Abstract

Microgrid polarimeters operate by integrating a focal plane array with an array of micropolarizers. The Stokes parameters are estimated by comparing polarization measurements from pixels in a neighborhood around the point of interest. The main drawback is that the measurements used to estimate the Stokes vector are made at different locations, leading to a false polarization signature owing to instantaneous field-of-view (IFOV) errors. We demonstrate for the first time, to our knowledge, that spatially band limited polarization images can be ideally reconstructed with no IFOV error by using a linear system framework.

© 2009 Optical Society of America

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B. M. Ratliff, C. F. Lacasse, and J. S. Tyo, Opt. Express 17, 9112 (2009).
[CrossRef] [PubMed]

B. M. Ratliff, J. S. Tyo, C. F. LaCasse, and W. T. Black, Proc. SPIE 7461, 74610K (2009).
[CrossRef]

2008

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, Opt. Eng. 47, 046403 (2008).
[CrossRef]

M. W. Kudenov, L. Pezzaniti, E. L. Dereniak, and G. R. Gerhart, Opt. Express 16, 13720 (2008).
[CrossRef] [PubMed]

2006

2003

2002

C. K. Harnett and H. G. Craighead, Appl. Opt. 41, 1291 (2002).
[CrossRef] [PubMed]

A. G. Andreou and Z. K. Kalayjian, IEEE Sens. J. 2, 566 (2002).
[CrossRef]

1999

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, Proc. SPIE 3754, 169 (1999).
[CrossRef]

1998

1994

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

Andreou, A. G.

A. G. Andreou and Z. K. Kalayjian, IEEE Sens. J. 2, 566 (2002).
[CrossRef]

Black, W. T.

B. M. Ratliff, J. S. Tyo, C. F. LaCasse, and W. T. Black, Proc. SPIE 7461, 74610K (2009).
[CrossRef]

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, Opt. Eng. 47, 046403 (2008).
[CrossRef]

Boger, J. K.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, Opt. Eng. 47, 046403 (2008).
[CrossRef]

Bowers, D. L.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, Opt. Eng. 47, 046403 (2008).
[CrossRef]

Chenault, D. B.

Chun, C. S. L.

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

Craighead, H. G.

Deguzman, P. C.

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, Proc. SPIE 3754, 169 (1999).
[CrossRef]

der Spiegel, J. V.

V. Gruev, K. Wu, J. V. der Spiegel, and N. Engheta, Proc. SPIE 6240, 6240O5 (2006).

Dereniak, E. L.

Engheta, N.

V. Gruev, K. Wu, J. V. der Spiegel, and N. Engheta, Proc. SPIE 6240, 6240O5 (2006).

J. S. Tyo, E. N. Pugh, and N. Engheta, J. Opt. Soc. Am. A 15, 367 (1998).
[CrossRef]

Fetrow, M. P.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, Opt. Eng. 47, 046403 (2008).
[CrossRef]

Fleming, D. L.

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

Gerhart, G. R.

Goldstein, D. H.

Gruev, V.

V. Gruev, K. Wu, J. V. der Spiegel, and N. Engheta, Proc. SPIE 6240, 6240O5 (2006).

Hagen, N.

Harnett, C. K.

Hubbs, J. E.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, Opt. Eng. 47, 046403 (2008).
[CrossRef]

Jones, M.

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, Proc. SPIE 3754, 169 (1999).
[CrossRef]

Kalayjian, Z. K.

A. G. Andreou and Z. K. Kalayjian, IEEE Sens. J. 2, 566 (2002).
[CrossRef]

Kaneko, T.

Kudenov, M. W.

Lacasse, C. F.

B. M. Ratliff, C. F. Lacasse, and J. S. Tyo, Opt. Express 17, 9112 (2009).
[CrossRef] [PubMed]

B. M. Ratliff, J. S. Tyo, C. F. LaCasse, and W. T. Black, Proc. SPIE 7461, 74610K (2009).
[CrossRef]

Luo, H.

Meier, J. T.

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, Proc. SPIE 3754, 169 (1999).
[CrossRef]

Nordin, G. P.

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, Proc. SPIE 3754, 169 (1999).
[CrossRef]

Oka, K.

Ortega, S. E.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, Opt. Eng. 47, 046403 (2008).
[CrossRef]

Pezzaniti, L.

Pugh, E. N.

Ratliff, B. M.

