Abstract

A scattering-media-characterization method that uses partially coherent radiation and polarization discrimination of multiply scattered light is described. The method is based on an analysis of the dependence of speckle contrast on the coherence length of the probe light. Polarization discrimination of detected speckles makes it possible to select scattered-light components that propagate in the probed medium at different distances. A theoretical analysis of the polarization-dependent speckle contrast as influenced by the probe-light coherence and parameters of the probed medium is presented. Experimental results obtained with various nondiffuse scattering samples are presented.

© 2004 Optical Society of America

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2002 (2)

V. Sankaran, J. T. Walsh, D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
[CrossRef] [PubMed]

S. L. Jacques, J. C. Ramella-Roman, K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
[CrossRef] [PubMed]

2001 (1)

D. A. Zimnyakov, Yu. P. Sinichkin, P. V. Zakharov, D. N. Agafonov, “Residual polarization of non-coherently backscattered linearly polarized light: the influence of the anisotropy parameter of the scattering medium,” Waves Random Media 11, 395–412 (2001).
[CrossRef]

2000 (5)

R. C. Studinski, I. A. Vitkin, “Methodology for examining polarized light interactionwith tissues and tissue-like media in the exact backscattering direction,” J. Biomed. Opt. 5, 330–337 (2000).
[CrossRef] [PubMed]

D. A. Zimnyakov, “On some manifestations of similarity in multiple scattering of coherent light,” Waves Random Media 10, 417–434 (2000).
[CrossRef]

S. L. Jacques, J. R. Roman, K. Lee, “Imaging superficial tissues with polarized light,” Lasers Surg. Med. 26, 119–129 (2000).
[CrossRef] [PubMed]

S. G. Demos, H. B. Radousky, R. R. Alfano, “Deep subsurface imaging in tissues using spectral and polarization filtering,” Opt. Express 7, 23–28 (2000), www.opticsexpress.org .
[CrossRef] [PubMed]

J. S. Tyo, “Enhancement of the point-spread function for imaging in scattering media by use of polarization-difference imaging,” J. Opt. Soc. Am. A 17, 1–10 (2000).
[CrossRef]

1999 (3)

1998 (4)

J. M. Schmitt, “Restoration of optical coherence images of living tissue using the CLEAN algorithm,” J. Biomed. Opt. 3, 66–75 (1998).
[CrossRef] [PubMed]

P.-A. Lemieux, M. U. Vera, D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: The role of ballistic transport and anisotropic scattering,” Phys. Rev. E 57, 4498–4515 (1998).
[CrossRef]

S. P. Schilders, X. S. Gan, M. Gu, “Resolution improvement in microscopic imaging through turbid media based on differential polarization imaging,” Appl. Opt. 37, 4300–4302 (1998).
[CrossRef]

L. Guniunas, R. Karkoskas, R. Danielius, “Accurate remote distance sensing by use of low-coherence interferometry: an industrial application,” Appl. Opt. 37, 6729–6733 (1998).
[CrossRef]

1997 (8)

1996 (6)

1995 (4)

D. J. Durian, “Accuracy of diffusing-wave spectroscopy theories,” Phys. Rev. E 51, 3350–3358 (1995).
[CrossRef]

E. E. Gorodnichev, D. B. Rogozkin, “Small-angle multiple scattering of light in a random medium,” Sov. Phys. JETP 80, 112–126 (1995).

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75, 1855–1858 (1995).
[CrossRef] [PubMed]

J. D. Briers, S. Webster, “Quasi-real time digital version of single-exposure speckle photography for full-field moni-toring of velocity or flow fields,” Opt. Commun. 116, 36–42 (1995).
[CrossRef]

1994 (1)

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattering waves by spherical diffusers: influence of size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

1993 (5)

D. Eliyahu, “Vector statistics of correlated Gaussian fields,” Phys. Rev. B 47, 2881–2892 (1993).
[CrossRef]

J. D. Briers, “Speckle fluctuations and biomedical optics: implications and applications,” Opt. Eng. 32, 277–283 (1993).
[CrossRef]

P. D. Kaplan, A. G. Yodh, D. F. Townsend, “Noninvasive study of gel formation in polymer-stabilized dense colloids using multiply scattered light,” J. Colloid Interface Sci. 155, 319–324 (1993).
[CrossRef]

D. Eliyahu, M. Rosenbluh, I. Freund, “Angular intensity and polarization dependence of diffuse transmission through random media,” J. Opt. Soc. Am. A 10, 477–491 (1993).
[CrossRef]

J. M. Schmitt, A. Knuttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6041 (1993).
[CrossRef] [PubMed]

1992 (6)

J. M. Schmitt, A. H. Gandjbakhche, R. F. Bonnar, “Use of polarized light to discriminate short-path photons in a multiply scattering medium,” Appl. Opt. 31, 6535–6546 (1992).
[CrossRef] [PubMed]

A. G. Yodh, D. J. Pine, P. D. Kaplan, M. H. Kao, N. Georgiades, “Speckle fluctuations and their use as probes of dense random media,” Mol. Cryst. Liq. Cryst. Sci. Technol. Sect. B 3, 149–160 (1992).

