Abstract

One of the key concerns in thin-film filter based spectral cameras is the presence of spectral shift in the measurements. This shift is caused by the sensitivity of the filters to the angle of incidence. In previous work, we showed that this shift can be corrected using a mathematical model. This model, however, requires knowledge of the distance to the exit pupil of the lens, which is not always readily available. We present a new model-based approach to estimate the distance to the exit pupil based on the observed spectral shift, making the method relevant for any thin-film Fabry-Perot based camera design. To implement the method, only a standard spectral camera setup and a well chosen spectral target are required. We also discuss how to optimally select such a target.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. N. Tack, A. Lambrechts, P. Soussan, and L. Haspeslagh, “A compact, high-speed, and low-cost hyperspectral imager,” Proc. SPIE 8266, 82660Q (2012).
    [Crossref]
  2. J. Pichette, W. Charle, and A. Lambrechts, “Fast and compact internal scanning CMOS-based hyperspectral camera: the Snapscan,” Proc. SPIE 10110, 1011014 (2017).
    [Crossref]
  3. P. Gonzalez, J. Pichette, B. Vereecke, B. Masschelein, L. Krasovitski, L. Bikov, and A. Lambrechts, “An extremely compact and high-speed line-scan hyperspectral imager covering the SWIR range,” in SPIE 10656, Image Sensing Technologies: Materials, Devices, Systems, and Applications V, vol. 10656 (2018), pp. 106560L–10656-9.
  4. C. Zhang and J. M. Kovacs, “The application of small unmanned aerial systems for precision agriculture: A review,” Precision Agric 13(6), 693–712 (2012).
    [Crossref]
  5. G. Lu and B. Fei, “Medical hyperspectral imaging: a review,” J. Biomed. Opt. 19(1), 010901 (2014).
    [Crossref]
  6. A. Gowen, C. O’Donnell, P. Cullen, G. Downey, and J. Frias, “Hyperspectral imaging – an emerging process analytical tool for food quality and safety control,” Trends Food Sci. Technol. 18(12), 590–598 (2007).
    [Crossref]
  7. P. Shippert, “Why Use Hyperspectral Imagery?” Photogramm. Eng. Remote Sens. 70, 377–379 (2004).
  8. H. A. Macleod, Thin-film Optical Filters (CRC Press, 2001).
  9. M. K. Yetzbacher, C. W. Miller, A. J. Boudreau, M. Christophersen, and M. J. Deprenger, “Multiple-order staircase etalon spectroscopy,” Proc. SPIE 9101, 910104 (2014).
    [Crossref]
  10. B. Geelen, N. Tack, and A. Lambrechts, “A compact snapshot multispectral imager with a monolithically integrated per-pixel filter mosaic,” Proc. SPIE 8974, 89740L (2014).
    [Crossref]
  11. I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
    [Crossref]
  12. M. K. Yetzbacher and M. J. DePrenger, “The effect of lens aperture for remote sensing of trace gases using Fabry-Perot interferometer-based cameras,” Proc. SPIE 10768, 1076802 (2018).
    [Crossref]
  13. T. Goossens, B. Geelen, J. Pichette, A. Lambrechts, and C. Van Hoof, “Finite aperture correction for spectral cameras with integrated thin-film Fabry-Perot filters,” Appl. Opt. 57(26), 7539–7549 (2018).
    [Crossref]
  14. T. Goossens, B. Geelen, A. Lambrechts, and C. Van Hoof, “Vignetted-aperture correction for spectral cameras with integrated thin-film Fabry-Perot filters,” Appl. Opt. 58(7), 1789 (2019).
    [Crossref]
  15. C. R. Pidgeon and S. D. Smith, “Resolving Power of Multilayer Filters in Nonparallel Light,” J. Opt. Soc. Am. 54(12), 1459 (1964).
    [Crossref]
  16. L. Hazra, “Introduction to Aberrations in Optical Imaging Systems by José Sasián,” J. Opt. 42(4), 293–294 (2013).
    [Crossref]

