Abstract

By use of a focusing configuration analogous to a Gregorian or a Cassegrain telescope, the on-axis aberration of a grazing-incidence spheric-based Kirkpatrick–Baez compound microscope may be precisely corrected. For finite fields, the off-axis performance degrades too rapidly for high-spatial-resolution imaging of even the smallest objects of interest. However, by use of ray-trace optimization it is possible to perturb the system such that the perfect, but impractical, on-axis performance is modestly degraded and uniformly distributed over a chosen object field. By use of this and other performance-enhancing features, two example ultrahigh-spatial-resolution laser-backlit x-ray microscope designs suitable for inertial confinement fusion (ICF) research have been developed. A companion paper [Appl. Opt. 40, 4588 (2001)] describing the tolerance analysis indicates that <0.5-µm spatial resolution at x-ray energies as high as 25 KeV is possible. As a prototype step, simpler noncompound devices are under consideration for Sandia National Laboratories’ Z accelerator/Z-Beamlet ICF facility.

© 2001 Optical Society of America

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2001 (4)

G. R. Bennett, J. A. Folta, “Advanced laser-backlit grazing-incidence x-ray imaging systems for inertial confinement fusion research. II. Tolerance analysis,” Appl. Opt. 40, 4588–4607 (2001).
[CrossRef]

O. L. Landen, D. R. Farley, S. G. Glendinning, L. M. Logory, P. M. Bell, J. A. Koch, F. D. Lee, D. K. Bradley, D. H. Kalantar, C. A. Back, R. E. Turner, “X-ray backlighting for the National Ignition Facility (invited),” Rev. Sci. Instrum. 72, 627–634 (2001).
[CrossRef]

J. Workman, G. A. Kyrala, “X-ray yield scaling studies performed on the OMEGA laser,” Rev. Sci. Instrum. 72, 678–681 (2001).
[CrossRef]

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]

2000 (3)

P. L. Thompson, J. E. Harvey, “Systems engineering analysis of aplantic Wolter type I x-ray telescopes,” Opt. Eng. 39, 1677–1691 (2000).
[CrossRef]

G. R. Bennett, J. M. Wallace, T. J. Murphy, R. E. Chrien, N. D. Delamater, P. L. Gobby, A. A. Hauer, K. A. Klare, J. A. Oertel, R. G. Watt, D. C. Wilson, W. S. Varnum, R. S. Craxton, V. Yu. Glebov, J. D. Schnittman, C. Stoeckl, S. M. Pollaine, R. E. Turner, “Moderate-convergence inertial confinement fusion implosions in tetrahedral hohlraums at Omega,” Phys. Plasmas 7, 2594–2603 (2000).
[CrossRef]

A. S. Bakulin, S. M. Durbin, T. Jach, J. Pedulla, “Fast imaging of hard x rays with a laboratory microscope,” Appl. Opt. 39, 3333–3337 (2000).
[CrossRef]

1999 (3)

T. A. Shelkovenko, S. A. Pikus, A. R. Mingaleev, D. A. Hammer, “Studies of plasmas formation from exploding wires and multiwire arrays using x-ray backlighting,” Rev. Sci. Instrum. 70, 667–670 (1999).
[CrossRef]

S. A. Pikuz, T. A. Shelkovenko, D. B. Sinars, J. B. Greenly, Y. S. Dimant, J. A. Hammer, “Mulitphase foamlike structure of exploding wire cores,” Phys. Rev. Lett. 83, 4313–4316 (1999).
[CrossRef]

L. J. Suter, O. L. Landen, J. I. Koch, “Prospect for fluorescence based imaging/visualization of hydrodynamic systems on the National Ignition Facility,” Rev. Sci. Instrum. 70, 663–666 (1999).
[CrossRef]

1998 (6)

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]

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 keV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (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]

J. A. Koch, O. L. Landen, T. W. Barbee, P. Celliers, L. B. DaSilva, S. G. Glendenning, B. A. Hammel, D. H. Kalantar, C. Brown, J. Seely, G. R. Bennett, W. Hsing, “High-energy x-ray microscopy techniques for laser-fusion plasma research at the National Ignition Facility,” Appl. Opt. 37, 1784–1795 (1998).
[CrossRef]

F. J. Marshall, M. M. Allen, J. P. Knauer, J. A. Oertel, T. Archuleta, “A high-resolution x-ray microscope for laser-driven planar-foil experiments,” Phys. Plasmas 3, 1118–1124 (1998).
[CrossRef]

D. C. Wilson, C. Adams, T. Asaki, G. R. Bennett, P. A. Bradley, S. Caldwell, N. D. Delamater, J. C. Fernandez, L. Foreman, S. R. Goldman, J. K. Hoffer, K. Klare, R. Margevicius, D. S. Montgomery, T. J. Murphy, L. Salazar, J. D. Sheliak, D. P. Smitherman, D. Thoma, J. Wallace, “Los Alamos progress toward achieving DT burn on the National Ignition Facility,” Fusion Technol. 34, 753–759 (1998).

1997 (5)

R. Kodama, H. Shiraga, M. Miyanaga, T. Matsushita, N. Nakai, H. Azechi, K. Mima, “Study of laser-imploded core plasmas with an advanced Kirkpatrick–Baez x-ray microscope,” Rev. Sci. Instrum. 68, 824–827 (1997).
[CrossRef]

R. Sauneuf, J. M. Dalmasso, T. Jalinaud, J. P. Le Breton, D. Schirmann, J. P. Marioge, F. Bridou, G. Tissot, J. Y. Clotaire, “Large-field high-resolution x-ray microscope for studying laser plasmas,” Rev. Sci. Instrum. 68, 3412–3420 (1997).
[CrossRef]

J. A. Oertel, “Los Alamos pinhole camera (LAPC): a new flexible x-ray pinhole camera” Rev. Sci. Instrum. 68, 786–788 (1997).
[CrossRef]

C. Brown, J. Seely, U. Feldman, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, A. Mostovych, Y. Aglitskiy, T. Lehecka, G. Holland, “High-resolution x-ray imaging of planar foils irradiated by the Nike KrF laser,” Phys. Plasmas 4, 1397–1401 (1997).
[CrossRef]

C. Brown, J. Seely, U. Feldman, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, V. Serlin, J. Sethian, “X-ray imaging of targets irradiated by the Nike KrF laser,” Rev. Sci. Instrum. 68, 1099–1102 (1997).
[CrossRef]

1996 (3)

1995 (3)

F. J. Marshall, Q. Su, “Quantitative measurements with x-ray microscopes in laser-fusion experiments,” Rev. Sci. Instrum. 66, 725–727 (1995).
[CrossRef]

