Abstract

We report a study and comparison of continuous-wave, optical polarization difference imaging (PDI) and polarization modulation imaging (PMI) for imaging through scattering media. The problem is cast in the framework of a theoretical estimation, and the comparison is based on three visualization parameters, namely, the magnitude, the degree, and the orientation of the polarization. We show that PDI is superior in estimating the first two parameters in active imaging under specific conditions, while the PMI is suitable for passive imaging and is the only way to estimate polarization orientation. We also propose new schemes for rendering polarization information as a color image and for applying the newly introduced polarization-orientation imaging for segmentation. Simulation and experimental results verify the theoretical conclusions.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. C. Hebden, S. R. Arridge, and D. T. Delpy, "Optical imaging in medicine. I. Experimental techniques," Phys. Med. Biol. 42, 825-840 (1997).
  2. R. S. Umesh, A. G. Ramakrishnan, R. Srikanth, and R. Hema, "Estimation theoretic framework for comparing polarization based, continuous-wave direct imaging schemes," in International Conference on Signal Processing and Communications (IEEE, 2004), pp. 535-539.
  3. M. P. Rowe, E. N. Pugh, Jr., J. S. Tyo, and N. Engheta, "Polarization-difference imaging: a biologically inspired technique for observation through scattering media," Opt. Lett. 20, 608-610 (1995).
    [CrossRef] [PubMed]
  4. J. S. Tyo, M. P. Rowe, E. N. Pugh, Jr., and N. Engheta, "Target detection in optically scattering media by polarization-difference imaging," Appl. Opt. 35, 1855-1870 (1996).
    [CrossRef] [PubMed]
  5. R. Hema and N. Andal, "Two-dimensional imaging through turbid media using a continuous wave light source," Opt. Commun. 154, 255-260 (1998).
    [CrossRef]
  6. O. Emile, F. Bretenaker, and A. Le Floch, "Rotating polarization imaging in turbid media," Opt. Lett. 21, 1706-1708 (1996).
    [CrossRef] [PubMed]
  7. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
    [CrossRef]
  8. W. S. Bickel and W. M. Bailey, "Stokes vectors, Mueller matrices, and polarized scattered light," Am. J. Phys. 53, 468-478 (1985).
    [CrossRef]
  9. S. Huard, Polarization of Light (Wiley, 1997).
  10. C. Brosseau, Fundamentals of Polarized Light--A Statistical Optics Approach (Wiley, 1998).
  11. J. G. Walker, P. C. Y. Chang, and K. I. Hopcraft, "Visibility depth improvement in active polarization imaging in scattering media," Appl. Opt. 39, 4993-4941 (2000).
    [CrossRef]
  12. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 1993).
  13. P. Stoica, H. Li, and J. Li, "Amplitude estimation of sinusoidal signals: survey, new results, and an application," IEEE Trans. Signal Process. 48, 338-352 (2000).
    [CrossRef]
  14. G. M. P. van Kempen and L. J. van Vliet, "Mean and variance of ratio estimators used in fluorescence ratio imaging," Cytometry 39, 300-305 (2000).
    [CrossRef] [PubMed]
  15. R. S. Umesh, "Algorithms for processing polarization-rich optical imaging data," M. S. thesis (Indian Institute of Science, Bangalore, 2004), http://etd.ncsi.iisc.ernet.in/handle/2005/96.

2000

J. G. Walker, P. C. Y. Chang, and K. I. Hopcraft, "Visibility depth improvement in active polarization imaging in scattering media," Appl. Opt. 39, 4993-4941 (2000).
[CrossRef]

P. Stoica, H. Li, and J. Li, "Amplitude estimation of sinusoidal signals: survey, new results, and an application," IEEE Trans. Signal Process. 48, 338-352 (2000).
[CrossRef]

G. M. P. van Kempen and L. J. van Vliet, "Mean and variance of ratio estimators used in fluorescence ratio imaging," Cytometry 39, 300-305 (2000).
[CrossRef] [PubMed]

1998

R. Hema and N. Andal, "Two-dimensional imaging through turbid media using a continuous wave light source," Opt. Commun. 154, 255-260 (1998).
[CrossRef]

1996

1995

1985

W. S. Bickel and W. M. Bailey, "Stokes vectors, Mueller matrices, and polarized scattered light," Am. J. Phys. 53, 468-478 (1985).
[CrossRef]

Andal, N.

R. Hema and N. Andal, "Two-dimensional imaging through turbid media using a continuous wave light source," Opt. Commun. 154, 255-260 (1998).
[CrossRef]

Arridge, S. R.

