Abstract

We present an implementation of an absolute distance measurement system which uses frequency scanning interferometry (FSI). The technique, referred to as dynamic FSI, uses two frequency scanning lasers, a gas absorption cell and a reference interferometer to determine the unknown optical path length difference (OPD) of one or many measurement interferometers. The gas absorption cell is the length reference for the measurement system and is traceable to international standards through knowledge of the frequencies of its absorption features. The OPD of the measurement interferometers can vary during the measurement and the variation is measured at the sampling rate of the system (2.77 MHz in the system described here). The system is shown to measure distances from 0.2 m to 20 m with a combined relative uncertainty of 0.41 × 10−6 at the two sigma level (k = 2). It will be shown that within a scan the change in OPD of the measurement interferometer can be determined to a resolution of 40 nm.

© 2014 Optical Society of America

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References

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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]
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2013 (1)

2009 (1)

2008 (1)

2005 (1)

2002 (2)

W. Estler, K. Edmundson, G. Peggs, and D. Parker, “Large scale metrology—an update,” CIRP Ann. Manuf. Technol. 51, 587–609 (2002).
[Crossref]

T. Kinder and K.-D. Salewski, “Absolute distance interferometer with grating-stabilized tunable diode laser at 633 nm,” J. Opt. A: Pure Appl. Opt. 4, 364–368 (2002).
[Crossref]

2001 (1)

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10 (2001).
[Crossref]

1999 (1)

1996 (1)

1992 (2)

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. i. fundamentals,” Proc. IEEE 80, 520–538 (1992).
[Crossref]

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. ii. algorithms and applications,” Proc. IEEE 80, 540–568 (1992).
[Crossref]

1975 (1)

F. James and M. Roos, “Minuit: A System for Function Minimization and Analysis of the Parameter Errors and Correlations,” Comput. Phys. Commun. 10, 343–367 (1975).
[Crossref]

1930 (1)

S. Butterworth, “On the theory of filter amplifiers,” Wireless Eng. 7, 536–541 (1930).

Abou-Zeid, A.

Amann, M.-C.

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10 (2001).
[Crossref]

Baumann, E.

Boashash, B.

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. i. fundamentals,” Proc. IEEE 80, 520–538 (1992).
[Crossref]

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. ii. algorithms and applications,” Proc. IEEE 80, 540–568 (1992).
[Crossref]

Bosch, T.

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10 (2001).
[Crossref]

Butterworth, S.

S. Butterworth, “On the theory of filter amplifiers,” Wireless Eng. 7, 536–541 (1930).

Ciddor, P. E.

Coddington, I.

Coe, P. A.

P. A. Coe, “An investigation of frequency scanning interferometry for the alignment of the ATLAS semiconductor tracker,” Ph.D. thesis, University Of Oxford (2001).

Dale, J.

J. Dale, “A study of interferometric distance measurement systems on a prototype rapid tunnel reference surveyor and the effects of reference network errors at the international linear collider,” Ph.D thesis, University Of Oxford (2009).

Edmundson, K.

W. Estler, K. Edmundson, G. Peggs, and D. Parker, “Large scale metrology—an update,” CIRP Ann. Manuf. Technol. 51, 587–609 (2002).
[Crossref]

Estler, W.

W. Estler, K. Edmundson, G. Peggs, and D. Parker, “Large scale metrology—an update,” CIRP Ann. Manuf. Technol. 51, 587–609 (2002).
[Crossref]

Floch, S. L.

Gilbert, S. L.

Giorgetta, F. R.

Green, J.

J. Green, “Development of a prototype frequency scanning interferometric absolute distance measurement system for the survey & alignment of the international linear collider,” Ph.D. thesis, University Of Oxford (2007).

Hecht, E.

E. Hecht, Optics,, 4th ed. (Addison Wesley, 2001).

Howard, L.

James, F.

F. James and M. Roos, “Minuit: A System for Function Minimization and Analysis of the Parameter Errors and Correlations,” Comput. Phys. Commun. 10, 343–367 (1975).
[Crossref]

Kinder, T.

