Abstract

We present both experimental and Monte Carlo–based simulation results for the diffusely backscattered intensity patterns that arise from illumination of a turbid medium with a polarized laser beam. A numerical method that allows the calculation of all 16 elements of the two-dimensional Muller matrix is used; moreover, it is shown that only seven matrix elements are independent. To validate our method, we compared our simulations with experimental measurements, using a turbid medium consisting of 2.02µm-diameter polystyrene spheres suspended in deionized water. By varying the incident polarization and the analyzer optics for the experimental measurements, we obtained the diffuse backscattering Mueller matrix elements. The experimental and the numerical results are in good agreement.

© 1998 Optical Society of America

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Errata

Brent D. Cameron, M. J. Raković, Mehrübe Mehrübeoǧlu, George W. Kattawar, Sohi Rastegar, Lihong V. Wang, and Gerard L. Coté, "Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium: errata," Opt. Lett. 23, 1630-1630 (1998)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-23-20-1630

References

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  1. A. H. Hielscher, J. R. Mourant, and I. J. Bigio, Appl. Opt. 36, 125 (1997).
    [CrossRef] [PubMed]
  2. A. I. Carswell and S. R. Pal, Appl. Opt. 19, 4123 (1980).
    [CrossRef] [PubMed]
  3. S. R. Pal and A. I. Carswell, Appl. Opt. 24, 3464 (1985).
    [CrossRef]
  4. S. L. Jacques, M. Ostemeyer, L. Wang, and D. Stephens, Proc. SPIE 2671, 199 (1996).
    [CrossRef]
  5. S. G. Demos and R. R. Alfano, Appl. Opt. 36, 150 (1997).
    [CrossRef] [PubMed]
  6. A. H. Hielscher, A. A. Eick, J. R. Mourant, and I. J. Bigio, Proc. SPIE 2976, 298 (1997).
    [CrossRef]
  7. M. Dogariu and T. Asakura, Opt. Eng. 35, 2234 (1996).
    [CrossRef]
  8. W. S. Bickel and W. M. Bailey, Am. J. Phys. 53, 468 (1985).
    [CrossRef]
  9. A. Ambirajan and D. C. Look, J. Quant. Spectrosc. Radiat. Transfer 58, 171 (1997).
    [CrossRef]
  10. R. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), p. 150.
  11. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
  12. G. W. Kattawar and C. N. Adams, Limnol. Oceanogr. 48, 1453 (1989).
    [CrossRef]

1997 (4)

A. H. Hielscher, J. R. Mourant, and I. J. Bigio, Appl. Opt. 36, 125 (1997).
[CrossRef] [PubMed]

S. G. Demos and R. R. Alfano, Appl. Opt. 36, 150 (1997).
[CrossRef] [PubMed]

A. H. Hielscher, A. A. Eick, J. R. Mourant, and I. J. Bigio, Proc. SPIE 2976, 298 (1997).
[CrossRef]

A. Ambirajan and D. C. Look, J. Quant. Spectrosc. Radiat. Transfer 58, 171 (1997).
[CrossRef]

1996 (2)

M. Dogariu and T. Asakura, Opt. Eng. 35, 2234 (1996).
[CrossRef]

S. L. Jacques, M. Ostemeyer, L. Wang, and D. Stephens, Proc. SPIE 2671, 199 (1996).
[CrossRef]

1989 (1)

G. W. Kattawar and C. N. Adams, Limnol. Oceanogr. 48, 1453 (1989).
[CrossRef]

1985 (2)

S. R. Pal and A. I. Carswell, Appl. Opt. 24, 3464 (1985).
[CrossRef]

W. S. Bickel and W. M. Bailey, Am. J. Phys. 53, 468 (1985).
[CrossRef]

1980 (1)

Adams, C. N.

G. W. Kattawar and C. N. Adams, Limnol. Oceanogr. 48, 1453 (1989).
[CrossRef]

Alfano, R. R.

Ambirajan, A.

A. Ambirajan and D. C. Look, J. Quant. Spectrosc. Radiat. Transfer 58, 171 (1997).
[CrossRef]

Asakura, T.

M. Dogariu and T. Asakura, Opt. Eng. 35, 2234 (1996).
[CrossRef]

Azzam, R.

R. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), p. 150.

Bailey, W. M.

W. S. Bickel and W. M. Bailey, Am. J. Phys. 53, 468 (1985).
[CrossRef]

Bashara, N. M.

R. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), p. 150.

Bickel, W. S.

W. S. Bickel and W. M. Bailey, Am. J. Phys. 53, 468 (1985).
[CrossRef]

Bigio, I. J.

A. H. Hielscher, A. A. Eick, J. R. Mourant, and I. J. Bigio, Proc. SPIE 2976, 298 (1997).
[CrossRef]

A. H. Hielscher, J. R. Mourant, and I. J. Bigio, Appl. Opt. 36, 125 (1997).
[CrossRef] [PubMed]

Carswell, A. I.

