Abstract

We describe two different, double-sided interferometer designs for measuring material stability. Both designs are balanced interferometers where the only optical path difference is the sample and the reference beams are located within the interferometer. One interferometer is a double-pass design, whereas the other is a single-pass system. Based on a tolerancing analysis, the single-pass system is less susceptible to initial component misalignment and motions during experiments. This single-pass interferometer was tested with an 86nm thin-film silver sample for both short-term repeatability and long-term stability. In 66 repeatability tests of 30min each, the mean measured drift rate was less than 1pm/h rms. In two long-term tests (>9h), the mean drift rate was less than 1.1pm/h, which shows good agreement between the short- and long-term measurements. In these experiments, the mean measured length change was 2nm rms.

© 2009 Optical Society of America

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  1. R. S. Elliott, N. Triantafyllidis, and J. A. Shaw, “Stability of crystalline solids--I: continuum and atomic lattice considerations,” J. Mech. Phys. Solids 54, 161-192 (2006).
    [Crossref]
  2. Y. W. Bao, S. B. Su, J. J. Yang, L. Sun, and J. H. Gong, “Nondestructively determining local strength and residual stress of glass by Hertzian indentation,” Acta Mater. 50, 4659-4666 (2002).
    [Crossref]
  3. M. Bergoglio, A. Calcatelli, M. Plassa, and P. Chen, “Gas adsorption-desorption and materials stability,” Vacuum 41, 2089-2092 (1990).
    [Crossref]
  4. Y. Kuriyama, Y. Yokoyama, Y. Ishii, J. Ishikawa, and H. Makino, “Development of a new interferometric measurement system for determining the main characteristics of gauge blocks,” CIRP Ann. 55, 563-566 (2006).
    [Crossref]
  5. R. Schödel, Ultra-high accuracy thermal expansion measurements with PTB's precision interferometer,” Meas. Sci. Technol. 19, 084003 (2008).
    [Crossref]
  6. S. J. Bennett, “An absolute interferometric dilatometer,” J. Phys. E 10, 525-530 (1977).
  7. K. P. Birch, “An automatic absolute interferometric dilatometer,” J. Phys. E 201387-1392 (1987).
    [Crossref]
  8. M. Okaji and H. Imai, “A practical measurement system for the accurate determination of linear thermal expansion coefficients,” J. Phys. E 17, 669-673 (1984).
    [Crossref]
  9. J. Suska and J. Tschirnich, “An interferometric device for precise thermal expansion measurements on bar-shaped materials,” Meas. Sci. Technol. 10, N55-N59 (1999).
    [Crossref]
  10. E. G. Wolff and R. C. Savedra, “Precision interferometric dilatometer,” Rev. Sci. Instrum. 56, 1313-1319 (1985).
    [Crossref]
  11. J. D. Ellis, K. Joo, A. Verlaan, J. W. Spronck, and R.-H. Munnig Schmidt, “Uncertainty considerations for interferometric stability testing,” presented at Annual Meeting of the American Society for Precision Engineering 2008, Portland, Oreg., USA (23 Oct. 2008).
  12. D. Ren, K. M. Lawton, and J. A. Miller, “A double-pass interferometer for measurement of dimensional changes,” Meas. Sci. Technol. 19, 025303 (2008).
    [Crossref]
  13. J. D. Ellis, J. W. Spronck, and R.-H. Munnig Schmidt, “Optically balanced, multi-pass displacement interferometry for picometer stability testing,” presented at Annual Meeting of the American Society for Precision Engineering 2007, Dallas, Tex., USA (16-17 Oct. 2007).
  14. W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91-98 (1992).
    [Crossref]
  15. T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13, 222-225(2002).
    [Crossref]
  16. K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
    [Crossref]
  17. J. Rutman and F. L. Walls, “Characterization of frequency stability in precision frequency sources,” Proc. IEEE 79, 952-960 (1991).
    [Crossref]

2008 (2)

R. Schödel, Ultra-high accuracy thermal expansion measurements with PTB's precision interferometer,” Meas. Sci. Technol. 19, 084003 (2008).
[Crossref]

D. Ren, K. M. Lawton, and J. A. Miller, “A double-pass interferometer for measurement of dimensional changes,” Meas. Sci. Technol. 19, 025303 (2008).
[Crossref]

2006 (2)

Y. Kuriyama, Y. Yokoyama, Y. Ishii, J. Ishikawa, and H. Makino, “Development of a new interferometric measurement system for determining the main characteristics of gauge blocks,” CIRP Ann. 55, 563-566 (2006).
[Crossref]