J. Lindl, “Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain,” Phys. Plasmas 2, 3933–4024 (1995).
[CrossRef]

D. K. Bradley, P. M. Bell, O. L. Landen, J. D. Kilkenny, J. Oertel, “Development and characterization of a pair of 30–40 ps x-ray framing cameras,” Rev. Sci. Instrum. 66, 716–718 (1995).
[CrossRef]

1994 (2)

F. J. Marshall, J. A. Delettrez, R. Epstein, B. Yaakobi, “Diagnosis of laser-target implosions by space-resolved continuum absorption x-ray spectroscopy,” Phys. Rev. E 49, 4381–4390 (1994).
[CrossRef]

C. Welnak, G. Chen, F. Cerrina, “Shadow: a synchrotron radiation and x-ray optics simulation tool,” Nucl. Instrum. Methods A 347, 344–347 (1994).
[CrossRef]

1993 (1)

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 (2)

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).
[CrossRef]

1991 (2)

J. B. Kortright, “Nonspecular x-ray scattering from multilayer structures,” J. Appl. Phys. 70, 3620–3625 (1991).
[CrossRef]

B. A. Remington, S. W. Hann, S. G. Glendinning, J. D. Kilkenny, D. H. Munro, R. J. Wallace, “Large growth Rayleigh–Taylor experiments using shaped laser pulses,” Phys. Rev. Lett. 67, 3259–3262 (1991).
[CrossRef] [PubMed]

1990 (1)

R. J. Ellis, J. E. Trebes, D. W. Phillion, J. D. Kilkenny, S. G. Glendinning, J. D. Wielwald, R. A. Levesque, “Four-frame gated Wolter x-ray microscope,” Rev. Sci. Instrum. 61, 2759–2761 (1990).
[CrossRef]

1986 (3)

J. H. Underwood, “Multilayer mirrors for x-rays and the extreme UV,” Opt. News (March1986), pp. 20–25.

J. H. Underwood, “High-energy x-ray microscopy with multilayer reflectors,” Rev. Sci. Instrum. 57, 2119–2123 (1986).
[CrossRef]

J. H. Underwood, T. W. Barbee, C. Frieber, “X-ray microscope with multilayer mirrors,” Appl. Opt. 25, 1730–1732 (1986).
[CrossRef] [PubMed]

1981 (1)

1952 (3)

J. Dyson, “Optics of the focusing x-ray microscope,” Proc. Phys. Soc. London Sec. B 65, 580–589 (1952).
[CrossRef]

H. Wolter, “Mirror systems with glancing incidence on image producing optics for x-rays,” Ann. Phys. (N.Y.) 10, 94–114 (1952).

H. Wolter, “Generalized Schwarzchild mirror systems with glancing incidence as optics for x-rays,” Ann. Phys. (N.Y.) 10, 286–295 (1952).

1948 (1)

Adams, C.

D. C. Wilson, C. Adams, T. Asaki, G. R. Bennett, P. A. Bradley, S. Caldwell, N. D. Delamater, J. C. Fernandez, L. Foreman, S. R. Goldman, J. K. Hoffer, K. Klare, R. Margevicius, D. S. Montgomery, T. J. Murphy, L. Salazar, J. D. Sheliak, D. P. Smitherman, D. Thoma, J. Wallace, “Los Alamos progress toward achieving DT burn on the National Ignition Facility,” Fusion Technol. 34, 753–759 (1998).

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]

C. Brown, J. Seely, U. Feldman, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, A. Mostovych, Y. Aglitskiy, T. Lehecka, G. Holland, “High-resolution x-ray imaging of planar foils irradiated by the Nike KrF laser,” Phys. Plasmas 4, 1397–1401 (1997).
[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]

Allen, M. M.

F. J. Marshall, M. M. Allen, J. P. Knauer, J. A. Oertel, T. Archuleta, “A high-resolution x-ray microscope for laser-driven planar-foil experiments,” Phys. Plasmas 3, 1118–1124 (1998).
[CrossRef]

Archuleta, T.

F. J. Marshall, M. M. Allen, J. P. Knauer, J. A. Oertel, T. Archuleta, “A high-resolution x-ray microscope for laser-driven planar-foil experiments,” Phys. Plasmas 3, 1118–1124 (1998).
[CrossRef]

Asaki, T.

D. C. Wilson, C. Adams, T. Asaki, G. R. Bennett, P. A. Bradley, S. Caldwell, N. D. Delamater, J. C. Fernandez, L. Foreman, S. R. Goldman, J. K. Hoffer, K. Klare, R. Margevicius, D. S. Montgomery, T. J. Murphy, L. Salazar, J. D. Sheliak, D. P. Smitherman, D. Thoma, J. Wallace, “Los Alamos progress toward achieving DT burn on the National Ignition Facility,” Fusion Technol. 34, 753–759 (1998).

Attwood, D.

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

Azechi, H.

R. Kodama, H. Shiraga, M. Miyanaga, T. Matsushita, N. Nakai, H. Azechi, K. Mima, “Study of laser-imploded core plasmas with an advanced Kirkpatrick–Baez x-ray microscope,” Rev. Sci. Instrum. 68, 824–827 (1997).
[CrossRef]

Back, C. A.

O. L. Landen, D. R. Farley, S. G. Glendinning, L. M. Logory, P. M. Bell, J. A. Koch, F. D. Lee, D. K. Bradley, D. H. Kalantar, C. A. Back, R. E. Turner, “X-ray backlighting for the National Ignition Facility (invited),” Rev. Sci. Instrum. 72, 627–634 (2001).
[CrossRef]

Baez, A. V.

P. Kirkpatrick, A. V. Baez, “Formation of optical images by x-rays,” J. Opt. Soc. Am. 38, 766–774 (1948).
[CrossRef] [PubMed]

A. V. Baez, X-ray Microscopy and Microradiography (Academic, New York, 1957), p. 186.

Bakulin, A. S.

Barbee, T. W.

Bell, P. M.

