Abstract

Frequency changes induced by bias or temperature modulation of injection diode lasers can provide an economical and effective method of applying phase-stepping interferometry to optical metrology. However, the intrinsic frequency instability of these devices limits their use in gauge block interferometry where precise and repeatable phase steps must be maintained simultaneously on two discontinuous surfaces and over relatively long path lengths. We demonstrate a method using a visible injection diode laser, the frequency of which is locked by using a Fabry–Perot interferometer. Small changes to the length of the Fabry–Perot interferometer shift the frequency of the laser producing proportional and repeatable phase steps to the gauge block interferogram. This method has been successfully implemented with a Fizeau-type gauge block interferometer with a phase measurement resolution of 0.005λ. The phase data are then processed to map the surface form of gauge blocks up to 100  mm in length and to objectively assess surface shape parameters.

© 2006 Optical Society of America

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References

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  1. ISO3650: Geometrical Product Specifications-Length Standards-Gauge Blocks (International Standards Organization, Geneva, 1999).
  2. Bureau International des Poids et Mesures, "Documents concerning the new definition of the metre," Metrologia 19,163-177, (1984).
  3. T. J. Quinn, "Practical realisation of the definition of the metre, including recommended radiations of other optical frequency standards (2001)," Metrologia 40, 103-133 (2003).
    [CrossRef]
  4. K. P. Birch and M. J. Downs, "Correction to the updated Edlén equation for the refractive index of air," Metrologia 31, 315-316 (1994).
    [CrossRef]
  5. K. G. Birch, Uncertainties in the Measurement of Gauge Blocks by Interferometry, Technical Rep. MOM 29 (National Physical Laboratory, London, 1978).
  6. J. E. Decker and J. R. Pekelsky, "Uncertainty evaluation for the measurement of gauge blocks by optical interferometry," Metrologia 34, 479-493 (1997).
    [CrossRef]
  7. A. J. Lewis, "Measurement of length, surface form and thermal expansion coefficient of length bars up to 1.5 m using multiple wavelength phase-stepping interferometry," Meas. Sci. Technol. 5, 694-703 (1994).
    [CrossRef]
  8. J. E. Decker, R. Schödel, and G. Bönsch, "Considerations for the evaluation of measurement uncertainty in interferometric gauge block calibration applying methods of phase step interferometry," Metrologia 41, L11-L17 (2004).
    [CrossRef]
  9. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
    [CrossRef]
  10. S. Kaiser, T. Maier, A. Grossmann, and C. Zimmermann, "Fizeau interferometer for phase shifting interferometry in ultra-high vacuum," Rev. Sci. Instrum 72, 3726-3327 (2001).
    [CrossRef]
  11. P. de Groot, "Measurement of transparent plates with wavelength-tuned phase-shifting interferometry," Appl. Opt. 39, 2658-2663 (2000).
    [CrossRef]
  12. Y. Ishii, "Wavelength-tunable laser diode interferometer," Opt. Rev. 6, 273-283 (1999).
    [CrossRef]
  13. P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, Y. Gilliand , C. H. Freund, A. J. Leistner, J. A. Seckold, and C. J. Walsh, "300-mm-aperture phase-shifting Fizeau interfer ometer," Opt. Eng. 38, 1371-1380 (1999).
    [CrossRef]
  14. Y. C. Chung, "Frequency-locked 1.3-μ-m and 1.5-μ-m semiconductor-lasers for lightwave systems applications," J. Lightwave Technol. 8, 869-876 (1990).
    [CrossRef]
  15. C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "Absolute frequency stabilisation of a 637 nm laser diode using Doppler free I2 spectra," Electron. Lett. 31, 796-797 (1995).
    [CrossRef]
  16. S. P. Poole and J. H. Dowell, "Application of interferometry to the routine measurement of block gauges," in Optics in Metrology (Pergamon, 1958), pp. 405-419.
  17. M. O'Hora, S. Peyton, B. Bowe, and V. Toal, "Modernisation of a Hilger & Watts gauge block interferometer," Opt. Eng. 44, 035601 (2005).
    [CrossRef]
  18. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2002).
  19. G. Bönsch and H. Böhme, "Phase-determination of Fizeau interferences by phase-shifting interferometry," Optik 82, 161-164 (1989).
  20. K. G. Larkin and B. F. Oreb, "Design and assessment of symmetrical phase-shifting algorithms," J. Opt. Soc. Am. A 9, 1740-1748 (1992).
    [CrossRef]
  21. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, "Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts," J. Opt. Soc. Am. A 14, 918-930 (1997).
    [CrossRef]
  22. Y. Surrel, "Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts: comment," J. Opt. Soc. Am. A 15, 805-807 (1998).
    [CrossRef]
  23. K. Hibino, "Error-compensating phase measuring algorithms in a Fizeau interferometer," Opt. Rev. 6, 529-538 (1999).
    [CrossRef]