R. S. Elliott, N. Triantafyllidis, and J. A. Shaw, “Stability of crystalline solids--I: continuum and atomic lattice considerations,” J. Mech. Phys. Solids 54, 161-192 (2006).
[Crossref]

2002 (2)

Y. W. Bao, S. B. Su, J. J. Yang, L. Sun, and J. H. Gong, “Nondestructively determining local strength and residual stress of glass by Hertzian indentation,” Acta Mater. 50, 4659-4666 (2002).
[Crossref]

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13, 222-225(2002).
[Crossref]

1999 (1)

J. Suska and J. Tschirnich, “An interferometric device for precise thermal expansion measurements on bar-shaped materials,” Meas. Sci. Technol. 10, N55-N59 (1999).
[Crossref]

1993 (1)

K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
[Crossref]

1992 (1)

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91-98 (1992).
[Crossref]

1991 (1)

J. Rutman and F. L. Walls, “Characterization of frequency stability in precision frequency sources,” Proc. IEEE 79, 952-960 (1991).
[Crossref]

1990 (1)

M. Bergoglio, A. Calcatelli, M. Plassa, and P. Chen, “Gas adsorption-desorption and materials stability,” Vacuum 41, 2089-2092 (1990).
[Crossref]

1987 (1)

K. P. Birch, “An automatic absolute interferometric dilatometer,” J. Phys. E 201387-1392 (1987).
[Crossref]

1985 (1)

E. G. Wolff and R. C. Savedra, “Precision interferometric dilatometer,” Rev. Sci. Instrum. 56, 1313-1319 (1985).
[Crossref]

1984 (1)

M. Okaji and H. Imai, “A practical measurement system for the accurate determination of linear thermal expansion coefficients,” J. Phys. E 17, 669-673 (1984).
[Crossref]

1977 (1)

S. J. Bennett, “An absolute interferometric dilatometer,” J. Phys. E 10, 525-530 (1977).

Bao, Y. W.

Y. W. Bao, S. B. Su, J. J. Yang, L. Sun, and J. H. Gong, “Nondestructively determining local strength and residual stress of glass by Hertzian indentation,” Acta Mater. 50, 4659-4666 (2002).
[Crossref]

Bennett, S. J.

S. J. Bennett, “An absolute interferometric dilatometer,” J. Phys. E 10, 525-530 (1977).

Bergoglio, M.

M. Bergoglio, A. Calcatelli, M. Plassa, and P. Chen, “Gas adsorption-desorption and materials stability,” Vacuum 41, 2089-2092 (1990).
[Crossref]

Birch, K. P.

K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
[Crossref]

K. P. Birch, “An automatic absolute interferometric dilatometer,” J. Phys. E 201387-1392 (1987).
[Crossref]

Calcatelli, A.

M. Bergoglio, A. Calcatelli, M. Plassa, and P. Chen, “Gas adsorption-desorption and materials stability,” Vacuum 41, 2089-2092 (1990).
[Crossref]

Chen, P.

M. Bergoglio, A. Calcatelli, M. Plassa, and P. Chen, “Gas adsorption-desorption and materials stability,” Vacuum 41, 2089-2092 (1990).
[Crossref]

Choi, H.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13, 222-225(2002).
[Crossref]

Choi, T.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13, 222-225(2002).
[Crossref]

Downs, M. J.

K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
[Crossref]

Elliott, R. S.

R. S. Elliott, N. Triantafyllidis, and J. A. Shaw, “Stability of crystalline solids--I: continuum and atomic lattice considerations,” J. Mech. Phys. Solids 54, 161-192 (2006).
[Crossref]

Ellis, J. D.

J. D. Ellis, K. Joo, A. Verlaan, J. W. Spronck, and R.-H. Munnig Schmidt, “Uncertainty considerations for interferometric stability testing,” presented at Annual Meeting of the American Society for Precision Engineering 2008, Portland, Oreg., USA (23 Oct. 2008).

J. D. Ellis, J. W. Spronck, and R.-H. Munnig Schmidt, “Optically balanced, multi-pass displacement interferometry for picometer stability testing,” presented at Annual Meeting of the American Society for Precision Engineering 2007, Dallas, Tex., USA (16-17 Oct. 2007).

Eom, T.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13, 222-225(2002).
[Crossref]

Gong, J. H.

