Abstract

The inhomogeneity of high-reflectivity mirror coatings is a potential error source in the application of the cavity ringdown technique. Here, the ringdown times for different transverse modes were recorded. Together with the observed spatial distribution of these modes the ringdown times can be used to approximately locate the position of coating defects. A simple model based on a weighted sum of Hermite–Gaussian mode functions is used to explain the experimental results.

© 2014 Optical Society of America

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References

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  1. Y. He and B. J. Orr, “Detection of trace gases by rapidly-swept continuous-wave cavity ringdown spectroscopy: pushing the limits of sensitivity,” Appl. Phys. B 85, 355–364 (2006).
    [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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    [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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    [CrossRef]

2012

2011

A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-Drever-Hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011).
[CrossRef]

2010

2009

Y. Gong, Y. Han, and B. Li, “Effect of threshold value on high reflectivity measurement with optical feedback cavity ring-down technique,” Proc. SPIE 7283, 72830U (2009).
[CrossRef]

2007

2006

Y. He and B. J. Orr, “Detection of trace gases by rapidly-swept continuous-wave cavity ringdown spectroscopy: pushing the limits of sensitivity,” Appl. Phys. B 85, 355–364 (2006).
[CrossRef]

J. T. Hodges and D. Lisak, “Frequency-stabilized cavity ring-down spectrometer for high-sensitivity measurements of water vapor concentration,” Appl. Phys. B 85, 375–382 (2006).
[CrossRef]

2005

M. Mazurenka, A. J. Orr-Ewing, R. Peverall, and G. A. D. Ritchie, “Cavity ring-down and cavity enhanced spectroscopy using diode lasers,” Ann. Rep. Prog. Chem., Sect. C 101, 100–142 (2005).

C. Vallance, “Innovations in cavity ringdown spectroscopy,” New J. Chem. 29, 867–874 (2005).
[CrossRef]

T. Klaassen, J. de Jong, M. van Exter, and J. P. Woerdman, “Transverse mode coupling in an optical resonator,” Opt. Lett. 30, 1959–1961 (2005).
[CrossRef]

B. A. Paldus and A. A. Kachanov, “An historical overview of cavity-enhanced methods,” Can. J. Phys. 83, 975–999 (2005).
[CrossRef]

2000

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565–607 (2000).
[CrossRef]

1998

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

1997

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, “CW cavity ring down spectroscopy,” Chem. Phys. Lett. 264, 316–322 (1997).
[CrossRef]

1996

K. K. Lehmann and D. Romanini, “The superposition principle and cavity ring-down spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
[CrossRef]

1993

D. Romanini and K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Chem. Phys. 99, 6287–6301 (1993).
[CrossRef]

1984

1980

Abe, H.

A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-Drever-Hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011).
[CrossRef]

Anderson, D. Z.

Benard, D. J.

Berden, G.

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565–607 (2000).
[CrossRef]

Bielska, K.

A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-Drever-Hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011).
[CrossRef]

Boyson, T. K.

Calzada, M. E.

Ciurylo, R.

A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-Drever-Hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011).
[CrossRef]

Cygan, A.

A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-Drever-Hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011).
[CrossRef]

de Jong, J.

Domyslawska, J.

A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-Drever-Hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011).
[CrossRef]

Frisch, J. C.

Gong, Y.

Y. Gong, Y. Han, and B. Li, “Effect of threshold value on high reflectivity measurement with optical feedback cavity ring-down technique,” Proc. SPIE 7283, 72830U (2009).
[CrossRef]

Han, Y.

Y. Gong, Y. Han, and B. Li, “Effect of threshold value on high reflectivity measurement with optical feedback cavity ring-down technique,” Proc. SPIE 7283, 72830U (2009).
[CrossRef]

Harb, C. C.

Harris, J. S.

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

He, Y.

Y. He and B. J. Orr, “Detection of trace gases by rapidly-swept continuous-wave cavity ringdown spectroscopy: pushing the limits of sensitivity,” Appl. Phys. B 85, 355–364 (2006).
[CrossRef]

Herbelin, J. M.

