. A. Kyrala, J. C. J. Gauthier, eds., Proc. SPIE3157, 104–115 (1997).
[CrossRef]

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991).

Pawley, C.

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “High-resolution monochromatic x-ray imaging system based on spherically bent crystals,” Appl. Opt. 37, 5253–5261 (1998).
[CrossRef]

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “The use of spherically bent crystals for the Nike laser plasmas spectral diagnostics and monochromatic imaging,” in Applications of X Rays Generated from Lasers and Other Bright Sources, G. A. Kyrala, J. C. J. Gauthier, eds., Proc. SPIE3157, 104–115 (1997).
[CrossRef]

Peterson, D. L.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Porter, J. L.

G. R. Bennett, O. L. Landen, R. G. Adams, J. L. Porter, L. E. Ruggles, W. W. Simpson, C. Wakefield, “X-ray imaging techniques on Z using the Z-Beamlet laser,” Rev. Sci. Instrum. 72, 657–662 (2001).
[CrossRef]

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Ruggles, L. E.

G. R. Bennett, O. L. Landen, R. G. Adams, J. L. Porter, L. E. Ruggles, W. W. Simpson, C. Wakefield, “X-ray imaging techniques on Z using the Z-Beamlet laser,” Rev. Sci. Instrum. 72, 657–662 (2001).
[CrossRef]

Saha, T. T.

Sanford, T. W. L.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Schmidt, M. A.

J. A. Folta, S. Bajt, T. W. Barbee, R. F. Grabner, P. B. Mirkarimi, T. Nguyen, M. A. Schmidt, E. Spiller, C. C. Walton, M. Wedowski, C. Montcalm, “Advances in multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 702–709 (1999).
[CrossRef]

Seamen, J. F.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Seely, J.

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “High-resolution monochromatic x-ray imaging system based on spherically bent crystals,” Appl. Opt. 37, 5253–5261 (1998).
[CrossRef]

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “The use of spherically bent crystals for the Nike laser plasmas spectral diagnostics and monochromatic imaging,” in Applications of X Rays Generated from Lasers and Other Bright Sources, G. A. Kyrala, J. C. J. Gauthier, eds., Proc. SPIE3157, 104–115 (1997).
[CrossRef]

Sethian, J.

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “High-resolution monochromatic x-ray imaging system based on spherically bent crystals,” Appl. Opt. 37, 5253–5261 (1998).
[CrossRef]

Y. Aglitskiy, T. Lehecka, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, C. M. Brown, J. Seely, U. Feldman, G. Holland, “The use of spherically bent crystals for the Nike laser plasmas spectral diagnostics and monochromatic imaging,” in Applications of X Rays Generated from Lasers and Other Bright Sources, G. A. Kyrala, J. C. J. Gauthier, eds., Proc. SPIE3157, 104–115 (1997).
[CrossRef]

Simpson, W. W.

G. R. Bennett, O. L. Landen, R. G. Adams, J. L. Porter, L. E. Ruggles, W. W. Simpson, C. Wakefield, “X-ray imaging techniques on Z using the Z-Beamlet laser,” Rev. Sci. Instrum. 72, 657–662 (2001).
[CrossRef]

Slomba, A.

A. Slomba, R. Babish, P. Glenn, “Mirror surface metrology and polishing for AXAF/TMA,” in X-Ray Instrumentation in Astronomy, J. L. Culhane, ed., Proc. SPIE597, 40–54 (1985).
[CrossRef]

Smith, W. J.

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems, 2nd ed. (McGraw-Hill, New York, 1990).

Spielman, R. B.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Spiller, E.

E. Spiller, D. Stearns, M. Krumrey, “Multilayer x-ray mirrors: interfacial roughness, scattering, and image quality,” J. Appl. Phys. 74, 107–118 (1993).
[CrossRef]

E. Spiller, J. Wilczynski, D. Stearns, L. Golub, G. Nystrom, “Imaging performance of multilayer x-ray mirrors,” Appl. Phys. Lett. 61, 1481–1483 (1992).
[CrossRef]

E. Spiller, J. Wilczynski, D. Stearns, L. Golub, G. Nystrom, “Erratum: imaging performance of multilayer x-ray mirrors [Appl. Phys. Lett. 61, 1481 (1992)],” Appl. Phys. Lett. 61, 3195 (1992).

