Abstract

In recent years there has been increasing interest in the use of polarization for imaging objects in a cluttered environment. Examples are optical imaging through clouds, optical detection of objects in a biological medium, and microwave detection of objects in clutter. We extend previous studies of continuous-wave scattering to pulse-polarization scattering in discrete scatterers. We solve the time-dependent vector radiative transfer equation for a plane-parallel medium by using Mie scattering and the discrete ordinates method. The time-dependent degree of polarization and cross-polarization discrimination are calculated and verify the advantages of circular over linear polarization in maintaining greater copolarized components rather than cross-polarized components.

© 2001 Optical Society of America

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References

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  1. D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
    [CrossRef]
  2. S. G. Demos, R. R. Alfano, “Optical polarization imaging,” Appl. Opt. 36, 150–155 (1997).
    [CrossRef] [PubMed]
  3. K. M. Yoo, R. R. Alfano, “Time resolved depolarization of multiple backscattered light from random media,” Phys. Lett. A 142, 531–536 (1989).
    [CrossRef]
  4. G. D. Lewis, D. L. Jordan, P. J. Roberts, “Backscattering target detection in a turbid medium by polarization discrimination,” Appl. Opt. 38, 3937–3944 (1999).
    [CrossRef]
  5. M. Moscoso, J. B. Keller, G. C. Papanicolaou, “Depolarization and blurring of optical images by biological tissue,” J. Opt. Soc. Am. A 18, 948–960 (2001).
    [CrossRef]
  6. A. D. Kim, S. Jaruwatanadilok, A. Ishimaru, Y. Kuga, “Polarized light propagation and scattering in random media,” in Laser–Tissue Interaction XII: Photochemical, Photothermal, and Photomechanical, D. D. Duncan, S. L. Jacques, P. C. Johnson, eds., Proc. SPIE4257, 90–100 (2001).
  7. P. Bruscaglioni, G. Zaccanti, Q. Wei, “Transmission of a pulsed polarized light beam through thick turbid media: numerical results,” Appl. Opt. 32, 6142–6150 (1993).
    [CrossRef] [PubMed]
  8. A. Ishimaru, Wave Propagation and Scattering in Random Media (Institute of Electrical and Electronics Engineers, New York, 1997).
  9. A. Ishimaru, R. L.-T. Cheung, “Multiple scattering effects on wave propagation due to rain,” Ann. Telecommun. 35, 373–379 (1980).
  10. R. L.-T. Cheung, A. Ishimaru, “Transmission backscattering and depolarization of waves in randomly distributed spherical particles,” Appl. Opt. 21, 3792–3798 (1982).
    [CrossRef] [PubMed]
  11. Z. Sekera, “Scattering matrices and reciprocity relationships for various representations of the state of polarization,” J. Opt. Soc. Am. 56, 1732–1740 (1966).
    [CrossRef]
  12. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

2001

1999

1997

1994

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

1993

1989

K. M. Yoo, R. R. Alfano, “Time resolved depolarization of multiple backscattered light from random media,” Phys. Lett. A 142, 531–536 (1989).
[CrossRef]

1982

1980

A. Ishimaru, R. L.-T. Cheung, “Multiple scattering effects on wave propagation due to rain,” Ann. Telecommun. 35, 373–379 (1980).

1966

Alfano, R. R.

S. G. Demos, R. R. Alfano, “Optical polarization imaging,” Appl. Opt. 36, 150–155 (1997).
[CrossRef] [PubMed]

K. M. Yoo, R. R. Alfano, “Time resolved depolarization of multiple backscattered light from random media,” Phys. Lett. A 142, 531–536 (1989).
[CrossRef]

Bicout, D.

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

Brosseau, C.

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

Bruscaglioni, P.

Cheung, R. L.-T.

R. L.-T. Cheung, A. Ishimaru, “Transmission backscattering and depolarization of waves in randomly distributed spherical particles,” Appl. Opt. 21, 3792–3798 (1982).
[CrossRef] [PubMed]

A. Ishimaru, R. L.-T. Cheung, “Multiple scattering effects on wave propagation due to rain,” Ann. Telecommun. 35, 373–379 (1980).

Demos, S. G.

Ishimaru, A.

R. L.-T. Cheung, A. Ishimaru, “Transmission backscattering and depolarization of waves in randomly distributed spherical particles,” Appl. Opt. 21, 3792–3798 (1982).
[CrossRef] [PubMed]

A. Ishimaru, R. L.-T. Cheung, “Multiple scattering effects on wave propagation due to rain,” Ann. Telecommun. 35, 373–379 (1980).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Institute of Electrical and Electronics Engineers, New York, 1997).

A. D. Kim, S. Jaruwatanadilok, A. Ishimaru, Y. Kuga, “Polarized light propagation and scattering in random media,” in Laser–Tissue Interaction XII: Photochemical, Photothermal, and Photomechanical, D. D. Duncan, S. L. Jacques, P. C. Johnson, eds., Proc. SPIE4257, 90–100 (2001).

Jaruwatanadilok, S.