Hodges, J. T.

A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-Drever-Hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011).
[CrossRef]

J. T. Hodges and D. Lisak, “Frequency-stabilized cavity ring-down spectrometer for high-sensitivity measurements of water vapor concentration,” Appl. Phys. B 85, 375–382 (2006).
[CrossRef]

Huang, H. F.

Kachanov, A. A.

B. A. Paldus and A. A. Kachanov, “An historical overview of cavity-enhanced methods,” Can. J. Phys. 83, 975–999 (2005).
[CrossRef]

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, “CW cavity ring down spectroscopy,” Chem. Phys. Lett. 264, 316–322 (1997).
[CrossRef]

Kallapur, A. G.

Kirkbride, K. P.

Klaassen, T.

Kogelnik, H.

H. Kogelnik and T. Li, “Laser beams and resonators,” in Proceedings of the Institute of Electrical and Electronics Engineers (1966), Vol. 54, p. 1312.

Kwok, M. A.

Lehmann, K. K.

H. F. Huang and K. K. Lehmann, “Noise in cavity ring-down spectroscopy caused by transverse mode coupling,” Opt. Express 15, 8745–8759 (2007).
[CrossRef]

K. K. Lehmann and D. Romanini, “The superposition principle and cavity ring-down spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
[CrossRef]

D. Romanini and K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Chem. Phys. 99, 6287–6301 (1993).
[CrossRef]

Li, B.

Y. Gong, Y. Han, and B. Li, “Effect of threshold value on high reflectivity measurement with optical feedback cavity ring-down technique,” Proc. SPIE 7283, 72830U (2009).
[CrossRef]

Li, T.

H. Kogelnik and T. Li, “Laser beams and resonators,” in Proceedings of the Institute of Electrical and Electronics Engineers (1966), Vol. 54, p. 1312.

Lisak, D.

A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-Drever-Hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011).
[CrossRef]

J. T. Hodges and D. Lisak, “Frequency-stabilized cavity ring-down spectrometer for high-sensitivity measurements of water vapor concentration,” Appl. Phys. B 85, 375–382 (2006).
[CrossRef]

Long, X.

Long, X. W.

Maslowski, P.

A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-Drever-Hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011).
[CrossRef]

Masser, C. S.

Mazurenka, M.

M. Mazurenka, A. J. Orr-Ewing, R. Peverall, and G. A. D. Ritchie, “Cavity ring-down and cavity enhanced spectroscopy using diode lasers,” Ann. Rep. Prog. Chem., Sect. C 101, 100–142 (2005).

McKay, J. A.

Meijer, G.

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565–607 (2000).
[CrossRef]

Moore, D. S.

Orr, B. J.

Y. He and B. J. Orr, “Detection of trace gases by rapidly-swept continuous-wave cavity ringdown spectroscopy: pushing the limits of sensitivity,” Appl. Phys. B 85, 355–364 (2006).
[CrossRef]

Orr-Ewing, A. J.

M. Mazurenka, A. J. Orr-Ewing, R. Peverall, and G. A. D. Ritchie, “Cavity ring-down and cavity enhanced spectroscopy using diode lasers,” Ann. Rep. Prog. Chem., Sect. C 101, 100–142 (2005).

Paldus, B. A.

B. A. Paldus and A. A. Kachanov, “An historical overview of cavity-enhanced methods,” Can. J. Phys. 83, 975–999 (2005).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

Peeters, R.

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565–607 (2000).
[CrossRef]

Petersen, I. R.

Peverall, R.

M. Mazurenka, A. J. Orr-Ewing, R. Peverall, and G. A. D. Ritchie, “Cavity ring-down and cavity enhanced spectroscopy using diode lasers,” Ann. Rep. Prog. Chem., Sect. C 101, 100–142 (2005).

Ritchie, G. A. D.

