Abstract

A new probe of multiple scattering material is demonstrated experimentally. Light from a tunable wavelength source is focused to a point on the surface of an opaque slab. A fraction of this light penetrates into the slab, is multiply scattered, and reemerges at the surface creating a surface speckle pattern. The full spatial and frequency speckle can be easily and quickly recorded using a CCD and an acoustooptical tunable filter. Both the average intensity and frequency correlations of intensity are analyzed as a function of the distance to the source. This method is demonstrated experimentally for white paint. The resulting model yields information about both the static and dynamic transport properties of the sample. The technique has prospects for both static and time resolved diffuse imaging in strongly scattering materials. The setup can be easily used as an add-on to a standard bright field microscope.

© 2014 Optical Society of America

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References

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2013

M. Alfeld, J. A.C. Broekaert, “Mobile depth profiling and sub-surface imaging techniques for historical paintings - review,” Spectrochimica Acta Part B: Atomic Spectroscopy 88(0), 211–230 (2013).
[CrossRef]

2010

T. Durduran, R. Choe, W. B Baker, A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Reports on Progress in Physics 73(7), 076701 (2010).
[CrossRef]

2009

2005

A. P. Gibson, J. C. Hebden, S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[CrossRef] [PubMed]

2004

2003

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68(1), 016604 (2003).
[CrossRef]

2000

D.J. Young, N.C. Beaulieu, “The generation of correlated rayleigh random variates by inverse discrete fourier transform,” Communications, IEEE Transactions on 48(7), 1114–1127 (2000).
[CrossRef]

1999

M. C. W. van Rossum, Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71(1), 313–371 (1999).
[CrossRef]

1997

1991

1990

A. Z. Genack, J. M. Drake, “Relationship between optical intensity, fluctuations and pulse propagation in random media,” EPL (Europhysics Letters) 11(4), 331–336 (1990).
[CrossRef]

1989

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt 28(12), 2331–2336 (1989).
[CrossRef] [PubMed]

1988

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. France 49(1), 77–98 (1988).
[CrossRef]

1977

F. F. Jobsis, ”Noninvasive, infrared monitoring of cerebral and myocardial oxygen, sufficiency and circulatory parameters,” Science 198(4323), 1264–1267 (1977).
[CrossRef] [PubMed]

Akkermans, E.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. France 49(1), 77–98 (1988).
[CrossRef]

Alfeld, M.

M. Alfeld, J. A.C. Broekaert, “Mobile depth profiling and sub-surface imaging techniques for historical paintings - review,” Spectrochimica Acta Part B: Atomic Spectroscopy 88(0), 211–230 (2013).
[CrossRef]

Arridge, S. R.

A. P. Gibson, J. C. Hebden, S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[CrossRef] [PubMed]

Aulbach, J.

J. Aulbach, Spatiotemporal Control of Light in Turbid Media (PhD thesis, University of Twente, 2013).

Baker, W. B

T. Durduran, R. Choe, W. B Baker, A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Reports on Progress in Physics 73(7), 076701 (2010).
[CrossRef]

Beaulieu, N.C.

D.J. Young, N.C. Beaulieu, “The generation of correlated rayleigh random variates by inverse discrete fourier transform,” Communications, IEEE Transactions on 48(7), 1114–1127 (2000).
[CrossRef]

Berndt, K. W.

Bret, B. P. J.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68(1), 016604 (2003).
[CrossRef]

Broekaert, J. A.C.

M. Alfeld, J. A.C. Broekaert, “Mobile depth profiling and sub-surface imaging techniques for historical paintings - review,” Spectrochimica Acta Part B: Atomic Spectroscopy 88(0), 211–230 (2013).
[CrossRef]

Chance, B.

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt 28(12), 2331–2336 (1989).
[CrossRef] [PubMed]

Choe, R.

T. Durduran, R. Choe, W. B Baker, A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Reports on Progress in Physics 73(7), 076701 (2010).
[CrossRef]

Contini, D.

de Boer, J. F.

J. F. de Boer, Optical fluctuations on the tranmsission and reflection of mesoscopic systems (PhD thesis, University of Amsterdam, 1995).

Drake, J. M.

A. Z. Genack, J. M. Drake, “Relationship between optical intensity, fluctuations and pulse propagation in random media,” EPL (Europhysics Letters) 11(4), 331–336 (1990).
[CrossRef]

Durduran, T.

T. Durduran, R. Choe, W. B Baker, A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Reports on Progress in Physics 73(7), 076701 (2010).
[CrossRef]

Fernando Rojas-Ochoa, L.

Genack, A. Z.

A. Z. Genack, J. M. Drake, “Relationship between optical intensity, fluctuations and pulse propagation in random media,” EPL (Europhysics Letters) 11(4), 331–336 (1990).
[CrossRef]

Gibson, A. P.

A. P. Gibson, J. C. Hebden, S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[CrossRef] [PubMed]

Gómez Rivas, J.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68(1), 016604 (2003).
[CrossRef]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[CrossRef] [PubMed]

Imhof, A.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68(1), 016604 (2003).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, 1978).