Y. W. Bao, S. B. Su, J. J. Yang, L. Sun, and J. H. Gong, “Nondestructively determining local strength and residual stress of glass by Hertzian indentation,” Acta Mater. 50, 4659-4666 (2002).
[Crossref]

Hou, W.

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91-98 (1992).
[Crossref]

Imai, H.

M. Okaji and H. Imai, “A practical measurement system for the accurate determination of linear thermal expansion coefficients,” J. Phys. E 17, 669-673 (1984).
[Crossref]

Ishii, Y.

Y. Kuriyama, Y. Yokoyama, Y. Ishii, J. Ishikawa, and H. Makino, “Development of a new interferometric measurement system for determining the main characteristics of gauge blocks,” CIRP Ann. 55, 563-566 (2006).
[Crossref]

Ishikawa, J.

Y. Kuriyama, Y. Yokoyama, Y. Ishii, J. Ishikawa, and H. Makino, “Development of a new interferometric measurement system for determining the main characteristics of gauge blocks,” CIRP Ann. 55, 563-566 (2006).
[Crossref]

Joo, K.

J. D. Ellis, K. Joo, A. Verlaan, J. W. Spronck, and R.-H. Munnig Schmidt, “Uncertainty considerations for interferometric stability testing,” presented at Annual Meeting of the American Society for Precision Engineering 2008, Portland, Oreg., USA (23 Oct. 2008).

Kuriyama, Y.

Y. Kuriyama, Y. Yokoyama, Y. Ishii, J. Ishikawa, and H. Makino, “Development of a new interferometric measurement system for determining the main characteristics of gauge blocks,” CIRP Ann. 55, 563-566 (2006).
[Crossref]

Lawton, K. M.

D. Ren, K. M. Lawton, and J. A. Miller, “A double-pass interferometer for measurement of dimensional changes,” Meas. Sci. Technol. 19, 025303 (2008).
[Crossref]

Lee, K.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13, 222-225(2002).
[Crossref]

Lee, S.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13, 222-225(2002).
[Crossref]

Makino, H.

Y. Kuriyama, Y. Yokoyama, Y. Ishii, J. Ishikawa, and H. Makino, “Development of a new interferometric measurement system for determining the main characteristics of gauge blocks,” CIRP Ann. 55, 563-566 (2006).
[Crossref]

Miller, J. A.

D. Ren, K. M. Lawton, and J. A. Miller, “A double-pass interferometer for measurement of dimensional changes,” Meas. Sci. Technol. 19, 025303 (2008).
[Crossref]

Munnig Schmidt, R. H.

J. D. Ellis, K. Joo, A. Verlaan, J. W. Spronck, and R.-H. Munnig Schmidt, “Uncertainty considerations for interferometric stability testing,” presented at Annual Meeting of the American Society for Precision Engineering 2008, Portland, Oreg., USA (23 Oct. 2008).

J. D. Ellis, J. W. Spronck, and R.-H. Munnig Schmidt, “Optically balanced, multi-pass displacement interferometry for picometer stability testing,” presented at Annual Meeting of the American Society for Precision Engineering 2007, Dallas, Tex., USA (16-17 Oct. 2007).

Okaji, M.

M. Okaji and H. Imai, “A practical measurement system for the accurate determination of linear thermal expansion coefficients,” J. Phys. E 17, 669-673 (1984).
[Crossref]

Plassa, M.

M. Bergoglio, A. Calcatelli, M. Plassa, and P. Chen, “Gas adsorption-desorption and materials stability,” Vacuum 41, 2089-2092 (1990).
[Crossref]

Ren, D.

D. Ren, K. M. Lawton, and J. A. Miller, “A double-pass interferometer for measurement of dimensional changes,” Meas. Sci. Technol. 19, 025303 (2008).
[Crossref]

Rutman, J.

J. Rutman and F. L. Walls, “Characterization of frequency stability in precision frequency sources,” Proc. IEEE 79, 952-960 (1991).
[Crossref]

Savedra, R. C.

E. G. Wolff and R. C. Savedra, “Precision interferometric dilatometer,” Rev. Sci. Instrum. 56, 1313-1319 (1985).
[Crossref]

Schödel, R.

R. Schödel, Ultra-high accuracy thermal expansion measurements with PTB's precision interferometer,” Meas. Sci. Technol. 19, 084003 (2008).
[Crossref]

Shaw, J. A.