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical ba-sis for the determination of optical pathlengths in tissue:temporal and frequency analysis,” Phys. Med. Biol. 17, 1531–1560 (1992).
[CrossRef]

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, P. M. Chaikin, “Nonergodicity and light scattering from polymer gels,” Phys. Rev. A 46, 6550–6553 (1992).
[CrossRef] [PubMed]

I. I. Tarhan, G. H. Watson, “Polarization microstatistics of laser speckle,” Phys. Rev. A 45, 6013–6018 (1992).
[CrossRef] [PubMed]

I. Freund, M. Kaveh, “Comment on Polarization memory of multiply scattered light,” Phys. Rev. B 45, 8162–8164 (1992).
[CrossRef]

1991 (7)

I. Freund, M. Kaveh, R. Berkovits, M. Rosenbluh, “Universal polarization correlations and microstatistics of optical waves in random media,” Phys. Rev. B 42, 2613–2616 (1991).
[CrossRef]

S. M. Cohen, D. Eliyahu, I. Freund, M. Kaveh, “Vector statistics of multiply-scattered waves in random systems,” Phys. Rev. A 43, 5748–5751 (1991).
[CrossRef] [PubMed]

R. R. Anderson, “Polarized light examination and photography of the skin,” Arch. Dermatol. 127, 1000–1005 (1991).
[CrossRef] [PubMed]

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–689 (1991).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

A. A. Middleton, D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B 43, 5934–5938 (1991).
[CrossRef]

B. L. Danielson, C. Y. Boisrobert, “Absolute optical ranging using low coherence interferometry,” Appl. Opt. 30, 2975–2979 (1991).
[CrossRef] [PubMed]

1990 (2)

Z. Zhang, S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef] [PubMed]

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

1989 (3)

F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive index of some mammalian tissues using a fiber optics cladding method,” Appl. Opt. 28, 2297–2303 (1989).
[CrossRef] [PubMed]

F. C. MacKintosh, S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2382–2406 (1989).
[CrossRef]

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

1988 (2)

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

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

1987 (1)

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motions of scatterers,” Z. Phys. B 65, 409–413 (1987).
[CrossRef]

1986 (2)

A. Y. Val’kov, V. P. Romanov, “Characteristics of propagation and scattering of light in nematic liquid crystals,” Sov. Phys. JETP 63, 737–743 (1986).

M. J. Stephen, G. Cwillich, “Rayleigh scattering and weak localization: effects of polarization,” Phys. Rev. B 34, 7564–7572 (1986).
[CrossRef]

1985 (1)

R. Barakat, “The statistical properties of partially polarized light,” Opt. Acta 32, 295–312 (1985).
[CrossRef]

1941 (1)

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Agafonov, D. N.

D. A. Zimnyakov, Yu. P. Sinichkin, P. V. Zakharov, D. N. Agafonov, “Residual polarization of non-coherently backscattered linearly polarized light: the influence of the anisotropy parameter of the scattering medium,” Waves Random Media 11, 395–412 (2001).
[CrossRef]

Akkermans, E.

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

Alfano, R. R.

Anderson, R. R.

R. R. Anderson, “Polarized light examination and photography of the skin,” Arch. Dermatol. 127, 1000–1005 (1991).
[CrossRef] [PubMed]

Arridge, S. R.

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical ba-sis for the determination of optical pathlengths in tissue:temporal and frequency analysis,” Phys. Med. Biol. 17, 1531–1560 (1992).
[CrossRef]

Barakat, R.

R. Barakat, “The statistical properties of partially polarized light,” Opt. Acta 32, 295–312 (1985).
[CrossRef]

Barton, J. K.

J. A. Izatt, M. D. Kulkarni, K. Kobayashi, M. V. Sivak, J. K. Barton, A. J. Welsh, “Optical coherence tomography for biodiagnostics,” Opt. Photon. News, August1997, pp. 41–47.

Berkovits, R.