Jobsis, F. F.

F. F. Jobsis, ”Noninvasive, infrared monitoring of cerebral and myocardial oxygen, sufficiency and circulatory parameters,” Science 198(4323), 1264–1267 (1977).
[CrossRef] [PubMed]

Johnson, P. M.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68(1), 016604 (2003).
[CrossRef]

Lacoste, D.

Lagendijk, A.

O. L. Muskens, A. Lagendijk, “Method for broadband spectroscopy of light transport through opaque scattering media,” Opt. Lett. 34, 395–397 (2009).
[CrossRef] [PubMed]

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68(1), 016604 (2003).
[CrossRef]

Lakowicz, J. R.

Lenke, R.

Maret, G.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. France 49(1), 77–98 (1988).
[CrossRef]

Martelli, F.

Maynard, R.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. France 49(1), 77–98 (1988).
[CrossRef]

Moulton, J. D.

Muskens, O. L.

Nieuwenhuizen, Th. M.

M. C. W. van Rossum, Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71(1), 313–371 (1999).
[CrossRef]

Patterson, M. S.

M. S. Patterson, J. D. Moulton, Br. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30(31), 4474–4476 (1991).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt 28(12), 2331–2336 (1989).
[CrossRef] [PubMed]

Scheffold, F.

Schurtenberger, P.

van Rossum, M. C. W.

M. C. W. van Rossum, Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71(1), 313–371 (1999).
[CrossRef]

Wilson, B. C.

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt 28(12), 2331–2336 (1989).
[CrossRef] [PubMed]

Wilson, Br. C.

Wolf, P. E.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. France 49(1), 77–98 (1988).
[CrossRef]

Yodh, A. G.

T. Durduran, R. Choe, W. B Baker, A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Reports on Progress in Physics 73(7), 076701 (2010).
[CrossRef]

Young, D.J.

D.J. Young, N.C. Beaulieu, “The generation of correlated rayleigh random variates by inverse discrete fourier transform,” Communications, IEEE Transactions on 48(7), 1114–1127 (2000).
[CrossRef]

Zaccanti, G.

Appl. Opt

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt 28(12), 2331–2336 (1989).
[CrossRef] [PubMed]

Appl. Opt.

Communications, IEEE Transactions on

D.J. Young, N.C. Beaulieu, “The generation of correlated rayleigh random variates by inverse discrete fourier transform,” Communications, IEEE Transactions on 48(7), 1114–1127 (2000).
[CrossRef]

EPL (Europhysics Letters)

A. Z. Genack, J. M. Drake, “Relationship between optical intensity, fluctuations and pulse propagation in random media,” EPL (Europhysics Letters) 11(4), 331–336 (1990).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. France

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. France 49(1), 77–98 (1988).
[CrossRef]

Opt. Lett.

Phys. Med. Biol.

A. P. Gibson, J. C. Hebden, S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[CrossRef] [PubMed]

Phys. Rev. E

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68(1), 016604 (2003).
[CrossRef]

Reports on Progress in Physics

T. Durduran, R. Choe, W. B Baker, A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Reports on Progress in Physics 73(7), 076701 (2010).
[CrossRef]

Rev. Mod. Phys.

M. C. W. van Rossum, Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71(1), 313–371 (1999).
[CrossRef]

Science

F. F. Jobsis, ”Noninvasive, infrared monitoring of cerebral and myocardial oxygen, sufficiency and circulatory parameters,” Science 198(4323), 1264–1267 (1977).
[CrossRef] [PubMed]

Spectrochimica Acta Part B: Atomic Spectroscopy

M. Alfeld, J. A.C. Broekaert, “Mobile depth profiling and sub-surface imaging techniques for historical paintings - review,” Spectrochimica Acta Part B: Atomic Spectroscopy 88(0), 211–230 (2013).
[CrossRef]

Other

J. Aulbach, Spatiotemporal Control of Light in Turbid Media (PhD thesis, University of Twente, 2013).

Merriam Webster online, http://www.merriam-webster.com/ .

J. F. de Boer, Optical fluctuations on the tranmsission and reflection of mesoscopic systems (PhD thesis, University of Amsterdam, 1995).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, 1978).

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Figures (7)

Figure 1
Figure 1

Diagram of the experimental setup. The tunable source (inside the dotted lines) is created by combining a supercontinuum laser with a high resolution acousto-optic tunable filter (AOTF). The light from the laser passes through a polarizer (P), followed by the AOTF. The single wavelength from the AOTF is spatially filtered (SP). A small percentage is then split off to a reference photodiode (R) with the bulk of the light traveling to a polarizing microscope, where it is focussed to a spot. The diffuse light is imaged onto a CCD for each wavelength.

Figure 2
Figure 2

Reflectivity per unit μm2 the sample (smoothed in contour plot and not smoothed in the inset). The isointensity lines starting from the center are 64, 32, 16, 8, 4, 2, 1, 0.5, 0.25 × 10−3. The main data has been filtered with a low pass digital square boxcar filter of size 2.5 × 2.5 μm2 to reduce the spatial speckle. The inset shows a 2.5μm square image of the unfiltered data near the focus, which shows the speckle pattern.