B. M. Ratliff, C. F. Lacasse, and J. S. Tyo, Opt. Express 17, 9112 (2009).
[CrossRef] [PubMed]

B. M. Ratliff, J. S. Tyo, C. F. LaCasse, and W. T. Black, Proc. SPIE 7461, 74610K (2009).
[CrossRef]

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, Opt. Eng. 47, 046403 (2008).
[CrossRef]

Shaw, J. A.

Tkaczyk, T.

Torok, E. J.

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

Tyo, J. S.

B. M. Ratliff, C. F. Lacasse, and J. S. Tyo, Opt. Express 17, 9112 (2009).
[CrossRef] [PubMed]

B. M. Ratliff, J. S. Tyo, C. F. LaCasse, and W. T. Black, Proc. SPIE 7461, 74610K (2009).
[CrossRef]

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, Opt. Eng. 47, 046403 (2008).
[CrossRef]

J. S. Tyo, D. H. Goldstein, D. B. Chenault, and J. A. Shaw, Appl. Opt. 45, 5453 (2006).
[CrossRef] [PubMed]

J. S. Tyo, E. N. Pugh, and N. Engheta, J. Opt. Soc. Am. A 15, 367 (1998).
[CrossRef]

Wellems, L. D.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, Opt. Eng. 47, 046403 (2008).
[CrossRef]

Wu, K.

V. Gruev, K. Wu, J. V. der Spiegel, and N. Engheta, Proc. SPIE 6240, 6240O5 (2006).

Appl. Opt.

IEEE Sens. J.

A. G. Andreou and Z. K. Kalayjian, IEEE Sens. J. 2, 566 (2002).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, Opt. Eng. 47, 046403 (2008).
[CrossRef]

Opt. Express

Proc. SPIE

V. Gruev, K. Wu, J. V. der Spiegel, and N. Engheta, Proc. SPIE 6240, 6240O5 (2006).

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

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, Proc. SPIE 3754, 169 (1999).
[CrossRef]

B. M. Ratliff, J. S. Tyo, C. F. LaCasse, and W. T. Black, Proc. SPIE 7461, 74610K (2009).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Typical microgrid polarimeter uses four interlaced linear polarizer orientations to estimate s 0 , s 1 , and s 2 .

Fig. 2
Fig. 2

Fourier transform of I ( m , n ) for the excitation defined by Eqs. (6, 7, 8). The outer shaded regions represent the high-pass filters used to reconstruct s 1 and s 2 . The central shaded area is the low-pass filter used to reconstruct s 0 .

Fig. 3
Fig. 3

s 0 (left column) and s 1 (right column) error distributions for the ideal reconstruction strategy presented here (top row) and NLPN interpolation (bottom row).

Fig. 4
Fig. 4

Long-wave IR (8–10 μ m ) polarimetric imagery taken using a microgrid polarimeter described elsewhere [12]. The target is a spherical gray body at 50 ° C . A, Calibrated microgrid image with modulation present. B, Fourier transform of I ( m , n ) . C, Reconstruction using Eq. (5). D, Reconstruction using NLPN interpolation [5].

Equations (8)

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S = [ s 0 s 1 s 2 s 3 ] T = [ I H + I V I H I V I 45 I 135 I L I R ] T ,
I ( m , n ) = S A ( m , n ) T S i ( m , n ) ,
S A = ( m , n ) [ 1 1 2 ( cos ( m π ) + cos ( n π ) ) 1 2 ( cos ( m π ) cos ( n π ) ) 0 ] .
I ( m , n ) = s 0 ( m , n ) + 1 2 cos ( m π ) [ s 1 ( m , n ) + s 2 ( m , n ) ] + 1 2 cos ( n π ) [ s 1 ( m , n ) s 2 ( m , n ) ] .
I ̃ ( ξ , η ) = S ̃ 0 ( ξ , η ) + 1 4 [ S ̃ 1 ( ξ 1 2 , η ) + S ̃ 2 ( ξ 1 2 , η ) ] + 1 4 [ S ̃ 1 ( ξ , η 1 2 ) S ̃ 2 ( ξ , η 1 2 ) ] ,
s 0 ( n , m ) = e 36 ( n 2 + m 2 ) ,
s 1 ( n , m ) = 1 2 s 0 ( n , m ) erf ( 2 m ) ,
s 2 ( n , m ) = 1 2 s 0 ( n , m ) erf ( 2 n ) .

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