Abstract

We present experimental results of measurements of light backscattering from semi-infinite disordered media by low-coherence interferometry (LCI). These results are compared with the theory developed in part I [J. Opt. Soc. Am. A 17, 2024 (2000)]. A comparison of the experimental data with the theoretical formulas based on the coherent phase approximation allows us to extract substantial information about the structure of the studied media. Our results demonstrate that LCI is an effective optical technique for studying nonuniform media even in the case in which the dimensions of nonuniformities are much less than the wavelength of the scattered light.

© 2000 Optical Society of America

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References

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  1. A. Brodsky, S. Thurber, L. Burgess, “Low-coherence interferometry in random media. I. Theory,” J. Opt. Soc. Am. A 17, 2024–2033 (2000).
    [CrossRef]
  2. A. Brodsky, P. Shelley, S. Thurber, L. Burgess, “Low-coherence interferometry of particles distributed in a dielectric medium,” J. Opt. Soc. Am. A 14, 2263–2268 (1997).
    [CrossRef]
  3. (Duke Scientific Corporation, Palo Alto, Calif., 1996).
  4. Microparticle Reagent Optimization, Laboratory Reference Manual, Part Number 0347-835 (Seradyn Inc., Indianapolis,1994).
  5. R. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966).
  6. See, for example, M. A. Fiddy, D. A. Pommet, in Inverse Problems of Wave Propagation and Diffraction, G. Chavent, P. Sabatier, eds. (Springer, Berlin, 1997), Chap. 3, p. 58; D. A. Boas, “A fundamental limitation of linearized algorithms for diffuse optical tomography,” Opt. Expr. 1, 404–413 (1997).
    [CrossRef]
  7. V. Tuchin, “Light scattering study of tissues,” Usp. Fiz. Nauk 167, 517–543 (1997)[English translation in Phys. Usp. 40, 495–515 (1997)];B. R. Masters, “Early development of optical low coherence reflectometry and some recent biomedical applications,” J. Biomed. Opt. 4, 236–247 (1999).
    [CrossRef] [PubMed]

2000

1997

V. Tuchin, “Light scattering study of tissues,” Usp. Fiz. Nauk 167, 517–543 (1997)[English translation in Phys. Usp. 40, 495–515 (1997)];B. R. Masters, “Early development of optical low coherence reflectometry and some recent biomedical applications,” J. Biomed. Opt. 4, 236–247 (1999).
[CrossRef] [PubMed]

A. Brodsky, P. Shelley, S. Thurber, L. Burgess, “Low-coherence interferometry of particles distributed in a dielectric medium,” J. Opt. Soc. Am. A 14, 2263–2268 (1997).
[CrossRef]

Brodsky, A.

Burgess, L.

Fiddy, M. A.

See, for example, M. A. Fiddy, D. A. Pommet, in Inverse Problems of Wave Propagation and Diffraction, G. Chavent, P. Sabatier, eds. (Springer, Berlin, 1997), Chap. 3, p. 58; D. A. Boas, “A fundamental limitation of linearized algorithms for diffuse optical tomography,” Opt. Expr. 1, 404–413 (1997).
[CrossRef]

Newton, R.

R. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966).

Pommet, D. A.

See, for example, M. A. Fiddy, D. A. Pommet, in Inverse Problems of Wave Propagation and Diffraction, G. Chavent, P. Sabatier, eds. (Springer, Berlin, 1997), Chap. 3, p. 58; D. A. Boas, “A fundamental limitation of linearized algorithms for diffuse optical tomography,” Opt. Expr. 1, 404–413 (1997).
[CrossRef]

Shelley, P.

Thurber, S.

Tuchin, V.

V. Tuchin, “Light scattering study of tissues,” Usp. Fiz. Nauk 167, 517–543 (1997)[English translation in Phys. Usp. 40, 495–515 (1997)];B. R. Masters, “Early development of optical low coherence reflectometry and some recent biomedical applications,” J. Biomed. Opt. 4, 236–247 (1999).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Usp. Fiz. Nauk

V. Tuchin, “Light scattering study of tissues,” Usp. Fiz. Nauk 167, 517–543 (1997)[English translation in Phys. Usp. 40, 495–515 (1997)];B. R. Masters, “Early development of optical low coherence reflectometry and some recent biomedical applications,” J. Biomed. Opt. 4, 236–247 (1999).
[CrossRef] [PubMed]

Other

(Duke Scientific Corporation, Palo Alto, Calif., 1996).

Microparticle Reagent Optimization, Laboratory Reference Manual, Part Number 0347-835 (Seradyn Inc., Indianapolis,1994).

R. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966).

