Abstract

We present transmission optical coherence tomography (transmission OCT) as a versatile tool to measure optical material properties of turbid media. The transmission OCT signal is described in detail and it is demonstrated how the group refractive index (ng), group velocity dispersion (GVD) and optical attenuation can be determined from this signal. We experimentally validate the refractive index properties of glasses, liquids and glucose water solutions in terms of ng and GVD. Measurements of scattering coefficients are determined using transmission OCT for suspensions of silica particles. Quantitative agreement is obtained with a dependent scattering model, both for the average as well as the wavenumber resolved optical attenuation coefficient. Good agreement is observed between our measurements and literature values.

© 2015 Optical Society of America

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References

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    [Crossref]

2013 (2)

2012 (2)

S. Kedenburg, M. Vieweg, T. Gissibl, and H. Giessen, “Linear refractive index and absorption measurements of nonlinear optical liquids in the visible and near-infrared spectral region,” Opt. Mater. Express 2, 1588–1611 (2012).
[Crossref]

S. R. Kachiraju and D. A. Gregory, “Determining the refractive index of liquids using a modified Michelson interferometer,” Opt. and Laser Technol. 44, 2361–2365 (2012).
[Crossref]

2011 (5)

Y. Verma, P. Nandi, K. D. Rao, M. Sharma, and P. K. Gupta, “Use of common path phase sensitive spectral domain optical coherence tomography for refractive index measurements,” Appl. Optics 50, E7–E12 (2011).
[Crossref]

K. Barwari, D. M. de Bruin, E. C. Cauberg, D. J. Faber, T. G. van Leeuwen, H. Wijkstra, J. de la Rosette, and M. P. Laguna, “Advanced diagnostics in renal mass using optical coherence tomography: a preliminary report,” J. Endourol. 25, 311–315 (2011).
[Crossref] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, and M. C. Aalders, “In vivo low-coherence spectroscopic measurements of local hemoglobin absorption spectra in human skin,” J. Biomed. Opt. 16, 100504 (2011).
[Crossref] [PubMed]

R. H. Bremmer, S. C. Kanick, N. Laan, A. Amelink, T. G. van Leeuwen, and M. C. Aalders, “Non-contact spectroscopic determination of large blood volume fractions in turbid media,” Biomed. Opt. Express 2, 396–407 (2011).
[Crossref] [PubMed]

Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 11, 116017 (2011).
[Crossref]

2007 (1)

M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl Opt. 46, 3811–3820 (2007).
[Crossref] [PubMed]

2005 (1)

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[Crossref]

2004 (1)

2003 (2)

2002 (1)

2001 (1)

1997 (1)

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601 (1997).
[Crossref]

1993 (1)

M. R. Hee, E. A. Swanson, J. A. Izatt, J. M. Jacobson, and J. G. Fujimoto, “Femtosecond transillumination optical coherence tomography,” Opt. Lett 18, 950–952 (1993).
[Crossref] [PubMed]

1988 (1)

1984 (1)

B. Tatian, “Fitting refractive-index data with the sellmeier dispersion formula,” Appl. Optics 23, 4477–4485 (1984).
[Crossref]

1980 (1)

H. H. Li, “Refractive index of alkaline earth halides and its wavelength and temperature derivatives,” J. Phys. and Chem. Ref. Data 9, 161–290 (1980).
[Crossref]

1965 (1)

1963 (1)

1962 (1)

Aalders, M. C.

R. H. Bremmer, S. C. Kanick, N. Laan, A. Amelink, T. G. van Leeuwen, and M. C. Aalders, “Non-contact spectroscopic determination of large blood volume fractions in turbid media,” Biomed. Opt. Express 2, 396–407 (2011).
[Crossref] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, and M. C. Aalders, “In vivo low-coherence spectroscopic measurements of local hemoglobin absorption spectra in human skin,” J. Biomed. Opt. 16, 100504 (2011).
[Crossref] [PubMed]

Aernouts, B.

Alexandrov, S. A.

Amelink, A.

Armstrong, J. J.

Balla, A.

Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 11, 116017 (2011).
[Crossref]

Barwari, K.

K. Barwari, D. M. de Bruin, E. C. Cauberg, D. J. Faber, T. G. van Leeuwen, H. Wijkstra, J. de la Rosette, and M. P. Laguna, “Advanced diagnostics in renal mass using optical coherence tomography: a preliminary report,” J. Endourol. 25, 311–315 (2011).
[Crossref] [PubMed]

Bosschaart, N.