2005

M. O'Hora, S. Peyton, B. Bowe, and V. Toal, "Modernisation of a Hilger & Watts gauge block interferometer," Opt. Eng. 44, 035601 (2005).
[CrossRef]

2004

J. E. Decker, R. Schödel, and G. Bönsch, "Considerations for the evaluation of measurement uncertainty in interferometric gauge block calibration applying methods of phase step interferometry," Metrologia 41, L11-L17 (2004).
[CrossRef]

2003

T. J. Quinn, "Practical realisation of the definition of the metre, including recommended radiations of other optical frequency standards (2001)," Metrologia 40, 103-133 (2003).
[CrossRef]

2001

S. Kaiser, T. Maier, A. Grossmann, and C. Zimmermann, "Fizeau interferometer for phase shifting interferometry in ultra-high vacuum," Rev. Sci. Instrum 72, 3726-3327 (2001).
[CrossRef]

2000

1999

K. Hibino, "Error-compensating phase measuring algorithms in a Fizeau interferometer," Opt. Rev. 6, 529-538 (1999).
[CrossRef]

Y. Ishii, "Wavelength-tunable laser diode interferometer," Opt. Rev. 6, 273-283 (1999).
[CrossRef]

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, Y. Gilliand , C. H. Freund, A. J. Leistner, J. A. Seckold, and C. J. Walsh, "300-mm-aperture phase-shifting Fizeau interfer ometer," Opt. Eng. 38, 1371-1380 (1999).
[CrossRef]

1998

Y. Surrel, "Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts: comment," J. Opt. Soc. Am. A 15, 805-807 (1998).
[CrossRef]

1997

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, "Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts," J. Opt. Soc. Am. A 14, 918-930 (1997).
[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]

1995

C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "Absolute frequency stabilisation of a 637 nm laser diode using Doppler free I2 spectra," Electron. Lett. 31, 796-797 (1995).
[CrossRef]

1994

A. J. Lewis, "Measurement of length, surface form and thermal expansion coefficient of length bars up to 1.5 m using multiple wavelength phase-stepping interferometry," Meas. Sci. Technol. 5, 694-703 (1994).
[CrossRef]

K. P. Birch and M. J. Downs, "Correction to the updated Edlén equation for the refractive index of air," Metrologia 31, 315-316 (1994).
[CrossRef]

1992

1990

Y. C. Chung, "Frequency-locked 1.3-μ-m and 1.5-μ-m semiconductor-lasers for lightwave systems applications," J. Lightwave Technol. 8, 869-876 (1990).
[CrossRef]

1989

G. Bönsch and H. Böhme, "Phase-determination of Fizeau interferences by phase-shifting interferometry," Optik 82, 161-164 (1989).

Barwood, G. P.

C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "Absolute frequency stabilisation of a 637 nm laser diode using Doppler free I2 spectra," Electron. Lett. 31, 796-797 (1995).
[CrossRef]

Birch, K. G.

K. G. Birch, Uncertainties in the Measurement of Gauge Blocks by Interferometry, Technical Rep. MOM 29 (National Physical Laboratory, London, 1978).

Birch, K. P.

K. P. Birch and M. J. Downs, "Correction to the updated Edlén equation for the refractive index of air," Metrologia 31, 315-316 (1994).
[CrossRef]

Böhme, H.

G. Bönsch and H. Böhme, "Phase-determination of Fizeau interferences by phase-shifting interferometry," Optik 82, 161-164 (1989).

Bönsch, G.

J. E. Decker, R. Schödel, and G. Bönsch, "Considerations for the evaluation of measurement uncertainty in interferometric gauge block calibration applying methods of phase step interferometry," Metrologia 41, L11-L17 (2004).
[CrossRef]

G. Bönsch and H. Böhme, "Phase-determination of Fizeau interferences by phase-shifting interferometry," Optik 82, 161-164 (1989).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2002).

