Abstract

A combined X-ray and optical interferometer capable of centimeter displacements has been made to measure the lattice parameter of Si crystals to within a 3×10-9 relative uncertainty. This paper relates the results of test measurements carried out to assess the capabilities of the apparatus.

© 2008 Optical Society of America

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  1. P. Becker, P. de Biévre, K. Fujii, M. Glaeser, B. Inglis, H. Luebbig, and G. Mana, "Considerations on future redefinitions of the kilogram, the mole and of other units," Metrologia 44, 1-14 (2007).
    [CrossRef]
  2. P. Becker, "Tracing the definition of the kilogram to the Avogadro constant using a silicon single crystal," Metrologia 40, 366-375 (2003).
    [CrossRef]
  3. G. Basile, A. Bergamin, G. Cavagnero, G. Mana, E. Vittone, and G. Zosi, "A measurement of the silicon (220) lattice spacing," Phys. Rev. Lett. 72, 3133-3136 (1994).
    [CrossRef] [PubMed]
  4. A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-ray interferometry and the silicon lattice parameter: towards 10�??9 relative uncertainty?" Eur. Phys. J. B 9, 225-232 (1999).
    [CrossRef]
  5. G. Cavagnero, H. Fujimoto, G. Mana, E. Massa, and K. Nakayama, "Measurement repetitions of the Si(220) lattice spacing," Metrologia 41, 56-64 (2004); ibid. at 445-447 (2204).
    [CrossRef]
  6. P. Becker, G. Cavagnero, U. Kuetgens, G. Mana, and E. Massa, "Confirmation of the INRiM and PTB determinations of the Si lattice parameter," IEEE Trans. Instrum. Meas. 56, (230-234) (2007).
    [CrossRef]
  7. U. Bonse, W. Graeff, and G. Materlik, "X-ray interferometry and lattice parameter investigation," Rev Phys.Appl. 11, 83-87 (1976).
    [CrossRef]
  8. G. Basile, A. Bergamin, G. Cavagnero, G. Mana, and G. Zosi, "Progress at IMGC in the absolute determination of the silicon d220 lattice spacing," IEEE Trans. Instrum. Meas. 38, 210-216 (1989).
    [CrossRef]
  9. P. Becker and G. Mana, "The lattice parameter of silicon: a survey," Metrologia 31, 203-209 (1994).
    [CrossRef]
  10. A. Bergamin, G. Cavagnero, and G. Mana, "A displacement-angle interferometer with sub-atomic resolution," Rev. Sci. Instrum. 64, 3076-3081 (1993).
    [CrossRef]
  11. A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-Ray Interferometry Over a Millimeter Baseline," IEEE Trans. Instru. Meas. 46, 576-579 (1997).
    [CrossRef]
  12. A. Bergamin, G. Cavagnero, G. Durando, G. Mana, and E. Massa, "A two-axis tip-tilt platform for x-ray interferometry," Meas. Sci. Technol. 14, 717723 (2003).
    [CrossRef]
  13. D. Windisch and P. Becker, "Silicon lattice parameter as an absolute scale of length for high precision measurement of fundamental constants," Phys. Stat. Sol. A 118, 379-388 (1990).
    [CrossRef]
  14. H. Siegert and P. Becker, "Systematic uncertainties in the determination of the lattice spacing d(220) in silicon," in Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, eds. Natl. Bur. Stand., Spec. Publ. 617, (U.S. GPO, Washington, 1984), pp. 321-324.
  15. A. Bergamin, G. Cavagnero, L. Cordiali, and G. Mana, "A Fourier optics model of two-beam scanning laser interferometers," Eur. Phys. J. D 5, 433-440 (1999).
    [CrossRef]
  16. G. Mana and E. Vittone, "Scanning LLL X-ray interferometry II. Aberration analysis," Z. Phys. B 102, 197-206 (1997).
    [CrossRef]
  17. A. Bergamin, G. Cavagnero, and G. Mana, "Observation of Fresnel diffraction in a two-beam laser interferometer," Phys. Rev. A 49, 2167-2172 (1994).
    [CrossRef] [PubMed]

2007

P. Becker, P. de Biévre, K. Fujii, M. Glaeser, B. Inglis, H. Luebbig, and G. Mana, "Considerations on future redefinitions of the kilogram, the mole and of other units," Metrologia 44, 1-14 (2007).
[CrossRef]

