Abstract

Diode-laser-based absorption spectroscopy for the evaluation of embedded gas concentrations in porous materials is demonstrated in measurements of molecular oxygen dispersed throughout scattering polystyrene foam, used here as a generic test material. The mean path length of light scattered in the material is determined with the temporal characteristics of the radiation transmitted through the sample. This combined with sensitive gas-absorption measurements employing wavelength-modulation spectroscopy yields an oxygen concentration in polystyrene foam of 20.4% corresponding to a foam porosity of 98%, which is consistent with manufacturing specifications. This feasibility study opens many possibilities for quantitative measurements by using the method of gas-in-scattering-media absorption spectroscopy.

© 2002 Optical Society of America

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2001

2000

1998

1993

1992

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical path lengths in tissue: temporal and frequency analysis, “Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Pattersson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

1990

1989

1988

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

1966

Alnis, J.

Andersen, P. E.

Andersson-Engels, S.

Arridge, S. R.

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical path lengths in tissue: temporal and frequency analysis, “Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Berg, R.

Boretsky, R.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Chance, B.

M. S. Pattersson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef]

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Cohen, P.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Cope, M.

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical path lengths in tissue: temporal and frequency analysis, “Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Dalgaard, T.

Dam, J. S.

Delpy, D. T.

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical path lengths in tissue: temporal and frequency analysis, “Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Farrell, T. J.

T. J. Farrell, M. S. Pattersson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Finander, M.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Fishkin, J. B.

J. B. Fishkin, E. Gratton, M. J. Vande Ven, W. W. Mantulin, “Diffusion of intensity-modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

Gratton, E.

J. B. Fishkin, E. Gratton, M. J. Vande Ven, W. W. Mantulin, “Diffusion of intensity-modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

Greenfeld, R.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Gustafsson, U.

Jarlman, O.

Kaufmann, K.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Leigh, J. S.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Levy, W.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Link, J. K.

Mantulin, W. W.

J. B. Fishkin, E. Gratton, M. J. Vande Ven, W. W. Mantulin, “Diffusion of intensity-modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

Miyake, H.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Nioka, S.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Pattersson, M. S.

T. J. Farrell, M. S. Pattersson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

M. S. Pattersson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef]

Platt, U.

U. Platt, Institute for Environmental Physic, University of Heidelberg, Heidelberg, Germany (personal communication, 2000).

Sjöholm, M.

Smith, D. S.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Somesfalean, G.

Svanberg, S.

Vande Ven, M. J.

J. B. Fishkin, E. Gratton, M. J. Vande Ven, W. W. Mantulin, “Diffusion of intensity-modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

Wilson, B.

T. J. Farrell, M. S. Pattersson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Wilson, B. C.

Yoshioka, H.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Young, M.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

Med. Phys.

T. J. Farrell, M. S. Pattersson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Med. Biol.

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical path lengths in tissue: temporal and frequency analysis, “Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in the brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Other

U. Platt, Institute for Environmental Physic, University of Heidelberg, Heidelberg, Germany (personal communication, 2000).

J. B. Fishkin, E. Gratton, M. J. Vande Ven, W. W. Mantulin, “Diffusion of intensity-modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Analytical time dispersion curve obtained for transillumination of a 39-mm-thick slab with optical parameters μ a = 0.002 cm-1 and μ s ′ = 40 cm-1 by using short-pulsed light. For clarity the direct absorption signals corresponding to photons that have traveled distances of different lengths in the material are intentionally exaggerated. The mean traveling time in the limit of small absorptions is shown in the inset.

Fig. 2
Fig. 2

(a) Direct absorption and (b) second-harmonic component of the WMS spectrum for the R7R7 line in the oxygen A band measured along a 10-m-long path in air. (c) Low-finesse fringes from a 2.43-GHz free spectral range Fabry-Perot etalon used for calibration of the frequency scale.

Fig. 3
Fig. 3

Experimental setup used for time-resolved measurements: PD, photodiode; PMT, photomultiplier tube; Amp, amplifier; CFD, constant fraction discriminator; TAC, time-to-amplitude converter.

Fig. 4
Fig. 4

Recorded time dispersion curve obtained when transilluminating a 39-mm-thick slab of polystyrene foam by using a diode laser source pulsed at 10 MHz. A fit of a theoretical curve and the instrumental transfer function are also depicted.

Fig. 5
Fig. 5

Standard-addition plot for molecular oxygen obtained with the GASMAS setup showing the extrapolated equivalent mean path length for a 9.4-mm-thick slab of polystyrene foam. The WMS signal obtained with the light-injecting collimator in direct contact with the sample is shown in the inset.

Fig. 6
Fig. 6

(a) Recorded mean time of flight through a 9.4-mm-thick slab of polystyrene foam measured with a pulsed Ti:Sapphire laser. Solid curve, theoretical curve corresponding to the evaluated optical parameters (μ a = 0.002 cm-1, μ s ′ = 40 cm-1). (b) Dotted line, quotient between the GASMAS signal and the mean traveling time of the photons together with a least-squares fit of the factor k gt .

Fig. 7
Fig. 7

Spatially resolved transmission recordings measured with the GASMAS setup on two polystyrene foam slabs (a), (b) 9.4 mm and (c), (d) 39 mm thick: upper curves, transmitted intensity; lower curves, detected oxygen absorption signal amplitude for different injector-detector separation distances. Fits according to the evaluated effective attenuation coefficient (μeff = 0.5 cm-1) are also indicated. A schematic of the transillumination setup is shown in the insets, and dashed lines at the zero position mark the symmetry axis.

Fig. 8
Fig. 8

Plot of the equivalent mean path length corresponding to oxygen absorption measured through slabs of polystyrene foam with different thicknesses by using a diode laser. The mean time of flight is proportional to the square of the slab thickness. Solid line, theoretical curve evaluated with μ a = 0.002 cm-1 and μ s ′ = 40 cm-1.

Equations (11)

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

Iλ=I0λexp-σλcL=I0λexp-a,
Lsm=l=vt,
Iρ, d, t=4πDv-3/2 t-5/2×exp-μavt-ρ24Dvt×k=0+z-k exp-r-k24Dvt-z+k exp-r+k24Dvt,
t=k=0z+kr+kexp-μeff r+k-z-kr-kexp-μeff r-k2vD k=0z+kr+k31+μeff r+kexp-μeff r+k-z-kr-k31+μeff r-kexp-μeff r-k,
Iρ, d=12πk=0z-kr-k31+μeffr-kexp-μeffr-k-z+kr+k31+μeffr+kexp-μeffr+k.
cairLeq=csmLsm,
gSWMSSDir,
kgLgL,
csm=cairLeqvt=gtcairvkgL,
nsm=Pnair+1-Pnb,
P=VgasVtot=csmcair,

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