O. L. Landen, D. R. Farley, S. G. Glendinning, L. M. Logory, P. M. Bell, J. A. Koch, F. D. Lee, D. K. Bradley, D. H. Kalantar, C. A. Back, R. E. Turner, “X-ray backlighting for the National Ignition Facility (invited),” Rev. Sci. Instrum. 72, 627–634 (2001).
[CrossRef]

D. K. Bradley, P. M. Bell, O. L. Landen, J. D. Kilkenny, J. Oertel, “Development and characterization of a pair of 30–40 ps x-ray framing cameras,” Rev. Sci. Instrum. 66, 716–718 (1995).
[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, J. A. Folta, “Advanced laser-backlit grazing-incidence x-ray imaging systems for inertial confinement fusion research. II. Tolerance analysis,” Appl. Opt. 40, 4588–4607 (2001).
[CrossRef]

G. R. Bennett, J. M. Wallace, T. J. Murphy, R. E. Chrien, N. D. Delamater, P. L. Gobby, A. A. Hauer, K. A. Klare, J. A. Oertel, R. G. Watt, D. C. Wilson, W. S. Varnum, R. S. Craxton, V. Yu. Glebov, J. D. Schnittman, C. Stoeckl, S. M. Pollaine, R. E. Turner, “Moderate-convergence inertial confinement fusion implosions in tetrahedral hohlraums at Omega,” Phys. Plasmas 7, 2594–2603 (2000).
[CrossRef]

J. A. Koch, O. L. Landen, T. W. Barbee, P. Celliers, L. B. DaSilva, S. G. Glendenning, B. A. Hammel, D. H. Kalantar, C. Brown, J. Seely, G. R. Bennett, W. Hsing, “High-energy x-ray microscopy techniques for laser-fusion plasma research at the National Ignition Facility,” Appl. Opt. 37, 1784–1795 (1998).
[CrossRef]

D. C. Wilson, C. Adams, T. Asaki, G. R. Bennett, P. A. Bradley, S. Caldwell, N. D. Delamater, J. C. Fernandez, L. Foreman, S. R. Goldman, J. K. Hoffer, K. Klare, R. Margevicius, D. S. Montgomery, T. J. Murphy, L. Salazar, J. D. Sheliak, D. P. Smitherman, D. Thoma, J. Wallace, “Los Alamos progress toward achieving DT burn on the National Ignition Facility,” Fusion Technol. 34, 753–759 (1998).

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]

C. Brown, J. Seely, U. Feldman, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, A. Mostovych, Y. Aglitskiy, T. Lehecka, G. Holland, “High-resolution x-ray imaging of planar foils irradiated by the Nike KrF laser,” Phys. Plasmas 4, 1397–1401 (1997).
[CrossRef]

C. Brown, J. Seely, U. Feldman, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, V. Serlin, J. Sethian, “X-ray imaging of targets irradiated by the Nike KrF laser,” Rev. Sci. Instrum. 68, 1099–1102 (1997).
[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]

Boutin, J.-Y.

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 keV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[CrossRef]

Bradley, D. K.

O. L. Landen, D. R. Farley, S. G. Glendinning, L. M. Logory, P. M. Bell, J. A. Koch, F. D. Lee, D. K. Bradley, D. H. Kalantar, C. A. Back, R. E. Turner, “X-ray backlighting for the National Ignition Facility (invited),” Rev. Sci. Instrum. 72, 627–634 (2001).
[CrossRef]

D. K. Bradley, P. M. Bell, O. L. Landen, J. D. Kilkenny, J. Oertel, “Development and characterization of a pair of 30–40 ps x-ray framing cameras,” Rev. Sci. Instrum. 66, 716–718 (1995).
[CrossRef]

Bradley, P. A.

D. C. Wilson, C. Adams, T. Asaki, G. R. Bennett, P. A. Bradley, S. Caldwell, N. D. Delamater, J. C. Fernandez, L. Foreman, S. R. Goldman, J. K. Hoffer, K. Klare, R. Margevicius, D. S. Montgomery, T. J. Murphy, L. Salazar, J. D. Sheliak, D. P. Smitherman, D. Thoma, J. Wallace, “Los Alamos progress toward achieving DT burn on the National Ignition Facility,” Fusion Technol. 34, 753–759 (1998).

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]

Bridou, F.

R. Sauneuf, J. M. Dalmasso, T. Jalinaud, J. P. Le Breton, D. Schirmann, J. P. Marioge, F. Bridou, G. Tissot, J. Y. Clotaire, “Large-field high-resolution x-ray microscope for studying laser plasmas,” Rev. Sci. Instrum. 68, 3412–3420 (1997).
[CrossRef]

Brown, C.

J. A. Koch, O. L. Landen, T. W. Barbee, P. Celliers, L. B. DaSilva, S. G. Glendenning, B. A. Hammel, D. H. Kalantar, C. Brown, J. Seely, G. R. Bennett, W. Hsing, “High-energy x-ray microscopy techniques for laser-fusion plasma research at the National Ignition Facility,” Appl. Opt. 37, 1784–1795 (1998).
[CrossRef]

C. Brown, J. Seely, U. Feldman, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, A. Mostovych, Y. Aglitskiy, T. Lehecka, G. Holland, “High-resolution x-ray imaging of planar foils irradiated by the Nike KrF laser,” Phys. Plasmas 4, 1397–1401 (1997).
[CrossRef]

C. Brown, J. Seely, U. Feldman, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, V. Serlin, J. Sethian, “X-ray imaging of targets irradiated by the Nike KrF laser,” Rev. Sci. Instrum. 68, 1099–1102 (1997).
[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]

Caldwell, S.

D. C. Wilson, C. Adams, T. Asaki, G. R. Bennett, P. A. Bradley, S. Caldwell, N. D. Delamater, J. C. Fernandez, L. Foreman, S. R. Goldman, J. K. Hoffer, K. Klare, R. Margevicius, D. S. Montgomery, T. J. Murphy, L. Salazar, J. D. Sheliak, D. P. Smitherman, D. Thoma, J. Wallace, “Los Alamos progress toward achieving DT burn on the National Ignition Facility,” Fusion Technol. 34, 753–759 (1998).

Cash, W.

D. Gallagher, W. Cash, S. Jelsma, J. Farmer, “Sub-arcsec x-ray telescope for imaging the solar corona in the 0.25–1.2 keV band,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2805, 121–132 (1996).
[CrossRef]

Cauchon, G.

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 keV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[CrossRef]

Celliers, P.

Cerrina, F.

C. Welnak, G. Chen, F. Cerrina, “Shadow: a synchrotron radiation and x-ray optics simulation tool,” Nucl. Instrum. Methods A 347, 344–347 (1994).
[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]

Chen, G.

C. Welnak, G. Chen, F. Cerrina, “Shadow: a synchrotron radiation and x-ray optics simulation tool,” Nucl. Instrum. Methods A 347, 344–347 (1994).
[CrossRef]

Chrien, R. E.

G. R. Bennett, J. M. Wallace, T. J. Murphy, R. E. Chrien, N. D. Delamater, P. L. Gobby, A. A. Hauer, K. A. Klare, J. A. Oertel, R. G. Watt, D. C. Wilson, W. S. Varnum, R. S. Craxton, V. Yu. Glebov, J. D. Schnittman, C. Stoeckl, S. M. Pollaine, R. E. Turner, “Moderate-convergence inertial confinement fusion implosions in tetrahedral hohlraums at Omega,” Phys. Plasmas 7, 2594–2603 (2000).
[CrossRef]

Clotaire, J. Y.