Bowe, B.

M. O'Hora, S. Peyton, B. Bowe, and V. Toal, "Modernisation of a Hilger & Watts gauge block interferometer," Opt. Eng. 44, 035601 (2005).
[CrossRef]

Chung, Y. C.

Y. C. Chung, "Frequency-locked 1.3-μ-m and 1.5-μ-m semiconductor-lasers for lightwave systems applications," J. Lightwave Technol. 8, 869-876 (1990).
[CrossRef]

de Groot, P.

Decker, J. E.

J. E. Decker, R. Schödel, and G. Bönsch, "Considerations for the evaluation of measurement uncertainty in interferometric gauge block calibration applying methods of phase step interferometry," Metrologia 41, L11-L17 (2004).
[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]

Dowell, J. H.

S. P. Poole and J. H. Dowell, "Application of interferometry to the routine measurement of block gauges," in Optics in Metrology (Pergamon, 1958), pp. 405-419.

Downs, M. J.

K. P. Birch and M. J. Downs, "Correction to the updated Edlén equation for the refractive index of air," Metrologia 31, 315-316 (1994).
[CrossRef]

Edwards, C. S.

C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "Absolute frequency stabilisation of a 637 nm laser diode using Doppler free I2 spectra," Electron. Lett. 31, 796-797 (1995).
[CrossRef]

Fairman, P. S.

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, Y. Gilliand , C. H. Freund, A. J. Leistner, J. A. Seckold, and C. J. Walsh, "300-mm-aperture phase-shifting Fizeau interfer ometer," Opt. Eng. 38, 1371-1380 (1999).
[CrossRef]

Farrant, D. I.

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, Y. Gilliand , C. H. Freund, A. J. Leistner, J. A. Seckold, and C. J. Walsh, "300-mm-aperture phase-shifting Fizeau interfer ometer," Opt. Eng. 38, 1371-1380 (1999).
[CrossRef]

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, "Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts," J. Opt. Soc. Am. A 14, 918-930 (1997).
[CrossRef]

Freund, C. H.

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, Y. Gilliand , C. H. Freund, A. J. Leistner, J. A. Seckold, and C. J. Walsh, "300-mm-aperture phase-shifting Fizeau interfer ometer," Opt. Eng. 38, 1371-1380 (1999).
[CrossRef]

Gill, P.

C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "Absolute frequency stabilisation of a 637 nm laser diode using Doppler free I2 spectra," Electron. Lett. 31, 796-797 (1995).
[CrossRef]

Gilliand, Y.

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, Y. Gilliand , C. H. Freund, A. J. Leistner, J. A. Seckold, and C. J. Walsh, "300-mm-aperture phase-shifting Fizeau interfer ometer," Opt. Eng. 38, 1371-1380 (1999).
[CrossRef]

Grossmann, A.

S. Kaiser, T. Maier, A. Grossmann, and C. Zimmermann, "Fizeau interferometer for phase shifting interferometry in ultra-high vacuum," Rev. Sci. Instrum 72, 3726-3327 (2001).
[CrossRef]

Hibino, K.

Ishii, Y.

Y. Ishii, "Wavelength-tunable laser diode interferometer," Opt. Rev. 6, 273-283 (1999).
[CrossRef]

Kaiser, S.

S. Kaiser, T. Maier, A. Grossmann, and C. Zimmermann, "Fizeau interferometer for phase shifting interferometry in ultra-high vacuum," Rev. Sci. Instrum 72, 3726-3327 (2001).
[CrossRef]

Larkin, K. G.

Leistner, A. J.

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, Y. Gilliand , C. H. Freund, A. J. Leistner, J. A. Seckold, and C. J. Walsh, "300-mm-aperture phase-shifting Fizeau interfer ometer," Opt. Eng. 38, 1371-1380 (1999).
[CrossRef]

Lewis, A. J.

A. J. Lewis, "Measurement of length, surface form and thermal expansion coefficient of length bars up to 1.5 m using multiple wavelength phase-stepping interferometry," Meas. Sci. Technol. 5, 694-703 (1994).
[CrossRef]

Maier, T.