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, and M. C. Aalders, “In vivo low-coherence spectroscopic measurements of local hemoglobin absorption spectra in human skin,” J. Biomed. Opt. 16, 100504 (2011).
[Crossref] [PubMed]

Bouma, B.

Bremmer, R. H.

Cauberg, E. C.

K. Barwari, D. M. de Bruin, E. C. Cauberg, D. J. Faber, T. G. van Leeuwen, H. Wijkstra, J. de la Rosette, and M. P. Laguna, “Advanced diagnostics in renal mass using optical coherence tomography: a preliminary report,” J. Endourol. 25, 311–315 (2011).
[Crossref] [PubMed]

Cense, B.

Chen, T. C.

Daimon, M.

M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl Opt. 46, 3811–3820 (2007).
[Crossref] [PubMed]

M. Daimon and A. Masumura, “High-accuracy measurements of the refractive index and its temperature coefficient of calcium fluoride in a wide wavelength range from 138 to 2326 nm,” Appl. Opt. 41, 5275–5281 (2002).
[Crossref] [PubMed]

de Boer, J. F.

de Bruin, D. M.

K. Barwari, D. M. de Bruin, E. C. Cauberg, D. J. Faber, T. G. van Leeuwen, H. Wijkstra, J. de la Rosette, and M. P. Laguna, “Advanced diagnostics in renal mass using optical coherence tomography: a preliminary report,” J. Endourol. 25, 311–315 (2011).
[Crossref] [PubMed]

de la Rosette, J.

K. Barwari, D. M. de Bruin, E. C. Cauberg, D. J. Faber, T. G. van Leeuwen, H. Wijkstra, J. de la Rosette, and M. P. Laguna, “Advanced diagnostics in renal mass using optical coherence tomography: a preliminary report,” J. Endourol. 25, 311–315 (2011).
[Crossref] [PubMed]

Decraemer, W. F.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[Crossref]

Del Bianco, S.

Dirckx, J. J. J.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[Crossref]

Faber, D. J.

V. D. Nguyen, D. J. Faber, E. van der Pol, T. G. van Leeuwen, and J. Kalkman, “Dependent and multiple scattering in transmission and backscattering optical coherence tomography,” Opt. Express 21, 29145–29156 (2013).
[Crossref]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, and M. C. Aalders, “In vivo low-coherence spectroscopic measurements of local hemoglobin absorption spectra in human skin,” J. Biomed. Opt. 16, 100504 (2011).
[Crossref] [PubMed]

K. Barwari, D. M. de Bruin, E. C. Cauberg, D. J. Faber, T. G. van Leeuwen, H. Wijkstra, J. de la Rosette, and M. P. Laguna, “Advanced diagnostics in renal mass using optical coherence tomography: a preliminary report,” J. Endourol. 25, 311–315 (2011).
[Crossref] [PubMed]

Fercher, A. F.

Fujimoto, J. G.

M. R. Hee, E. A. Swanson, J. A. Izatt, J. M. Jacobson, and J. G. Fujimoto, “Femtosecond transillumination optical coherence tomography,” Opt. Lett 18, 950–952 (1993).
[Crossref] [PubMed]

Giessen, H.

Gissibl, T.

Gregory, D. A.

S. R. Kachiraju and D. A. Gregory, “Determining the refractive index of liquids using a modified Michelson interferometer,” Opt. and Laser Technol. 44, 2361–2365 (2012).
[Crossref]

Gupta, P. K.

Y. Verma, P. Nandi, K. D. Rao, M. Sharma, and P. K. Gupta, “Use of common path phase sensitive spectral domain optical coherence tomography for refractive index measurements,” Appl. Optics 50, E7–E12 (2011).
[Crossref]

Hee, M. R.

M. R. Hee, E. A. Swanson, J. A. Izatt, J. M. Jacobson, and J. G. Fujimoto, “Femtosecond transillumination optical coherence tomography,” Opt. Lett 18, 950–952 (1993).
[Crossref] [PubMed]

Heraeus,

Heraeus, Quartz Glass for Optics Data and Properties(2015).

Hikari,

Hikari, “Optical catalogue,” (2015).

Hillman, T. R.

Hitzenberger, C. K.

Izatt, J. A.

