Abstract

We model the infrared polarization emissivity from spherical particles on a plane surface. The emissivity and polarization is primarily a function of the density of particles multiplied by their cross-sectional area. The presence of particles tends to reduce the polarization. As the emission angle increases from near-normal incidence, the polarization tends to pass through a maximum, followed by a minimum and a final sharp rise at near grazing angles. The mechanism for this structure is the shadowing of different portions of the spherical particles by other particles.

© 2003 Optical Society of America

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References

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  1. J. A. Shaw, “Degree of linear polarization in spectral radiances from water-viewing infrared radiometers,” Appl. Opt. 38, 3157–3165 (1999).
    [CrossRef]
  2. P. C. Y. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. Jordan, J. G. Walker, “Importance of shadowing and multiple reflections in emission polarization,” Waves Random Media 12, 1–19 (2002).
    [CrossRef]
  3. D. L. Jordan, G. D. Lewis, E. Jakeman, “Emission polarization of roughened glass and aluminum surfaces,” Appl. Opt. 35, 3583–3590 (1996).
    [CrossRef] [PubMed]
  4. S. V. Nghiem, M. E. Veysoglu, J. A. Kong, R. T. Shin, “Polarimetric passive remote sensing of a periodic soil surface: microwave measurements and analysis,” J. Electromagn. Waves Appl. 5, 997–1005 (1991).
    [CrossRef]
  5. R. D. Tooley, “Man-made target detection using infrared polarization,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. SPIE1166, 52–58 (1989).
    [CrossRef]
  6. A. W. Cooper, W. J. Lentz, P. L. Walker, “Infrared polarization ship images and contrast in the MAPTIP experiment,” in Image Propagation through the Atmosphere, L. R. Bissonnette, C. Dainty, eds., Proc. SPIE2828, 85–96 (1996).
    [CrossRef]
  7. D. Ligon, Army Research Laboratory, Adelphi, Md. (personal communication, 2003).

2002

P. C. Y. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. Jordan, J. G. Walker, “Importance of shadowing and multiple reflections in emission polarization,” Waves Random Media 12, 1–19 (2002).
[CrossRef]

1999

1996

1991

S. V. Nghiem, M. E. Veysoglu, J. A. Kong, R. T. Shin, “Polarimetric passive remote sensing of a periodic soil surface: microwave measurements and analysis,” J. Electromagn. Waves Appl. 5, 997–1005 (1991).
[CrossRef]

Chang, P. C. Y.

P. C. Y. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. Jordan, J. G. Walker, “Importance of shadowing and multiple reflections in emission polarization,” Waves Random Media 12, 1–19 (2002).
[CrossRef]

Cooper, A. W.

A. W. Cooper, W. J. Lentz, P. L. Walker, “Infrared polarization ship images and contrast in the MAPTIP experiment,” in Image Propagation through the Atmosphere, L. R. Bissonnette, C. Dainty, eds., Proc. SPIE2828, 85–96 (1996).
[CrossRef]

Flitton, J. C.

P. C. Y. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. Jordan, J. G. Walker, “Importance of shadowing and multiple reflections in emission polarization,” Waves Random Media 12, 1–19 (2002).
[CrossRef]

Hopcraft, K. I.

P. C. Y. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. Jordan, J. G. Walker, “Importance of shadowing and multiple reflections in emission polarization,” Waves Random Media 12, 1–19 (2002).
[CrossRef]

Jakeman, E.

P. C. Y. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. Jordan, J. G. Walker, “Importance of shadowing and multiple reflections in emission polarization,” Waves Random Media 12, 1–19 (2002).
[CrossRef]

D. L. Jordan, G. D. Lewis, E. Jakeman, “Emission polarization of roughened glass and aluminum surfaces,” Appl. Opt. 35, 3583–3590 (1996).
[CrossRef] [PubMed]

Jordan, D.

P. C. Y. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. Jordan, J. G. Walker, “Importance of shadowing and multiple reflections in emission polarization,” Waves Random Media 12, 1–19 (2002).
[CrossRef]

Jordan, D. L.

Kong, J. A.

S. V. Nghiem, M. E. Veysoglu, J. A. Kong, R. T. Shin, “Polarimetric passive remote sensing of a periodic soil surface: microwave measurements and analysis,” J. Electromagn. Waves Appl. 5, 997–1005 (1991).
[CrossRef]

Lentz, W. J.

A. W. Cooper, W. J. Lentz, P. L. Walker, “Infrared polarization ship images and contrast in the MAPTIP experiment,” in Image Propagation through the Atmosphere, L. R. Bissonnette, C. Dainty, eds., Proc. SPIE2828, 85–96 (1996).
[CrossRef]

Lewis, G. D.

Ligon, D.

