Abstract

A new interferometric method for ultra-precise measurement of laser-beam angular deflection is proposed. The angular tilt of a measuring device in relation to the beam axis also can be measured. The method is based on interference fringe period analysis in the selected plane of measurement. The theoretical basis and experimental verification of the method are presented. It is shown that by using the proposed technique, it is possible to measure the laser beam angular deflection or instability with ultrahigh resolution reaching single nanoradians. The proposed method allows the measurement and further compensation of laser beam deflections in a very compact design.

© 2013 Optical Society of America

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References

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  1. “Lasers and laser-related equipment—test methods for laser beam parameters—beam positional stability,” International Standard , April2003.
  2. “Measuring laser position & pointing stability—application note,” Photon Inc. Precision Beam Profiling, Photonics Online, 2009, http://www.photonicsonline.com/article.mvc/Measuring-Laser-Position-Pointing-Stability-0002 .
  3. http://www.ophiropt.com/laser-measurement-instruments/beam-profilers/products/slit-based-profilers/nanoscan .
  4. C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” Appl. Phys. 72, 6–12 (1992).
    [CrossRef]
  5. G. Meyer and N. M. Amer, “Optical beam deflection atomic force microscopy: the NaCl (001) surface,” Appl. Phys. Lett. 56, 2100–2101 (1990).
    [CrossRef]
  6. M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux, and M. Tiedtke, “Laser pointing stability measurements,” Proc. SPIE 2870, 216–224 (1996).
    [CrossRef]
  7. P. S. Huang, S. Kiyono, and O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt. 31, 6047–6055 (1992).
    [CrossRef]
  8. P. S. Huang and J. Ni, “Angle measurement based on the internal-reflection effect using elongated critical-angle prisms,” Appl. Opt. 35, 2239–2241 (1996).
    [CrossRef]
  9. A. García-Valenzuela, “Detection limits of an internal-reflection sensor for the optical beam deflection method,” Appl. Opt. 36, 4456–4462 (1997).
    [CrossRef]
  10. A. García-Valenzuela, G. E. Sandoval-Romero, and C. Sánchez-Pérez, “High-resolution optical angle sensors: approaching the diffraction limit to the sensitivity,” Appl. Opt. 43, 4311–4321 (2004).
    [CrossRef]
  11. J. Villatoro and A. García-Valenzuela, “Measuring optical power transmission near the critical angle for sensing beam deflection,” Appl. Opt. 37, 6649–6653 (1998).
  12. S. Zhang, S. Kiyono, and Y. Uda, “Nanoradian angle sensor and in situ self-calibration,” Appl. Opt. 37, 4154–4159 (1998).
    [CrossRef]
  13. P. S. Huang, “Use of thin films for high-sensitivity angle measurement,” Appl. Opt. 38, 4831–4836 (1999).
    [CrossRef]
  14. A. Zhang and P. S. Huang, “Total internal reflection for precision small-angle measurement,” Appl. Opt. 40, 1617–1622 (2001).
    [CrossRef]
  15. J. Gray, P. Thomas, and X. D. Zhu, “Laser pointing stability measured by an oblique-incidence optical transmittance difference technique,” Rev. Sci. Instrum. 72, 3714–3717 (2001).
    [CrossRef]
  16. A. García-Valenzuela, M. Peña-Gomar, and J. Villatoro, “Sensitivity analysis of angle sensitive detectors based on a film resonator,” Opt. Eng. 42, 1084–1092 (2003).
    [CrossRef]
  17. A. García-Valenzuela and R. Díaz-Uribe, “Approach to improve the angle sensitivity and resolution of the optical beam deflection method using a passive interferometer and a Ronchi grating,” Opt. Eng. 36, 1770–1778 (1997).
    [CrossRef]
  18. E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, “Automatic alignment of optical interferometers,” Appl. Opt. 33, 5041–5049 (1994).
    [CrossRef]
  19. P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78, 073103 (2007).
    [CrossRef]
  20. P. Kwee, “Laser characterization and stabilization for precision interferometry,” Ph.D. thesis (Von der Fakultat fur Mathematik und Physik der Gottfried Wilhelm Leibniz Universitat Hannover zur Erlangung des Grades, 2010).
  21. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  22. M. Dobosz and O. Iwasińska-Kowalska, “Measuring method for angular deviations of the laser beam and an interferometer for measuring the angular deviations of the laser beam,” Polish patent application P-397925 (January27, 2012) (in Polish).
  23. O. Iwasińska-Kowalska, “A system for precise laser beam angular steering,” Metrol. Meas. Syst.XXI (2014), to be published.
  24. M. Dobosz, “Laser diode distance measuring interferometer—metrological properties,” Metrol. Meas. Syst. XIX, 553–564 (2012).
  25. R. Caulcutt and R. Boddy, Statistics for Analytical Chemists (Chapman & Hall, 1983).
  26. E. C. Fieller, “Some problems in interval estimation,” J. R. Stat. Soc. Ser. B 16, 175–185 (1954).