R. S. Elliott, N. Triantafyllidis, and J. A. Shaw, “Stability of crystalline solids--I: continuum and atomic lattice considerations,” J. Mech. Phys. Solids 54, 161-192 (2006).
[Crossref]

Spronck, J. W.

J. D. Ellis, K. Joo, A. Verlaan, J. W. Spronck, and R.-H. Munnig Schmidt, “Uncertainty considerations for interferometric stability testing,” presented at Annual Meeting of the American Society for Precision Engineering 2008, Portland, Oreg., USA (23 Oct. 2008).

J. D. Ellis, J. W. Spronck, and R.-H. Munnig Schmidt, “Optically balanced, multi-pass displacement interferometry for picometer stability testing,” presented at Annual Meeting of the American Society for Precision Engineering 2007, Dallas, Tex., USA (16-17 Oct. 2007).

Su, S. B.

Y. W. Bao, S. B. Su, J. J. Yang, L. Sun, and J. H. Gong, “Nondestructively determining local strength and residual stress of glass by Hertzian indentation,” Acta Mater. 50, 4659-4666 (2002).
[Crossref]

Sun, L.

Y. W. Bao, S. B. Su, J. J. Yang, L. Sun, and J. H. Gong, “Nondestructively determining local strength and residual stress of glass by Hertzian indentation,” Acta Mater. 50, 4659-4666 (2002).
[Crossref]

Suska, J.

J. Suska and J. Tschirnich, “An interferometric device for precise thermal expansion measurements on bar-shaped materials,” Meas. Sci. Technol. 10, N55-N59 (1999).
[Crossref]

Triantafyllidis, N.

R. S. Elliott, N. Triantafyllidis, and J. A. Shaw, “Stability of crystalline solids--I: continuum and atomic lattice considerations,” J. Mech. Phys. Solids 54, 161-192 (2006).
[Crossref]

Tschirnich, J.

J. Suska and J. Tschirnich, “An interferometric device for precise thermal expansion measurements on bar-shaped materials,” Meas. Sci. Technol. 10, N55-N59 (1999).
[Crossref]

Verlaan, A.

J. D. Ellis, K. Joo, A. Verlaan, J. W. Spronck, and R.-H. Munnig Schmidt, “Uncertainty considerations for interferometric stability testing,” presented at Annual Meeting of the American Society for Precision Engineering 2008, Portland, Oreg., USA (23 Oct. 2008).

Walls, F. L.

J. Rutman and F. L. Walls, “Characterization of frequency stability in precision frequency sources,” Proc. IEEE 79, 952-960 (1991).
[Crossref]

Wilkening, G.

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91-98 (1992).
[Crossref]

Wolff, E. G.

E. G. Wolff and R. C. Savedra, “Precision interferometric dilatometer,” Rev. Sci. Instrum. 56, 1313-1319 (1985).
[Crossref]

Yang, J. J.

Y. W. Bao, S. B. Su, J. J. Yang, L. Sun, and J. H. Gong, “Nondestructively determining local strength and residual stress of glass by Hertzian indentation,” Acta Mater. 50, 4659-4666 (2002).
[Crossref]

Yokoyama, Y.

Y. Kuriyama, Y. Yokoyama, Y. Ishii, J. Ishikawa, and H. Makino, “Development of a new interferometric measurement system for determining the main characteristics of gauge blocks,” CIRP Ann. 55, 563-566 (2006).
[Crossref]

Acta Mater. (1)

Y. W. Bao, S. B. Su, J. J. Yang, L. Sun, and J. H. Gong, “Nondestructively determining local strength and residual stress of glass by Hertzian indentation,” Acta Mater. 50, 4659-4666 (2002).
[Crossref]

CIRP Ann. (1)

Y. Kuriyama, Y. Yokoyama, Y. Ishii, J. Ishikawa, and H. Makino, “Development of a new interferometric measurement system for determining the main characteristics of gauge blocks,” CIRP Ann. 55, 563-566 (2006).
[Crossref]

J. Mech. Phys. Solids (1)

R. S. Elliott, N. Triantafyllidis, and J. A. Shaw, “Stability of crystalline solids--I: continuum and atomic lattice considerations,” J. Mech. Phys. Solids 54, 161-192 (2006).
[Crossref]

J. Phys. E (3)

S. J. Bennett, “An absolute interferometric dilatometer,” J. Phys. E 10, 525-530 (1977).

K. P. Birch, “An automatic absolute interferometric dilatometer,” J. Phys. E 201387-1392 (1987).
[Crossref]

M. Okaji and H. Imai, “A practical measurement system for the accurate determination of linear thermal expansion coefficients,” J. Phys. E 17, 669-673 (1984).
[Crossref]