C. Montcalm, S. Bajt, P. B. Mirkarimi, E. Spiller, F. J. Weber, J. A. Folta, “Multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies II, Y. Vladimirsky, ed., Proc. SPIE3331, 42–51 (1998).
[CrossRef]

C. Montcalm, E. Spiller, M. Wedowski, E. M. Gullikson, J. A. Folta, “Multilayer coating of 10× projection optics for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 710–716 (1999).
[CrossRef]

J. A. Folta, S. Bajt, T. W. Barbee, R. F. Grabner, P. B. Mirkarimi, T. Nguyen, M. A. Schmidt, E. Spiller, C. C. Walton, M. Wedowski, C. Montcalm, “Advances in multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 702–709 (1999).
[CrossRef]

Stearns, D.

E. Spiller, D. Stearns, M. Krumrey, “Multilayer x-ray mirrors: interfacial roughness, scattering, and image quality,” J. Appl. Phys. 74, 107–118 (1993).
[CrossRef]

E. Spiller, J. Wilczynski, D. Stearns, L. Golub, G. Nystrom, “Imaging performance of multilayer x-ray mirrors,” Appl. Phys. Lett. 61, 1481–1483 (1992).
[CrossRef]

E. Spiller, J. Wilczynski, D. Stearns, L. Golub, G. Nystrom, “Erratum: imaging performance of multilayer x-ray mirrors [Appl. Phys. Lett. 61, 1481 (1992)],” Appl. Phys. Lett. 61, 3195 (1992).

Stover, J. C.

J. C. Stover, Optical Scattering, Measurement and Analysis (McGraw-Hill, New York, 1990).

Struve, K. W.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Stygar, W. A.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Thompson, P. L.

P. L. Thompson, J. E. Harvey, “Systems engineering analysis of aplantic Wolter type I x-ray telescope,” Opt. Eng. 36, 1677–1691 (2000).
[CrossRef]

Torres, J. A.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Vargas, M.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Wagoner, T.

R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, D. L. Peterson, “Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ,” Phys. Plasmas 5, 2105–2111 (1998).
[CrossRef]

Wakefield, C.

G. R. Bennett, O. L. Landen, R. G. Adams, J. L. Porter, L. E. Ruggles, W. W. Simpson, C. Wakefield, “X-ray imaging techniques on Z using the Z-Beamlet laser,” Rev. Sci. Instrum. 72, 657–662 (2001).
[CrossRef]

Walton, C. C.

J. A. Folta, S. Bajt, T. W. Barbee, R. F. Grabner, P. B. Mirkarimi, T. Nguyen, M. A. Schmidt, E. Spiller, C. C. Walton, M. Wedowski, C. Montcalm, “Advances in multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 702–709 (1999).
[CrossRef]

Weber, F. J.

C. Montcalm, S. Bajt, P. B. Mirkarimi, E. Spiller, F. J. Weber, J. A. Folta, “Multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies II, Y. Vladimirsky, ed., Proc. SPIE3331, 42–51 (1998).
[CrossRef]

Wedowski, M.

J. A. Folta, S. Bajt, T. W. Barbee, R. F. Grabner, P. B. Mirkarimi, T. Nguyen, M. A. Schmidt, E. Spiller, C. C. Walton, M. Wedowski, C. Montcalm, “Advances in multilayer reflective coatings for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 702–709 (1999).
[CrossRef]

C. Montcalm, E. Spiller, M. Wedowski, E. M. Gullikson, J. A. Folta, “Multilayer coating of 10× projection optics for extreme-ultraviolet lithography,” in Emerging Lithographic Technologies III, Y. Vladimirsky, ed., Proc. SPIE3676, 710–716 (1999).
[CrossRef]

Wilczynski, J.

E. Spiller, J. Wilczynski, D. Stearns, L. Golub, G. Nystrom, “Imaging performance of multilayer x-ray mirrors,” Appl. Phys. Lett. 61, 1481–1483 (1992).
[CrossRef]

E. Spiller, J. Wilczynski, D. Stearns, L. Golub, G. Nystrom, “Erratum: imaging performance of multilayer x-ray mirrors [Appl. Phys. Lett. 61, 1481 (1992)],” Appl. Phys. Lett. 61, 3195 (1992).

Zagar, D. M.

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Figures (11)

Fig. 1
Fig. 1

The four grazing-incidence mirrors (grazing angles and radii of curvature not shown) of the 2-D KB microscope are in optical contact with a large, flat fused-silica base, manufactured from the same material as the mirrors. A second fused-silica slab is in contact with the first to provide a precise right angle against which the mirrors rest. The slabs and mirrors should be thick enough to negate the bending effects of gravity.

