Abstract

Air refractive index fluctuation (Δnair) is one of the largest uncertainty sources in precision interferometry systems that require a resolution of nanometer order or less. We introduce a method for the active suppression of Δnair inside a normal air-environment chamber using a Fabry–Perot cavity and a piezoelectric volume actuator. The temporal air refractive index (nair) at a local point is maintained constant with an expanded uncertainty of 4.2×109 (k=2), a sufficiently low uncertainty for precise measurements unaffected by Δnair to be made inside a chamber.

© 2010 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009

T. Q. Banh, M. Ishige, Y. Ohkubo, and M. Aketagawa, “Measurement of air refractive index fluctuation from laser frequency shift with uncertainty of order 10−9,” Meas. Sci. Technol. 20, 125302–125309 (2009).
[CrossRef]

2008

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

2007

O. Cip, F. Petru, Z. Buchta, and J. Lazar, “Small displacement measurements with subatomic resolution by beat frequency measurements,” Meas. Sci. Technol. 18, 2005–2013 (2007).
[CrossRef]

2006

2005

D. Karabacak, T. Kouh, and K. L. Ekinci, “Analysis of optical interferometric displacement detection in nanoelectromechanical systems,” J. Appl. Phys. 98, 124309–124318 (2005).
[CrossRef]

1998

T. E. Carlsson, J. Gustafsson, and N. H. Abramson, “Method for fringe enhancement in holographic interferometry for measurement of in-plane displacements,” Appl. Opt. 37, 1845–1847 (1998).
[CrossRef]

N. Khelifa, H. Fang, J. Xu, P. Juncar, and M. Himbert, “Refractometer for tracking changes in the refractive index of air near 780nm,” Appl. Opt. 37, 156–161 (1998).
[CrossRef]

M. Aketagawa, K. Takada, K. Kobayashi, N. Takeshima, M. Noro, and Y. Nakayama, “Length measurement using a regular crystalline lattice and a dual tunneling unit scanning tunneling microscope in a thermo-stabilized cell,” Meas. Sci. Technol. 9, 1076–1081 (1998).
[CrossRef]

1997

1996

1993

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

1991

S. Hosoe, “Laser interferometric system for displacement measurement with high precision,” Nanotechnology 2, 88–92(1991).
[CrossRef]

1989

1988

1983

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

1979

J. B. Bryan, “Design and construction of an ultraprecision 84 inch diamond turning machine,” Precis. Eng. 1, 13–17 (1979).
[CrossRef]

1972

1953

Abramson, N. H.

Aketagawa, M.

T. Q. Banh, M. Ishige, Y. Ohkubo, and M. Aketagawa, “Measurement of air refractive index fluctuation from laser frequency shift with uncertainty of order 10−9,” Meas. Sci. Technol. 20, 125302–125309 (2009).
[CrossRef]

M. Aketagawa, K. Takada, K. Kobayashi, N. Takeshima, M. Noro, and Y. Nakayama, “Length measurement using a regular crystalline lattice and a dual tunneling unit scanning tunneling microscope in a thermo-stabilized cell,” Meas. Sci. Technol. 9, 1076–1081 (1998).
[CrossRef]

Banh, T. Q.

T. Q. Banh, M. Ishige, Y. Ohkubo, and M. Aketagawa, “Measurement of air refractive index fluctuation from laser frequency shift with uncertainty of order 10−9,” Meas. Sci. Technol. 20, 125302–125309 (2009).
[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]

Bitou, Y.

Bryan, J. B.

J. B. Bryan, “Design and construction of an ultraprecision 84 inch diamond turning machine,” Precis. Eng. 1, 13–17 (1979).
[CrossRef]

Buchta, Z.

O. Cip, F. Petru, Z. Buchta, and J. Lazar, “Small displacement measurements with subatomic resolution by beat frequency measurements,” Meas. Sci. Technol. 18, 2005–2013 (2007).
[CrossRef]

Carlsson, T. E.

Chen, H. Y.

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

Ciddor, P. E.

Cip, O.

O. Cip, F. Petru, Z. Buchta, and J. Lazar, “Small displacement measurements with subatomic resolution by beat frequency measurements,” Meas. Sci. Technol. 18, 2005–2013 (2007).
[CrossRef]

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]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Edlen, B.

Eickhoff, M. L.

Ekinci, K. L.

D. Karabacak, T. Kouh, and K. L. Ekinci, “Analysis of optical interferometric displacement detection in nanoelectromechanical systems,” J. Appl. Phys. 98, 124309–124318 (2005).
[CrossRef]

Fang, H.

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Golubkova, V. P.

Gustafsson, J.

Hall, J. L.