R. Sauneuf, J. M. Dalmasso, T. Jalinaud, J. P. Le Breton, D. Schirmann, J. P. Marioge, F. Bridou, G. Tissot, J. Y. Clotaire, “Large-field high-resolution x-ray microscope for studying laser plasmas,” Rev. Sci. Instrum. 68, 3412–3420 (1997).
[CrossRef]

Craxton, R. S.

G. R. Bennett, J. M. Wallace, T. J. Murphy, R. E. Chrien, N. D. Delamater, P. L. Gobby, A. A. Hauer, K. A. Klare, J. A. Oertel, R. G. Watt, D. C. Wilson, W. S. Varnum, R. S. Craxton, V. Yu. Glebov, J. D. Schnittman, C. Stoeckl, S. M. Pollaine, R. E. Turner, “Moderate-convergence inertial confinement fusion implosions in tetrahedral hohlraums at Omega,” Phys. Plasmas 7, 2594–2603 (2000).
[CrossRef]

Dalmasso, J. M.

R. Sauneuf, J. M. Dalmasso, T. Jalinaud, J. P. Le Breton, D. Schirmann, J. P. Marioge, F. Bridou, G. Tissot, J. Y. Clotaire, “Large-field high-resolution x-ray microscope for studying laser plasmas,” Rev. Sci. Instrum. 68, 3412–3420 (1997).
[CrossRef]

DaSilva, L. B.

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]

Delamater, N. D.

G. R. Bennett, J. M. Wallace, T. J. Murphy, R. E. Chrien, N. D. Delamater, P. L. Gobby, A. A. Hauer, K. A. Klare, J. A. Oertel, R. G. Watt, D. C. Wilson, W. S. Varnum, R. S. Craxton, V. Yu. Glebov, J. D. Schnittman, C. Stoeckl, S. M. Pollaine, R. E. Turner, “Moderate-convergence inertial confinement fusion implosions in tetrahedral hohlraums at Omega,” Phys. Plasmas 7, 2594–2603 (2000).
[CrossRef]

D. C. Wilson, C. Adams, T. Asaki, G. R. Bennett, P. A. Bradley, S. Caldwell, N. D. Delamater, J. C. Fernandez, L. Foreman, S. R. Goldman, J. K. Hoffer, K. Klare, R. Margevicius, D. S. Montgomery, T. J. Murphy, L. Salazar, J. D. Sheliak, D. P. Smitherman, D. Thoma, J. Wallace, “Los Alamos progress toward achieving DT burn on the National Ignition Facility,” Fusion Technol. 34, 753–759 (1998).

Delettrez, J. A.

F. J. Marshall, J. A. Delettrez, R. Epstein, B. Yaakobi, “Diagnosis of laser-target implosions by space-resolved continuum absorption x-ray spectroscopy,” Phys. Rev. E 49, 4381–4390 (1994).
[CrossRef]

Dhez, P.

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 keV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[CrossRef]

Dimant, Y. S.

S. A. Pikuz, T. A. Shelkovenko, D. B. Sinars, J. B. Greenly, Y. S. Dimant, J. A. Hammer, “Mulitphase foamlike structure of exploding wire cores,” Phys. Rev. Lett. 83, 4313–4316 (1999).
[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]

Durbin, S. M.

Dyson, J.

J. Dyson, “Optics of the focusing x-ray microscope,” Proc. Phys. Soc. London Sec. B 65, 580–589 (1952).
[CrossRef]

Ellis, R. J.

R. J. Ellis, J. E. Trebes, D. W. Phillion, J. D. Kilkenny, S. G. Glendinning, J. D. Wielwald, R. A. Levesque, “Four-frame gated Wolter x-ray microscope,” Rev. Sci. Instrum. 61, 2759–2761 (1990).
[CrossRef]

Epstein, R.

F. J. Marshall, J. A. Delettrez, R. Epstein, B. Yaakobi, “Diagnosis of laser-target implosions by space-resolved continuum absorption x-ray spectroscopy,” Phys. Rev. E 49, 4381–4390 (1994).
[CrossRef]

Farley, D. R.

O. L. Landen, D. R. Farley, S. G. Glendinning, L. M. Logory, P. M. Bell, J. A. Koch, F. D. Lee, D. K. Bradley, D. H. Kalantar, C. A. Back, R. E. Turner, “X-ray backlighting for the National Ignition Facility (invited),” Rev. Sci. Instrum. 72, 627–634 (2001).
[CrossRef]

Farmer, J.

D. Gallagher, W. Cash, S. Jelsma, J. Farmer, “Sub-arcsec x-ray telescope for imaging the solar corona in the 0.25–1.2 keV band,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2805, 121–132 (1996).
[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]

C. Brown, J. Seely, U. Feldman, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, A. Mostovych, Y. Aglitskiy, T. Lehecka, G. Holland, “High-resolution x-ray imaging of planar foils irradiated by the Nike KrF laser,” Phys. Plasmas 4, 1397–1401 (1997).
[CrossRef]

C. Brown, J. Seely, U. Feldman, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, V. Serlin, J. Sethian, “X-ray imaging of targets irradiated by the Nike KrF laser,” Rev. Sci. Instrum. 68, 1099–1102 (1997).
[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]

Fernandez, J. C.

D. C. Wilson, C. Adams, T. Asaki, G. R. Bennett, P. A. Bradley, S. Caldwell, N. D. Delamater, J. C. Fernandez, L. Foreman, S. R. Goldman, J. K. Hoffer, K. Klare, R. Margevicius, D. S. Montgomery, T. J. Murphy, L. Salazar, J. D. Sheliak, D. P. Smitherman, D. Thoma, J. Wallace, “Los Alamos progress toward achieving DT burn on the National Ignition Facility,” Fusion Technol. 34, 753–759 (1998).

Folta, J. A.

Foreman, L.

D. C. Wilson, C. Adams, T. Asaki, G. R. Bennett, P. A. Bradley, S. Caldwell, N. D. Delamater, J. C. Fernandez, L. Foreman, S. R. Goldman, J. K. Hoffer, K. Klare, R. Margevicius, D. S. Montgomery, T. J. Murphy, L. Salazar, J. D. Sheliak, D. P. Smitherman, D. Thoma, J. Wallace, “Los Alamos progress toward achieving DT burn on the National Ignition Facility,” Fusion Technol. 34, 753–759 (1998).

Frieber, C.

Gallagher, D.

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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, “Erratum: imaging performance of multilayer x-ray mirrors [Appl. Phys. Lett. 61, 1481 (1992)],” Appl. Phys. Lett. 61, 3195 (1992).
[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]

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, “Erratum: imaging performance of multilayer x-ray mirrors [Appl. Phys. Lett. 61, 1481 (1992)],” Appl. Phys. Lett. 61, 3195 (1992).
[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]

Stoeckl, C.