J. C. Hebden, S. R. Arridge, and D. T. Delpy, "Optical imaging in medicine. I. Experimental techniques," Phys. Med. Biol. 42, 825-840 (1997).

Bailey, W. M.

W. S. Bickel and W. M. Bailey, "Stokes vectors, Mueller matrices, and polarized scattered light," Am. J. Phys. 53, 468-478 (1985).
[CrossRef]

Bickel, W. S.

W. S. Bickel and W. M. Bailey, "Stokes vectors, Mueller matrices, and polarized scattered light," Am. J. Phys. 53, 468-478 (1985).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Bretenaker, F.

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light--A Statistical Optics Approach (Wiley, 1998).

Chang, P. C. Y.

J. G. Walker, P. C. Y. Chang, and K. I. Hopcraft, "Visibility depth improvement in active polarization imaging in scattering media," Appl. Opt. 39, 4993-4941 (2000).
[CrossRef]

Delpy, D. T.

J. C. Hebden, S. R. Arridge, and D. T. Delpy, "Optical imaging in medicine. I. Experimental techniques," Phys. Med. Biol. 42, 825-840 (1997).

Emile, O.

Engheta, N.

Hebden, J. C.

J. C. Hebden, S. R. Arridge, and D. T. Delpy, "Optical imaging in medicine. I. Experimental techniques," Phys. Med. Biol. 42, 825-840 (1997).

Hema, R.

R. Hema and N. Andal, "Two-dimensional imaging through turbid media using a continuous wave light source," Opt. Commun. 154, 255-260 (1998).
[CrossRef]

R. S. Umesh, A. G. Ramakrishnan, R. Srikanth, and R. Hema, "Estimation theoretic framework for comparing polarization based, continuous-wave direct imaging schemes," in International Conference on Signal Processing and Communications (IEEE, 2004), pp. 535-539.

Hopcraft, K. I.

J. G. Walker, P. C. Y. Chang, and K. I. Hopcraft, "Visibility depth improvement in active polarization imaging in scattering media," Appl. Opt. 39, 4993-4941 (2000).
[CrossRef]

Huard, S.

S. Huard, Polarization of Light (Wiley, 1997).

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 1993).

Le Floch, A.

Li, H.

P. Stoica, H. Li, and J. Li, "Amplitude estimation of sinusoidal signals: survey, new results, and an application," IEEE Trans. Signal Process. 48, 338-352 (2000).
[CrossRef]

Li, J.

P. Stoica, H. Li, and J. Li, "Amplitude estimation of sinusoidal signals: survey, new results, and an application," IEEE Trans. Signal Process. 48, 338-352 (2000).
[CrossRef]

Pugh, E. N.

Ramakrishnan, A. G.

R. S. Umesh, A. G. Ramakrishnan, R. Srikanth, and R. Hema, "Estimation theoretic framework for comparing polarization based, continuous-wave direct imaging schemes," in International Conference on Signal Processing and Communications (IEEE, 2004), pp. 535-539.

Rowe, M. P.

Srikanth, R.

R. S. Umesh, A. G. Ramakrishnan, R. Srikanth, and R. Hema, "Estimation theoretic framework for comparing polarization based, continuous-wave direct imaging schemes," in International Conference on Signal Processing and Communications (IEEE, 2004), pp. 535-539.

Stoica, P.

P. Stoica, H. Li, and J. Li, "Amplitude estimation of sinusoidal signals: survey, new results, and an application," IEEE Trans. Signal Process. 48, 338-352 (2000).
[CrossRef]

Tyo, J. S.

Umesh, R. S.

R. S. Umesh, "Algorithms for processing polarization-rich optical imaging data," M. S. thesis (Indian Institute of Science, Bangalore, 2004), http://etd.ncsi.iisc.ernet.in/handle/2005/96.

R. S. Umesh, A. G. Ramakrishnan, R. Srikanth, and R. Hema, "Estimation theoretic framework for comparing polarization based, continuous-wave direct imaging schemes," in International Conference on Signal Processing and Communications (IEEE, 2004), pp. 535-539.

van Kempen, G. M. P.

G. M. P. van Kempen and L. J. van Vliet, "Mean and variance of ratio estimators used in fluorescence ratio imaging," Cytometry 39, 300-305 (2000).
[CrossRef] [PubMed]

van Vliet, L. J.

G. M. P. van Kempen and L. J. van Vliet, "Mean and variance of ratio estimators used in fluorescence ratio imaging," Cytometry 39, 300-305 (2000).
[CrossRef] [PubMed]

Walker, J. G.

J. G. Walker, P. C. Y. Chang, and K. I. Hopcraft, "Visibility depth improvement in active polarization imaging in scattering media," Appl. Opt. 39, 4993-4941 (2000).
[CrossRef]

Am. J. Phys.