2012 (1)

M. Dobosz, “Laser diode distance measuring interferometer—metrological properties,” Metrol. Meas. Syst. XIX, 553–564 (2012).

2007 (1)

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

2004 (1)

2003 (1)

A. García-Valenzuela, M. Peña-Gomar, and J. Villatoro, “Sensitivity analysis of angle sensitive detectors based on a film resonator,” Opt. Eng. 42, 1084–1092 (2003).
[CrossRef]

2001 (2)

A. Zhang and P. S. Huang, “Total internal reflection for precision small-angle measurement,” Appl. Opt. 40, 1617–1622 (2001).
[CrossRef]

J. Gray, P. Thomas, and X. D. Zhu, “Laser pointing stability measured by an oblique-incidence optical transmittance difference technique,” Rev. Sci. Instrum. 72, 3714–3717 (2001).
[CrossRef]

1999 (1)

1998 (2)

J. Villatoro and A. García-Valenzuela, “Measuring optical power transmission near the critical angle for sensing beam deflection,” Appl. Opt. 37, 6649–6653 (1998).

S. Zhang, S. Kiyono, and Y. Uda, “Nanoradian angle sensor and in situ self-calibration,” Appl. Opt. 37, 4154–4159 (1998).
[CrossRef]

1997 (2)

A. García-Valenzuela, “Detection limits of an internal-reflection sensor for the optical beam deflection method,” Appl. Opt. 36, 4456–4462 (1997).
[CrossRef]

A. García-Valenzuela and R. Díaz-Uribe, “Approach to improve the angle sensitivity and resolution of the optical beam deflection method using a passive interferometer and a Ronchi grating,” Opt. Eng. 36, 1770–1778 (1997).
[CrossRef]

1996 (2)

P. S. Huang and J. Ni, “Angle measurement based on the internal-reflection effect using elongated critical-angle prisms,” Appl. Opt. 35, 2239–2241 (1996).
[CrossRef]

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux, and M. Tiedtke, “Laser pointing stability measurements,” Proc. SPIE 2870, 216–224 (1996).
[CrossRef]

1994 (1)

1992 (2)

P. S. Huang, S. Kiyono, and O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt. 31, 6047–6055 (1992).
[CrossRef]

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” Appl. Phys. 72, 6–12 (1992).
[CrossRef]

1990 (1)

G. Meyer and N. M. Amer, “Optical beam deflection atomic force microscopy: the NaCl (001) surface,” Appl. Phys. Lett. 56, 2100–2101 (1990).
[CrossRef]

1954 (1)

E. C. Fieller, “Some problems in interval estimation,” J. R. Stat. Soc. Ser. B 16, 175–185 (1954).

Amer, N. M.

G. Meyer and N. M. Amer, “Optical beam deflection atomic force microscopy: the NaCl (001) surface,” Appl. Phys. Lett. 56, 2100–2101 (1990).
[CrossRef]

Boddy, R.

R. Caulcutt and R. Boddy, Statistics for Analytical Chemists (Chapman & Hall, 1983).

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Caulcutt, R.

R. Caulcutt and R. Boddy, Statistics for Analytical Chemists (Chapman & Hall, 1983).

Champagne, Y.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux, and M. Tiedtke, “Laser pointing stability measurements,” Proc. SPIE 2870, 216–224 (1996).
[CrossRef]

Danzmann, K.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

De Grooth, B. G.