G. R. Bennett, J. M. Wallace, T. J. Murphy, R. E. Chrien, N. D. Delamater, P. L. Gobby, A. A. Hauer, K. A. Klare, J. A. Oertel, R. G. Watt, D. C. Wilson, W. S. Varnum, R. S. Craxton, V. Yu. Glebov, J. D. Schnittman, C. Stoeckl, S. M. Pollaine, R. E. Turner, “Moderate-convergence inertial confinement fusion implosions in tetrahedral hohlraums at Omega,” Phys. Plasmas 7, 2594–2603 (2000).
[CrossRef]

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]

Su, Q.

F. J. Marshall, Q. Su, “Quantitative measurements with x-ray microscopes in laser-fusion experiments,” Rev. Sci. Instrum. 66, 725–727 (1995).
[CrossRef]

Suter, L. J.

L. J. Suter, O. L. Landen, J. I. Koch, “Prospect for fluorescence based imaging/visualization of hydrodynamic systems on the National Ignition Facility,” Rev. Sci. Instrum. 70, 663–666 (1999).
[CrossRef]

Takeshi, K.

Thoma, D.

D. C. Wilson, C. Adams, T. Asaki, G. R. Bennett, P. A. Bradley, S. Caldwell, N. D. Delamater, J. C. Fernandez, L. Foreman, S. R. Goldman, J. K. Hoffer, K. Klare, R. Margevicius, D. S. Montgomery, T. J. Murphy, L. Salazar, J. D. Sheliak, D. P. Smitherman, D. Thoma, J. Wallace, “Los Alamos progress toward achieving DT burn on the National Ignition Facility,” Fusion Technol. 34, 753–759 (1998).

Thompson, P. L.

P. L. Thompson, J. E. Harvey, “Systems engineering analysis of aplantic Wolter type I x-ray telescopes,” Opt. Eng. 39, 1677–1691 (2000).
[CrossRef]

J. E. Harvey, P. L. Thompson, “Generalized Wolter type I design for the solar x-ray imager (SXI),” in X-Ray Optics, Instruments, and Missions II, R. B. Hoover, A. B. Walker eds., Proc. SPIE3766, 173–183 (1999).
[CrossRef]

Tissot, G.

R. Sauneuf, J. M. Dalmasso, T. Jalinaud, J. P. Le Breton, D. Schirmann, J. P. Marioge, F. Bridou, G. Tissot, J. Y. Clotaire, “Large-field high-resolution x-ray microscope for studying laser plasmas,” Rev. Sci. Instrum. 68, 3412–3420 (1997).
[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]

Trebes, J. E.

R. J. Ellis, J. E. Trebes, D. W. Phillion, J. D. Kilkenny, S. G. Glendinning, J. D. Wielwald, R. A. Levesque, “Four-frame gated Wolter x-ray microscope,” Rev. Sci. Instrum. 61, 2759–2761 (1990).
[CrossRef]

Troussel, P.

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 keV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[CrossRef]

Turner, R. E.

O. L. Landen, D. R. Farley, S. G. Glendinning, L. M. Logory, P. M. Bell, J. A. Koch, F. D. Lee, D. K. Bradley, D. H. Kalantar, C. A. Back, R. E. Turner, “X-ray backlighting for the National Ignition Facility (invited),” Rev. Sci. Instrum. 72, 627–634 (2001).
[CrossRef]

G. R. Bennett, J. M. Wallace, T. J. Murphy, R. E. Chrien, N. D. Delamater, P. L. Gobby, A. A. Hauer, K. A. Klare, J. A. Oertel, R. G. Watt, D. C. Wilson, W. S. Varnum, R. S. Craxton, V. Yu. Glebov, J. D. Schnittman, C. Stoeckl, S. M. Pollaine, R. E. Turner, “Moderate-convergence inertial confinement fusion implosions in tetrahedral hohlraums at Omega,” Phys. Plasmas 7, 2594–2603 (2000).
[CrossRef]

Underwood, J. H.

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]

Varnum, W. S.

G. R. Bennett, J. M. Wallace, T. J. Murphy, R. E. Chrien, N. D. Delamater, P. L. Gobby, A. A. Hauer, K. A. Klare, J. A. Oertel, R. G. Watt, D. C. Wilson, W. S. Varnum, R. S. Craxton, V. Yu. Glebov, J. D. Schnittman, C. Stoeckl, S. M. Pollaine, R. E. Turner, “Moderate-convergence inertial confinement fusion implosions in tetrahedral hohlraums at Omega,” Phys. Plasmas 7, 2594–2603 (2000).
[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]

Wallace, J.

D. C. Wilson, C. Adams, T. Asaki, G. R. Bennett, P. A. Bradley, S. Caldwell, N. D. Delamater, J. C. Fernandez, L. Foreman, S. R. Goldman, J. K. Hoffer, K. Klare, R. Margevicius, D. S. Montgomery, T. J. Murphy, L. Salazar, J. D. Sheliak, D. P. Smitherman, D. Thoma, J. Wallace, “Los Alamos progress toward achieving DT burn on the National Ignition Facility,” Fusion Technol. 34, 753–759 (1998).

Wallace, J. M.

G. R. Bennett, J. M. Wallace, T. J. Murphy, R. E. Chrien, N. D. Delamater, P. L. Gobby, A. A. Hauer, K. A. Klare, J. A. Oertel, R. G. Watt, D. C. Wilson, W. S. Varnum, R. S. Craxton, V. Yu. Glebov, J. D. Schnittman, C. Stoeckl, S. M. Pollaine, R. E. Turner, “Moderate-convergence inertial confinement fusion implosions in tetrahedral hohlraums at Omega,” Phys. Plasmas 7, 2594–2603 (2000).
[CrossRef]

Wallace, R. J.

B. A. Remington, S. W. Hann, S. G. Glendinning, J. D. Kilkenny, D. H. Munro, R. J. Wallace, “Large growth Rayleigh–Taylor experiments using shaped laser pulses,” Phys. Rev. Lett. 67, 3259–3262 (1991).
[CrossRef] [PubMed]

Watt, R. G.

G. R. Bennett, J. M. Wallace, T. J. Murphy, R. E. Chrien, N. D. Delamater, P. L. Gobby, A. A. Hauer, K. A. Klare, J. A. Oertel, R. G. Watt, D. C. Wilson, W. S. Varnum, R. S. Craxton, V. Yu. Glebov, J. D. Schnittman, C. Stoeckl, S. M. Pollaine, R. E. Turner, “Moderate-convergence inertial confinement fusion implosions in tetrahedral hohlraums at Omega,” Phys. Plasmas 7, 2594–2603 (2000).
[CrossRef]

Welnak, C.

C. Welnak, G. Chen, F. Cerrina, “Shadow: a synchrotron radiation and x-ray optics simulation tool,” Nucl. Instrum. Methods A 347, 344–347 (1994).
[CrossRef]

Wielwald, J. D.