Figure 3
Figure 3

The diffuse intensity, averaged azimuthally, as a function of radius for parallel (circles) and perpendicular (triangles) orientation of the analyzer with the fit (line) to Eq. (12) with ω = 0. The errors bars are the standard error calculated from the azimuthal averaging. The inset shows the same plot at larger radii to highlight the quality of the fit even above 30 microns.

Figure 4
Figure 4

Resulting fitting parameters over the green, yellow, and red wavelengths. The absorption time τa decreases systematically while the depolarization time τp and the mean free path l remain constant. (both τa and τp are given in units of 0.75τmf), The bottom plot shows the goodness of fit for the entire range.

Figure 5
Figure 5

Selected speckle patterns at 3 different radii: ρ = 0, 4, and 10 microns for the top, middle, and bottom plots respectively. The frequency correlation decreases markedly as the radii increases.

Figure 6
Figure 6

Top: ρ̄,ω̄, (δω) for several values of ρ̄ (0, 4, 8, and 14 microns for the squares, circles, up triangles, and down triangles respectively) at a constant average frequency of ω̄ = 3.03 fs−1(λ̄ = 0.620 μm) averaged over a range of δω = 0.107 fs−1(δλ = 0.022 μm). The correlation becomes weaker (narrower) as the radius increases. Bottom: ρ̄,ω̄, (δω) for several values of ω̄ (3.03, 3.14, 3.25, and 3.35 fs−1) for the squares, circles, up triangles, and down triangles respectively) at a constant radius of ρ̄ = 6 μm. The frequency dependence of the correlation function at this radius is below the measurement uncertainty.

Figure 7
Figure 7

The full width at half max (FWHM) of (, ω̄, δωk) as a function of radius crossed polarization case. The FWHM decreases with increasing radius due to the longer flight times in the material. The two theoretical curves are the analytical result (dashed line) from Eq. (12) and the simulated result (solid line) using the method described in section 3.2.

Equations (15)

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

I ¯ ( ρ i , ω ¯ ) I ( ρ i , ω j ) j | | ω j ω ¯ | Δ ω 2 ,
I ¯ ( ρ ¯ , ω ¯ ) I ¯ ( ρ i , ω ¯ ) i | | r i r ¯ | Δ r 2 .
C ρ i , ω ¯ ( δ ω k ) = ( I ( ρ i , ω j ) I ¯ ( ρ i , ω ¯ ) ) ( I ( ρ i , ω j + k ) I ¯ ( ρ i , ω ¯ ) ) j | | ω j ω ¯ | Δ ω 2 ( I ( ρ i , ω j ) I ¯ ( ρ i , ω ¯ ) ) 2 j | | ω j ω ¯ | Δ ω 2 ,
C ¯ ρ ¯ , ω ¯ , ( δ ω k ) = C ρ i , ω ¯ ( δ ω k ) i | | r i r ¯ | Δ r 2 .
C ¯ ρ ¯ , ω ¯ ( δ ω k ) = ( I ( ρ i , ω j ) I ¯ ( ρ ¯ , ω ¯ ) ) ( I ( ρ i , ω j + k ) I ¯ ( ρ ¯ , ω ¯ ) ) i | | ρ i ρ ¯ | Δ ρ 2 j | | ω j ω ¯ | Δ ω 2 ( I ( ρ i , ω j ) I ¯ ( ρ ¯ , ω ¯ ) ) 2 i | | ρ i ρ ¯ | Δ ρ 2 j | | ω j ω ¯ | Δ ω 2 ,
t U ( r , t ) = D 2 U ( r , t ) τ a 1 U ( r , t ) + S ( r , t ) ,
U ( z , ρ , t ) τ a = A t 3 / 2 e t / τ a n = 0 1 ( 1 ) n e r n 2 / t
U ( z , ρ , ω ) τ a = A 1 n = 0 1 ( 1 ) n e r n Γ r n
R ( ρ , ω ) τ a = A 2 n = 0 1 ( 1 ) n e r n Γ r n 3 ( 1 + r n Γ ) d z n | z = 0
U , ( z , ρ , t ) τ a U ( z , ρ , t ) τ a ( 1 2 ± exp ( t τ p ) )
U , ( z , ρ , t ) 1 2 ( U ( z , ρ , t ) τ a ± U ( z , ρ , t ) τ ap )
R , ( ρ , ω ) τ a , τ p 1 2 ( R ( ρ , ω ) τ a ± R ( ρ , ω ) τ ap )
R ( z , ρ , t ) τ a , finite = A 1 t 3 / 2 e t / τ a m = n = 0 1 ( 1 ) n e r n , m 2 / t .
R ( ρ , t ) τ a = 2 l 3 τ m f A t 5 / 3 e t / τ a n = 0 1 ( 1 ) n e r n 2 / t d z n | z = 0
R , ( ρ , t ) τ a , τ p 1 2 ( R ( ρ , t ) τ a ± R ( ρ , t ) τ ap )

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