W. S. Bickel and W. M. Bailey, "Stokes vectors, Mueller matrices, and polarized scattered light," Am. J. Phys. 53, 468-478 (1985).
[CrossRef]

Appl. Opt.

J. G. Walker, P. C. Y. Chang, and K. I. Hopcraft, "Visibility depth improvement in active polarization imaging in scattering media," Appl. Opt. 39, 4993-4941 (2000).
[CrossRef]

J. S. Tyo, M. P. Rowe, E. N. Pugh, Jr., and N. Engheta, "Target detection in optically scattering media by polarization-difference imaging," Appl. Opt. 35, 1855-1870 (1996).
[CrossRef] [PubMed]

Cytometry

G. M. P. van Kempen and L. J. van Vliet, "Mean and variance of ratio estimators used in fluorescence ratio imaging," Cytometry 39, 300-305 (2000).
[CrossRef] [PubMed]

IEEE Trans. Signal Process.

P. Stoica, H. Li, and J. Li, "Amplitude estimation of sinusoidal signals: survey, new results, and an application," IEEE Trans. Signal Process. 48, 338-352 (2000).
[CrossRef]

Opt. Commun.

R. Hema and N. Andal, "Two-dimensional imaging through turbid media using a continuous wave light source," Opt. Commun. 154, 255-260 (1998).
[CrossRef]

Opt. Lett.

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

R. S. Umesh, "Algorithms for processing polarization-rich optical imaging data," M. S. thesis (Indian Institute of Science, Bangalore, 2004), http://etd.ncsi.iisc.ernet.in/handle/2005/96.

J. C. Hebden, S. R. Arridge, and D. T. Delpy, "Optical imaging in medicine. I. Experimental techniques," Phys. Med. Biol. 42, 825-840 (1997).

R. S. Umesh, A. G. Ramakrishnan, R. Srikanth, and R. Hema, "Estimation theoretic framework for comparing polarization based, continuous-wave direct imaging schemes," in International Conference on Signal Processing and Communications (IEEE, 2004), pp. 535-539.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 1993).

S. Huard, Polarization of Light (Wiley, 1997).

C. Brosseau, Fundamentals of Polarized Light--A Statistical Optics Approach (Wiley, 1998).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Performance of PII estimators. (a) Variance of PII estimators in white noise. (b) Variance of PII estimators in AR1 noise.

Fig. 2
Fig. 2

Performance of DOLP estimators. (a) Variance of DOLP estimators in white noise. (b) Variance of DOLP estimators in AR1 noise.

Fig. 3
Fig. 3

Performance of PO estimators. (a) Variance of PO estimators in white noise. (b) Variance of PO estimators in AR1 noise.

Fig. 4
Fig. 4

Result of fusing the visualization parameters. (a) Break-up of synthetic images. (b) A representative of the 32 images in the series. (c) Result of histogram equalizing (b). (d) PMI magnitude estimation result. (e) PMI DOLP estimation results. (f) PMI PO estimation result. (g) Result of fusing (d), (e), and (f).

Fig. 5
Fig. 5

Experimental results. Details of the experimental setup are given in Table 1. (a) Actual object. (b) Unprocessed image. (c) PDI result. (d) PMI result. (e) APES result.

Fig. 6
Fig. 6

Segmentation of a POI result. (a) Image without scattering. (b) Result of PMI POI; N = 512. (c) 9 9 block processing result. (d) 15 15 block processing result. (e) Histogram of (d). (f) Result of segmenting (e).

Tables (1)

Tables Icon

Table 1 Elements of Experimental Setup Shown in Fig. 5

Equations (135)

Equations on this page are rendered with MathJax. Learn more.