D. Ligon, Army Research Laboratory, Adelphi, Md. (personal communication, 2003).

Nghiem, S. V.

S. V. Nghiem, M. E. Veysoglu, J. A. Kong, R. T. Shin, “Polarimetric passive remote sensing of a periodic soil surface: microwave measurements and analysis,” J. Electromagn. Waves Appl. 5, 997–1005 (1991).
[CrossRef]

Shaw, J. A.

Shin, R. T.

S. V. Nghiem, M. E. Veysoglu, J. A. Kong, R. T. Shin, “Polarimetric passive remote sensing of a periodic soil surface: microwave measurements and analysis,” J. Electromagn. Waves Appl. 5, 997–1005 (1991).
[CrossRef]

Tooley, R. D.

R. D. Tooley, “Man-made target detection using infrared polarization,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. SPIE1166, 52–58 (1989).
[CrossRef]

Veysoglu, M. E.

S. V. Nghiem, M. E. Veysoglu, J. A. Kong, R. T. Shin, “Polarimetric passive remote sensing of a periodic soil surface: microwave measurements and analysis,” J. Electromagn. Waves Appl. 5, 997–1005 (1991).
[CrossRef]

Walker, J. G.

P. C. Y. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. Jordan, J. G. Walker, “Importance of shadowing and multiple reflections in emission polarization,” Waves Random Media 12, 1–19 (2002).
[CrossRef]

Walker, P. L.

A. W. Cooper, W. J. Lentz, P. L. Walker, “Infrared polarization ship images and contrast in the MAPTIP experiment,” in Image Propagation through the Atmosphere, L. R. Bissonnette, C. Dainty, eds., Proc. SPIE2828, 85–96 (1996).
[CrossRef]

Appl. Opt.

J. Electromagn. Waves Appl.

S. V. Nghiem, M. E. Veysoglu, J. A. Kong, R. T. Shin, “Polarimetric passive remote sensing of a periodic soil surface: microwave measurements and analysis,” J. Electromagn. Waves Appl. 5, 997–1005 (1991).
[CrossRef]

Waves Random Media

P. C. Y. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. Jordan, J. G. Walker, “Importance of shadowing and multiple reflections in emission polarization,” Waves Random Media 12, 1–19 (2002).
[CrossRef]

Other

R. D. Tooley, “Man-made target detection using infrared polarization,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. SPIE1166, 52–58 (1989).
[CrossRef]

A. W. Cooper, W. J. Lentz, P. L. Walker, “Infrared polarization ship images and contrast in the MAPTIP experiment,” in Image Propagation through the Atmosphere, L. R. Bissonnette, C. Dainty, eds., Proc. SPIE2828, 85–96 (1996).
[CrossRef]

D. Ligon, Army Research Laboratory, Adelphi, Md. (personal communication, 2003).

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Figures (2)

Fig. 1
Fig. 1

(a). For small emission angles α, shadowing is nonexistent or minimal (dashed). As α increases, the contribution of the lower portion of droplets may be intercepted by other droplets before it can reach the detector (solid). (b). Different quadrants of the droplet have a different contribution to the polarization state. The top and bottom have a positive contribution, and the sides have a negative contribution. (c). Shadowed portion of the droplet is modeled from chord of length d.

Fig. 2
Fig. 2

Emission polarization P (α) for ρa 2 of (a) 0.0001 (b), 0.01 (c) 0.04 (d) 0.16, (e) 0.64 and (f) 2.56. System parameters are m d = 1.33, m s = 1.55.

Equations (13)

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dIT*=1-RT*dA,
RTEm, θdA=cos θdA-m1-1/m2 sin2 θdA1/2cos θdA+m1-1/m2 sin2 θdA1/22
RTMm, θdA=m cos θdA-cos1-1/m2 sin2 θdA1/2m cosθdA+cos1-1/m2 sin2 θdA1/22,
IT*=1-RT*m, αA-S,
ITEITM=02π0π/21-RTEm, α1-RTMm, α×cos2ϕsin2ϕsin2ϕcos2ϕa2 cos α sin αdαdϕ,
P=ITE-ITMITE+ITM.
ITEITM=02π0π/2 δU1-RTEm, α1-RTMm, α×cos2ϕsin2ϕsin2ϕcos2ϕa2 cos α sin αdαdϕ,
AUP=A-Nπa2/cos α+AMP,
AMP=ASSNπa2/cos αA+ASS.
AMP/A=ρ2π2a4-1+cos αcos α-cos α-ρπa2+ρπa2 cos α,
AUP/A=cos α1-ρπa2ρπa2+cos α1-ρπa2.
ε=1-AMPNπa2/cosα =1-ρπa2-1+cos α-cos α-ρπa2+ρπa2 cos α.
ε=πa2-ACSπa2=2π-β- sin β2π.

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