P. Becker, G. Cavagnero, U. Kuetgens, G. Mana, and E. Massa, "Confirmation of the INRiM and PTB determinations of the Si lattice parameter," IEEE Trans. Instrum. Meas. 56, (230-234) (2007).
[CrossRef]

2003

P. Becker, "Tracing the definition of the kilogram to the Avogadro constant using a silicon single crystal," Metrologia 40, 366-375 (2003).
[CrossRef]

A. Bergamin, G. Cavagnero, G. Durando, G. Mana, and E. Massa, "A two-axis tip-tilt platform for x-ray interferometry," Meas. Sci. Technol. 14, 717723 (2003).
[CrossRef]

1999

A. Bergamin, G. Cavagnero, L. Cordiali, and G. Mana, "A Fourier optics model of two-beam scanning laser interferometers," Eur. Phys. J. D 5, 433-440 (1999).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-ray interferometry and the silicon lattice parameter: towards 10�??9 relative uncertainty?" Eur. Phys. J. B 9, 225-232 (1999).
[CrossRef]

1997

G. Mana and E. Vittone, "Scanning LLL X-ray interferometry II. Aberration analysis," Z. Phys. B 102, 197-206 (1997).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-Ray Interferometry Over a Millimeter Baseline," IEEE Trans. Instru. Meas. 46, 576-579 (1997).
[CrossRef]

1994

A. Bergamin, G. Cavagnero, and G. Mana, "Observation of Fresnel diffraction in a two-beam laser interferometer," Phys. Rev. A 49, 2167-2172 (1994).
[CrossRef] [PubMed]

P. Becker and G. Mana, "The lattice parameter of silicon: a survey," Metrologia 31, 203-209 (1994).
[CrossRef]

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, E. Vittone, and G. Zosi, "A measurement of the silicon (220) lattice spacing," Phys. Rev. Lett. 72, 3133-3136 (1994).
[CrossRef] [PubMed]

1993

A. Bergamin, G. Cavagnero, and G. Mana, "A displacement-angle interferometer with sub-atomic resolution," Rev. Sci. Instrum. 64, 3076-3081 (1993).
[CrossRef]

1990

D. Windisch and P. Becker, "Silicon lattice parameter as an absolute scale of length for high precision measurement of fundamental constants," Phys. Stat. Sol. A 118, 379-388 (1990).
[CrossRef]

1989

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, and G. Zosi, "Progress at IMGC in the absolute determination of the silicon d220 lattice spacing," IEEE Trans. Instrum. Meas. 38, 210-216 (1989).
[CrossRef]

1976

U. Bonse, W. Graeff, and G. Materlik, "X-ray interferometry and lattice parameter investigation," Rev Phys.Appl. 11, 83-87 (1976).
[CrossRef]

Basile, G.

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, E. Vittone, and G. Zosi, "A measurement of the silicon (220) lattice spacing," Phys. Rev. Lett. 72, 3133-3136 (1994).
[CrossRef] [PubMed]

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, and G. Zosi, "Progress at IMGC in the absolute determination of the silicon d220 lattice spacing," IEEE Trans. Instrum. Meas. 38, 210-216 (1989).
[CrossRef]

Becker, P.

P. Becker, P. de Biévre, K. Fujii, M. Glaeser, B. Inglis, H. Luebbig, and G. Mana, "Considerations on future redefinitions of the kilogram, the mole and of other units," Metrologia 44, 1-14 (2007).
[CrossRef]

P. Becker, G. Cavagnero, U. Kuetgens, G. Mana, and E. Massa, "Confirmation of the INRiM and PTB determinations of the Si lattice parameter," IEEE Trans. Instrum. Meas. 56, (230-234) (2007).
[CrossRef]

P. Becker, "Tracing the definition of the kilogram to the Avogadro constant using a silicon single crystal," Metrologia 40, 366-375 (2003).
[CrossRef]

P. Becker and G. Mana, "The lattice parameter of silicon: a survey," Metrologia 31, 203-209 (1994).
[CrossRef]

D. Windisch and P. Becker, "Silicon lattice parameter as an absolute scale of length for high precision measurement of fundamental constants," Phys. Stat. Sol. A 118, 379-388 (1990).
[CrossRef]

Bergamin, A.

