Abstract

For almost 20 years, microgrid polarimetric imaging systems have been built using a 2×2 repeating pattern of polarization analyzers. In this Letter, we show that superior spatial resolution is achieved over this 2×2 case when the analyzers are arranged in a 2×4 repeating pattern. This unconventional result, in which a more distributed sampling pattern results in finer spatial resolution, is also achieved without affecting the conditioning of the polarimetric data-reduction matrix. Proof is provided theoretically and through Stokes image reconstruction of synthesized data.

© 2014 Optical Society of America

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References

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  1. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, Appl. Opt. 45, 5453 (2006).
    [CrossRef]
  2. C. S. L. Chun, D. L. Fleming, and E. J. Torok, Proc. SPIE 2234, 275 (1994).
    [CrossRef]
  3. J. S. Tyo, C. F. LaCasse, and B. M. Ratliff, Opt. Lett. 34, 3187 (2009).
    [CrossRef]
  4. C. F. LaCasse, J. S. Tyo, and R. A. Chipman, Opt. Lett. 37, 1097 (2012).
    [CrossRef]
  5. K. Hirakawa and P. J. Wolfe, IEEE Trans. Image Process. 17, 1876 (2008).
    [CrossRef]
  6. D. Alleysson, S. Susstrunk, and J. Hérault, IEEE Trans. Image Process. 14, 439 (2005).
    [CrossRef]
  7. B. Leung, G. Jeon, and E. Dubois, IEEE Trans. Image Process. 20, 1885 (2011).
    [CrossRef]
  8. R. Gonzalez and R. Woods, Digital Image Processing, 3rd ed. (Pearson, 2011).

2012 (1)

2011 (1)

B. Leung, G. Jeon, and E. Dubois, IEEE Trans. Image Process. 20, 1885 (2011).
[CrossRef]

2009 (1)

2008 (1)

K. Hirakawa and P. J. Wolfe, IEEE Trans. Image Process. 17, 1876 (2008).
[CrossRef]

2006 (1)

2005 (1)

D. Alleysson, S. Susstrunk, and J. Hérault, IEEE Trans. Image Process. 14, 439 (2005).
[CrossRef]

1994 (1)

C. S. L. Chun, D. L. Fleming, and E. J. Torok, Proc. SPIE 2234, 275 (1994).
[CrossRef]

Alleysson, D.

D. Alleysson, S. Susstrunk, and J. Hérault, IEEE Trans. Image Process. 14, 439 (2005).
[CrossRef]

Chenault, D. B.

Chipman, R. A.

Chun, C. S. L.

C. S. L. Chun, D. L. Fleming, and E. J. Torok, Proc. SPIE 2234, 275 (1994).
[CrossRef]

Dubois, E.

B. Leung, G. Jeon, and E. Dubois, IEEE Trans. Image Process. 20, 1885 (2011).
[CrossRef]

Fleming, D. L.

C. S. L. Chun, D. L. Fleming, and E. J. Torok, Proc. SPIE 2234, 275 (1994).
[CrossRef]

Goldstein, D. L.

Gonzalez, R.

R. Gonzalez and R. Woods, Digital Image Processing, 3rd ed. (Pearson, 2011).

Hérault, J.

D. Alleysson, S. Susstrunk, and J. Hérault, IEEE Trans. Image Process. 14, 439 (2005).
[CrossRef]

Hirakawa, K.

K. Hirakawa and P. J. Wolfe, IEEE Trans. Image Process. 17, 1876 (2008).
[CrossRef]

Jeon, G.

B. Leung, G. Jeon, and E. Dubois, IEEE Trans. Image Process. 20, 1885 (2011).
[CrossRef]

LaCasse, C. F.

Leung, B.

B. Leung, G. Jeon, and E. Dubois, IEEE Trans. Image Process. 20, 1885 (2011).
[CrossRef]

Ratliff, B. M.

Shaw, J. A.

Susstrunk, S.

