Abstract

The results of experiments in developing a method for extracting three-dimensional information from a scene by means of a polarimetric passive imaging sensor are summarized. This sensor provides a full Stokes vector at each sensor pixel location from which degree and angle of linear polarization are computed. The angle of linear polarization provides the azimuth angle of the surface normal vector. The depression angle of this surface normal vector is obtained in terms of the emitting object’s index of refraction from the solution of an equation derived from Fresnel equations, Snell’s law, and percent of linear polarization. Results of the application of this approach to simulated infrared polarimetric data are provided.

© 2007 Optical Society of America

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References

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  1. L. B. Wolff and T. E. B. Boult, IEEE Trans. Pattern Anal. Mach. Intell. 13, 635 (1991).
    [CrossRef]
  2. M. Saito, Y. Sato, K. Ikeuchi, and H. Kashiwagi, J. Opt. Soc. Am. A 16, 2286 (1999).
    [CrossRef]
  3. M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).
  4. F. A. Sadjadi and C. L. Chun, Opt. Lett. 28, 531 (2003).
    [CrossRef] [PubMed]

2003 (1)

1999 (1)

1991 (1)

L. B. Wolff and T. E. B. Boult, IEEE Trans. Pattern Anal. Mach. Intell. 13, 635 (1991).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Boult, T. E. B.

L. B. Wolff and T. E. B. Boult, IEEE Trans. Pattern Anal. Mach. Intell. 13, 635 (1991).
[CrossRef]

Chun, C. L.

Ikeuchi, K.

Kashiwagi, H.

Sadjadi, F. A.

Saito, M.

Sato, Y.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Wolff, L. B.

L. B. Wolff and T. E. B. Boult, IEEE Trans. Pattern Anal. Mach. Intell. 13, 635 (1991).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

L. B. Wolff and T. E. B. Boult, IEEE Trans. Pattern Anal. Mach. Intell. 13, 635 (1991).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Other (1)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

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Figures (7)

Fig. 1
Fig. 1

Plots of the two solutions for ϕ in terms of r ( P LP ) and n (relative refractive index).

Fig. 2
Fig. 2

First two Stokes parameter polarimetric imagery of a scene showing an M35 truck.

Fig. 3
Fig. 3

Third Stokes parameter and angle of linear polarization (surface normal angle ψ) imagery of a scene showing an M35 truck.

Fig. 4
Fig. 4

Percent of linear polarization and surface normal depression angle ϕ 1 imagery of a scene showing an M35 truck at n = 1.1 and threshold 0.3.

Fig. 5
Fig. 5

First two Stokes parameter polarimetric imagery of a scene showing a T72 tank.

Fig. 6
Fig. 6

Third Stokes parameter and angle of linear polarization (surface normal depression angle ψ) imagery of a scene showing a T72 tank.

Fig. 7
Fig. 7

Percent of linear polarization and surface normal depression angle ϕ 1 imagery of a scene showing a T72 tank at n = 1.1 and threshold 0.3.

Tables (1)

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Table 1 Sensitivity of Surface Normal Depression Angles (in degrees) with Respect to the Index of Refraction

Equations (9)

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A = [ E H E H * + E V E V * E H E H * E V E V * 2 Re ( E H E V * ) 2 Im ( E H E V * ) ] = [ a 2 a 2 cos ( 2 χ ) cos ( 2 ψ ) a 2 cos ( 2 χ ) sin ( 2 ψ ) a 2 sin ( 2 χ ) ] ,
E = Re ( E H h + E V v ) exp [ ( r κ t ω ) ] ,
P LP = S 2 + S 3 S 1 ,
Ang LP = 1 2 tan 1 ( S 3 S 2 ) .
I = sin ( 2 ϕ i ) sin ( 2 ϕ t ) sin 2 ( ϕ i + ϕ t ) cos 2 ( ϕ i ϕ t ) ,
I = sin ( 2 ϕ i ) sin ( 2 ϕ t ) sin 2 ( ϕ i + ϕ t ) ,
P LP = I I I + I ,
ϕ 1 = sin 1 ( 1 r 1 + r 1 2 n ( 1 r 1 + r ) 1 2 1 n 2 1 ) 1 2 ,
ϕ 2 = sin 1 ( 1 r 1 + r 1 2 n ( 1 r 1 + r ) 1 2 1 n 2 1 ) 1 2 ,

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