A. D. Kim, S. Jaruwatanadilok, A. Ishimaru, Y. Kuga, “Polarized light propagation and scattering in random media,” in Laser–Tissue Interaction XII: Photochemical, Photothermal, and Photomechanical, D. D. Duncan, S. L. Jacques, P. C. Johnson, eds., Proc. SPIE4257, 90–100 (2001).

Jordan, D. L.

Keller, J. B.

Kim, A. D.

A. D. Kim, S. Jaruwatanadilok, A. Ishimaru, Y. Kuga, “Polarized light propagation and scattering in random media,” in Laser–Tissue Interaction XII: Photochemical, Photothermal, and Photomechanical, D. D. Duncan, S. L. Jacques, P. C. Johnson, eds., Proc. SPIE4257, 90–100 (2001).

Kuga, Y.

A. D. Kim, S. Jaruwatanadilok, A. Ishimaru, Y. Kuga, “Polarized light propagation and scattering in random media,” in Laser–Tissue Interaction XII: Photochemical, Photothermal, and Photomechanical, D. D. Duncan, S. L. Jacques, P. C. Johnson, eds., Proc. SPIE4257, 90–100 (2001).

Lewis, G. D.

Martinez, A. S.

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

Moscoso, M.

Papanicolaou, G. C.

Roberts, P. J.

Schmitt, J. M.

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

Sekera, Z.

van de Hulst, H. C.

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

Wei, Q.

Yoo, K. M.

K. M. Yoo, R. R. Alfano, “Time resolved depolarization of multiple backscattered light from random media,” Phys. Lett. A 142, 531–536 (1989).
[CrossRef]

Zaccanti, G.

Ann. Telecommun.

A. Ishimaru, R. L.-T. Cheung, “Multiple scattering effects on wave propagation due to rain,” Ann. Telecommun. 35, 373–379 (1980).

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Phys. Lett. A

K. M. Yoo, R. R. Alfano, “Time resolved depolarization of multiple backscattered light from random media,” Phys. Lett. A 142, 531–536 (1989).
[CrossRef]

Phys. Rev. E

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

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (Institute of Electrical and Electronics Engineers, New York, 1997).

A. D. Kim, S. Jaruwatanadilok, A. Ishimaru, Y. Kuga, “Polarized light propagation and scattering in random media,” in Laser–Tissue Interaction XII: Photochemical, Photothermal, and Photomechanical, D. D. Duncan, S. L. Jacques, P. C. Johnson, eds., Proc. SPIE4257, 90–100 (2001).

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

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Figures (11)

Fig. 1
Fig. 1

The incident wave is a linearly or a circularly polarized wave. The medium comprises randomly distributed spherical scatterers.

Fig. 2
Fig. 2

Degree of polarization (in decibels) versus optical depth when size parameter (ka) varies.

Fig. 3
Fig. 3

(a) DOP and (b) XPD in the forward direction (in decibels) as a function of optical depth.

Fig. 4
Fig. 4

(a) DOP and (b) XPD in the backward direction (in decibels) as a function of optical depth.

Fig. 5
Fig. 5

Total intensity of the snake waves (in decibels) as a function of optical depth. CO-PO, copolarized; X-PO, cross polarized.

Fig. 6
Fig. 6

(a) DOP and (b) XPD of the forward direction (in decibels) as a function of time (τ0 = 10).

Fig. 7
Fig. 7

(a) DOP and (b) XPD of the backward direction (in decibels) as a function of time (τ0 = 10).

Fig. 8
Fig. 8

Total intensity of the snake waves (in decibels) as a function of time: (a) τ0 = 1 and (b) τ0 = 10.

Fig. 9
Fig. 9

(a) DOP and (b) XPD of the forward direction (in decibels) as a function of time (fog, λ = 1 µm).

Fig. 10
Fig. 10

(a) DOP and (b) XPD of the backward direction (in decibels) as a function of time (fog, λ = 1 µm).

Fig. 11
Fig. 11

Total intensity of the snake waves (in decibels) as a function of time (fog, λ = 1 µm).

Tables (2)

Tables Icon

Table 1 Particle-Size Distribution of Latex Spheres

Tables Icon

Table 2 Particle-Size Distribution of Fog

Equations (39)