D. Alleysson, S. Susstrunk, and J. Hérault, IEEE Trans. Image Process. 14, 439 (2005).
[CrossRef]

Torok, E. J.

C. S. L. Chun, D. L. Fleming, and E. J. Torok, Proc. SPIE 2234, 275 (1994).
[CrossRef]

Tyo, J. S.

Wolfe, P. J.

K. Hirakawa and P. J. Wolfe, IEEE Trans. Image Process. 17, 1876 (2008).
[CrossRef]

Woods, R.

R. Gonzalez and R. Woods, Digital Image Processing, 3rd ed. (Pearson, 2011).

Appl. Opt. (1)

IEEE Trans. Image Process. (3)

K. Hirakawa and P. J. Wolfe, IEEE Trans. Image Process. 17, 1876 (2008).
[CrossRef]

D. Alleysson, S. Susstrunk, and J. Hérault, IEEE Trans. Image Process. 14, 439 (2005).
[CrossRef]

B. Leung, G. Jeon, and E. Dubois, IEEE Trans. Image Process. 20, 1885 (2011).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (1)

C. S. L. Chun, D. L. Fleming, and E. J. Torok, Proc. SPIE 2234, 275 (1994).
[CrossRef]

Other (1)

R. Gonzalez and R. Woods, Digital Image Processing, 3rd ed. (Pearson, 2011).

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Figures (5)

Fig. 1.
Fig. 1.

Conventional 2×2 microgrid array.

Fig. 2.
Fig. 2.

One permutation of the proposed 2×4 array.

Fig. 3.
Fig. 3.

Log-scale spectra of MPA sampled sensor data.

Fig. 4.
Fig. 4.

Reconstructed S0 images.

Fig. 5.
Fig. 5.

Reconstructed DOLP images.

Tables (1)

Tables Icon

Table 1. Root Mean Square Error Comparison (Units of Digital Counts) Between the True Image and the Reconstructed Images

Equations (19)

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X=[12Dcos(2θ)Dsin(2θ)]AθS,
X(n)=Aθ(n)S(n)=S0(n)+Dcos(2θ(n))S1(n)+Dsin(2θ(n))S2(n).
X(n)={A0(n)S(n)n1andn2evenAπ/4(n)S(n)n1even;n2oddAπ/2(n)S(n)n1andn2oddA3π/4(n)S(n)n1odd;n2even=S0(n)+(D2)(1)n1(S1(n)+S2(n))+(D2)(1)n2(S1(n)S2(n)).
X^(ω)=S^0(ω)+(D2){S^1+S^2}(ω(π0))+(D2){S^1S^2}(ω(0π)).
θ(n)=12ω0Tn,
Y(n)=Aθ(n)S(n)=S0(n)+Dcos(ω0Tn)S1(n)+Dsin(ω0Tn)S2(n).
Y^(ω)=S^0(ω)+(D2){S^1jS^2}(ωω0)+(D2){S^1+jS^2}(ω+ω0),
S0(n)=H0(n)X(n),
(D/2){S1(n)+S2(n)}=H1(n){ej(0,π)nX(n)},
(D/2){S1(n)S2(n)}=H1(n){ej(π,0)nX(n)},
S^0(ω)=H^0(ω)X^(ω),
(D/2){S^1(ω)+S^2(ω)}=H^1(ω)X^(ω(0π)),
(D/2){S^1(ω)S^2(ω)}=H^1(ω)X^(ω(π0)),
(S^0S^1S^2)=(10001D1D01D1D)(S^0D2(S^1+S^2)D2(S^1S^2)).
S0(n)=H0(n)X(n),
(D/2){S1(n)+jS2(n)}=H1(n){ejω0TnX(n)},
(D/2){S1(n)jS2(n)}=H1(n){ejω0TnX(n)},
(S^0S^1S^2)=(10001D1D0jDjD)(S^0D2(S^1+jS^2)D2(S^1jS^2)).
P(n)=S12(n)+S22(n)S0(n).

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