R. J. Ellis, J. E. Trebes, D. W. Phillion, J. D. Kilkenny, S. G. Glendinning, J. D. Wielwald, R. A. Levesque, “Four-frame gated Wolter x-ray microscope,” Rev. Sci. Instrum. 61, 2759–2761 (1990).
[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).
[CrossRef]

Wilson, D. C.

G. R. Bennett, J. M. Wallace, T. J. Murphy, R. E. Chrien, N. D. Delamater, P. L. Gobby, A. A. Hauer, K. A. Klare, J. A. Oertel, R. G. Watt, D. C. Wilson, W. S. Varnum, R. S. Craxton, V. Yu. Glebov, J. D. Schnittman, C. Stoeckl, S. M. Pollaine, R. E. Turner, “Moderate-convergence inertial confinement fusion implosions in tetrahedral hohlraums at Omega,” Phys. Plasmas 7, 2594–2603 (2000).
[CrossRef]

D. C. Wilson, C. Adams, T. Asaki, G. R. Bennett, P. A. Bradley, S. Caldwell, N. D. Delamater, J. C. Fernandez, L. Foreman, S. R. Goldman, J. K. Hoffer, K. Klare, R. Margevicius, D. S. Montgomery, T. J. Murphy, L. Salazar, J. D. Sheliak, D. P. Smitherman, D. Thoma, J. Wallace, “Los Alamos progress toward achieving DT burn on the National Ignition Facility,” Fusion Technol. 34, 753–759 (1998).

Wolter, H.

H. Wolter, “Mirror systems with glancing incidence on image producing optics for x-rays,” Ann. Phys. (N.Y.) 10, 94–114 (1952).

H. Wolter, “Generalized Schwarzchild mirror systems with glancing incidence as optics for x-rays,” Ann. Phys. (N.Y.) 10, 286–295 (1952).

Workman, J.

J. Workman, G. A. Kyrala, “X-ray yield scaling studies performed on the OMEGA laser,” Rev. Sci. Instrum. 72, 678–681 (2001).
[CrossRef]

Yaakobi, B.

F. J. Marshall, J. A. Delettrez, R. Epstein, B. Yaakobi, “Diagnosis of laser-target implosions by space-resolved continuum absorption x-ray spectroscopy,” Phys. Rev. E 49, 4381–4390 (1994).
[CrossRef]

Zagar, D. 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]

Ann. Phys. (N.Y.) (2)

H. Wolter, “Mirror systems with glancing incidence on image producing optics for x-rays,” Ann. Phys. (N.Y.) 10, 94–114 (1952).

H. Wolter, “Generalized Schwarzchild mirror systems with glancing incidence as optics for x-rays,” Ann. Phys. (N.Y.) 10, 286–295 (1952).

Appl. Opt. (8)

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).
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G. R. Bennett, J. A. Folta, “Advanced laser-backlit grazing-incidence x-ray imaging systems for inertial confinement fusion research. II. Tolerance analysis,” Appl. Opt. 40, 4588–4607 (2001).
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J. A. Koch, O. L. Landen, T. W. Barbee, P. Celliers, L. B. DaSilva, S. G. Glendenning, B. A. Hammel, D. H. Kalantar, C. Brown, J. Seely, G. R. Bennett, W. Hsing, “High-energy x-ray microscopy techniques for laser-fusion plasma research at the National Ignition Facility,” Appl. Opt. 37, 1784–1795 (1998).
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J. H. Underwood, T. W. Barbee, C. Frieber, “X-ray microscope with multilayer mirrors,” Appl. Opt. 25, 1730–1732 (1986).
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A. S. Bakulin, S. M. Durbin, T. Jach, J. Pedulla, “Fast imaging of hard x rays with a laboratory microscope,” Appl. Opt. 39, 3333–3337 (2000).
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J. F. Seely, M. P. Kowalski, W. R. Hunter, G. Gutman, “Reflectance of a wideband multilayer x-ray mirror at normal and grazing incidences,” Appl. Opt. 35, 4408–4412 (1996).
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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), and references therein.

Appl. Phys. Lett. (2)

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).
[CrossRef]

Fusion Technol. (1)

D. C. Wilson, C. Adams, T. Asaki, G. R. Bennett, P. A. Bradley, S. Caldwell, N. D. Delamater, J. C. Fernandez, L. Foreman, S. R. Goldman, J. K. Hoffer, K. Klare, R. Margevicius, D. S. Montgomery, T. J. Murphy, L. Salazar, J. D. Sheliak, D. P. Smitherman, D. Thoma, J. Wallace, “Los Alamos progress toward achieving DT burn on the National Ignition Facility,” Fusion Technol. 34, 753–759 (1998).

J. Appl. Phys. (2)

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

J. B. Kortright, “Nonspecular x-ray scattering from multilayer structures,” J. Appl. Phys. 70, 3620–3625 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

Nucl. Instrum. Methods A (1)

C. Welnak, G. Chen, F. Cerrina, “Shadow: a synchrotron radiation and x-ray optics simulation tool,” Nucl. Instrum. Methods A 347, 344–347 (1994).
[CrossRef]

Opt. Eng. (1)

P. L. Thompson, J. E. Harvey, “Systems engineering analysis of aplantic Wolter type I x-ray telescopes,” Opt. Eng. 39, 1677–1691 (2000).
[CrossRef]

Opt. Lett. (1)

Opt. News (1)

J. H. Underwood, “Multilayer mirrors for x-rays and the extreme UV,” Opt. News (March1986), pp. 20–25.

Phys. Plasmas (5)

G. R. Bennett, J. M. Wallace, T. J. Murphy, R. E. Chrien, N. D. Delamater, P. L. Gobby, A. A. Hauer, K. A. Klare, J. A. Oertel, R. G. Watt, D. C. Wilson, W. S. Varnum, R. S. Craxton, V. Yu. Glebov, J. D. Schnittman, C. Stoeckl, S. M. Pollaine, R. E. Turner, “Moderate-convergence inertial confinement fusion implosions in tetrahedral hohlraums at Omega,” Phys. Plasmas 7, 2594–2603 (2000).
[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]

F. J. Marshall, M. M. Allen, J. P. Knauer, J. A. Oertel, T. Archuleta, “A high-resolution x-ray microscope for laser-driven planar-foil experiments,” Phys. Plasmas 3, 1118–1124 (1998).
[CrossRef]

C. Brown, J. Seely, U. Feldman, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, J. Sethian, A. Mostovych, Y. Aglitskiy, T. Lehecka, G. Holland, “High-resolution x-ray imaging of planar foils irradiated by the Nike KrF laser,” Phys. Plasmas 4, 1397–1401 (1997).
[CrossRef]

J. Lindl, “Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain,” Phys. Plasmas 2, 3933–4024 (1995).
[CrossRef]

Phys. Rev. E (1)