M. R. Hee, E. A. Swanson, J. A. Izatt, J. M. Jacobson, and J. G. Fujimoto, “Femtosecond transillumination optical coherence tomography,” Opt. Lett 18, 950–952 (1993).
[Crossref] [PubMed]

Jacobson, J. M.

M. R. Hee, E. A. Swanson, J. A. Izatt, J. M. Jacobson, and J. G. Fujimoto, “Femtosecond transillumination optical coherence tomography,” Opt. Lett 18, 950–952 (1993).
[Crossref] [PubMed]

Kachiraju, S. R.

S. R. Kachiraju and D. A. Gregory, “Determining the refractive index of liquids using a modified Michelson interferometer,” Opt. and Laser Technol. 44, 2361–2365 (2012).
[Crossref]

Kalkman, J.

Kanick, S. C.

Karamata, B.

Kasap, S. O.

W. C. Tan, K. Koughia, J. Singh, and S. O. Kasap, “Fundamental optical properties of materials I,” in Optical Properties of Condensed Matter and Applications, J. Singh, ed. (John Wiley and Sons, Ltd, Chichester, UK. 2006)
[Crossref]

Kedenburg, S.

Köser, J.

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601 (1997).
[Crossref]

Koughia, K.

W. C. Tan, K. Koughia, J. Singh, and S. O. Kasap, “Fundamental optical properties of materials I,” in Optical Properties of Condensed Matter and Applications, J. Singh, ed. (John Wiley and Sons, Ltd, Chichester, UK. 2006)
[Crossref]

Kuypers, L. C.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[Crossref]

Laan, N.

Laguna, M. P.

K. Barwari, D. M. de Bruin, E. C. Cauberg, D. J. Faber, T. G. van Leeuwen, H. Wijkstra, J. de la Rosette, and M. P. Laguna, “Advanced diagnostics in renal mass using optical coherence tomography: a preliminary report,” J. Endourol. 25, 311–315 (2011).
[Crossref] [PubMed]

Lammertyn, J.

Lasser, T.

Li, H. H.

H. H. Li, “Refractive index of alkaline earth halides and its wavelength and temperature derivatives,” J. Phys. and Chem. Ref. Data 9, 161–290 (1980).
[Crossref]

Malitson, I. H.

Martelli, F.

Masumura, A.

M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl Opt. 46, 3811–3820 (2007).
[Crossref] [PubMed]

M. Daimon and A. Masumura, “High-accuracy measurements of the refractive index and its temperature coefficient of calcium fluoride in a wide wavelength range from 138 to 2326 nm,” Appl. Opt. 41, 5275–5281 (2002).
[Crossref] [PubMed]

Mätzler, C.

C. Mätzler, “MATLAB functions for Mie scattering and absorption, version 2,” IAP Res. Rep.8 (2002).

Nandi, P.

Y. Verma, P. Nandi, K. D. Rao, M. Sharma, and P. K. Gupta, “Use of common path phase sensitive spectral domain optical coherence tomography for refractive index measurements,” Appl. Optics 50, E7–E12 (2011).
[Crossref]

Nassif, N.

Nguyen, V. D.

Park, B.

Pierce, M.

Popescu, G.

Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 11, 116017 (2011).
[Crossref]

Rahman, A. B.

Rao, K. D.

Y. Verma, P. Nandi, K. D. Rao, M. Sharma, and P. K. Gupta, “Use of common path phase sensitive spectral domain optical coherence tomography for refractive index measurements,” Appl. Optics 50, E7–E12 (2011).
[Crossref]

Rheims, J.

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601 (1997).
[Crossref]

Saeys, W.

Sampson, D.

Schott,

Schott, “Optical glass data sheets,” (2012).

Sharma, M.

Y. Verma, P. Nandi, K. D. Rao, M. Sharma, and P. K. Gupta, “Use of common path phase sensitive spectral domain optical coherence tomography for refractive index measurements,” Appl. Optics 50, E7–E12 (2011).
[Crossref]

Silva, K. K.

Singh, J.

W. C. Tan, K. Koughia, J. Singh, and S. O. Kasap, “Fundamental optical properties of materials I,” in Optical Properties of Condensed Matter and Applications, J. Singh, ed. (John Wiley and Sons, Ltd, Chichester, UK. 2006)
[Crossref]

Sticker, M.

Sumita,

Sumita, “Optical glass,” (2015).