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Díaz-Uribe, R.

A. García-Valenzuela and R. Díaz-Uribe, “Approach to improve the angle sensitivity and resolution of the optical beam deflection method using a passive interferometer and a Ronchi grating,” Opt. Eng. 36, 1770–1778 (1997).
[CrossRef]

Dobosz, M.

M. Dobosz, “Laser diode distance measuring interferometer—metrological properties,” Metrol. Meas. Syst. XIX, 553–564 (2012).

M. Dobosz and O. Iwasińska-Kowalska, “Measuring method for angular deviations of the laser beam and an interferometer for measuring the angular deviations of the laser beam,” Polish patent application P-397925 (January27, 2012) (in Polish).

Fieller, E. C.

E. C. Fieller, “Some problems in interval estimation,” J. R. Stat. Soc. Ser. B 16, 175–185 (1954).

Galarneau, P.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux, and M. Tiedtke, “Laser pointing stability measurements,” Proc. SPIE 2870, 216–224 (1996).
[CrossRef]

García-Valenzuela, A.

A. García-Valenzuela, G. E. Sandoval-Romero, and C. Sánchez-Pérez, “High-resolution optical angle sensors: approaching the diffraction limit to the sensitivity,” Appl. Opt. 43, 4311–4321 (2004).
[CrossRef]

A. García-Valenzuela, M. Peña-Gomar, and J. Villatoro, “Sensitivity analysis of angle sensitive detectors based on a film resonator,” Opt. Eng. 42, 1084–1092 (2003).
[CrossRef]

J. Villatoro and A. García-Valenzuela, “Measuring optical power transmission near the critical angle for sensing beam deflection,” Appl. Opt. 37, 6649–6653 (1998).

A. García-Valenzuela and R. Díaz-Uribe, “Approach to improve the angle sensitivity and resolution of the optical beam deflection method using a passive interferometer and a Ronchi grating,” Opt. Eng. 36, 1770–1778 (1997).
[CrossRef]

A. García-Valenzuela, “Detection limits of an internal-reflection sensor for the optical beam deflection method,” Appl. Opt. 36, 4456–4462 (1997).
[CrossRef]

Gray, J.

J. Gray, P. Thomas, and X. D. Zhu, “Laser pointing stability measured by an oblique-incidence optical transmittance difference technique,” Rev. Sci. Instrum. 72, 3714–3717 (2001).
[CrossRef]

Greve, J.

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Huang, P. S.

Iwasinska-Kowalska, O.

M. Dobosz and O. Iwasińska-Kowalska, “Measuring method for angular deviations of the laser beam and an interferometer for measuring the angular deviations of the laser beam,” Polish patent application P-397925 (January27, 2012) (in Polish).

O. Iwasińska-Kowalska, “A system for precise laser beam angular steering,” Metrol. Meas. Syst.XXI (2014), to be published.

Kamada, O.

Kiyono, S.

Kwee, P.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

P. Kwee, “Laser characterization and stabilization for precision interferometry,” Ph.D. thesis (Von der Fakultat fur Mathematik und Physik der Gottfried Wilhelm Leibniz Universitat Hannover zur Erlangung des Grades, 2010).

Levesque, M.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux, and M. Tiedtke, “Laser pointing stability measurements,” Proc. SPIE 2870, 216–224 (1996).
[CrossRef]

Mailloux, A.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux, and M. Tiedtke, “Laser pointing stability measurements,” Proc. SPIE 2870, 216–224 (1996).
[CrossRef]

Meers, B. J.

Meyer, G.

G. Meyer and N. M. Amer, “Optical beam deflection atomic force microscopy: the NaCl (001) surface,” Appl. Phys. Lett. 56, 2100–2101 (1990).
[CrossRef]

Morin, M.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux, and M. Tiedtke, “Laser pointing stability measurements,” Proc. SPIE 2870, 216–224 (1996).
[CrossRef]

Morrison, E.

Ni, J.

Peña-Gomar, M.