2019 (1)

2018 (2)

M. K. Yetzbacher and M. J. DePrenger, “The effect of lens aperture for remote sensing of trace gases using Fabry-Perot interferometer-based cameras,” Proc. SPIE 10768, 1076802 (2018).
[Crossref]

T. Goossens, B. Geelen, J. Pichette, A. Lambrechts, and C. Van Hoof, “Finite aperture correction for spectral cameras with integrated thin-film Fabry-Perot filters,” Appl. Opt. 57(26), 7539–7549 (2018).
[Crossref]

2017 (1)

J. Pichette, W. Charle, and A. Lambrechts, “Fast and compact internal scanning CMOS-based hyperspectral camera: the Snapscan,” Proc. SPIE 10110, 1011014 (2017).
[Crossref]

2016 (1)

I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
[Crossref]

2014 (3)

M. K. Yetzbacher, C. W. Miller, A. J. Boudreau, M. Christophersen, and M. J. Deprenger, “Multiple-order staircase etalon spectroscopy,” Proc. SPIE 9101, 910104 (2014).
[Crossref]

B. Geelen, N. Tack, and A. Lambrechts, “A compact snapshot multispectral imager with a monolithically integrated per-pixel filter mosaic,” Proc. SPIE 8974, 89740L (2014).
[Crossref]

G. Lu and B. Fei, “Medical hyperspectral imaging: a review,” J. Biomed. Opt. 19(1), 010901 (2014).
[Crossref]

2013 (1)

L. Hazra, “Introduction to Aberrations in Optical Imaging Systems by José Sasián,” J. Opt. 42(4), 293–294 (2013).
[Crossref]

2012 (2)

C. Zhang and J. M. Kovacs, “The application of small unmanned aerial systems for precision agriculture: A review,” Precision Agric 13(6), 693–712 (2012).
[Crossref]

N. Tack, A. Lambrechts, P. Soussan, and L. Haspeslagh, “A compact, high-speed, and low-cost hyperspectral imager,” Proc. SPIE 8266, 82660Q (2012).
[Crossref]

2007 (1)

A. Gowen, C. O’Donnell, P. Cullen, G. Downey, and J. Frias, “Hyperspectral imaging – an emerging process analytical tool for food quality and safety control,” Trends Food Sci. Technol. 18(12), 590–598 (2007).
[Crossref]

2004 (1)

P. Shippert, “Why Use Hyperspectral Imagery?” Photogramm. Eng. Remote Sens. 70, 377–379 (2004).

1964 (1)

Bergström, D.

I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
[Crossref]

Bikov, L.

P. Gonzalez, J. Pichette, B. Vereecke, B. Masschelein, L. Krasovitski, L. Bikov, and A. Lambrechts, “An extremely compact and high-speed line-scan hyperspectral imager covering the SWIR range,” in SPIE 10656, Image Sensing Technologies: Materials, Devices, Systems, and Applications V, vol. 10656 (2018), pp. 106560L–10656-9.

Boudreau, A. J.

M. K. Yetzbacher, C. W. Miller, A. J. Boudreau, M. Christophersen, and M. J. Deprenger, “Multiple-order staircase etalon spectroscopy,” Proc. SPIE 9101, 910104 (2014).
[Crossref]

Charle, W.

J. Pichette, W. Charle, and A. Lambrechts, “Fast and compact internal scanning CMOS-based hyperspectral camera: the Snapscan,” Proc. SPIE 10110, 1011014 (2017).
[Crossref]

Christophersen, M.

M. K. Yetzbacher, C. W. Miller, A. J. Boudreau, M. Christophersen, and M. J. Deprenger, “Multiple-order staircase etalon spectroscopy,” Proc. SPIE 9101, 910104 (2014).
[Crossref]

Cullen, P.