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μ τIt, τ, μ, ϕ+1+1τ0tIt, τ, μ, ϕ=02π-11Sμ, ϕ, μ, ϕ]It, τ, μ, ϕdμdϕ+F0μ, ϕft, τ,  0ττ0,
I=I1 I2 U VT=E1E1*E2E2*2 ReE1E2*2 ImE1E2*T,
Iτ=0=0  0μ1,Iτ=τ0=0  -1μ0,
ft, τ=exp-τδt-τ/τ0.
ft, τ=1π T0exp-τ-t-τ/τ02T02,
μ τIω, τ, μ, ϕ+1-i ωτ0Iω, τ, μ, ϕ=02π-11Sμ, ϕ, μ, ϕ]Iω, τ, μ, ϕdμdϕ+F0τ, μ, ϕfω, τ,  0ττ0,
Iω, τ, μ, ϕ= It, τ, μ, ϕexpiωtdt
fω, τ=exp-1-i ωτ0τ
fω, τ=exp-ω2T024exp-1-i ωτ0τ
Sμ, ϕ, μ, ϕ=σt |f11|2|f12|2Ref11f12*-Imf11f12*|f21|2|f22|2Ref21f22*-Imf21f22*2 Ref11f21*2 Ref12f22*Ref11f12*+f12f21*-Imf11f12*-f12f21*2 Imf11f21*2 Imf12f22*Imf11f22*+f12f21*Ref11f22*-f12f21*,
S=S1S3S2S4.
Iω, τ=Idω, τexpi ωτ0 τ
μ τIdω, τ, μ, ϕ+1+μ-1i ωτ0×Idω, τ, μ, ϕ=02π-11Sμ, ϕ, μ, ϕ]Idω, τ, μ, ϕdμdϕ+F0τ, μ, ϕfdω, τ,  0ττ0,
fdω, τ=exp-τdelta function pulseexp-τexp-ω2T024Gaussian pulse.
Idt, τ=12π  Idω, τexpi ωτ0 τ-iωtdω,
Idt, τ=I1t, τ I2t, τ Ut, τ Vt, τT.
Irit, τ=1 0 0 0T exp-τ.
Idt, τ, μ, ϕ=Id0t, τ, μ+n=1Idcnt, τ, μcosnϕ+Idsnt, τ, μsinnϕ.
μ τId0ω, τ, μ+1+μ-1i ωτ0×Id0ω, τ, μ=-11L10μ, μ]Id0ω, τ, μdμ+F00μfdω, τ, 0ττ0,
Id0τ, μ=I10τ, μI20τ, μ,F00μ=12σt|Allμ||Arrμ|,
L10μ, μ=02πS1μ, μ, ϕ-ϕdϕ-ϕ.
μ τId2ω, τ, μ+1+μ-1i ωτ0×Id2ω, τ, μ=-11L2μ, μ]Id2ω, τ, μdμ+F02μfdω, τ,  0ττ0,
Id2τ, μ=I1c2τ, μI1c2τ, μUs2τ, μVs2τ, μ,F02μ=12σt|Allμ|-|Arrμ|-2 ReAllμArr*μ-2 ImAllμArr*μ,
L2=L12L22L32L42,
L12μ, μ=02πS1μ, μ, ϕ-ϕ×cos2ϕ-ϕdϕ-ϕ,L22μ, μ=02πS2μ, μ, ϕ-ϕ×sin2ϕ-ϕdϕ-ϕ,L32μ, μ=02πS3μ, μ, ϕ-ϕ×sin2ϕ-ϕdϕ-ϕ,L42μ, μ=02πS4μ, μ, ϕ-ϕ×cos2ϕ-ϕdϕ-ϕ.
Idt, τ, μ, ϕ=Id0t, τ, μ+Idc2t, τ, μcosnϕ+Ids2t, τ, μsinnϕ=I10t, τ, μI20t, τ, μ00+I1c2t, τ, μcos2ϕI2c2t, τ, μcos2ϕUs2t, τ, μsin2ϕVs2t, τ, μsin2ϕ.
Irit, τ=1/2 1/2 0 1T exp-τ.
μ τId10ω, τ, μ+1+μ-1i ωτ0×Id10ω, τ, μ=-11L10μ, μ]Id12ω, τ, μdμ+F10μfdω, τ,  0ττ0,
μ τId20ω, τ, μ+1+μ-1i ωτ0×Id20ω, τ, μ=-11L40μ, μ]Id22ω, τ, μdμ+F20μfdω, τ,  0ττ0,
Id10τ, μ=I10τ, μI20τ, μ,F10μ=12σt|Allμ||Arrμ|,
Id20τ, μ=U0τ, μV0τ, μ,F20μ=1σt-ImAllμArr*μReAllμArr*μ.
Idt, τ, μ=Id10t, τ, μ+Id20t, τ, μ=I10τ, μ I20τ, μ U0τ, μ×V0τ, μTI1 I2 U2 V2T.
Ilhc=I1+I2+V/2,  Irhc=I1+I2-V/2.
m=I1-I22+U2+V21/2I1+I2.
XPD=10 logIco-polIx-pol.
Itotalt=Iri+πθ2Idt.
f11=l, lT1+r, rT2,f12=-r, lT1+l, rT2,f21=-l, rT1+r, lT2,f22=r, rT1+l, lT2,l, l=1-μ21-μ21/2+μμ cosϕ-ϕ,l, r=-μ sinϕ-ϕ,r, l=μ sinϕ-ϕ,r, r=cosϕ-ϕ,T1x=Arrχ-χAllχ1-χ2,T2x=Allχ-χArrχ1-χ2,
χ=cos Θ=1-μ21-μ21/2 cosϕ-ϕ+μμ,μ=cos θ, μ=cos θ.
All=is2*/k,  Arr=is1*/k.

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