A. García-Valenzuela, M. Peña-Gomar, and J. Villatoro, “Sensitivity analysis of angle sensitive detectors based on a film resonator,” Opt. Eng. 42, 1084–1092 (2003).
[CrossRef]

Plomteux, O.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux, and M. Tiedtke, “Laser pointing stability measurements,” Proc. SPIE 2870, 216–224 (1996).
[CrossRef]

Putman, C. A. J.

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Robertson, D. I.

Sánchez-Pérez, C.

Sandoval-Romero, G. E.

Seifert, F.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

Thomas, P.

J. Gray, P. Thomas, and X. D. Zhu, “Laser pointing stability measured by an oblique-incidence optical transmittance difference technique,” Rev. Sci. Instrum. 72, 3714–3717 (2001).
[CrossRef]

Tiedtke, M.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux, and M. Tiedtke, “Laser pointing stability measurements,” Proc. SPIE 2870, 216–224 (1996).
[CrossRef]

Uda, Y.

van de Hulst, N. F.

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Villatoro, J.

A. García-Valenzuela, M. Peña-Gomar, and J. Villatoro, “Sensitivity analysis of angle sensitive detectors based on a film resonator,” Opt. Eng. 42, 1084–1092 (2003).
[CrossRef]

J. Villatoro and A. García-Valenzuela, “Measuring optical power transmission near the critical angle for sensing beam deflection,” Appl. Opt. 37, 6649–6653 (1998).

Ward, H.

Willke, B.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Zhang, A.

Zhang, S.

Zhu, X. D.

J. Gray, P. Thomas, and X. D. Zhu, “Laser pointing stability measured by an oblique-incidence optical transmittance difference technique,” Rev. Sci. Instrum. 72, 3714–3717 (2001).
[CrossRef]

Appl. Opt. (9)

Appl. Phys. (1)

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Appl. Phys. Lett. (1)

G. Meyer and N. M. Amer, “Optical beam deflection atomic force microscopy: the NaCl (001) surface,” Appl. Phys. Lett. 56, 2100–2101 (1990).
[CrossRef]

J. R. Stat. Soc. Ser. B (1)

E. C. Fieller, “Some problems in interval estimation,” J. R. Stat. Soc. Ser. B 16, 175–185 (1954).

Metrol. Meas. Syst. (1)

M. Dobosz, “Laser diode distance measuring interferometer—metrological properties,” Metrol. Meas. Syst. XIX, 553–564 (2012).

Opt. Eng. (2)

A. García-Valenzuela, M. Peña-Gomar, and J. Villatoro, “Sensitivity analysis of angle sensitive detectors based on a film resonator,” Opt. Eng. 42, 1084–1092 (2003).
[CrossRef]

A. García-Valenzuela and R. Díaz-Uribe, “Approach to improve the angle sensitivity and resolution of the optical beam deflection method using a passive interferometer and a Ronchi grating,” Opt. Eng. 36, 1770–1778 (1997).
[CrossRef]

Proc. SPIE (1)

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux, and M. Tiedtke, “Laser pointing stability measurements,” Proc. SPIE 2870, 216–224 (1996).
[CrossRef]

Rev. Sci. Instrum. (2)

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

J. Gray, P. Thomas, and X. D. Zhu, “Laser pointing stability measured by an oblique-incidence optical transmittance difference technique,” Rev. Sci. Instrum. 72, 3714–3717 (2001).
[CrossRef]

Other (8)

P. Kwee, “Laser characterization and stabilization for precision interferometry,” Ph.D. thesis (Von der Fakultat fur Mathematik und Physik der Gottfried Wilhelm Leibniz Universitat Hannover zur Erlangung des Grades, 2010).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

M. Dobosz and O. Iwasińska-Kowalska, “Measuring method for angular deviations of the laser beam and an interferometer for measuring the angular deviations of the laser beam,” Polish patent application P-397925 (January27, 2012) (in Polish).

O. Iwasińska-Kowalska, “A system for precise laser beam angular steering,” Metrol. Meas. Syst.XXI (2014), to be published.

“Lasers and laser-related equipment—test methods for laser beam parameters—beam positional stability,” International Standard , April2003.