I. Freund, M. Kaveh, R. Berkovits, M. Rosenbluh, “Universal polarization correlations and microstatistics of optical waves in random media,” Phys. Rev. B 42, 2613–2616 (1991).
[CrossRef]

Bicout, D.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattering waves by spherical diffusers: influence of size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
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Townsend, D. F.

P. D. Kaplan, A. G. Yodh, D. F. Townsend, “Noninvasive study of gel formation in polymer-stabilized dense colloids using multiply scattered light,” J. Colloid Interface Sci. 155, 319–324 (1993).
[CrossRef]

Tuchin, V. V.

D. A. Zimnyakov, J. D. Briers, V. V. Tuchin. “Speckle technologies for monitoring and imaging of tissues and tissue-like phantoms,” in Handbook of Optical Medical Diagnostics, V. V. Tuchin, ed. (SPIE Press, Bellingham, Wash., 2002), pp. 987–1036.

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A. Y. Val’kov, V. P. Romanov, “Characteristics of propagation and scattering of light in nematic liquid crystals,” Sov. Phys. JETP 63, 737–743 (1986).

Vera, M. U.

P.-A. Lemieux, M. U. Vera, D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: The role of ballistic transport and anisotropic scattering,” Phys. Rev. E 57, 4498–4515 (1998).
[CrossRef]

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R. C. Studinski, I. A. Vitkin, “Methodology for examining polarized light interactionwith tissues and tissue-like media in the exact backscattering direction,” J. Biomed. Opt. 5, 330–337 (2000).
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V. Sankaran, J. T. Walsh, D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
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D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–689 (1991).
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F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
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J. A. Izatt, M. D. Kulkarni, K. Kobayashi, M. V. Sivak, J. K. Barton, A. J. Welsh, “Optical coherence tomography for biodiagnostics,” Opt. Photon. News, August1997, pp. 41–47.

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M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1970).

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G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motions of scatterers,” Z. Phys. B 65, 409–413 (1987).
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J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, P. M. Chaikin, “Nonergodicity and light scattering from polymer gels,” Phys. Rev. A 46, 6550–6553 (1992).
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J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, P. M. Chaikin, “Nonergodicity and light scattering from polymer gels,” Phys. Rev. A 46, 6550–6553 (1992).
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A. G. Yodh, D. J. Pine, P. D. Kaplan, M. H. Kao, N. Georgiades, “Speckle fluctuations and their use as probes of dense random media,” Mol. Cryst. Liq. Cryst. Sci. Technol. Sect. B 3, 149–160 (1992).

Yung, K. M.

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography: an overview,” in Saratov Fall Meeting ’98: Light Scattering Technologies for Mechanics, Biomedicine, and Material Science, V. V. Tuchin, V. P. Ryabukho, D. A. Zimnyakov, eds. Proc. SPIE3726, 450–461 (1999).
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D. A. Zimnyakov, Yu. P. Sinichkin, P. V. Zakharov, D. N. Agafonov, “Residual polarization of non-coherently backscattered linearly polarized light: the influence of the anisotropy parameter of the scattering medium,” Waves Random Media 11, 395–412 (2001).
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F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
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Zimnyakov, D. A.

D. A. Zimnyakov, Yu. P. Sinichkin, P. V. Zakharov, D. N. Agafonov, “Residual polarization of non-coherently backscattered linearly polarized light: the influence of the anisotropy parameter of the scattering medium,” Waves Random Media 11, 395–412 (2001).
[CrossRef]

D. A. Zimnyakov, “On some manifestations of similarity in multiple scattering of coherent light,” Waves Random Media 10, 417–434 (2000).
[CrossRef]

D. A. Zimnyakov, J. D. Briers, V. V. Tuchin. “Speckle technologies for monitoring and imaging of tissues and tissue-like phantoms,” in Handbook of Optical Medical Diagnostics, V. V. Tuchin, ed. (SPIE Press, Bellingham, Wash., 2002), pp. 987–1036.

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J. Colloid Interface Sci. (1)

P. D. Kaplan, A. G. Yodh, D. F. Townsend, “Noninvasive study of gel formation in polymer-stabilized dense colloids using multiply scattered light,” J. Colloid Interface Sci. 155, 319–324 (1993).
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Phys. Rev. B (7)

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Phys. Rev. Lett. (3)

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75, 1855–1858 (1995).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Z. Zhang, S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
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Science (3)

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Sov. Phys. JETP (2)

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Sov. Phys. Usp. (1)

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Figures (8)

Fig. 1
Fig. 1

Schematic of the experimental setup. (a) Transmitted-light detection, (b) backscattered-light detection. 1, light source (laser diode with collimator); 2, beam splitter; 3 and 5, polarizers; 4, probed sample; 6, CCD camera with imaging lens; 7, fiber-optic bundle; 9, grating spectrophotometer; 9, personal computer.