M. L. Eickhoff and J. L. Hall, “Real-time precision refractometry: new approaches,” Appl. Opt. 36, 1223–1234 (1997).
[CrossRef] [PubMed]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Higuchi, K.

Himbert, M.

Hong, F. L.

Hosoe, S.

S. Hosoe, “Laser interferometric system for displacement measurement with high precision,” Nanotechnology 2, 88–92(1991).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Hsu, C. C.

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

Inaba, H.

Ishige, M.

T. Q. Banh, M. Ishige, Y. Ohkubo, and M. Aketagawa, “Measurement of air refractive index fluctuation from laser frequency shift with uncertainty of order 10−9,” Meas. Sci. Technol. 20, 125302–125309 (2009).
[CrossRef]

Juncar, P.

Karabacak, D.

D. Karabacak, T. Kouh, and K. L. Ekinci, “Analysis of optical interferometric displacement detection in nanoelectromechanical systems,” J. Appl. Phys. 98, 124309–124318 (2005).
[CrossRef]

Khelifa, N.

Kiryanov, V. P.

Kobayashi, K.

M. Aketagawa, K. Takada, K. Kobayashi, N. Takeshima, M. Noro, and Y. Nakayama, “Length measurement using a regular crystalline lattice and a dual tunneling unit scanning tunneling microscope in a thermo-stabilized cell,” Meas. Sci. Technol. 9, 1076–1081 (1998).
[CrossRef]

Koronkevitch, V. P.

Kouh, T.

D. Karabacak, T. Kouh, and K. L. Ekinci, “Analysis of optical interferometric displacement detection in nanoelectromechanical systems,” J. Appl. Phys. 98, 124309–124318 (2005).
[CrossRef]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Lazar, J.

O. Cip, F. Petru, Z. Buchta, and J. Lazar, “Small displacement measurements with subatomic resolution by beat frequency measurements,” Meas. Sci. Technol. 18, 2005–2013 (2007).
[CrossRef]

Lee, J. Y.

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

Lenkova, G. A.

Lokhmatov, A. I.

Maruyama, T.

Matienko, B. G.

Matsumoto, H.

Minoshima, K.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Nakayama, Y.

M. Aketagawa, K. Takada, K. Kobayashi, N. Takeshima, M. Noro, and Y. Nakayama, “Length measurement using a regular crystalline lattice and a dual tunneling unit scanning tunneling microscope in a thermo-stabilized cell,” Meas. Sci. Technol. 9, 1076–1081 (1998).
[CrossRef]

Noro, M.

M. Aketagawa, K. Takada, K. Kobayashi, N. Takeshima, M. Noro, and Y. Nakayama, “Length measurement using a regular crystalline lattice and a dual tunneling unit scanning tunneling microscope in a thermo-stabilized cell,” Meas. Sci. Technol. 9, 1076–1081 (1998).
[CrossRef]

Ohkubo, Y.

T. Q. Banh, M. Ishige, Y. Ohkubo, and M. Aketagawa, “Measurement of air refractive index fluctuation from laser frequency shift with uncertainty of order 10−9,” Meas. Sci. Technol. 20, 125302–125309 (2009).
[CrossRef]

Onae, A.

Petru, F.

O. Cip, F. Petru, Z. Buchta, and J. Lazar, “Small displacement measurements with subatomic resolution by beat frequency measurements,” Meas. Sci. Technol. 18, 2005–2013 (2007).
[CrossRef]

Sasaki, O.

Schibli, T. R.

Suzuki, T.

Takada, K.

M. Aketagawa, K. Takada, K. Kobayashi, N. Takeshima, M. Noro, and Y. Nakayama, “Length measurement using a regular crystalline lattice and a dual tunneling unit scanning tunneling microscope in a thermo-stabilized cell,” Meas. Sci. Technol. 9, 1076–1081 (1998).
[CrossRef]

Takahashi, K.

Takeshima, N.

M. Aketagawa, K. Takada, K. Kobayashi, N. Takeshima, M. Noro, and Y. Nakayama, “Length measurement using a regular crystalline lattice and a dual tunneling unit scanning tunneling microscope in a thermo-stabilized cell,” Meas. Sci. Technol. 9, 1076–1081 (1998).
[CrossRef]

Tsherbatchenko, A. M.

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Weng, H. F.

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

Wu, C. C.

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

Xu, J.

Appl. Opt.

Appl. Phys. B

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

J. Appl. Phys.

D. Karabacak, T. Kouh, and K. L. Ekinci, “Analysis of optical interferometric displacement detection in nanoelectromechanical systems,” J. Appl. Phys. 98, 124309–124318 (2005).
[CrossRef]

J. Opt. Soc. Am.

Meas. Sci. Technol.

