Abstract

We report an exploitation of the optical comb of a femtosecond pulse laser as the wavelength ruler for the task of absolute length calibration of gauge blocks. To that end, the optical comb was stabilized to the Rb clock of frequency standard and an optical frequency synthesizer was constructed by tuning an external single-frequency laser to the optical comb. The absolute height of gauge blocks was measured by means of multiwavelength interferometry using multiple beams of different wavelengths consecutively provided by the optical frequency synthesizer. The wavelength uncertainty was measured 1.9×10-10 that leads to an overall calibration uncertainty of 15 nm (k=1) in determining the absolute length of gauge blocks.

© 2006 Optical Society of America

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References

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  1. H. Darnedde, "High-precision calibration of long gauge blocks using the vacuum wavelength comparator," Metrologia 29, 349-359 (1992).
    [CrossRef]
  2. E. Ikonen and K. Riski, "Gauge-block interferometer based on one stabilized laser and a white-light source," Metrologia 30, 95-104 (1993).
    [CrossRef]
  3. K. J. Siemsen, R. F. Siemsen, J. E. Decker, L. Marmet, and J. R. Pekelsky, "A multiple frequency heterodyne technique for the measurement of long gauges," Metrologia 33, 555-563 (1996).
    [CrossRef]
  4. V. M. Khavinson, "Ring interferometer for two-sided measurement of the absolute lengths of end standards," Appl. Opt. 38, 126-135 (1999).
    [CrossRef]
  5. S. Lu, C. Chiueh, and C. Lee, "Differential wavelength-scanning heterodyne interferometer for measuring large step height," Appl. Opt. 41, 5866-5871 (2002).
    [CrossRef] [PubMed]
  6. J. E. Decker, J. R. Miles, A. A. Madej, R. F. Siemsen, K. J. Siemsen, S. de Bonth, K. Bustraan, S. Temple, and J. R. Pekelsky, "Increasing the range of unambiguity in step-height measurement with multiple-wavelength interferometry-application to absolute long gauge block measurement," Appl. Opt. 42, 5670-5678 (2003).
    [CrossRef] [PubMed]
  7. T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, "Absolute optical frequency measurement of the cesium D1 line with a mode-locked laser," Phy. Rev. Lett. 82, 3568-3571 (1999).
    [CrossRef]
  8. D. J. Jones, S. A. Diddams, J. K. Randka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
    [CrossRef] [PubMed]
  9. J. D. Jost, J. L. Hall, and J. Ye, "Continuously tunable, precise, single frequency optical signal generator," Opt. Express 10, 515-520 (2002).
    [PubMed]
  10. M. Tsai, H. Huang, M. Itoh, and T. Yatagai, "Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness," Opt. Rev. 6, 449-454 (1999).
    [CrossRef]
  11. K. P. Birch and M. J. Downs, "An updated Edlen equation for the refractive index of air," Metrologia 30, 155-162 (1993).
    [CrossRef]
  12. J. E. Decker and J. R. Pekelsky, "Uncertainty evaluation for the measurement of gauge blocks by optical interferometry," Metrologia 34, 479-493 (1997).
    [CrossRef]
  13. Guide to the expression of uncertainty in measurement, (International organization for standardization, 1993).

2003

2002

2000

D. J. Jones, S. A. Diddams, J. K. Randka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

1999

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, "Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness," Opt. Rev. 6, 449-454 (1999).
[CrossRef]

V. M. Khavinson, "Ring interferometer for two-sided measurement of the absolute lengths of end standards," Appl. Opt. 38, 126-135 (1999).
[CrossRef]

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, "Absolute optical frequency measurement of the cesium D1 line with a mode-locked laser," Phy. Rev. Lett. 82, 3568-3571 (1999).
[CrossRef]

1997

J. E. Decker and J. R. Pekelsky, "Uncertainty evaluation for the measurement of gauge blocks by optical interferometry," Metrologia 34, 479-493 (1997).
[CrossRef]

1996

K. J. Siemsen, R. F. Siemsen, J. E. Decker, L. Marmet, and J. R. Pekelsky, "A multiple frequency heterodyne technique for the measurement of long gauges," Metrologia 33, 555-563 (1996).
[CrossRef]

1993

E. Ikonen and K. Riski, "Gauge-block interferometer based on one stabilized laser and a white-light source," Metrologia 30, 95-104 (1993).
[CrossRef]

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

1992

H. Darnedde, "High-precision calibration of long gauge blocks using the vacuum wavelength comparator," Metrologia 29, 349-359 (1992).
[CrossRef]

Birch, K. P.