Swanson, E. A.

M. R. Hee, E. A. Swanson, J. A. Izatt, J. M. Jacobson, and J. G. Fujimoto, “Femtosecond transillumination optical coherence tomography,” Opt. Lett 18, 950–952 (1993).
[Crossref] [PubMed]

Tan, W. C.

W. C. Tan, K. Koughia, J. Singh, and S. O. Kasap, “Fundamental optical properties of materials I,” in Optical Properties of Condensed Matter and Applications, J. Singh, ed. (John Wiley and Sons, Ltd, Chichester, UK. 2006)
[Crossref]

Tangella, K.

Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 11, 116017 (2011).
[Crossref]

Tatian, B.

B. Tatian, “Fitting refractive-index data with the sellmeier dispersion formula,” Appl. Optics 23, 4477–4485 (1984).
[Crossref]

Tearney, G. J.

Tsuta, M.

Tsuzuki, T.

Van Beers, R.

van der Pol, E.

van Leeuwen, T. G.

V. D. Nguyen, D. J. Faber, E. van der Pol, T. G. van Leeuwen, and J. Kalkman, “Dependent and multiple scattering in transmission and backscattering optical coherence tomography,” Opt. Express 21, 29145–29156 (2013).
[Crossref]

R. H. Bremmer, S. C. Kanick, N. Laan, A. Amelink, T. G. van Leeuwen, and M. C. Aalders, “Non-contact spectroscopic determination of large blood volume fractions in turbid media,” Biomed. Opt. Express 2, 396–407 (2011).
[Crossref] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, and M. C. Aalders, “In vivo low-coherence spectroscopic measurements of local hemoglobin absorption spectra in human skin,” J. Biomed. Opt. 16, 100504 (2011).
[Crossref] [PubMed]

K. Barwari, D. M. de Bruin, E. C. Cauberg, D. J. Faber, T. G. van Leeuwen, H. Wijkstra, J. de la Rosette, and M. P. Laguna, “Advanced diagnostics in renal mass using optical coherence tomography: a preliminary report,” J. Endourol. 25, 311–315 (2011).
[Crossref] [PubMed]

Verma, Y.

Y. Verma, P. Nandi, K. D. Rao, M. Sharma, and P. K. Gupta, “Use of common path phase sensitive spectral domain optical coherence tomography for refractive index measurements,” Appl. Optics 50, E7–E12 (2011).
[Crossref]

Vieweg, M.

Wang, L.

Wang, Z.

Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 11, 116017 (2011).
[Crossref]

Watté, R.

Wijkstra, H.

K. Barwari, D. M. de Bruin, E. C. Cauberg, D. J. Faber, T. G. van Leeuwen, H. Wijkstra, J. de la Rosette, and M. P. Laguna, “Advanced diagnostics in renal mass using optical coherence tomography: a preliminary report,” J. Endourol. 25, 311–315 (2011).
[Crossref] [PubMed]

Wriedt, T.

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601 (1997).
[Crossref]

Yun, S.

Yunus, W. M.

Zaccanti, G.

Zamora-Rojas, E.

Zawadzki, R.

Zvyagin, A. V.

Appl Opt. (1)

M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl Opt. 46, 3811–3820 (2007).
[Crossref] [PubMed]

Appl. Opt. (4)

Appl. Optics (2)

Y. Verma, P. Nandi, K. D. Rao, M. Sharma, and P. K. Gupta, “Use of common path phase sensitive spectral domain optical coherence tomography for refractive index measurements,” Appl. Optics 50, E7–E12 (2011).
[Crossref]

B. Tatian, “Fitting refractive-index data with the sellmeier dispersion formula,” Appl. Optics 23, 4477–4485 (1984).
[Crossref]

Biomed. Opt. Express (1)

J. Biomed. Opt. (3)

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, and M. C. Aalders, “In vivo low-coherence spectroscopic measurements of local hemoglobin absorption spectra in human skin,” J. Biomed. Opt. 16, 100504 (2011).
[Crossref] [PubMed]

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[Crossref]

Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 11, 116017 (2011).
[Crossref]

J. Endourol. (1)

K. Barwari, D. M. de Bruin, E. C. Cauberg, D. J. Faber, T. G. van Leeuwen, H. Wijkstra, J. de la Rosette, and M. P. Laguna, “Advanced diagnostics in renal mass using optical coherence tomography: a preliminary report,” J. Endourol. 25, 311–315 (2011).
[Crossref] [PubMed]