A. Bergamin, G. Cavagnero, G. Durando, G. Mana, and E. Massa, "A two-axis tip-tilt platform for x-ray interferometry," Meas. Sci. Technol. 14, 717723 (2003).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-ray interferometry and the silicon lattice parameter: towards 10�??9 relative uncertainty?" Eur. Phys. J. B 9, 225-232 (1999).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, and G. Mana, "A Fourier optics model of two-beam scanning laser interferometers," Eur. Phys. J. D 5, 433-440 (1999).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-Ray Interferometry Over a Millimeter Baseline," IEEE Trans. Instru. Meas. 46, 576-579 (1997).
[CrossRef]

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, E. Vittone, and G. Zosi, "A measurement of the silicon (220) lattice spacing," Phys. Rev. Lett. 72, 3133-3136 (1994).
[CrossRef] [PubMed]

A. Bergamin, G. Cavagnero, and G. Mana, "Observation of Fresnel diffraction in a two-beam laser interferometer," Phys. Rev. A 49, 2167-2172 (1994).
[CrossRef] [PubMed]

A. Bergamin, G. Cavagnero, and G. Mana, "A displacement-angle interferometer with sub-atomic resolution," Rev. Sci. Instrum. 64, 3076-3081 (1993).
[CrossRef]

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, and G. Zosi, "Progress at IMGC in the absolute determination of the silicon d220 lattice spacing," IEEE Trans. Instrum. Meas. 38, 210-216 (1989).
[CrossRef]

Bonse, U.

U. Bonse, W. Graeff, and G. Materlik, "X-ray interferometry and lattice parameter investigation," Rev Phys.Appl. 11, 83-87 (1976).
[CrossRef]

Cavagnero, G.

P. Becker, G. Cavagnero, U. Kuetgens, G. Mana, and E. Massa, "Confirmation of the INRiM and PTB determinations of the Si lattice parameter," IEEE Trans. Instrum. Meas. 56, (230-234) (2007).
[CrossRef]

A. Bergamin, G. Cavagnero, G. Durando, G. Mana, and E. Massa, "A two-axis tip-tilt platform for x-ray interferometry," Meas. Sci. Technol. 14, 717723 (2003).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-ray interferometry and the silicon lattice parameter: towards 10�??9 relative uncertainty?" Eur. Phys. J. B 9, 225-232 (1999).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, and G. Mana, "A Fourier optics model of two-beam scanning laser interferometers," Eur. Phys. J. D 5, 433-440 (1999).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-Ray Interferometry Over a Millimeter Baseline," IEEE Trans. Instru. Meas. 46, 576-579 (1997).
[CrossRef]

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, E. Vittone, and G. Zosi, "A measurement of the silicon (220) lattice spacing," Phys. Rev. Lett. 72, 3133-3136 (1994).
[CrossRef] [PubMed]

A. Bergamin, G. Cavagnero, and G. Mana, "Observation of Fresnel diffraction in a two-beam laser interferometer," Phys. Rev. A 49, 2167-2172 (1994).
[CrossRef] [PubMed]

A. Bergamin, G. Cavagnero, and G. Mana, "A displacement-angle interferometer with sub-atomic resolution," Rev. Sci. Instrum. 64, 3076-3081 (1993).
[CrossRef]

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, and G. Zosi, "Progress at IMGC in the absolute determination of the silicon d220 lattice spacing," IEEE Trans. Instrum. Meas. 38, 210-216 (1989).
[CrossRef]

Cordiali, L.

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-ray interferometry and the silicon lattice parameter: towards 10�??9 relative uncertainty?" Eur. Phys. J. B 9, 225-232 (1999).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, and G. Mana, "A Fourier optics model of two-beam scanning laser interferometers," Eur. Phys. J. D 5, 433-440 (1999).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-Ray Interferometry Over a Millimeter Baseline," IEEE Trans. Instru. Meas. 46, 576-579 (1997).
[CrossRef]

de Biévre, P.

P. Becker, P. de Biévre, K. Fujii, M. Glaeser, B. Inglis, H. Luebbig, and G. Mana, "Considerations on future redefinitions of the kilogram, the mole and of other units," Metrologia 44, 1-14 (2007).
[CrossRef]

Durando, G.

A. Bergamin, G. Cavagnero, G. Durando, G. Mana, and E. Massa, "A two-axis tip-tilt platform for x-ray interferometry," Meas. Sci. Technol. 14, 717723 (2003).
[CrossRef]

Fujii, K.