T. Kinder and K.-D. Salewski, “Absolute distance interferometer with grating-stabilized tunable diode laser at 633 nm,” J. Opt. A: Pure Appl. Opt. 4, 364–368 (2002).
[Crossref]

Knabe, K.

Krakiwsky, E.

D. Wells and E. Krakiwsky, The Method Of Least Squares (University Of New Brunswick, 1971).

Lescure, M.

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10 (2001).
[Crossref]

Lévêque, S.

Meiners-Hagen, K.

Myllyla, R.

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10 (2001).
[Crossref]

Newbury, N. R.

Parker, D.

W. Estler, K. Edmundson, G. Peggs, and D. Parker, “Large scale metrology—an update,” CIRP Ann. Manuf. Technol. 51, 587–609 (2002).
[Crossref]

Peggs, G.

W. Estler, K. Edmundson, G. Peggs, and D. Parker, “Large scale metrology—an update,” CIRP Ann. Manuf. Technol. 51, 587–609 (2002).
[Crossref]

Pollinger, F.

Rioux, M.

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10 (2001).
[Crossref]

Roos, M.

F. James and M. Roos, “Minuit: A System for Function Minimization and Analysis of the Parameter Errors and Correlations,” Comput. Phys. Commun. 10, 343–367 (1975).
[Crossref]

Salewski, K.-D.

T. Kinder and K.-D. Salewski, “Absolute distance interferometer with grating-stabilized tunable diode laser at 633 nm,” J. Opt. A: Pure Appl. Opt. 4, 364–368 (2002).
[Crossref]

Salvad, Y.

Schuhler, N.

Schwenke, H.

H. Schwenke, Etalon AG, Hinter dem Turme 20, 38114, Braunschweig, Germany (Personal Communication, 2011).

Sinclair, L. C.

Stejskal, A.

Stone, J. A.

Swann, W. C.

Urner, D.

M. Warden and D. Urner, “Apparatus and method for measuring distance,” International Patent number wo2012022956, (2010).

Warden, M.

M. Warden and D. Urner, “Apparatus and method for measuring distance,” International Patent number wo2012022956, (2010).

M. Warden, “Absolute distance metrology using frequency swept lasers,” Ph.D. thesis, University Of Oxford (2011).

Wedde, M.

Wells, D.

D. Wells and E. Krakiwsky, The Method Of Least Squares (University Of New Brunswick, 1971).

Appl. Opt. (4)

CIRP Ann. Manuf. Technol. (1)

W. Estler, K. Edmundson, G. Peggs, and D. Parker, “Large scale metrology—an update,” CIRP Ann. Manuf. Technol. 51, 587–609 (2002).
[Crossref]

Comput. Phys. Commun. (1)

F. James and M. Roos, “Minuit: A System for Function Minimization and Analysis of the Parameter Errors and Correlations,” Comput. Phys. Commun. 10, 343–367 (1975).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

T. Kinder and K.-D. Salewski, “Absolute distance interferometer with grating-stabilized tunable diode laser at 633 nm,” J. Opt. A: Pure Appl. Opt. 4, 364–368 (2002).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Eng. (1)

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10 (2001).
[Crossref]

Opt. Lett. (1)

Proc. IEEE (2)

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. i. fundamentals,” Proc. IEEE 80, 520–538 (1992).
[Crossref]

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. ii. algorithms and applications,” Proc. IEEE 80, 540–568 (1992).
[Crossref]

Wireless Eng. (1)

S. Butterworth, “On the theory of filter amplifiers,” Wireless Eng. 7, 536–541 (1930).

Other (10)

International Organization for Standardization, “Evaluation of measurement data - Guide to the expression of uncertainty in measurement,” International Organization for Standardization, Geneva (2008).