A. Gowen, C. O’Donnell, P. Cullen, G. Downey, and J. Frias, “Hyperspectral imaging – an emerging process analytical tool for food quality and safety control,” Trends Food Sci. Technol. 18(12), 590–598 (2007).
[Crossref]

DePrenger, M. J.

M. K. Yetzbacher and M. J. DePrenger, “The effect of lens aperture for remote sensing of trace gases using Fabry-Perot interferometer-based cameras,” Proc. SPIE 10768, 1076802 (2018).
[Crossref]

M. K. Yetzbacher, C. W. Miller, A. J. Boudreau, M. Christophersen, and M. J. Deprenger, “Multiple-order staircase etalon spectroscopy,” Proc. SPIE 9101, 910104 (2014).
[Crossref]

Downey, G.

A. Gowen, C. O’Donnell, P. Cullen, G. Downey, and J. Frias, “Hyperspectral imaging – an emerging process analytical tool for food quality and safety control,” Trends Food Sci. Technol. 18(12), 590–598 (2007).
[Crossref]

Fei, B.

G. Lu and B. Fei, “Medical hyperspectral imaging: a review,” J. Biomed. Opt. 19(1), 010901 (2014).
[Crossref]

Frias, J.

A. Gowen, C. O’Donnell, P. Cullen, G. Downey, and J. Frias, “Hyperspectral imaging – an emerging process analytical tool for food quality and safety control,” Trends Food Sci. Technol. 18(12), 590–598 (2007).
[Crossref]

Geelen, B.

Gonzalez, P.

P. Gonzalez, J. Pichette, B. Vereecke, B. Masschelein, L. Krasovitski, L. Bikov, and A. Lambrechts, “An extremely compact and high-speed line-scan hyperspectral imager covering the SWIR range,” in SPIE 10656, Image Sensing Technologies: Materials, Devices, Systems, and Applications V, vol. 10656 (2018), pp. 106560L–10656-9.

Goossens, T.

Gowen, A.

A. Gowen, C. O’Donnell, P. Cullen, G. Downey, and J. Frias, “Hyperspectral imaging – an emerging process analytical tool for food quality and safety control,” Trends Food Sci. Technol. 18(12), 590–598 (2007).
[Crossref]

Haspeslagh, L.

N. Tack, A. Lambrechts, P. Soussan, and L. Haspeslagh, “A compact, high-speed, and low-cost hyperspectral imager,” Proc. SPIE 8266, 82660Q (2012).
[Crossref]

Hazra, L.

L. Hazra, “Introduction to Aberrations in Optical Imaging Systems by José Sasián,” J. Opt. 42(4), 293–294 (2013).
[Crossref]

Hedborg, J.

I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
[Crossref]

Kovacs, J. M.

C. Zhang and J. M. Kovacs, “The application of small unmanned aerial systems for precision agriculture: A review,” Precision Agric 13(6), 693–712 (2012).
[Crossref]

Krasovitski, L.

P. Gonzalez, J. Pichette, B. Vereecke, B. Masschelein, L. Krasovitski, L. Bikov, and A. Lambrechts, “An extremely compact and high-speed line-scan hyperspectral imager covering the SWIR range,” in SPIE 10656, Image Sensing Technologies: Materials, Devices, Systems, and Applications V, vol. 10656 (2018), pp. 106560L–10656-9.

Lambrechts, A.

T. Goossens, B. Geelen, A. Lambrechts, and C. Van Hoof, “Vignetted-aperture correction for spectral cameras with integrated thin-film Fabry-Perot filters,” Appl. Opt. 58(7), 1789 (2019).
[Crossref]

T. Goossens, B. Geelen, J. Pichette, A. Lambrechts, and C. Van Hoof, “Finite aperture correction for spectral cameras with integrated thin-film Fabry-Perot filters,” Appl. Opt. 57(26), 7539–7549 (2018).
[Crossref]