P. Becker, P. de Biévre, K. Fujii, M. Glaeser, B. Inglis, H. Luebbig, and G. Mana, "Considerations on future redefinitions of the kilogram, the mole and of other units," Metrologia 44, 1-14 (2007).
[CrossRef]

Glaeser, M.

P. Becker, P. de Biévre, K. Fujii, M. Glaeser, B. Inglis, H. Luebbig, and G. Mana, "Considerations on future redefinitions of the kilogram, the mole and of other units," Metrologia 44, 1-14 (2007).
[CrossRef]

Graeff, W.

U. Bonse, W. Graeff, and G. Materlik, "X-ray interferometry and lattice parameter investigation," Rev Phys.Appl. 11, 83-87 (1976).
[CrossRef]

Inglis, B.

P. Becker, P. de Biévre, K. Fujii, M. Glaeser, B. Inglis, H. Luebbig, and G. Mana, "Considerations on future redefinitions of the kilogram, the mole and of other units," Metrologia 44, 1-14 (2007).
[CrossRef]

Kuetgens, U.

P. Becker, G. Cavagnero, U. Kuetgens, G. Mana, and E. Massa, "Confirmation of the INRiM and PTB determinations of the Si lattice parameter," IEEE Trans. Instrum. Meas. 56, (230-234) (2007).
[CrossRef]

Luebbig, H.

P. Becker, P. de Biévre, K. Fujii, M. Glaeser, B. Inglis, H. Luebbig, and G. Mana, "Considerations on future redefinitions of the kilogram, the mole and of other units," Metrologia 44, 1-14 (2007).
[CrossRef]

Mana, G.

P. Becker, P. de Biévre, K. Fujii, M. Glaeser, B. Inglis, H. Luebbig, and G. Mana, "Considerations on future redefinitions of the kilogram, the mole and of other units," Metrologia 44, 1-14 (2007).
[CrossRef]

P. Becker, G. Cavagnero, U. Kuetgens, G. Mana, and E. Massa, "Confirmation of the INRiM and PTB determinations of the Si lattice parameter," IEEE Trans. Instrum. Meas. 56, (230-234) (2007).
[CrossRef]

A. Bergamin, G. Cavagnero, G. Durando, G. Mana, and E. Massa, "A two-axis tip-tilt platform for x-ray interferometry," Meas. Sci. Technol. 14, 717723 (2003).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-ray interferometry and the silicon lattice parameter: towards 10�??9 relative uncertainty?" Eur. Phys. J. B 9, 225-232 (1999).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, and G. Mana, "A Fourier optics model of two-beam scanning laser interferometers," Eur. Phys. J. D 5, 433-440 (1999).
[CrossRef]

G. Mana and E. Vittone, "Scanning LLL X-ray interferometry II. Aberration analysis," Z. Phys. B 102, 197-206 (1997).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-Ray Interferometry Over a Millimeter Baseline," IEEE Trans. Instru. Meas. 46, 576-579 (1997).
[CrossRef]

P. Becker and G. Mana, "The lattice parameter of silicon: a survey," Metrologia 31, 203-209 (1994).
[CrossRef]

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, E. Vittone, and G. Zosi, "A measurement of the silicon (220) lattice spacing," Phys. Rev. Lett. 72, 3133-3136 (1994).
[CrossRef] [PubMed]

A. Bergamin, G. Cavagnero, and G. Mana, "Observation of Fresnel diffraction in a two-beam laser interferometer," Phys. Rev. A 49, 2167-2172 (1994).
[CrossRef] [PubMed]

A. Bergamin, G. Cavagnero, and G. Mana, "A displacement-angle interferometer with sub-atomic resolution," Rev. Sci. Instrum. 64, 3076-3081 (1993).
[CrossRef]

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, and G. Zosi, "Progress at IMGC in the absolute determination of the silicon d220 lattice spacing," IEEE Trans. Instrum. Meas. 38, 210-216 (1989).
[CrossRef]

Massa, E.

P. Becker, G. Cavagnero, U. Kuetgens, G. Mana, and E. Massa, "Confirmation of the INRiM and PTB determinations of the Si lattice parameter," IEEE Trans. Instrum. Meas. 56, (230-234) (2007).
[CrossRef]

A. Bergamin, G. Cavagnero, G. Durando, G. Mana, and E. Massa, "A two-axis tip-tilt platform for x-ray interferometry," Meas. Sci. Technol. 14, 717723 (2003).
[CrossRef]

Materlik, G.