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

Bustraan, K.

Chiueh, C.

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Randka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Darnedde, H.

H. Darnedde, "High-precision calibration of long gauge blocks using the vacuum wavelength comparator," Metrologia 29, 349-359 (1992).
[CrossRef]

de Bonth, S.

Decker, J. E.

J. E. Decker, J. R. Miles, A. A. Madej, R. F. Siemsen, K. J. Siemsen, S. de Bonth, K. Bustraan, S. Temple, and J. R. Pekelsky, "Increasing the range of unambiguity in step-height measurement with multiple-wavelength interferometry-application to absolute long gauge block measurement," Appl. Opt. 42, 5670-5678 (2003).
[CrossRef] [PubMed]

J. E. Decker and J. R. Pekelsky, "Uncertainty evaluation for the measurement of gauge blocks by optical interferometry," Metrologia 34, 479-493 (1997).
[CrossRef]

K. J. Siemsen, R. F. Siemsen, J. E. Decker, L. Marmet, and J. R. Pekelsky, "A multiple frequency heterodyne technique for the measurement of long gauges," Metrologia 33, 555-563 (1996).
[CrossRef]

Diddams, S. A.

D. J. Jones, S. A. Diddams, J. K. Randka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Downs, M. J.

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

Hall, J. L.

J. D. Jost, J. L. Hall, and J. Ye, "Continuously tunable, precise, single frequency optical signal generator," Opt. Express 10, 515-520 (2002).
[PubMed]

D. J. Jones, S. A. Diddams, J. K. Randka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Hänsch, T. W.

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, "Absolute optical frequency measurement of the cesium D1 line with a mode-locked laser," Phy. Rev. Lett. 82, 3568-3571 (1999).
[CrossRef]

Holzwarth, R.

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, "Absolute optical frequency measurement of the cesium D1 line with a mode-locked laser," Phy. Rev. Lett. 82, 3568-3571 (1999).
[CrossRef]

Huang, H.

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, "Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness," Opt. Rev. 6, 449-454 (1999).
[CrossRef]

Ikonen, E.

E. Ikonen and K. Riski, "Gauge-block interferometer based on one stabilized laser and a white-light source," Metrologia 30, 95-104 (1993).
[CrossRef]

Itoh, M.

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, "Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness," Opt. Rev. 6, 449-454 (1999).
[CrossRef]

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Randka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Jost, J. D.

Khavinson, V. M.

Lee, C.

Lu, S.

Madej, A. A.

Marmet, L.

K. J. Siemsen, R. F. Siemsen, J. E. Decker, L. Marmet, and J. R. Pekelsky, "A multiple frequency heterodyne technique for the measurement of long gauges," Metrologia 33, 555-563 (1996).
[CrossRef]

Miles, J. R.

Pekelsky, J. R.

J. E. Decker, J. R. Miles, A. A. Madej, R. F. Siemsen, K. J. Siemsen, S. de Bonth, K. Bustraan, S. Temple, and J. R. Pekelsky, "Increasing the range of unambiguity in step-height measurement with multiple-wavelength interferometry-application to absolute long gauge block measurement," Appl. Opt. 42, 5670-5678 (2003).
[CrossRef] [PubMed]

J. E. Decker and J. R. Pekelsky, "Uncertainty evaluation for the measurement of gauge blocks by optical interferometry," Metrologia 34, 479-493 (1997).
[CrossRef]

K. J. Siemsen, R. F. Siemsen, J. E. Decker, L. Marmet, and J. R. Pekelsky, "A multiple frequency heterodyne technique for the measurement of long gauges," Metrologia 33, 555-563 (1996).
[CrossRef]

Randka, J. K.