J. Pichette, W. Charle, and A. Lambrechts, “Fast and compact internal scanning CMOS-based hyperspectral camera: the Snapscan,” Proc. SPIE 10110, 1011014 (2017).
[Crossref]

B. Geelen, N. Tack, and A. Lambrechts, “A compact snapshot multispectral imager with a monolithically integrated per-pixel filter mosaic,” Proc. SPIE 8974, 89740L (2014).
[Crossref]

N. Tack, A. Lambrechts, P. Soussan, and L. Haspeslagh, “A compact, high-speed, and low-cost hyperspectral imager,” Proc. SPIE 8266, 82660Q (2012).
[Crossref]

P. Gonzalez, J. Pichette, B. Vereecke, B. Masschelein, L. Krasovitski, L. Bikov, and A. Lambrechts, “An extremely compact and high-speed line-scan hyperspectral imager covering the SWIR range,” in SPIE 10656, Image Sensing Technologies: Materials, Devices, Systems, and Applications V, vol. 10656 (2018), pp. 106560L–10656-9.

Letalick, D.

I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
[Crossref]

Lu, G.

G. Lu and B. Fei, “Medical hyperspectral imaging: a review,” J. Biomed. Opt. 19(1), 010901 (2014).
[Crossref]

Macleod, H. A.

H. A. Macleod, Thin-film Optical Filters (CRC Press, 2001).

Masschelein, B.

P. Gonzalez, J. Pichette, B. Vereecke, B. Masschelein, L. Krasovitski, L. Bikov, and A. Lambrechts, “An extremely compact and high-speed line-scan hyperspectral imager covering the SWIR range,” in SPIE 10656, Image Sensing Technologies: Materials, Devices, Systems, and Applications V, vol. 10656 (2018), pp. 106560L–10656-9.

Miller, C. W.

M. K. Yetzbacher, C. W. Miller, A. J. Boudreau, M. Christophersen, and M. J. Deprenger, “Multiple-order staircase etalon spectroscopy,” Proc. SPIE 9101, 910104 (2014).
[Crossref]

Möller, S.

I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
[Crossref]

O’Donnell, C.

A. Gowen, C. O’Donnell, P. Cullen, G. Downey, and J. Frias, “Hyperspectral imaging – an emerging process analytical tool for food quality and safety control,” Trends Food Sci. Technol. 18(12), 590–598 (2007).
[Crossref]

Pichette, J.

T. Goossens, B. Geelen, J. Pichette, A. Lambrechts, and C. Van Hoof, “Finite aperture correction for spectral cameras with integrated thin-film Fabry-Perot filters,” Appl. Opt. 57(26), 7539–7549 (2018).
[Crossref]

J. Pichette, W. Charle, and A. Lambrechts, “Fast and compact internal scanning CMOS-based hyperspectral camera: the Snapscan,” Proc. SPIE 10110, 1011014 (2017).
[Crossref]

P. Gonzalez, J. Pichette, B. Vereecke, B. Masschelein, L. Krasovitski, L. Bikov, and A. Lambrechts, “An extremely compact and high-speed line-scan hyperspectral imager covering the SWIR range,” in SPIE 10656, Image Sensing Technologies: Materials, Devices, Systems, and Applications V, vol. 10656 (2018), pp. 106560L–10656-9.

Pidgeon, C. R.

Renhorn, I. G. E.

I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
[Crossref]

Shippert, P.

P. Shippert, “Why Use Hyperspectral Imagery?” Photogramm. Eng. Remote Sens. 70, 377–379 (2004).

Smith, S. D.

Soussan, P.

N. Tack, A. Lambrechts, P. Soussan, and L. Haspeslagh, “A compact, high-speed, and low-cost hyperspectral imager,” Proc. SPIE 8266, 82660Q (2012).
[Crossref]

Tack, N.