S. Kaiser, T. Maier, A. Grossmann, and C. Zimmermann, "Fizeau interferometer for phase shifting interferometry in ultra-high vacuum," Rev. Sci. Instrum 72, 3726-3327 (2001).
[CrossRef]

O'Hora, M.

M. O'Hora, S. Peyton, B. Bowe, and V. Toal, "Modernisation of a Hilger & Watts gauge block interferometer," Opt. Eng. 44, 035601 (2005).
[CrossRef]

Oreb, B. F.

Pekelsky, J. R.

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

Peyton, S.

M. O'Hora, S. Peyton, B. Bowe, and V. Toal, "Modernisation of a Hilger & Watts gauge block interferometer," Opt. Eng. 44, 035601 (2005).
[CrossRef]

Poole, S. P.

S. P. Poole and J. H. Dowell, "Application of interferometry to the routine measurement of block gauges," in Optics in Metrology (Pergamon, 1958), pp. 405-419.

Quinn, T. J.

T. J. Quinn, "Practical realisation of the definition of the metre, including recommended radiations of other optical frequency standards (2001)," Metrologia 40, 103-133 (2003).
[CrossRef]

Rowley, W. R. C.

C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "Absolute frequency stabilisation of a 637 nm laser diode using Doppler free I2 spectra," Electron. Lett. 31, 796-797 (1995).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Schödel, R.

J. E. Decker, R. Schödel, and G. Bönsch, "Considerations for the evaluation of measurement uncertainty in interferometric gauge block calibration applying methods of phase step interferometry," Metrologia 41, L11-L17 (2004).
[CrossRef]

Seckold, J. A.

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, Y. Gilliand , C. H. Freund, A. J. Leistner, J. A. Seckold, and C. J. Walsh, "300-mm-aperture phase-shifting Fizeau interfer ometer," Opt. Eng. 38, 1371-1380 (1999).
[CrossRef]

Surrel, Y.

Y. Surrel, "Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts: comment," J. Opt. Soc. Am. A 15, 805-807 (1998).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Toal, V.

M. O'Hora, S. Peyton, B. Bowe, and V. Toal, "Modernisation of a Hilger & Watts gauge block interferometer," Opt. Eng. 44, 035601 (2005).
[CrossRef]

Walsh, C. J.

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, Y. Gilliand , C. H. Freund, A. J. Leistner, J. A. Seckold, and C. J. Walsh, "300-mm-aperture phase-shifting Fizeau interfer ometer," Opt. Eng. 38, 1371-1380 (1999).
[CrossRef]

Ward, B. K.

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, Y. Gilliand , C. H. Freund, A. J. Leistner, J. A. Seckold, and C. J. Walsh, "300-mm-aperture phase-shifting Fizeau interfer ometer," Opt. Eng. 38, 1371-1380 (1999).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2002).

Zimmermann, C.

S. Kaiser, T. Maier, A. Grossmann, and C. Zimmermann, "Fizeau interferometer for phase shifting interferometry in ultra-high vacuum," Rev. Sci. Instrum 72, 3726-3327 (2001).
[CrossRef]

Appl. Opt.

Electron. Lett.

C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "Absolute frequency stabilisation of a 637 nm laser diode using Doppler free I2 spectra," Electron. Lett. 31, 796-797 (1995).
[CrossRef]

J. Lightwave Technol.

Y. C. Chung, "Frequency-locked 1.3-μ-m and 1.5-μ-m semiconductor-lasers for lightwave systems applications," J. Lightwave Technol. 8, 869-876 (1990).
[CrossRef]

J. Opt. Soc. Am. A

Meas. Sci. Technol.

A. J. Lewis, "Measurement of length, surface form and thermal expansion coefficient of length bars up to 1.5 m using multiple wavelength phase-stepping interferometry," Meas. Sci. Technol. 5, 694-703 (1994).
[CrossRef]

Metrologia

J. E. Decker, R. Schödel, and G. Bönsch, "Considerations for the evaluation of measurement uncertainty in interferometric gauge block calibration applying methods of phase step interferometry," Metrologia 41, L11-L17 (2004).
[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]

T. J. Quinn, "Practical realisation of the definition of the metre, including recommended radiations of other optical frequency standards (2001)," Metrologia 40, 103-133 (2003).
[CrossRef]

K. P. Birch and M. J. Downs, "Correction to the updated Edlén equation for the refractive index of air," Metrologia 31, 315-316 (1994).
[CrossRef]

Opt. Eng.