D. J. Jones, S. A. Diddams, J. K. Randka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Reichert, J.

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, "Absolute optical frequency measurement of the cesium D1 line with a mode-locked laser," Phy. Rev. Lett. 82, 3568-3571 (1999).
[CrossRef]

Riski, K.

E. Ikonen and K. Riski, "Gauge-block interferometer based on one stabilized laser and a white-light source," Metrologia 30, 95-104 (1993).
[CrossRef]

Siemsen, K. J.

Siemsen, R. F.

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Randka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Temple, S.

Tsai, M.

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, "Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness," Opt. Rev. 6, 449-454 (1999).
[CrossRef]

Udem, T.

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, "Absolute optical frequency measurement of the cesium D1 line with a mode-locked laser," Phy. Rev. Lett. 82, 3568-3571 (1999).
[CrossRef]

Windeler, R. S.

D. J. Jones, S. A. Diddams, J. K. Randka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Yatagai, T.

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, "Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness," Opt. Rev. 6, 449-454 (1999).
[CrossRef]

Ye, J.

Appl. Opt.

Metrologia

H. Darnedde, "High-precision calibration of long gauge blocks using the vacuum wavelength comparator," Metrologia 29, 349-359 (1992).
[CrossRef]

E. Ikonen and K. Riski, "Gauge-block interferometer based on one stabilized laser and a white-light source," Metrologia 30, 95-104 (1993).
[CrossRef]

K. J. Siemsen, R. F. Siemsen, J. E. Decker, L. Marmet, and J. R. Pekelsky, "A multiple frequency heterodyne technique for the measurement of long gauges," Metrologia 33, 555-563 (1996).
[CrossRef]

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

J. E. Decker and J. R. Pekelsky, "Uncertainty evaluation for the measurement of gauge blocks by optical interferometry," Metrologia 34, 479-493 (1997).
[CrossRef]

Opt. Express

Opt. Rev.

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, "Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness," Opt. Rev. 6, 449-454 (1999).
[CrossRef]

Phy. Rev. Lett.

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, "Absolute optical frequency measurement of the cesium D1 line with a mode-locked laser," Phy. Rev. Lett. 82, 3568-3571 (1999).
[CrossRef]

Science

D. J. Jones, S. A. Diddams, J. K. Randka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Other

Guide to the expression of uncertainty in measurement, (International organization for standardization, 1993).

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Figures (3)

Fig. 1.
Fig. 1.

Overall hardware configuration for absolute length calibration of gauge blocks using the optical comb of a femtosecond laser. Blue dotted lines represent electric signals and orange curved lines are optical fibers. PLL: phase locked loop, APD: avalanche photo detector, ECLD: external cavity laser diode, CCD: charge coupled detector, CL: collimation lens, BS: beam splitter, M: mirror, IL: imaging lens, PH: pinhole, SMF: single mode fiber, PCF: photonic crystal fiber.

Fig. 2.
Fig. 2.

Observation of a 5 MHz beat note using a spectrum analyzer (LG Precision Co., SA-7270). Also seen are other peaks corresponding to the acoustic length variation of the ECLD at 10 MHz, (f r-f b) at 76 MHz, the repetition rate at 81 MHz, and (f r+f b) at 86 MHz.

Fig. 3.
Fig. 3.

Fringe analysis procedure to determine the excess fraction between the gauge block and base plate. Three representative lines are selected; line G along the center line of the gauge block, and line Ba and line Bb from the base plate at a same distance from line G. Fourier transform is adopted to obtain the phase value of each line, which finally leads to determination of the exact value of the excess fraction.

Tables (2)

Tables Icon

Table 1. Measurement result of a gauge block of 25 mm length.

Tables Icon

Table 2. Uncertainty evaluation of absolute calibration of gauge blocks. L 0 denotes the nominal length of a gauge block whose length is given in meter.

Equations (2)

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L = λ 1 2 ( m 1 + f 1 ) = λ 2 2 ( m 2 + f 2 ) = = λ N 2 ( m N + f N )
f = 1 360 ° [ ϕ G ( ϕ Ba + ϕ Bb 2 ) ]

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