B. Geelen, N. Tack, and A. Lambrechts, “A compact snapshot multispectral imager with a monolithically integrated per-pixel filter mosaic,” Proc. SPIE 8974, 89740L (2014).
[Crossref]

N. Tack, A. Lambrechts, P. Soussan, and L. Haspeslagh, “A compact, high-speed, and low-cost hyperspectral imager,” Proc. SPIE 8266, 82660Q (2012).
[Crossref]

Van Hoof, C.

Vereecke, B.

P. Gonzalez, J. Pichette, B. Vereecke, B. Masschelein, L. Krasovitski, L. Bikov, and A. Lambrechts, “An extremely compact and high-speed line-scan hyperspectral imager covering the SWIR range,” in SPIE 10656, Image Sensing Technologies: Materials, Devices, Systems, and Applications V, vol. 10656 (2018), pp. 106560L–10656-9.

Yetzbacher, M. K.

M. K. Yetzbacher and M. J. DePrenger, “The effect of lens aperture for remote sensing of trace gases using Fabry-Perot interferometer-based cameras,” Proc. SPIE 10768, 1076802 (2018).
[Crossref]

M. K. Yetzbacher, C. W. Miller, A. J. Boudreau, M. Christophersen, and M. J. Deprenger, “Multiple-order staircase etalon spectroscopy,” Proc. SPIE 9101, 910104 (2014).
[Crossref]

Zhang, C.

C. Zhang and J. M. Kovacs, “The application of small unmanned aerial systems for precision agriculture: A review,” Precision Agric 13(6), 693–712 (2012).
[Crossref]

Appl. Opt. (2)

J. Biomed. Opt. (1)

G. Lu and B. Fei, “Medical hyperspectral imaging: a review,” J. Biomed. Opt. 19(1), 010901 (2014).
[Crossref]

J. Opt. (1)

L. Hazra, “Introduction to Aberrations in Optical Imaging Systems by José Sasián,” J. Opt. 42(4), 293–294 (2013).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
[Crossref]

Photogramm. Eng. Remote Sens. (1)

P. Shippert, “Why Use Hyperspectral Imagery?” Photogramm. Eng. Remote Sens. 70, 377–379 (2004).

Precision Agric (1)

C. Zhang and J. M. Kovacs, “The application of small unmanned aerial systems for precision agriculture: A review,” Precision Agric 13(6), 693–712 (2012).
[Crossref]

Proc. SPIE (5)

M. K. Yetzbacher and M. J. DePrenger, “The effect of lens aperture for remote sensing of trace gases using Fabry-Perot interferometer-based cameras,” Proc. SPIE 10768, 1076802 (2018).
[Crossref]

M. K. Yetzbacher, C. W. Miller, A. J. Boudreau, M. Christophersen, and M. J. Deprenger, “Multiple-order staircase etalon spectroscopy,” Proc. SPIE 9101, 910104 (2014).
[Crossref]

B. Geelen, N. Tack, and A. Lambrechts, “A compact snapshot multispectral imager with a monolithically integrated per-pixel filter mosaic,” Proc. SPIE 8974, 89740L (2014).
[Crossref]

N. Tack, A. Lambrechts, P. Soussan, and L. Haspeslagh, “A compact, high-speed, and low-cost hyperspectral imager,” Proc. SPIE 8266, 82660Q (2012).
[Crossref]

J. Pichette, W. Charle, and A. Lambrechts, “Fast and compact internal scanning CMOS-based hyperspectral camera: the Snapscan,” Proc. SPIE 10110, 1011014 (2017).
[Crossref]

Trends Food Sci. Technol. (1)

A. Gowen, C. O’Donnell, P. Cullen, G. Downey, and J. Frias, “Hyperspectral imaging – an emerging process analytical tool for food quality and safety control,” Trends Food Sci. Technol. 18(12), 590–598 (2007).
[Crossref]

Other (2)

P. Gonzalez, J. Pichette, B. Vereecke, B. Masschelein, L. Krasovitski, L. Bikov, and A. Lambrechts, “An extremely compact and high-speed line-scan hyperspectral imager covering the SWIR range,” in SPIE 10656, Image Sensing Technologies: Materials, Devices, Systems, and Applications V, vol. 10656 (2018), pp. 106560L–10656-9.