Fig. 2
Fig. 2

(a) Figure error measured along a thin, 20-mm-length segment of a spherical concave superpolished mirror of 25 mm × 30 mm full aperture and 1200-mm radius of curvature. The 1-D error was measured with a Bauer Associates, Inc., Model 100 profilometer11-16 in an arbitrary direction. In the KB grazing-incidence configuration, any one mirror is illuminated only along an extremely thin strip. Therefore metrology is required in one dimension only. In this regard, (a) shows a 1-D surface that is <λ/150 peak to valley (λ = 6328 Å and the 2nd-order polynomial removed) and <λ/600 rms over 80% of the full aperture diameter. (b) As for (a) but with a 9th-order polynomial fit and a normalized x axis of -1 ≤ x ≤ 1.

Fig. 3
Fig. 3

(a) Spot diagram for the 13.1-keV 2-D KB microscope optimized over a 400 µm × 400 µm object field. Full design details are described in the companion paper.1 With the aperture stop adjusted to attain β = 5/2, a 0.35-µm Rayleigh criterion resolution diffraction limit is obtained in each plane. Therefore, after 100× magnification, the first zero of the sinc-squared diffraction PSF occurs about the 70 µm × 70 µm spot diagram edge. (b) The same 2-D KB device but with the inclusion, in all four mirrors in the most damaging combination, of the 9th-order polynomial figure-error fit shown in Fig. 2(b) and described by Eq. (1) but appropriately scaled in length and height. Note that the box has 0.14-mm sides, not 0.07 mm as in (a). (c) As for (b) but with no figure error in the primary mirrors. Note that a considerable spot size decrease is apparent, suggesting that the primary mirror figure errors are significantly more important to image quality than comparable defects in the secondary reflectors. If the mirrors in (b) were corrected by a thin-film correction technique to the level thought possible, only a mid- to high-spatial-frequency microroughness would remain.

Fig. 4
Fig. 4

(a) Thin-film deposition correction A applied to the 1-D figure error of Fig. 2(a), and residual surface error. This correction is almost exactly equivalent to subtracting the 9th-order polynomial fit shown in Fig. 2(b) and described by Eq. (1), from the measured surface profile. The surface error remaining is a mid- to high-spatial-frequency microroughness. (b) As for (a) but for correction B, which is more accurate but harder to achieve. Both corrections are thought to be possible. (c) Comparison of the remaining surface error after either correction A or B has been applied.

Fig. 5
Fig. 5

2-D KB spot diagram including errors in grazing angle, mirror-to-mirror alignment, etc., as described in the text, but with thin-film correction A applied to all mirrors. Therefore the appropriately scaled (in length and height) 9th-order polynomial surface error is not included. The most detrimental combination of grazing angle and radius measurement errors in both the tangential and the sagittal planes is used. Rigid body motion–induced grazing-angle errors are negligible compared with those of the mirrors and are therefore omitted. Although they are increased by ∼2.5× compared with those in Fig. 3(a), the 35-µm full width blur spots are still significantly smaller than the 70 µm × 70 µm zero contour of the diffraction PSF. Also, the optical path difference of each spot is <λ/4. This implies that the system can be approximately modeled by use of the product of the diffraction and scattering MTF components.

Fig. 6
Fig. 6

Flow chart for some of the 2-D KB microscope fabrication and performance prediction steps. The 2-D KB device is described in the companion paper.1 The tolerances shown result in an ∼2.5× increase in spot size. The most important error is in the product Rθ. Large increases in the other tolerances shown may only marginally increase spot size or in fact have no detectable effect. After the ray-tracing design steps described in Ref. 1 have been completed, mirrors A–D would be fabricated to the specified grazing angles, radii, etc. Then the radii of curvature would be measured to 0.003–0.03% precision and the values would be used in the real radius optimization step, as described in the text. Following this, 1-D profilometry along the relevant mirror segments would be performed, and then thin-film correction A would be used to remove the large-spatial-period figure errors.

Fig. 7
Fig. 7

Error budget tree of the 2-D KB tangential focusing plane. The corresponding tree for the independent and orthogonal sagittal plane is essentially identical. As the defects are independent and uncorrelated, each error contributes to an increase in the geometric spot size through a RSS accumulation. To restrict the unperturbed 14-µm spot size to a <2.5× enlargement, thereby ensuring an essentially diffraction-limited PSF, the allowable RSS spot size increase is ∼21 µm. As shown, the resulting RSS increase is 9 µm, implying that there is ∼19 µm of reserve. From the error tree it is evident that the dominant defect is in the Rθ product of the primary mirrors. Note that all the tolerances are realistic from a manufacturing point of view.