See, for example, M. A. Fiddy, D. A. Pommet, in Inverse Problems of Wave Propagation and Diffraction, G. Chavent, P. Sabatier, eds. (Springer, Berlin, 1997), Chap. 3, p. 58; D. A. Boas, “A fundamental limitation of linearized algorithms for diffuse optical tomography,” Opt. Expr. 1, 404–413 (1997).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

LCI signal for a highly scattering system: a single scan (the highly fluctuating curve) and an average of 50 individual scans (bold curve) for a 2.5% (by weight) solution of 308-nm-diameter polystyrene microspheres in deionized water. Here, l is the distance difference between the mirror position and the probe/sample interface with respect to the instrument coupler. The intensity of the high-frequency fluctuations depends at least partly on the Brownian motion of the particles and the nonuniformities. The fluctuations can be averaged out in liquid samples, but they remain strong even after averaging in solid samples. The dotted line corresponds to the exponential decay law (Beer’s law).

Fig. 2
Fig. 2

(a) Average of 50 reflectometer scans for a 1% (by weight) solution of polystyrene microspheres in deionized water as a function of particle diameters. The signal traces (from bottom to top) correspond to the following particle diameters: 41, 50, 60, 73, 83, 96, 126, and 204 nm. (b) Average of 50 scans for 1% (by weight) polystyrene microspheres in deionized water as a function of particle diameters. The diameters are (i) 223 nm, (ii) 401 nm, (iii) 543 nm, and (iv) 818 nm.

Fig. 3
Fig. 3

(a) Average of 50 reflectometer scans for different concentrations (by weight) of 126-nm-diameter polystyrene microspheres in deionized water: (i) 0.25%, (ii) 0.5%, (iii) 1%. (b) Averaged reflectometer signals for 0.25%, 0.5%, 1%, 1.25%, 2.5%, 5%, and 10% concentrations (by weight) of 308-nm-diameter polystyrene microspheres in deionized water.

Fig. 4
Fig. 4

Maximum signal intensities for different concentrations of Duke polystyrene microsphere standards (see the text) in deionized water as a function of the cubed radius of the particles: (i) 0.25%, (ii) 0.5%, (iii) 1%.

Fig. 5
Fig. 5

Maximum signal intensities for 0.5% (by weight) polystyrene microspheres in deionized water as a function of the cubed radius of the particles: ○, Duke standards3; ●, Seradyn standards.4

Fig. 6
Fig. 6

Maximium signal intensities as a function of particle concentration (by weight) in deionized water and the cubed radius of the particles: ◍, 0.0025%; ○, 0.0050%; ●, 0.010%; ⊘, 0.025%; ⊕, 0.050%; josaa-17-11-2034-i001 0.10%.

Fig. 7
Fig. 7

Critical particle radius (the radius at the point of the deviation from the linearity in Fig. 8) as a function of particle concentration.

Fig. 8
Fig. 8

Comparison of selected reflectometer signals with theory. The theoretical curves (bold) were calculated as constant×log [expression (48) from Ref. 1]. Shown are the averaged signal of 50 individual scans and the theoretical curve for the (i) 1% (by weight) solution of 50-nm-diameter polystyrene microspheres in deionized water, (ii) 1% (by weight) solution of 60-nm-diameter polystyrene microspheres in deionized water, (iii) 5% (by weight) solution of 308-nm-diameter polystyrene microspheres in deionized water, and (iv) (gray) 5% (by weight) solution of 401-nm-diameter polystyrene microspheres in deionized water.  

Tables (2)

Tables Icon

Table 1 Maximum Intensity of the Signal As a Function of Particle Size and Concentration for Duke Polystyrene Microspheres in Deionized Water (see text)

Tables Icon

Table 2 Maximum Intensity of the Signal As a Function of Particle Size and Concentration for Seradyne Polystyrene Microspheres in Deionized Water (see text)

Equations (16)

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JD=Rd[Jc+Jint(l)],
κ(ω)=λ22παNαAα(0),forκ2(ω0)<m(ω0),
Nα=ρα43πRα3,
Rαλ<1,
Aα(0)Rα3λ2c1+ic2Rαλ,
c1=32 [p(ω)-m(ω)] 1p(ω)+2,
c2=-38 [p(ω)-m(ω)]2,
Rαλ2[p(ω)-m(ω)].
Rcrc2ωm(p-m),
Δ=1N¯.
Re Δκ2(ω0)ρ¯0R¯3[p(ω)-m(ω)]1+OR¯λ2,
Im Δκ2(ω0)ρ¯0R¯3R¯[p(ω)-m(ω)]2λ×1+OR¯λ2,
ρ0=αρα,R¯=αραRαρ0.
JSUT(0)=Cρ0R¯3 forR¯<Rcr,
n(ω)nm(ω)>Re κ(ω)Im κ(ω).
akBTηR1/2/τ,

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