H. A. Macleod, Thin-film Optical Filters (CRC Press, 2001).

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Figures (6)

Fig. 1.
Fig. 1. The spectrum measured at an off-axis distance $d=7.7$ mm is shifted with respect to the on-axis measurement. For simplicity, without loss of generality, the entrance pupil and exit pupil coincide in Fig. 1a.
Fig. 2.
Fig. 2. The camera images a white diffuse surface. By placing a filter in front of the lens, the whole surface acts as one large uniform spectral target.
Fig. 3.
Fig. 3. The method can predict the exit pupil position with varying accuracy. The estimates made with filters that are further from the optical axis (larger $d$) are more accurate.
Fig. 4.
Fig. 4. When the exit pupil position is known ($x=29.6$ mm), undesired shifts for identical targets at different positions can be corrected using Eq. 2.
Fig. 5.
Fig. 5. Merit functions used to estimate exit pupil distance. The estimates are made at different off-axis distances. The global minimum for $x=39.6$ mm is less pronounced than for $x=29.6$ mm (Fig. 5a). The analytical approximations $\hat{E}(y)$ fit the real merit functions $E_{\textrm{lsq}}(y)$ well up to a common scalar factor.
Fig. 6.
Fig. 6. The transmittance of the Thorlabs FGB67S filter is highly oscillatory in the 400 to 1000 nm range.

Equations (20)

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

λ cwl new = λ cwl ( 1 θ CRA 2 2 n eff 2 θ cone 2 4 n eff 2 ) , with θ CRA = arctan d x .
λ cwl new = λ cwl ( 1 θ CRA 2 2 n eff 2 ) , with θ CRA = arctan d x .
λ cwl ( y ) = λ cwl ( 1 arctan 2 ( d y ) 1 2 n eff 2 ) .
ρ corr ( y ) = interp ( ( λ cwl ( y ) , ρ off ) , λ cwl ) .
x ^ = arg min y ρ corr ( y ) ρ on 2 2 ,
E lsq ( y ; d ) = ρ corr ( y ) ρ on 2 2 ,
r off ( λ ) = r ( λ ( 1 d 2 2 n eff 2 x 2 ) ) ,
r corr ( λ ) = r ( λ ( 1 d 2 2 n eff 2 x 2 + d 2 2 n eff 2 y 2 ) ) .
E ( y ) = Ω [ r corr ( λ ) r ( λ ) ] 2 d λ ,
x ^ = arg min y E ( y ) .
E ( y ) E ^ ( y ) , for y x = d 4 4 n eff 4 Ω ( λ r ) 2 d λ ( 1 x 2 1 y 2 ) 2 = d 4 4 n eff 4 f ( r ) ( 1 x 2 1 y 2 ) 2 .
E ^ ( y ) = d 4 x 6 n eff 4 f ( r ) ( x y ) 2 + O ( ( x y ) 3 ) .
E ( y ) = d 4 x 6 n eff 4 f ( r ) ( x y ) 2 + O ( ( x y ) 3 ) .
d 4 x 6 n eff 4 .
f ( r ) = Ω ( λ r ) 2 d λ .
λ cwl,on new = λ cwl ( 1 α 2 2 n eff 2 ) .
λ cwl,off new = λ cwl ( 1 θ CRA 2 2 n eff 2 ) = λ cwl ( 1 ( θ CRA + α ) 2 2 n eff 2 ) .
λ cwl,on new λ cwl,off new = λ cwl θ CRA ( 2 α + θ CRA ) 2 n eff 2 .
y = d θ CRA 1 + 2 α θ CRA x 1 + 2 α θ CRA x ( 1 α θ CRA ) , α θ CRA 0 ,
| Δ x x | | α θ CRA | .

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