M. O'Hora, S. Peyton, B. Bowe, and V. Toal, "Modernisation of a Hilger & Watts gauge block interferometer," Opt. Eng. 44, 035601 (2005).
[CrossRef]

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, Y. Gilliand , C. H. Freund, A. J. Leistner, J. A. Seckold, and C. J. Walsh, "300-mm-aperture phase-shifting Fizeau interfer ometer," Opt. Eng. 38, 1371-1380 (1999).
[CrossRef]

Opt. Rev.

Y. Ishii, "Wavelength-tunable laser diode interferometer," Opt. Rev. 6, 273-283 (1999).
[CrossRef]

K. Hibino, "Error-compensating phase measuring algorithms in a Fizeau interferometer," Opt. Rev. 6, 529-538 (1999).
[CrossRef]

Optik

G. Bönsch and H. Böhme, "Phase-determination of Fizeau interferences by phase-shifting interferometry," Optik 82, 161-164 (1989).

Rev. Sci. Instrum

S. Kaiser, T. Maier, A. Grossmann, and C. Zimmermann, "Fizeau interferometer for phase shifting interferometry in ultra-high vacuum," Rev. Sci. Instrum 72, 3726-3327 (2001).
[CrossRef]

Other

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

K. G. Birch, Uncertainties in the Measurement of Gauge Blocks by Interferometry, Technical Rep. MOM 29 (National Physical Laboratory, London, 1978).

ISO3650: Geometrical Product Specifications-Length Standards-Gauge Blocks (International Standards Organization, Geneva, 1999).

Bureau International des Poids et Mesures, "Documents concerning the new definition of the metre," Metrologia 19,163-177, (1984).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2002).

S. P. Poole and J. H. Dowell, "Application of interferometry to the routine measurement of block gauges," in Optics in Metrology (Pergamon, 1958), pp. 405-419.

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Figures (4)

Fig. 1
Fig. 1

Schematic of the optical configuration used for the calibration of absolute length of the gauge and the assessment of gauge block surface form by using the diode laser phase-stepping system.

Fig. 2
Fig. 2

Diode laser control methodology showing transmission vpd through the reference Fabry–Perot interferometer as a function of diode laser frequency ν ld. A control algorithm seeks to maintain a set point voltage Vs through injection current feedback into the diode. A change in the interferometer spacing h 1h 2 shifts the transmission peak, and hence the lasing frequency ν1 → ν2 stabilization point. This method is used to produce stable and proportional phase steps in the gauge block interferogram, Fig. 1, by spacing changes alone.

Fig. 3
Fig. 3

(a) Gauge block (25 mm) interferogram illuminated by a stabilized laser diode. The gauge surface is in the center of the field, reference fringes are significantly attenuated by the glass reference surface. (b) Reference surface fringes phase stepped by +π, gauge fringes are stepped by approximately +3π∕5 due to the longer path length. (c) Gauge fringes stepped by +π, reference fringes are stepped by +5π∕6.

Fig. 4
Fig. 4

(Color online) Surface length deviation of a 25 mm gauge block (ISO Grade 1), the interferograms of which are shown in Fig. 3. Surface parameters, deviation from nominal e = −0.06 μm; length variation v = 0.065 μm; and deviation from flatness fd = 0.054 μm.

Equations (6)

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

l o = ( M 1 + f 1 ) λ 1 2 = ( M 2 + f 2 ) λ 2 2 = = ( M n + f n ) λ n 2 ,
δ ν l d = c 2 π L δ φ r .
i ( x , y ) = A ( x , y ) ( 1 B 1 C cos φ ( x , y ) ) .
B = ( 1 r 1     2 ) ( 1 r 2     2 ) 1 + r 1     2 r 2     2 , C = 2 r 1 r 2 1 + r 1     2 r 2     2 .
i ( x , y ) = A { 1 B 1 C cos [ k v f p φ ( x , y ) ] } .
i ( x , y ) = [ A ( x , y ) + α v f p ] × { 1 B 1 C cos [ 2 π v f p / V 2 π + φ i ( x , y ) ] } + E ( x , y ) .

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