Meas. Sci. Technol. (4)

J. Suska and J. Tschirnich, “An interferometric device for precise thermal expansion measurements on bar-shaped materials,” Meas. Sci. Technol. 10, N55-N59 (1999).
[Crossref]

R. Schödel, Ultra-high accuracy thermal expansion measurements with PTB's precision interferometer,” Meas. Sci. Technol. 19, 084003 (2008).
[Crossref]

D. Ren, K. M. Lawton, and J. A. Miller, “A double-pass interferometer for measurement of dimensional changes,” Meas. Sci. Technol. 19, 025303 (2008).
[Crossref]

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13, 222-225(2002).
[Crossref]

Metrologia (1)

K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
[Crossref]

Precis. Eng. (1)

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91-98 (1992).
[Crossref]

Proc. IEEE (1)

J. Rutman and F. L. Walls, “Characterization of frequency stability in precision frequency sources,” Proc. IEEE 79, 952-960 (1991).
[Crossref]

Rev. Sci. Instrum. (1)

E. G. Wolff and R. C. Savedra, “Precision interferometric dilatometer,” Rev. Sci. Instrum. 56, 1313-1319 (1985).
[Crossref]

Vacuum (1)

M. Bergoglio, A. Calcatelli, M. Plassa, and P. Chen, “Gas adsorption-desorption and materials stability,” Vacuum 41, 2089-2092 (1990).
[Crossref]

Other (2)

J. D. Ellis, K. Joo, A. Verlaan, J. W. Spronck, and R.-H. Munnig Schmidt, “Uncertainty considerations for interferometric stability testing,” presented at Annual Meeting of the American Society for Precision Engineering 2008, Portland, Oreg., USA (23 Oct. 2008).

J. D. Ellis, J. W. Spronck, and R.-H. Munnig Schmidt, “Optically balanced, multi-pass displacement interferometry for picometer stability testing,” presented at Annual Meeting of the American Society for Precision Engineering 2007, Dallas, Tex., USA (16-17 Oct. 2007).

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Figures (9)

Fig. 1
Fig. 1

Double-pass, double-sided interferometer for measuring sample length changes. Including the reference beam within the interferometer reduces the effects of polarization mixing and component misalignments. PD s , PD r , photodetectors.

Fig. 2
Fig. 2

Single-pass, double-sided interferometer for measuring sample length changes. The input beams have a frequency offset but are the same polarization state. The vacuum tube (VT) has extended glass flanges to keep the paths common between all four beams.

Fig. 3
Fig. 3

Polarization schematic for the single-pass design. The black solid beams are horizontally polarized, the black dotted beams are right circularly polarized, the grey solid beams are vertically polarized, and the grey dotted beams are left circularly polarized.

Fig. 4
Fig. 4

Interferometer layout for measuring a zero-length sample to qualify the single-pass double-sided design. The size of PBS1 and PBS2 was 35 mm for these measurements. The total optical path after splitting is approximately 500 mm .

Fig. 5
Fig. 5

A total of 66 measurements of the silver thin-film sample overlaid on top of one another. The majority of measured length change is within an 8 nm band, and the average length change was 1.9 nm rms.

Fig. 6
Fig. 6

Linear drift rate (left axis) and rms length change (right axis) of each of the 66, 30 min measurements. The mean drift rate was 0.4 pm h 1 with a standard deviation of 16.5 pm h 1 . The mean length change was 1.9 nm rms.

Fig. 7
Fig. 7

Two long-term measurements over 12 and 9 h. Both measurements had a mean length change of 1.6 nm rms, and the linear drift rates were less than 1.1 pm h 1 .

Fig. 8
Fig. 8

Measured phase noise from the laser head, using a common polarizer and a 50% beam splitter. The phase between the two signals was measured by using the same signal processing parameters and electronics as in the thin-film measurements.

Fig. 9
Fig. 9

Allan variances of the two long-term measurements and the phase noise (translated to nanometers) from the source. The lack of upswing over time indicates a high stability in the system.

Equations (4)

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E s J p ( J sys , sm E sm + J sys , sr E sr ) ,
E r J p ( J sys , r 1 E r 1 + J sys , r 2 E r 2 ) ,
J sys , sm = J n J n 1 R θ J hwp R + θ J 1 ,
J sys , sr = J m R + θ J hwp R θ J 2 J 1 ,

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