T. Q. Banh, M. Ishige, Y. Ohkubo, and M. Aketagawa, “Measurement of air refractive index fluctuation from laser frequency shift with uncertainty of order 10−9,” Meas. Sci. Technol. 20, 125302–125309 (2009).
[CrossRef]

M. Aketagawa, K. Takada, K. Kobayashi, N. Takeshima, M. Noro, and Y. Nakayama, “Length measurement using a regular crystalline lattice and a dual tunneling unit scanning tunneling microscope in a thermo-stabilized cell,” Meas. Sci. Technol. 9, 1076–1081 (1998).
[CrossRef]

O. Cip, F. Petru, Z. Buchta, and J. Lazar, “Small displacement measurements with subatomic resolution by beat frequency measurements,” Meas. Sci. Technol. 18, 2005–2013 (2007).
[CrossRef]

Metrologia

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

Nanotechnology

S. Hosoe, “Laser interferometric system for displacement measurement with high precision,” Nanotechnology 2, 88–92(1991).
[CrossRef]

Opt. Commun.

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

Opt. Express

Precis. Eng.

J. B. Bryan, “Design and construction of an ultraprecision 84 inch diamond turning machine,” Precis. Eng. 1, 13–17 (1979).
[CrossRef]

Other

“International Technology Roadmap for Semiconductors,” http://public.itrs.net/.

“A roadmap for the development of United States astronomical adaptive optics,” http://www.noao.edu/system/aodp/AO_Roadmap2008_Final.pdf.

Agilent 10717A Wavelength Tracker, Agilent technologies 5301 Stevens Creek, Santa Clara, California. 95051, USA.

For example, Agilent Technologies, 5301 Stevens Creek Boulevard, Santa Clara, California 95051, USA.

For example, Ranishaw Plc. Old Town, Wotton-under-Edge, Gloucestershire, GL12 7DW, UK.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of system for suppressing Δ n air . FSL, frequency-stabilized He–Ne laser; FI, Faraday isolator; M, steering mirror; EOM, electro-optical modulator; PBS, polarization beam splitter; LIA, lock-in amplifier; LPF, low-pass filter; APD, avalanche photodetector; DSP, digital signal processor; PD, photodetector; P, pressure sensor; T, temperature sensor; PZT, piezoelectric volume actuator; SM/MM, single-mode/multimode fibers; FT, fiber through connector; Amp, amplifier; OSC, oscillator.

Fig. 2
Fig. 2

Schematic diagram of Δ n air measurement system. ECLD, external cavity laser diode; BS, beam splitter; PL, polarizer; FG, function generator. (a) Optical and electronic schematic of Δ n air measurement system. (b) Laser and electronic schematic of Δ n air measurement system.

Fig. 3
Fig. 3

(a) Temperature and pressure variations when bellows is moved by the PZT volume actuator. (b) Comparison of Δ n air measurement by the FP cavity based ECLD frequency change method and the Ciddor method, taken when bellows is moved by the PZT volume actuator.

Fig. 4
Fig. 4

(a) Photograph of Δ n air suppression system. (b) Photograph of the FP cavity and the associated optical components.

Fig. 5
Fig. 5

(a) Δ n air measurement by the Ciddor method and the Wavelength Tracker when bellows is not controlled. (b) Temperature and pressure variations during measurement when the bellows is not controlled.

Fig. 6
Fig. 6

(a) Evaluation of the stabilization of Δ n air using the Wavelength Tracker and the Ciddor method when the bellows is controlled. (b) Temperature and controlled pressure during the suppression of Δ n air .

Fig. 7
Fig. 7

Relationship between the LIA signal and the scanned pressure in the chamber.

Tables (1)

Tables Icon

Table 1 Total Uncertainty of the Measurement System

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

Δ n air = n air p Δ p + n air T Δ T .
p V = m R T ,
Δ p p = Δ V V + Δ T T ,
Δ n air = n air p p Δ V V + ( n air p p T + n air T ) Δ T .
n air L = c N 2 f ,
Δ n air n air = Δ f f Δ L L + Δ N N ,
Δ n air n air Δ N N .
Δ n air n air Δ f f ,
U Δ n air / n air = { U Δ f / f } 2 + { U Δ L / L } 2 + { U Δ N / N } 2 .
V LIA ( P ) a P ,
Δ V LIA = V LIA ( Δ P ) a Δ P .
Δ N ( N + 1 ) N = Δ N = Δ P P f .
N = 2 f L c .
U Δ N N = Δ N N = 9 × 10 6 3.16 × 10 5 2.8 × 10 11 .

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