π / 2
[ I s Q s U s V s ]
SV S i n = [ I s Q s U s V s ] T
I o = ( I s + Q s cos 2 θ + U s sin 2 θ ) .
I r ( n ) = ( I s + Q s cos 2 θ n + U s sin 2 θ n ) + v ( n ) ,
n = 0 , ..., N 1 ,
θ n
θ n
2 π / M
I r ( n ) = 1 2 [ I s + Q s     2 + U s     2     sin ( 4 π n M + 2 ϕ + α ) ] + v ( n ) ,
α = arctan ( Q s / U s ) .
I s / 2
( Q s     2 + U s     2 ) 1 / 2 / 2
I r ( n ) = I s c a t + I b a l sin ( 4 π n M + β ) + v ( n ) ,
n = 0 , ..., N 1 ,
2 ϕ + α
I b a l
f = 2 / M
M
N / 2
I
I
I
I ( n ) = I s c a t + I b a l sin ( β ) + w ( n ) ,
I ( n ) = I s c a t + I b a l sin ( β + π ) + w ( n ) ,
w ( n )
β = ( 2 ϕ + α )
I ^ b a l , P D I = 1 N n = 1 N / 2 [ I ( n ) I ( n ) ] .
I
I
I ^ b a l , P D I = I b a l sin β + w * ( n ) ,
σ 2 / N
σ 2
w ( n )
E { I ^ b a l , P D I } = I b a l sin β ,
var { I ^ b a l , P D I } = σ 2 / N .
I ^ b a l , P D I
β = π / 2
σ 2 / N
2 N / M
I b a l
I ^ b a l , P M I = 2 N | Π ( 2 N M ) | ,
I b a l
I b a l
I b a l
I b a l
I scat
I r ( n ) = I s c a t + I b a l cos β sin ( 4 π n M ) + I b a l sin β cos ( 4 π n M ) + w ( n ) ,
n = 0 , ..., N 1.
[ I r ( 0 ) I r ( 1 ) I r ( 2 ) ] I r = [ 1 0 1 1 sin ( 4 π / M ) cos ( 4 π / M ) 1 sin ( 8 π / M ) cos ( 8 π / M ) ] H [ I s c a t I b a l cos β I b a l sin β ] Θ + [ w ( 0 ) w ( 1 ) w ( 2 ) ] W ,
I r = H Θ + W .
I bal cos β
I b a l sin β
I b a l
Θ ̂ = ( H T C 1 H ) 1 H T C 1 I r ,
Θ ̂
I b a l cos β
I b a l sin β
I b a l
I ^ b a l , M L E = + [ ( I b a l cos β ) 2 + ( I b a l sin β ) 2 ] 1 / 2 .
I b a l
I ^ s c a t , M V U = 1 N n = 0 N 1 I r ( n ) ,
I ^ b a l cos β M V U = 2 N n = 0 N 1 I r ( n ) sin ( 4 π n M ) ,
I ^ b a l sin β M V U = 2 N n = 0 N 1 I r ( n ) cos ( 4 π n M ) ,
var { I ^ s c a t , M V U } = σ 2 N ,
var { I ^ b a l cos β M V U } = var { I ^ b a l sin β M V U } = 2 σ 2 N .
I b a l
β = π / 2
I b a l
I b a l
I b a l
I b a l
I b a l
σ 2 I
β = π / 2
3 π / 2
I s c a t
I b a l
I s c a t
I b a l
14   dB
+ 2 5   dB
a 1 = 0.50
a 2 = 0.125
π / 2
( at β = π / 2 )
D OLP = I I I + I .
I
I
β = π / 2
D O L P = I b a l I s c a t = [ Q s     2 + U s     2 ] 1 / 2 I s .
D O L P ̂ P D I 1 = n = 0 ( N / 2 ) 1 [ I ( n ) I ( n ) ] n = 0 ( N 2 ) 1 [ I ( n ) + I ( n ) ] ,
D O L P ̂ P D I 2 = 2 N n = 0 ( N / 2 ) 1 [ I ( n ) I ( n ) I ( n ) + I ( n ) ] .
β = π / 2
D O L P ̂ P D I
β 0
β = π / 2
I b a l
D O L P ̂ P D I
D O L P ̂ P D I 2
D O L P ̂ P D I 1
D O L P ̂ P D I 1
D O L P ̂ P D I 1
D O L P ̂ P D I 2
β π / 2
I b a l
I s c a t
D O L P ̂ = I ^ b a l / I ^ s c a t
β = π / 2
β π / 2
ϕ + γ
var { β ̂ } 2 σ 2 N I bal 2 = 1 N η ,
η = I bal 2 / 2 σ 2
β ^ MLE = arctan ( I ^ b a l sin β M V U I ^ b al cos β M VU ) = arctan [ n = 0 N 1 I r ( n ) cos ( 4 π n / M ) n = 0 N 1 I r ( n ) sin ( 4 π n / M ) ] ,
β ̂ M L E
β ̂ M L E
var β ̂ a 11 a 22 + ( a 11 a 23 a 12 a 13 ) sin 2 β a 12 2 cos 2 β a 13 2 sin 2 β I bal 2 det ( A ) ,
A = H T C 1 H
I b a l
β ̂ M L E
I s c a t
I b a l
4   dB
I b a l
2 π / 9
0 , 5 π / 18
15 π / 9
2.97   μm
0.11   μm
( 8   dB )
I b a l
I s c a t
I b a l
I s c a t

Metrics