U. Bonse, W. Graeff, and G. Materlik, "X-ray interferometry and lattice parameter investigation," Rev Phys.Appl. 11, 83-87 (1976).
[CrossRef]

Vittone, E.

G. Mana and E. Vittone, "Scanning LLL X-ray interferometry II. Aberration analysis," Z. Phys. B 102, 197-206 (1997).
[CrossRef]

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, E. Vittone, and G. Zosi, "A measurement of the silicon (220) lattice spacing," Phys. Rev. Lett. 72, 3133-3136 (1994).
[CrossRef] [PubMed]

Windisch, D.

D. Windisch and P. Becker, "Silicon lattice parameter as an absolute scale of length for high precision measurement of fundamental constants," Phys. Stat. Sol. A 118, 379-388 (1990).
[CrossRef]

Zosi, G.

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-ray interferometry and the silicon lattice parameter: towards 10�??9 relative uncertainty?" Eur. Phys. J. B 9, 225-232 (1999).
[CrossRef]

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-Ray Interferometry Over a Millimeter Baseline," IEEE Trans. Instru. Meas. 46, 576-579 (1997).
[CrossRef]

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, E. Vittone, and G. Zosi, "A measurement of the silicon (220) lattice spacing," Phys. Rev. Lett. 72, 3133-3136 (1994).
[CrossRef] [PubMed]

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, and G. Zosi, "Progress at IMGC in the absolute determination of the silicon d220 lattice spacing," IEEE Trans. Instrum. Meas. 38, 210-216 (1989).
[CrossRef]

Eur. Phys. J. B

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-ray interferometry and the silicon lattice parameter: towards 10�??9 relative uncertainty?" Eur. Phys. J. B 9, 225-232 (1999).
[CrossRef]

Eur. Phys. J. D

A. Bergamin, G. Cavagnero, L. Cordiali, and G. Mana, "A Fourier optics model of two-beam scanning laser interferometers," Eur. Phys. J. D 5, 433-440 (1999).
[CrossRef]

IEEE Trans. Instru. Meas.

A. Bergamin, G. Cavagnero, L. Cordiali, G. Mana, and G. Zosi, "Scanning X-Ray Interferometry Over a Millimeter Baseline," IEEE Trans. Instru. Meas. 46, 576-579 (1997).
[CrossRef]

IEEE Trans. Instrum. Meas.

P. Becker, G. Cavagnero, U. Kuetgens, G. Mana, and E. Massa, "Confirmation of the INRiM and PTB determinations of the Si lattice parameter," IEEE Trans. Instrum. Meas. 56, (230-234) (2007).
[CrossRef]

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, and G. Zosi, "Progress at IMGC in the absolute determination of the silicon d220 lattice spacing," IEEE Trans. Instrum. Meas. 38, 210-216 (1989).
[CrossRef]

Meas. Sci. Technol.

A. Bergamin, G. Cavagnero, G. Durando, G. Mana, and E. Massa, "A two-axis tip-tilt platform for x-ray interferometry," Meas. Sci. Technol. 14, 717723 (2003).
[CrossRef]

Metrologia

P. Becker and G. Mana, "The lattice parameter of silicon: a survey," Metrologia 31, 203-209 (1994).
[CrossRef]

P. Becker, P. de Biévre, K. Fujii, M. Glaeser, B. Inglis, H. Luebbig, and G. Mana, "Considerations on future redefinitions of the kilogram, the mole and of other units," Metrologia 44, 1-14 (2007).
[CrossRef]

P. Becker, "Tracing the definition of the kilogram to the Avogadro constant using a silicon single crystal," Metrologia 40, 366-375 (2003).
[CrossRef]

Phys. Rev. A

A. Bergamin, G. Cavagnero, and G. Mana, "Observation of Fresnel diffraction in a two-beam laser interferometer," Phys. Rev. A 49, 2167-2172 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett.

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, E. Vittone, and G. Zosi, "A measurement of the silicon (220) lattice spacing," Phys. Rev. Lett. 72, 3133-3136 (1994).
[CrossRef] [PubMed]

Phys. Stat. Sol. A

D. Windisch and P. Becker, "Silicon lattice parameter as an absolute scale of length for high precision measurement of fundamental constants," Phys. Stat. Sol. A 118, 379-388 (1990).
[CrossRef]

Rev Phys.