“Measuring laser position & pointing stability—application note,” Photon Inc. Precision Beam Profiling, Photonics Online, 2009, http://www.photonicsonline.com/article.mvc/Measuring-Laser-Position-Pointing-Stability-0002 .

http://www.ophiropt.com/laser-measurement-instruments/beam-profilers/products/slit-based-profilers/nanoscan .

R. Caulcutt and R. Boddy, Statistics for Analytical Chemists (Chapman & Hall, 1983).

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Figures (12)

Fig. 1.
Fig. 1.

Changing the direction of the beam reflected by a plane mirror when the angle of incidence is changed in the plane of reflection (here in the plane of the drawing).

Fig. 2.
Fig. 2.

Superposition of two mutually coherent plane wavefronts, inclined relative to each other spatially.

Fig. 3.
Fig. 3.

(a) Simple four-element photodetector to measure changes in interference fringe period. (b) Intensity distribution in relation to the proposed photodetector. Full line represents interference fringe distribution of period δ. Gray line refers to the interference fringe of period δ0, which matches twice the distance between the photoelements. A and C are the amplitude and constant of the interference signal, respectively.

Fig. 4.
Fig. 4.

Theoretical dependence I(θR): (a) 0<θR<6 and (b) 0.55<θR<1.45. θR is defined by Eq. (16).

Fig. 5.
Fig. 5.

Examples of possible optical setups for the interferometer. (a) Simplest setup for explanation of the idea of the measuring method. (b) Compact interferometer constructed using simple commercially available optical elements. (c) Low-dimensional compact interferometer based on pentaprism configuration.

Fig. 6.
Fig. 6.

(a) Effect of angular deviation of a beam reflected from a planar mirror due to the angular deviation of the incident beam in a plane perpendicular to the original plane of reflection. (b) Influence of the deviation of the interferometer input beam in the plane perpendicular to the initial plane of the interference on the position of the final plane of the interference.

Fig. 7.
Fig. 7.

Schematic diagram of the experimental setup.

Fig. 8.
Fig. 8.

Theoretical model according to Eq. (17) and experimental data (squares).

Fig. 9.
Fig. 9.

Observed angular fluctuations of the laser beam. Black line represents output voltage obtained from the TI. Gray line represents angular deflections measured by the reference AI.

Fig. 10.
Fig. 10.

Calibration line of the interferometer output voltage versus laser beam deflection angle.

Fig. 11.
Fig. 11.

Signal controlling laser beam deflections by means of the PM (gray points) and response of the TI (black points). Full lines represent results of applying moving average for digital data filtration.

Fig. 12.
Fig. 12.

Angular fluctuations of LB before and after closing the feedback loop of the stabilization system.

Equations (32)

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

Iθ=C+Acos[2ksinθy+Δφ],
k=2πλ.
δ=λ2sin(θ).
δλ2θ.
dδδdθθ,
I=I1+I4I2I3.
V=sinc(πwδ),
δ=δ0,
I1=C+VAcos(2πδ·3δ04)=I4,
I2=C+VAcos(2πδ·δ04)=I3,
I=2I12I2.
dIdδ=2(dI1dδdI2dδ).
dIdδ|δ=δ0=4πVAδ0.
dI4πVAθ0dθ,
δ0δθθ0=dfθR,
I=8VAcos(π2·θR)sin2(π2·θR).
8AV=334ΔIpp,
θ0=|θ0in|.
I1(α)=C+VAcos(3π2+α)=CVAsinα,
I2(α)=C+VAcos(π2+α)=C+VAsinα,
I3(α)=C+VAcos(π2+α)=CVAsinα,
I4(α)=C+VAcos(3π2+α)=C+VAsinα.
I(α)=I1(α)I3(α)+I2(α)I4(α)=0.
dI(new)b0b1±tαb1MSE(1m+1n+(dI(new)dI¯)2b12i=1n(dθ(i)dθ¯)2),
sin(π2·θR)=0
sin2(π2·θR)+2cos2(π2·θR)=0.
cos(π2·θR)=±13,
π2·θR=arccos13
π2·θR=arccos13.
Imin=16VA33
Imax=16VA33.
ΔIpp=ImaxImin=32VA33,

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