E. Hecht, Optics,, 4th ed. (Addison Wesley, 2001).

H. Schwenke, Etalon AG, Hinter dem Turme 20, 38114, Braunschweig, Germany (Personal Communication, 2011).

D. Wells and E. Krakiwsky, The Method Of Least Squares (University Of New Brunswick, 1971).

Etalon AG, http://www.etalon-ag.com/index.php/en .

M. Warden, “Absolute distance metrology using frequency swept lasers,” Ph.D. thesis, University Of Oxford (2011).

J. Dale, “A study of interferometric distance measurement systems on a prototype rapid tunnel reference surveyor and the effects of reference network errors at the international linear collider,” Ph.D thesis, University Of Oxford (2009).

P. A. Coe, “An investigation of frequency scanning interferometry for the alignment of the ATLAS semiconductor tracker,” Ph.D. thesis, University Of Oxford (2001).

J. Green, “Development of a prototype frequency scanning interferometric absolute distance measurement system for the survey & alignment of the international linear collider,” Ph.D. thesis, University Of Oxford (2007).

M. Warden and D. Urner, “Apparatus and method for measuring distance,” International Patent number wo2012022956, (2010).

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Figures (20)

Fig. 1
Fig. 1 A diagram of two fiber based Fizeau interferometers connected to a single laser.
Fig. 2
Fig. 2 A diagram of two Fizeau interferometers connected to two lasers and one gas absorption cell.
Fig. 3
Fig. 3 The normalised H13C14N absorption spectrum plotted against the phase of a reference interferometer.
Fig. 4
Fig. 4 Upper plot: Straight line fit to the reference phase at absorption peaks versus nominal frequency at the absorption peak. The reference phase is found by fitting to the absorption features in Fig. 3. Lower plot: The fit residual versus the laser frequency of the upper plot.
Fig. 5
Fig. 5 Photographs of the interferometers.
Fig. 6
Fig. 6 The Invar interferometers under construction.
Fig. 7
Fig. 7 Schematic of the calibration experiment.
Fig. 8
Fig. 8 The standard uncertainty of the LaserTRACER as defined in the text in section 3.1.
Fig. 9
Fig. 9 Upper Plot: Fit results from the calibration of a 165 mm long H13C14N cell. Middle Plot: Residual to the fit from the upper plot. Lower Plot: Relative residual to the fit from the upper plot.
Fig. 10
Fig. 10 Histogram of the relative residuals shown in the lower plot of Fig. 9.
Fig. 11
Fig. 11 Results from repeated calibrations of the 165 mm long H13C14N cell using both Invar interferometers. The error bars are the standard uncertainties of calibration constants.
Fig. 12
Fig. 12 Results from repeated calibrations of the 50 mm long H13C14N cell using both Invar interferometers. The error bars are the standard uncertainties of calibration constants.
Fig. 13
Fig. 13 Upper: Single FSI scan of a retro reflector on an oscillating piezo electric actuator. Lower: Fourier transform of the upper plot.
Fig. 14
Fig. 14 Upper Left: Multiple scans of a measurement interferometer with the target on a linear motion stage. Upper Right: Single scan at fastest linear motion stage speed. Lower Left: Zoom in of upper right with a straight line fit. Lower Right: Residual to the straight line fit in lower left.
Fig. 15
Fig. 15 Sub-scan measurement of an Invar interferometer.
Fig. 16
Fig. 16 Upper: The relative difference between the lengths measured by the two gas cells, one undergoing temperature variation, with and without temperature corrections applied. Lower: The temperature of the gas cell in the environmental chamber.
Fig. 17
Fig. 17 Histogram of the relative difference in the lengths measured by two different gas cells with temperature correction applied to the cell undergoing temperature variation.
Fig. 18
Fig. 18 Set-up of the long range tests.
Fig. 19
Fig. 19 Upper Plot: The residual of the fit to the long range test data. Lower Plot: The relative residual of the top plot
Fig. 20
Fig. 20 A histogram of the relative residual for the long range test data with a Gaussian fitted.

Tables (6)

Tables Icon

Table 1 The laser parameters used during the calibration experiment.