F. J. Marshall, J. A. Delettrez, R. Epstein, B. Yaakobi, “Diagnosis of laser-target implosions by space-resolved continuum absorption x-ray spectroscopy,” Phys. Rev. E 49, 4381–4390 (1994).
[CrossRef]

Phys. Rev. Lett. (2)

B. A. Remington, S. W. Hann, S. G. Glendinning, J. D. Kilkenny, D. H. Munro, R. J. Wallace, “Large growth Rayleigh–Taylor experiments using shaped laser pulses,” Phys. Rev. Lett. 67, 3259–3262 (1991).
[CrossRef] [PubMed]

S. A. Pikuz, T. A. Shelkovenko, D. B. Sinars, J. B. Greenly, Y. S. Dimant, J. A. Hammer, “Mulitphase foamlike structure of exploding wire cores,” Phys. Rev. Lett. 83, 4313–4316 (1999).
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J. Dyson, “Optics of the focusing x-ray microscope,” Proc. Phys. Soc. London Sec. B 65, 580–589 (1952).
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Rev. Sci. Instrum. (14)

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 keV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[CrossRef]

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]

O. L. Landen, D. R. Farley, S. G. Glendinning, L. M. Logory, P. M. Bell, J. A. Koch, F. D. Lee, D. K. Bradley, D. H. Kalantar, C. A. Back, R. E. Turner, “X-ray backlighting for the National Ignition Facility (invited),” Rev. Sci. Instrum. 72, 627–634 (2001).
[CrossRef]

J. Workman, G. A. Kyrala, “X-ray yield scaling studies performed on the OMEGA laser,” Rev. Sci. Instrum. 72, 678–681 (2001).
[CrossRef]

L. J. Suter, O. L. Landen, J. I. Koch, “Prospect for fluorescence based imaging/visualization of hydrodynamic systems on the National Ignition Facility,” Rev. Sci. Instrum. 70, 663–666 (1999).
[CrossRef]

R. Kodama, H. Shiraga, M. Miyanaga, T. Matsushita, N. Nakai, H. Azechi, K. Mima, “Study of laser-imploded core plasmas with an advanced Kirkpatrick–Baez x-ray microscope,” Rev. Sci. Instrum. 68, 824–827 (1997).
[CrossRef]

R. Sauneuf, J. M. Dalmasso, T. Jalinaud, J. P. Le Breton, D. Schirmann, J. P. Marioge, F. Bridou, G. Tissot, J. Y. Clotaire, “Large-field high-resolution x-ray microscope for studying laser plasmas,” Rev. Sci. Instrum. 68, 3412–3420 (1997).
[CrossRef]

R. J. Ellis, J. E. Trebes, D. W. Phillion, J. D. Kilkenny, S. G. Glendinning, J. D. Wielwald, R. A. Levesque, “Four-frame gated Wolter x-ray microscope,” Rev. Sci. Instrum. 61, 2759–2761 (1990).
[CrossRef]

F. J. Marshall, Q. Su, “Quantitative measurements with x-ray microscopes in laser-fusion experiments,” Rev. Sci. Instrum. 66, 725–727 (1995).
[CrossRef]

C. Brown, J. Seely, U. Feldman, S. Obenschain, S. Bodner, C. Pawley, K. Gerber, V. Serlin, J. Sethian, “X-ray imaging of targets irradiated by the Nike KrF laser,” Rev. Sci. Instrum. 68, 1099–1102 (1997).
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J. A. Oertel, “Los Alamos pinhole camera (LAPC): a new flexible x-ray pinhole camera” Rev. Sci. Instrum. 68, 786–788 (1997).
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D. K. Bradley, P. M. Bell, O. L. Landen, J. D. Kilkenny, J. Oertel, “Development and characterization of a pair of 30–40 ps x-ray framing cameras,” Rev. Sci. Instrum. 66, 716–718 (1995).
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T. A. Shelkovenko, S. A. Pikus, A. R. Mingaleev, D. A. Hammer, “Studies of plasmas formation from exploding wires and multiwire arrays using x-ray backlighting,” Rev. Sci. Instrum. 70, 667–670 (1999).
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[CrossRef]

http://www.breault.com , Breault Research Organization, Inc., home page.

http://www.xraylith.wisc.edu/shadow/shadow.html/ , Shadow, home page. University of Wisconsin at Madison.

http://www-cxro.lbl.gov/optical_constants/mirror2.html , thick layer reflectivity program. Accessed from the Ernest Orlando Lawrence Berkeley National Laboratory home page.

http://www-cxro.lbl.gov/optical_constants/pert_form.html , x-ray properties of the elements program. Accessed from the Ernest Orlando Lawrence Berkeley National Laboratory home page.

http://www-cxro.lbl.gov/optical_constants/multi2.html , multilayer reflectivity program. Accessed from the Ernest Orlando Lawrence Berkeley National Laboratory home page.

A. V. Baez, X-ray Microscopy and Microradiography (Academic, New York, 1957), p. 186.

http://www-cxro.lbl.gov/data_booklet/ , X-ray Data Booklet. Accessed from the Ernest Orlando Lawrence Berkeley National Laboratory home page.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).

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]

http://lasers.llnl.gov/inertial.html , Inertial Confinement Fusion Program, Lawrence Livermore National Laboratory, home page.

http://www.lanl.gov/ICF/ , Inertial Confinement Fusion and Radiation Physics Program, Los Alamos National Laboratory, home page.

http://www.llnl.gov/nif/index.html , National Ignition Facility, Lawrence Livermore National Laboratory, home page.

http://www.llnl.gov , Lawrence Livermore National Laboratory, home page.

R. Kodama, Institute of Laser Engineering, Osaka University, 2-6 Yamada-Oka, Suita, Osaka 565-0871, Japan (personal communication, October1997).

In this paper the details of how the laser-produced backlighter x rays are generated are not given, although it should be noted that direct laser irradiation of a metallic foil is a commonly used backlighting technique for multi-kiloelectron volt x-ray production.27–29 However, for ICF experiments that rely on self-emission it should be noted that in capsule implosion studies the central gaseous region is often doped with argon to enhance the core brightness. However, for the larger and more opaque NIF capsules, an emitter of higher energy K-shell radiation, for example, krypton, is required. For future backlighting applications that will require improved x-ray conversion efficiency at high photon energies it is notable that a new technique that uses laser-irradiated underdense radiators has been proposed by Suter et al. (Ref. 30 and references therein). Furthermore, a fluorescence-based illumination technique, pumped by underdense radiators or laser-hohlraum hot-corona radiation, has also been suggested.30 Interestingly, the same approach may also be useful for Sandia National Laboratories’ Z accelerator,31,32 for which fluorescence in germanium-doped ICF capsules, for example, could be pumped by the bremsstrahlung background.Although pinhole, curved crystal, and grazing incidence are the most commonly used ICF x-ray imaging techniques, it should be noted that laser-plasma point projection imaging (point source dental x-ray imaging with no actual pinhole or optic), can be a powerful but simple technique. Indeed, the new Z-Beamlet laser backlighter system33,34 at Sandia’s Z accelerator31,32 will be used extensively to point project image both ICF and high-energy density physics experiments. Furthermore, by use of a particularly small point source generated by a pulsed-power x pinch,35 this most simple of imaging techniques is also becoming important for other physics applications in which lower x-ray energies and less-precise timing are acceptable.36 Finally, although diffractive optics27 have been applied to the study of laser-produced plasmas with moderate resolution,37 their most productive use has been in areas unrelated to ICF, for example, x-ray synchrotron microprobes. However, with developments and improvements, diffractive-optic techniques may well become attractive for ICF experiments in the future.