J. Opt. Soc. Am. (2)

J. Phys. and Chem. Ref. Data (1)

H. H. Li, “Refractive index of alkaline earth halides and its wavelength and temperature derivatives,” J. Phys. and Chem. Ref. Data 9, 161–290 (1980).
[Crossref]

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[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Schematic diagram of the Fourier-domain transmission OCT system. I(k): detected intensity at the spectrometer, L: length of the sample, n(k,z): refractive index of the sample, µt(k,z): total attenuation, S(k): source intensity.
Fig. 2
Fig. 2 Schematic diagram of the experimental setup. BS: beam splitter, CA: camera, CL: collimation lens, FL: focusing lens, HG: holographic grating, NDF: Neutral density filter, PC: polarization controller, PH: pinhole, S: Sample, SLD: superluminescent diode, TS: translation stage
Fig. 3
Fig. 3 Schematic illustration of the analysis algorithm for the determination of the optical material properties.
Fig. 4
Fig. 4 Overview of the data processing steps for the fused silica sample (a) Reference and sample arm subtracted interference spectrum. (b) Phase of the original Hilbert transformed signal (blue, dashed), the spectrometer corrected signal (black, points), and the linear phase relation (red). (c) Phase difference between the linear phase and the original signal (blue, dashed) and to the setup dispersion corrected signal (red, solid). (d) z-Domain transmission OCT signal after inverse Fourier transform without dispersion correction (blue, dashed), after setup dispersion correction (black, points) and after material dispersion correction (red, solid).
Fig. 5
Fig. 5 Measured group refractive index (a) and group velocity dispersion (b) compared with literature values. The measured values are denoted in red and the literature values are visualized in shades of blue with the reference indicated above and below their respective bar.
Fig. 6
Fig. 6 Group index and group velocity dispersion for solutions with varying glucose concentration as determined with transmission OCT. The measurements (indicated with open symbols, red and blue) are fitted with a linear regression (dashed black lines).
Fig. 7
Fig. 7 Spatial domain transmission OCT data for several concentrations of 0.5 µm (a) and 1.5 µm (b) silica particles in water. Data separated for plotting by multiplication with powers of 10. (c) Measured scattering coefficients for the silica suspensions. The data is fitted using a dependent scattering model (black, solid), which is based on Mie calculations (gray, dashed).
Fig. 8
Fig. 8 (a) Measured absorption coefficient of water versus wavelength (blue, dots) and its comparison to literature [11] (black, solid). (b) Measured scattering coefficient versus wavelength for 2 vol.% 1.5 µm silica particles (blue, dots). Error margin is denoted by the dashed lines. The data is compared to the scattering coefficient obtained from dependent scattering calculations (black, solid).

Equations (11)

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E r e f ( k ) = [ α ( 1 α ) ] 1 2 E s ( k ) exp ( i k L ) ,
E s a m ( k ) = [ α ( 1 α ) ] 1 2 E s ( k ) exp ( 1 2 0 L μ t ( k , z ) d z ) exp ( i k 0 L n ( k , z ) d z ) ,
I int ( k ) = 2 α ( 1 α ) E s 2 ( k ) exp ( 1 2 L μ t ( k ) ) cos [ k L ( n ( k ) 1 ) ] .
n ( k ) = j = 0 J n j ( k k c k c ) j ,
I int ˜ ( k ) = I int ( k ) + i H { I int ( k ) } ,
φ ( k ) = tan 1 ( { I int ( k ) } I int ( k ) ) ,
φ ( k ) k c L = ( n 0 1 ) + ( n 0 1 + n 1 ) ( k k c k c ) + ( n 1 + n 2 ) ( k k c k c ) 2 .
I c ( z ) = 1 { | I int ˜ ( k ) | exp [ i Δ φ ( k ) ] } ,
a ( z ) = α ( 1 α ) exp ( 1 2 L μ t ) 1 { E s 2 ( k ) } ( z ) [ δ ( z L ( n g 1 ) ) + δ ( z + L ( n g 1 ) ) ] ,
μ t = 2 L ln ( max | a r e f | max | a s a m | ) .
| I int ˜ ( k ) | = α ( 1 α ) E s 2 ( k ) exp ( 1 2 L μ t ( k ) ) .

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