Demos, S. G.

Dogariu, M.

M. Dogariu and T. Asakura, Opt. Eng. 35, 2234 (1996).
[CrossRef]

Eick, A. A.

A. H. Hielscher, A. A. Eick, J. R. Mourant, and I. J. Bigio, Proc. SPIE 2976, 298 (1997).
[CrossRef]

Hielscher, A. H.

A. H. Hielscher, A. A. Eick, J. R. Mourant, and I. J. Bigio, Proc. SPIE 2976, 298 (1997).
[CrossRef]

A. H. Hielscher, J. R. Mourant, and I. J. Bigio, Appl. Opt. 36, 125 (1997).
[CrossRef] [PubMed]

Jacques, S. L.

S. L. Jacques, M. Ostemeyer, L. Wang, and D. Stephens, Proc. SPIE 2671, 199 (1996).
[CrossRef]

Kattawar, G. W.

G. W. Kattawar and C. N. Adams, Limnol. Oceanogr. 48, 1453 (1989).
[CrossRef]

Look, D. C.

A. Ambirajan and D. C. Look, J. Quant. Spectrosc. Radiat. Transfer 58, 171 (1997).
[CrossRef]

Mourant, J. R.

A. H. Hielscher, A. A. Eick, J. R. Mourant, and I. J. Bigio, Proc. SPIE 2976, 298 (1997).
[CrossRef]

A. H. Hielscher, J. R. Mourant, and I. J. Bigio, Appl. Opt. 36, 125 (1997).
[CrossRef] [PubMed]

Ostemeyer, M.

S. L. Jacques, M. Ostemeyer, L. Wang, and D. Stephens, Proc. SPIE 2671, 199 (1996).
[CrossRef]

Pal, S. R.

Stephens, D.

S. L. Jacques, M. Ostemeyer, L. Wang, and D. Stephens, Proc. SPIE 2671, 199 (1996).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).

Wang, L.

S. L. Jacques, M. Ostemeyer, L. Wang, and D. Stephens, Proc. SPIE 2671, 199 (1996).
[CrossRef]

Am. J. Phys. (1)

W. S. Bickel and W. M. Bailey, Am. J. Phys. 53, 468 (1985).
[CrossRef]

Appl. Opt. (4)

J. Quant. Spectrosc. Radiat. Transfer (1)

A. Ambirajan and D. C. Look, J. Quant. Spectrosc. Radiat. Transfer 58, 171 (1997).
[CrossRef]

Limnol. Oceanogr. (1)

G. W. Kattawar and C. N. Adams, Limnol. Oceanogr. 48, 1453 (1989).
[CrossRef]

Opt. Eng. (1)

M. Dogariu and T. Asakura, Opt. Eng. 35, 2234 (1996).
[CrossRef]

Proc. SPIE (2)

A. H. Hielscher, A. A. Eick, J. R. Mourant, and I. J. Bigio, Proc. SPIE 2976, 298 (1997).
[CrossRef]

S. L. Jacques, M. Ostemeyer, L. Wang, and D. Stephens, Proc. SPIE 2671, 199 (1996).
[CrossRef]

Other (2)

R. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), p. 150.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram of experimental setup used for the Mueller matrix imaging of the diffusely backscattered light from the sample.

Fig. 2
Fig. 2

Experimental and Monte Carlo–simulated diffusely backscattered Mueller matrix for a 2.02µm polystyrene sphere suspension. The approximate size of each image is 1.6 cm×1.6 cm. Each of the 16 experimental elements is calculated by addition or subtraction of a series of images. The individual images are represented by a two-letter combination that denotes the input polarization and the output analyzer orientation (i.e., HV denotes horizontal input polarized light and a vertical polarization analyzer). The corresponding symbols denoting polarization are V, vertical; H, horizontal; P, +45°; M, -45°; R, right; L, left; and O, open or no polarization optics. For the Monte Carlo simulations, the average number of collisions per trajectory is 10.

Equations (5)

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Sρ, ϕ; μs, μT=R-ϕLρs, ω¯R-ϕ, Lρ, ω¯=n=2ω¯n-2Lnρs, ρs=μTρ, ω¯=μsμT,
L2=00dz1dz2r2exp-z1+z2+r×Mπ-θMθ, r=ρs2+z1-z221/2, tanθ=ρsz2-z1,
L2=00dz1dz2r2exp-z1+z2+r×Mπ-θTθMπ-θ, r=ρs2+z1+z221/2, tanθ=ρsz2+z1.
Lnt=PLnP, Lt=PLP, P=[1000010000-100001].
S13=S12φ+π4, S21=S12, S31=S12φ-π4, S32=S23φ±π4, S33=-S22φ±π4, S34=S24φ-π4, S41=S14, S42=S24, S43=S24φ+π4,

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