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

http://zpinch.sandia.gov , Z accelerator, Sandia National Laboratories, home page.

http://www.z-beamlet.sandia.gov , Z-Beamlet, Sandia National Laboratories, home page.

H. H. Pattee, in X-Ray Microscopy and Microradiography (Academic, New York, 1957), p. 135.

J. F. McGee, in X-Ray Microscopy and Microradiography (Academic, New York, 1957), p. 164.

D. Gallagher, W. Cash, S. Jelsma, J. Farmer, “Sub-arcsec x-ray telescope for imaging the solar corona in the 0.25–1.2 keV band,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2805, 121–132 (1996).
[CrossRef]

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

http://www.focus-software.com , Focus Software, Inc., home page.

J. E. Harvey, P. L. Thompson, “Generalized Wolter type I design for the solar x-ray imager (SXI),” in X-Ray Optics, Instruments, and Missions II, R. B. Hoover, A. B. Walker eds., Proc. SPIE3766, 173–183 (1999).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Longitudinal and traverse spherical aberration of a concave spherical reflector with magnification M > 1. Equation (1) describes the grazing-incidence spherical aberration to a high degree of accuracy. θ is the principal ray grazing angle and R is the radius of curvature, where R > 0. For M < 1 the traverse departures lie below the optic axis. When both the object and the image lie upon the Rowland circle (circle of radius R/2 with tangent intersecting P as shown) for unity magnification, the spherical aberration is zero. (b) Standard KB configuration of two grazing-incidence mirrors (curvature not shown) placed orthogonally to each other. (c) Type IV configuration, as defined in the text, in which the concave spherical mirrors in both the tangential and the sagittal planes are facing the same way. The aperture stop, which is not shown, is placed between mirrors C and B.

Fig. 2
Fig. 2

The two basic focusing configurations investigated, with the object plane on the left in both cases; mirror curvatures not shown (concave primary and convex secondary for Cassegrain, concave primary and secondary for Gregorian). In the KB configuration the tangential and sagittal planes are essentially optically decoupled; therefore the foci locations are shown for only one of the two planes. The orthogonal plane will have the same basic focal configuration (Gregorian or Cassegrain) and magnification but with different values of U A , V A , U B , and V B . (a) Cassegrain configuration for type II facing; i.e., the mirror normals are pointing in approximately the same direction [type I (opposing) has mirrors’ normals pointing in approximately the opposite directions]; (b) Gregorian for type IV (facing) as shown in Fig. 1(c) [likewise, type III (opposing) has mirrors’ normals pointing in approximately opposite directions].

Fig. 3
Fig. 3

1-D KB on-axis spot diagram for (a) analytical and (b) ray-tracing optimized solutions to spherical-aberration correction (0.4 µm × 0.4 µm cross size). (c) Off-axis performance at the edge of a 0 µm × 500 µm field for a microscope with perfect on-axis performance (500 µm × 500 µm cross size), and (d) the same system but optimized to distribute performance smoothly over 11 equally spaced field points (20 µm × 20 µm cross size). (e) Cf. (d): optimum performance of a single-mirror 1-D KB microscope. In (d) and (e), only the on-axis and two extreme off-axis field points are shown. All other points within the designed field have similar or smaller blur spot sizes.

Fig. 4
Fig. 4

20 µm × 20 µm spot diagram for a 2-D KB microscope optimized over a 400 µm × 400 µm field. Only the four extreme off-axis points are shown. All other points within the designed field have similar blur spot sizes. To attain β = 5/2 the resultant aperture stop size incurs a 0.35-µm object plane Rayleigh criterion resolution diffraction limit.

Fig. 5
Fig. 5

(a) With the aperture stop of the 2-D KB microscope placed 135 mm behind mirror A, the rays illuminating the 400 µm × 400 µm object field appear to come from a large-area backlighter (the cone represents the instrument’s solid angle). However, when the stop is split into two separate orthogonal slits placed 185 and 235 mm behind mirror A for tangential and sagittal planes, respectively, the illuminating rays now appear to come from a backlighter of area smaller than the 400 µm × 400 µm object field. This is not true of course if the source is far away. Thus, if a high-power laser is focused onto a metallic foil in (b), more energy can be concentrated into a smaller area, implying an overall efficiency increase. The same point backlighter technique could be applied to the 1-D KB microscope and also to simpler KB microscopes with one mirror in each plane.

Equations (28)

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Δ=Δα, V, R, θ-3αV2Rθ-VR2θ3,
 Δ=¾αM-1M+1V/θ,
1U+1V=2Rθ=1f,
M=V/U.
S=αΔ/M.
S=34 α2M-1M+1VMθ.
Smax=34N.A.M2M-1M+1Uθ=34λ2γM2M-1M+1Uθ.
βSmax2+λ2N.A.21/2=α/γ4+γ21/2,
α=β 316Uθ λ22,  β1.
opt=3β 332Uθ λ21/3.
optλ1/3.
Hfy=1-γoptfy
=1-β 3216Uθ λ21/3 fy,
MB=UB/VB,
1UB+1VB=2RBθB,  VB<0, RB<0, UB>0 MB<0.
ΔBαB=34 αB1MB-11MB+1VB/θB.
ΔAα+ΔBα=0,
MA-1MA+1VA+1MB-11MB+1VB=0
ΔAα+ΔB-α=0,
MA-1MA+1VA=1MB-11MB+1VB
MA-1MA+1VA+1MB-11MB+1VB=0
MA-1MA+1VA=1MB-11MB+1VB
UB=M MA-1MA+1UAMAM-1MAM+1,
l1+MAUA±MAM+1MMA-1MA+1UA.
l1+MAUA+MAM+1M1-MAMA+1UA,
MA<1,  M  MA  MB  1.
MA-1MA+1VAθA=1MB-11MB+1VBθB
βSmaxMT2+λ2N.A.tan21/2.

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