Fig. 2
Fig. 2

(a) Typical emission spectrum of the laser diode that we used in the region of the generation threshold (pumping current is 12.3 mA). (b) Typical form of the coherence peak (time-domain presentation; pumping current is 9.8 mA). Circles, values calculated by the Fourier transform of the spectral envelope; dashed curve, exponential approximation. (c) Fragments of captured speckle patterns (for porcine adipose tissue, with transmitted light and co-polarized speckle pattern. Left panel, lc28 μm; right panel, lc380 μm).

Fig. 3
Fig. 3

Spectral dependencies of the extinction coefficient for samples 2 (solid curve) and 3 (dotted curve).

Fig. 4
Fig. 4

Dependencies of speckle contrast on the coherence length for sample 1. Solid curve and solid triangles, co-polarized speckle patterns; dashed curve and open triangles, cross-polarized speckle patterns. Curves represent theoretical results; symbols experimental results.

Fig. 5
Fig. 5

Dependencies of speckle contrast on coherence length for sample 2. Solid curve and solid circles, co-polarized speckle patterns, transmitted light; dashed curve and solid squares, cross-polarized speckle patterns, transmitted light; dashed–dotted curve and open circles, co-polarized speckle patterns, backscattered light; dotted curve and open squares, cross-polarized speckle patterns, backscattered light. Curves represent theoretical results; symbols, experimental results.

Fig. 6
Fig. 6

Dependencies of speckle contrast on coherence length for sample 3. Solid curve and solid circles, co-polarized speckle patterns, transmitted light; dashed–dotted curve and open circles, co-polarized speckle patterns, backscattered light; dotted curve and open squares, cross-polarized speckle patterns, backscattered mode. Curves represent theoretical results; symbols, experimental results.

Fig. 7
Fig. 7

Dependencies of speckle contrast on coherence length for sample 4. Solid curve and solid circles, co-polarized speckle patterns, transmitted light; dashed curve and solid squares, cross-polarized speckle patterns, transmitted light; dashed–dotted curve and open circles, co-polarized speckle patterns, backscattered light; dotted curve and open squares, cross-polarized speckle patterns, backscattered light. Curves represent theoretical results; symbols, experimental results. The thickness of tissue layer is equal to 0.70 mm. The value of the depolarization length ξ for transmitted and backscattered light obtained with the fitting procedure was found to be ≈3 µm).

Fig. 8
Fig. 8

Dependence of the normalization coefficient K on the reduced scattering coefficient μ˜s and the mode spacing parameter Δ˜ (the dimensionless values μ˜s and Δ˜ are normalized by the coherence length of probe light). The scattering and detection conditions were backscattering from a semi-infinite medium with expressed scattering anisotropy and co-polarized component detection. Inset: relative sensitivity of K to changes in μ˜s. Open circles, isotropic scattering; solid circles, anisotropic scattering.

Tables (1)

Tables Icon

Table 1 Optical Parameters of the Samples Used To Fit Speckle-Contrast Dependencies Cco(lc), Ccr(lc)

Equations (14)

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

InN|En|2, I2nN|En|22+nNnnN|En|2|En|2|g(Δsnn)|2×cos2[k¯Δsnn+Δϕnn+ψ(Δsnn)].
I|E|2N,
I2|E|4N2+(N2-N)k|g(Δsk)|2Pk.
C=I2-I2I20.5=1-1Nk|g(Δsk)|2Pk0.5.
C=0|g(Δs)|2ρ(Δs)d(Δs)0.5.
ρ(Δs)=0ρ(s)ρ(s+Δs)ds.
C=00|g(Δs)|2ρ(s)ρ(s+Δs)dsd(Δs)0.5.
C=00S(λ)S(λ)|J(λ,λ)|2dλdλ0.50S(λ)dλ.
ρ(s)=fii(s)ρ(s);ρ(s)=f(s)ρ(s).
fii(s)=[1+exp(-s/ξ)]/2;f(s)={1-exp(-s/ξ)}/2,
PL(t)={I(t)-I(t)}/{I(t)+I(t)}exp(-t/tL).
|g(Δs)|Δs0=i=0Ci exp(-|Δs-iΔ|/lc).
|g(Δs)|=i=0MΔsmax/ΔCi exp(-|Δs-iΔ|/lc),
K(K/n)ρ(Δs) Δs=0+2i-1Mρ(Δs) Δr=Δi0.5.

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