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Table 2 Gas cell calibration constants and uncertainties together with measurement relative uncertainty for systems using either gas cells.

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Table 3 Atmospheric elements of FSI measurement system uncertainties.

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Table 4 FSI measurement system uncertainties for the long gas cell.

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Table 5 FSI measurement system uncertainties for the short gas cell.

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Table 6 The laser settings used during the long range tests.

Equations (27)

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ϕ abs t i , R = 4 π c L R ν t i .
ϕ t i , R = 4 π c L R ν t i 4 π c L R ν t 0 = 4 π c L R Δ ν t i .
ϕ t i , M = 4 π c L M Δ ν t i .
ϕ t i , M ϕ t i , R = L M L R .
ϕ t i , R , 1 = 4 π c L R ν t i , 1 4 π c L R ν t 0 , 1
ϕ t i , R , 2 = 4 π c L R ν t i , 2 4 π c L R ν t 0 , 2
ϕ t i , M , 1 = 4 π c L t i , M ν t i , 1 4 π c L t 0 , M ν t 0 , 1
ϕ t i , M , 2 = 4 π c L t i , M ν t i , 2 4 π c L t 0 , M ν t 0 , 2
ϕ t a 1 , R , 1 = 4 π c L R ν t a 1 , 1 4 π c L R ν t 0 , 1
ϕ t a 2 , R , 2 = 4 π c L R ν t a 2 , 2 4 π c L R ν t 0 , 2
ϕ t a 3 , M , 1 = 4 π c L t a 3 , M ν t a 3 , 1 4 π c L t 0 , M ν t 0 , 1
ϕ t a 3 , M , 2 = 4 π c L t a 3 , M ν t a 3 , 2 4 π c L t 0 , M ν t 0 , 2
ϕ t i , R , 1 ϕ t a 1 , R , 1 + 4 π c L R ν t a 1 , 1 = 4 π c L R ν t i , 1
ϕ t i , R , 2 ϕ t a 2 , R , 2 + 4 π c L R ν t a 2 , 2 = 4 π c L R ν t i , 2
ϕ t i , M , 1 ϕ t a 3 , M , 1 + 4 π c L t a 3 , M ν t a 3 , 1 = 4 π c L t i , M ν t i , 1
ϕ t i , M , 2 ϕ t a 3 , M , 2 + 4 π c L t a 3 , M ν t a 3 , 2 = 4 π c L t i , M ν t i , 2
L t a 3 , M = ν t i , 2 ( ϕ t i , M , 1 ϕ t a 3 , M , 1 ) ν t i , 1 ( ϕ t i , M , 2 ϕ t a 3 , M , 2 ) 4 π c ( ν t a 3 , 2 ν t i , 1 ν t a 3 , 1 ν t i , 2 ) .
P V = n R T ,
P 0 / T 0 = n R / V .
P = P 0 × T T 0 .
L corrected = L measured C Gas Cell C Ciddor
F ( X , L ) = [ D 1 S ( ( x 1 x FSI ) 2 + ( y 1 y FSI ) 2 + ( z 1 z FSI ) 2 ) 1 / 2 D 2 S ( ( x 2 x FSI ) 2 + ( y 2 y FSI ) 2 + ( z 2 z FSI ) 2 ) 1 / 2 D n S ( ( x n x FSI ) 2 + ( y n y FSI ) 2 + ( z n z FSI ) 2 ) 1 / 2 ] = 0 .
x n = R n × sin ( θ n ) × cos ( ϕ n ) y n = R n × sin ( θ n ) × sin ( ϕ n ) z n = R n × cos ( θ n ) .
X = [ x FSI y FSI z FSI S ] .
L = [ R 0 θ 0 ϕ 0 D 0 . R n θ n ϕ n D n ] .
X ^ = ( A T ( B P 1 B T ) 1 A ) 1 A T ( B P 1 B T ) 1 W X 0 = X 0 + X ^
A = F ( X , L ) X | X 0 , L B = F ( X , L ) L | X 0 , L

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