Fig. 8
Fig. 8

Like Fig. 3(c) but with a 2.86× height scaling in mirror B and no figure error in mirrors A, C, and D (the tangential and sagittal primaries and the sagittal secondary). Thus the tangential secondary reflector, mirror B, has a departure from spherical equal to the 9th-order polynomial shown in Fig. 2(b), and described by Eq. (1) but increased in height by 10× and scaled to cover a 70-mm length. The two lower spot diagrams indicate a tangential resolution better than the otherwise pure spheric-based 2-D KB configuration of Fig. 3(a). This result may suggest that, with suitable thin-film deposition alterations, the secondary mirrors could be transformed into high-quality aspheres for possibly improved resolution. The primary mirrors could remain spherical, or for perhaps even higher resolution they could be transformed into aspherics.

Fig. 9
Fig. 9

(a) Solid curve, ACV of the sample mirror’s measured figure error, i.e., the ACV of the figure error plotted in Fig. 2(a), after the 2nd-order polynomial, best sphere has been removed. (b) Solid curve, ACV of the data in Fig. 2(a) after the 9th-order polynomial best fit has been removed. The fits in (a) and (b) were obtained over 0–10 and 0–5-mm shifts and are described by Eqs. (6) and (7), respectively.

Fig. 10
Fig. 10

(a) MTF of the 1-D KB x-ray microscope as a function of normalized spatial frequency. In the object plane the maximum imaging spatial frequency, limited by diffraction, is 1/0.30 µm-1 (reciprocal of the object plane Rayleigh criterion diffraction limit). Solid line, response for perfectly smooth mirrors, the pure diffraction limit. Long-dashed curve, product of Eqs. (14)(15)(16), where σhigh = 1.06 Å, l high′ = 10 µm, σmid = 1.28 Å, l mid = 5.21 mm, and a mid = 6.49 mm. Short-dashed curve, product of Eqs. (14) and (15) only; i.e., diffraction omitted. Application of the thin-film correction layer and the multilayer coating may slightly increase the high-spatial-frequency microroughness. The effects of pessimistically doubling σhigh to 2.12 Å are shown in (b), where solid, long-dashed, and short-dashed curves have the same meaning as in (a). Reasonable changes in the high-spatial-frequency correlation length l high will not affect the MTF in the area of interest. In both (a) and (b) the MTF is >20% at a normalized spatial frequency of 0.6. This implies >20% contrast for a spatial period of 0.5 µm in length, i.e. <0.5-µm spatial resolution.

Fig. 11
Fig. 11

Same as Fig. 10(a) but with the exit pupil size increased by 10×; i.e., 2w = 238.1 µm. If l mid is not significantly less than the length of the mirror being illuminated, the statistical argument from which the transfer function is derived is no longer valid (see Appendix A). With illumination lengths of ∼12 and ∼5 mm for mirrors A and B of the 1-D KB microscope and l high = 5.21 mm, it would appear that the MTFs of Fig. 10 are not precise. However, with mirror lengths increased to 120 and 50 mm by means of 10× enlargement of the exit pupil, the resultant statistically correct MTF indicates only slightly reduced performance. Therefore this modified MTF provides a lower bound to performance because scatter degradation effects are reduced with decreasing exit-pupil size.

Equations (57)