M. Mazurenka, A. J. Orr-Ewing, R. Peverall, and G. A. D. Ritchie, “Cavity ring-down and cavity enhanced spectroscopy using diode lasers,” Ann. Rep. Prog. Chem., Sect. C 101, 100–142 (2005).

Romanini, D.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, “CW cavity ring down spectroscopy,” Chem. Phys. Lett. 264, 316–322 (1997).
[CrossRef]

K. K. Lehmann and D. Romanini, “The superposition principle and cavity ring-down spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
[CrossRef]

D. Romanini and K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Chem. Phys. 99, 6287–6301 (1993).
[CrossRef]

Sadeghi, N.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, “CW cavity ring down spectroscopy,” Chem. Phys. Lett. 264, 316–322 (1997).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (including the author’s list of corrections), 1st ed. (University Science Books, 1986).

Silfvast, W. T.

W. T. Silfvast, Laser Fundamentals (Cambridge University, 2008).

Spence, T. G.

Spencer, D. J.

Stoeckel, F.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, “CW cavity ring down spectroscopy,” Chem. Phys. Lett. 264, 316–322 (1997).
[CrossRef]

Tan, Z. Q.

Trawinski, R. S.

A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-Drever-Hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011).
[CrossRef]

Ueunten, R. H.

Urevig, D. S.

Vallance, C.

C. Vallance, “Innovations in cavity ringdown spectroscopy,” New J. Chem. 29, 867–874 (2005).
[CrossRef]

van Exter, M.

Wilke, B.

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

Woerdman, J. P.

Wojtewicz, S.

A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-Drever-Hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011).
[CrossRef]

Wu, S.

Xie, J.

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

Yang, K.

Zare, R. N.

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

Ann. Rep. Prog. Chem., Sect. C

M. Mazurenka, A. J. Orr-Ewing, R. Peverall, and G. A. D. Ritchie, “Cavity ring-down and cavity enhanced spectroscopy using diode lasers,” Ann. Rep. Prog. Chem., Sect. C 101, 100–142 (2005).

Appl. Opt.

Appl. Phys. B

Y. He and B. J. Orr, “Detection of trace gases by rapidly-swept continuous-wave cavity ringdown spectroscopy: pushing the limits of sensitivity,” Appl. Phys. B 85, 355–364 (2006).
[CrossRef]

J. T. Hodges and D. Lisak, “Frequency-stabilized cavity ring-down spectrometer for high-sensitivity measurements of water vapor concentration,” Appl. Phys. B 85, 375–382 (2006).
[CrossRef]

Appl. Spectrosc.

Can. J. Phys.

B. A. Paldus and A. A. Kachanov, “An historical overview of cavity-enhanced methods,” Can. J. Phys. 83, 975–999 (2005).
[CrossRef]

Chem. Phys. Lett.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, “CW cavity ring down spectroscopy,” Chem. Phys. Lett. 264, 316–322 (1997).
[CrossRef]

Int. Rev. Phys. Chem.

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565–607 (2000).
[CrossRef]

J. Appl. Phys.

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

J. Chem. Phys.

K. K. Lehmann and D. Romanini, “The superposition principle and cavity ring-down spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
[CrossRef]

D. Romanini and K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Chem. Phys. 99, 6287–6301 (1993).
[CrossRef]

J. Opt. Soc. Am. B

New J. Chem.

C. Vallance, “Innovations in cavity ringdown spectroscopy,” New J. Chem. 29, 867–874 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

Y. Gong, Y. Han, and B. Li, “Effect of threshold value on high reflectivity measurement with optical feedback cavity ring-down technique,” Proc. SPIE 7283, 72830U (2009).
[CrossRef]

Rev. Sci. Instrum.

A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-Drever-Hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011).
[CrossRef]

Other

W. T. Silfvast, Laser Fundamentals (Cambridge University, 2008).

H. Kogelnik and T. Li, “Laser beams and resonators,” in Proceedings of the Institute of Electrical and Electronics Engineers (1966), Vol. 54, p. 1312.