U. Bonse, W. Graeff, and G. Materlik, "X-ray interferometry and lattice parameter investigation," Rev Phys.Appl. 11, 83-87 (1976).
[CrossRef]

Rev. Sci. Instrum.

A. Bergamin, G. Cavagnero, and G. Mana, "A displacement-angle interferometer with sub-atomic resolution," Rev. Sci. Instrum. 64, 3076-3081 (1993).
[CrossRef]

Z. Phys. B

G. Mana and E. Vittone, "Scanning LLL X-ray interferometry II. Aberration analysis," Z. Phys. B 102, 197-206 (1997).
[CrossRef]

Other

H. Siegert and P. Becker, "Systematic uncertainties in the determination of the lattice spacing d(220) in silicon," in Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, eds. Natl. Bur. Stand., Spec. Publ. 617, (U.S. GPO, Washington, 1984), pp. 321-324.

G. Cavagnero, H. Fujimoto, G. Mana, E. Massa, and K. Nakayama, "Measurement repetitions of the Si(220) lattice spacing," Metrologia 41, 56-64 (2004); ibid. at 445-447 (2204).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Left: the combined X-ray and optical interferometer. Right: the interferometer slide. On the top of the L shaped carriage is an active tripod, electronically controlled to compensate for sliding errors. The tripod supports the analyzer (XINT) and the reference electrode of a capacitive transducer. The analyzer front-surface is the movable mirror of the optical interferometer.

Fig. 2.
Fig. 2.

Top: d 220 variation in the MO*4 crystal. The measurements carried out on 2007-12- 18, 2008-02-04, and 2008-02-25 are in blue, green, and red. Bottom: Consistency of the measured d 220 values. The average - over the crystal slices indicated by the arrows - of the values in the top part are in red; the results of one-step measurements over the same slices are in green. The graduation is the sequence of possible d 220 values compatible with the X-ray fringe fraction in the 20 mm displacement.

Fig. 3.
Fig. 3.

The MO*4 crystal. The x axis is where the d 220 measurements were performed. The red spot is the laser beam, the blue box is the X-ray beam - see also Fig. 5.

Fig. 4.
Fig. 4.

Measurement repetitions of the mean (220) lattice spacing in the MO*4 crystal.

Fig. 5.
Fig. 5.

Schemes of the quadrant (left) and multianode (right) detectors. The spacings between the centers of the analyzer areas imaged by the quadrants and anodes are 1.5 mm and 1.4 mm - see also Fig. 3. Hypothetical optical and X-ray interference patterns - with enhanced misalignment fringes - are also rendered by scatter plots.

Fig. 6.
Fig. 6.

Left: Analyzer displacements in the anodes of the photomultiplier tube - at the coordinates z i ≈{-4.2,-2.8,-1.4,0,1.4,2.8,4.2,5.6} mm - when it is pitched (red) and yawed (green) about the center of the laser-beam spot. Right: d 220 values measured in the anodes of the photomultiplier tube.

Fig. 7.
Fig. 7.

Consistency of the measured lattice spacing values. The movement direction was intentionally varied and measurement results are plotted vs. the projection error. The solid line is the expected d 220 variation.

Fig. 8.
Fig. 8.

Difference between the d 220 values in the vertical and horizontal pairs of the quadrant detector; measurements carried out on 2007-12-18 and 2008-02-04 are in blue and green.

Fig. 9.
Fig. 9.

Top: Analyzer or (220) plane pitching - as sensed by the X-ray interferometer-when the analyzer pitch - as sensed by the optical interferometer - is kept to zero. Measurements carried out on 2008-02-04 and 2008-02-25 are in green and red. Bottom: Residuals from the best-fit line to the data.

Fig. 10.
Fig. 10.

History of the measurements of the mean (220) lattice spacing in the MO*4 crystal. The labels record the increasing scan-length and control-capability; numbers in brackets are the relevant references.

Tables (1)

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Table 1. Crystal MO*4 - corrections and uncertainties of d 220.

Equations (3)

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d 220 = ( m / n ) λ / 2 ,
d 220 = 192.0155508 ( 12 ) pm ,
d ( x i , z k ) = d 0 [ 1 + z k Δ ρ m λ / 2 ] ,

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