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zx=-5.7239-20.05x+92.27x2+428.07x3-266.58x4-1393.4x5+277.65x6+1607.6x7-102.34x8-643.21x9,
Hfx, fy=Hdifffx, fyHmidfx, fyHhighfx, fy,
Hscatterfx, fy=Hmidfx, fyHhighfx, fy,
Hmidfx, fy=exp-4πσmidλsin θ2×1-ACVmidλzifx2+λzifysin θ21/2σmid-2,
Hhighfx, fy=exp-4πσhighλsin θ2×1-ACVhighλzifx2+λzifysin θ21/2σhigh-2,
ACVt1, t2=EUt1Ut2-EUt1EUt2.
ACVλzifx, λzifz=EUλzifx2, λzifz2×U-λzifx2, -λzifz2.
λzifx2+λzify21/2.
ACVx, y=EUx2, y2U-x2, -y2=EUx, yU0, 0
ACVr=EUrU0.
ACVm=1N-mn=1N-m znzn+m,
n=1Nzn=0, ACV0=1Nn=1N zn2=σ2=σmid2+σhigh2,
ACVr=σ2 exp-r/bcos-r/c,
ACVr=σ9th2 exp-r/b9thcos-r/c9th,
ACVmidr=σmid2 exp-r/lmidcos-r/amid,
Hhighfx, fy=exp-4πσhighλsin θA2×1 - ACVhighλzifxUA+VA+VB/UA2+λzifyVB/VAsin θA21/2σhigh-2×exp-4πσhighλsin θB2×1 - ACVhigh(λzifx)2+λzifysin θB21/2σhigh-2,
Hmidfx, fy=exp-4πσmidλsin θA2×1-ACVmidλzifxUA+VA+VB/UA2+λzifyVB/VAsin θA21/2σmid-2×exp-4πσmidλsin θB2×1-ACVmidλzifx2+λzifysin θB21/2σmid-2,
Hmidε=exp-4πσmidλsin θA2×1-ACVmidε2wVB/VAsin θAσmid-2×exp-4πσmidλsin θB2×1-ACVmidε2wsin θBσmid-2,
Hhighε=exp-4πσhighλsin θA2×1-ACVhighε2wVB/VAsin θAσhigh-2×exp-4πσhighλsin θB2×1-ACVhighε2wsin θBσhigh-2,
ACVhighr=σhigh2 exp-r/lhigh,
Hhighε=exp-4πσhighλsin θA2×1-exp-ε2wVB/VAlhigh sin θA× exp-4πσhighλsin θB2×1-exp-ε2wlhigh sin θB.
Hmidε=exp-4πσmidλsin θA2×1-exp-ε2wVB/VAlmid sin θA×cos-ε2wVB/VAamid sin θA×exp-4πσmidλsin θB2×1-exp-ε2wlmid sin θB×cos-ε2wamid sin θB,
Hdiffε=1-ε,  0ε1,
Stan=exp-4πλ2σmid2+σhigh2×sin2 θA+sin2 θB,
Stan=exp-4πλ2σmid2+σhigh2)×(sin2 θC+sin2 θD.
Px, y=px, yexpikWx, y.
Hfx, fy=Afx,fy expikW1-W2dxdyA0,0dxdy,
W1=Wx+λzifx/2, y+λzify/2, W2=Wx-λzifx/2, y-λzify/2,
Hfx, fy=EAfx,fy expikW1-W2×expi2kU1-U2dxdyA0,0dxdy,
λzifx2+λzify21/2.
Eexpi2kU1-U2
Hfx, fy=Hscatterfx, fyHopticfx, fy,
Hscatterfx, fy=Eexpi2kU1-U2,
Hopticfx, fy=Afx,fy expikW1-W2dxdyA0,0dxdy.
fu1, u2=12πσ1σ21-r21/2exp-121-r2×u1-η12σ12-2r u1-η1u2-η2σ1σ2+u2-η22σ22,  |r|<1,
fu1, u2=12πσ21-r21/2exp-12σ21-r2×u12-2ru1u2+u22,  |r|<1,
fu1u1=- fu1, u2du2=1σ2πexp-u12/2σ2, fu2u2=- fu1, u2du1=1σ2πexp-u22/2σ2.
Hscatterfx, fy=Eexpi2kZ=-expi2kzfzzdz,
fzz=1σz2πexp-z-ηz2/2σz2Nηz, σz.
fxx=12πexp-x2/2.
Eexpi2kX=12π-expsxexp-x2/2dx,
s=i2k.
Eexpi2kX=12π-exp-x-s2/2dx×exps2/2=exps2/2=exp-2k2.
Eexpi2kZ=Eexpi2kσzX+ηz=exp-2k2σz2expi2kηz.
σz2=EZ-ηz2,
Z-ηz=U1-η1-U2-η2.
σz2=EU1-η1-U2-η22=EU1-η12+U2-η22-2U1-η1U2-η2=σ12+σ22-2rσ2=2σ2-2σ2r,
λzifx2+λzify21/2,
ACVλzifx, λzifz=EUλzifx2, λzifz2×U-λzifx2, -λzifz2.
ACV=σhigh2 exp-λzifxlhigh2+λzifzlhigh21/2+σmid2 exp-λzifxlmid2+λzifzlmid21/2,
σ2=σhigh2+σlow2.
Hscatterfx, fy=exp-4k2σ2-σ2r,
σ2-σ2r=σhigh21-exp-λzifxlhigh2+λzifzlhigh21/2+σmid21-exp-λzifxlmid2+λzifzlmid21/2,
Hhighfx, fy=exp-4πσhighλ2×1-exp-λzifxlhigh2+λzifylhigh21/2,
Hmidfx, fy=exp-4πσmidλ21-exp-λzifxlmid2+λzifylmid21/2
Hfx, fy=EAfx,fy p1p2 expikW1-W2expi2kU1-U2expi2kV1-V2dxdyAfx=0, fy=0 p1p2dxdy,
Eexpi2kU1-U2expi2kV1-V2=Eexpi2kU1-U2Eexpi2kV1-V2.

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