A. E. Siegman, Lasers (including the author’s list of corrections), 1st ed. (University Science Books, 1986).

G. Berden and R. Engeln, eds., Cavity Ring-Down Spectroscopy: Techniques and Applications (Wiley-Blackwell, 2009).

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Figures (7)

Fig. 1.
Fig. 1.

Simulated intensity distribution functions for a set of Hermite–Gaussian transverse cavity modes.

Fig. 2.
Fig. 2.

Intensity distribution function assuming an incoherent sum of all transverse mode intensities functions. The sum includes all Hermite–Gaussian basis functions of Fig. 1 with n, m=0 to 6. (A) All 49 simulated Hermite–Gaussian functions each contain a small defect, I¯(x,y)R(x,y). The defect is in the center of the red circle. (B) Sum of all 49 simulated Hermite–Gaussian functions without a defect but weighted according to the fraction by which each mode samples the defect, n,m=0N,Mcm,nIm,n(x,y). The differences to (A) are barely visible. (C) Ratio between (A) and (B) showing the simulated reconstruction of the defect location, R(x,y), as described in Eq. (7). The comparison with (A) shows that all modes sampling the defect (in the lower right maximum) are attenuated. (D) Difference between (A) and (B) showing the simulated reconstruction of the defect location, R(x,y), as described in Eq. (10).

Fig. 3.
Fig. 3.

Sketch of the experimental CRD apparatus.

Fig. 4.
Fig. 4.

Cavity decay signal of the second mode in Table 1 and its fit to a single exponential function giving τ0=28.46μs and Γ=139.8ppm for one of the three measurements. After contamination of the mirrors a shorter ringdown time τ0=16.34μs and Γ=244.4ppm is obtained from the transient of the highlighted mode in Fig. 6.

Fig. 5.
Fig. 5.

Photographs of 15 different transverse cavity modes with respective optical loss (in ppm) after exposure to ambient air.

Fig. 6.
Fig. 6.

Photographs of 13 different transverse cavity modes with respective optical loss (in ppm) after a spot was painted on one of the mirrors.

Fig. 7.
Fig. 7.

Composite image obtained by adding normalized photographs of all transverse modes. (A) Sum of all modes shown in Fig. 5 after background subtraction and normalizing their intensity. (B) Sum of the same modes after weighting each normalized image by a factor dependent on the associated optical loss. (C) Ratio of (A) and (B). (D) Difference between (A) and (B). (E) Sum of all modes shown in Fig. 6 after background subtraction and normalizing their intensity. (F) Sum of the same modes after weighting each normalized image by a factor dependent on the associated optical loss. (G) Ratio of (E) and (F). (H) Difference between (E) and (F).

Tables (1)

Tables Icon

Table 1. Ringdown Times and Optical Loss Associated with Seven Different Transverse Cavity Modes for the Clean Cavity.a

Equations (10)

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

HGm(x)=(2πw2)1/412mm!Hm(2xw)exp(x2w2)m=0,1,2,3,HGn(y)=(2πw2)1/412nn!Hn(2yw)exp(y2w2)n=0,1,2,3,,
Im,n(x,y)=Im,n0[HGm(x)]2[HGn(y)]2.
1=x=HG(x)2dx=y=HG(y)2dy.
I0=Im,n0=x,y=Im,n(x,y)dxdy.
I¯(x,y)=n,m=0N,MIm,n(x,y)(N+1)(M+1).
cm,n=1I0x,y=Im,n(x,y)R(x,y)dxdy.
R(x,y)=n,m=0N,Mcm,nIm,n(x,y)I¯(x,y)(N+1)(M+1)=n,m=0N,Mcm,nIm,n(x,y)n,m=0N,MIm,n(x,y).
Γn,m=1exp(tRTτn,m),
ΔΓn,m=exp(tRTτ0)exp(tRTτn,m),
R(x,y)=I¯(x,y)n,m=0N,Mcm,nIm,n(x,y)(N+1)(M+1).

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