Abstract

We discuss achievement of a long-standing technology goal: the first practical realization of a quantitative-grade, field-worthy snapshot imaging spectropolarimeter. The instrument employs Polarimetric Spectral Intensity Modulation (PSIM), a technique that enables full Stokes instantaneous “snapshot” spectropolarimetry with perfect channel registration. This is achieved with conventional single beam optics and a single focal plane array (FPA). Simultaneity and perfect registration are obtained by encoding the polarimetry onto the spectrum via a novel optical arrangement which enables sensing from moving platforms against dynamic scenes. PSIM is feasible across the electro-optical sensing range (UV-LWIR). We present measurement results from a prototype sensor that operates in the visible and near infrared regime (450–900 nm). We discuss in some detail the calibration and Stokes spectrum inversion algorithms that are presently achieving 0.5% polarimetric accuracy.

© 2004 Optical Society of America

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References

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    [CrossRef]
  2. J. Chowdhary, B. Cairns, M. Mishchenko and L. Travis, �??Retrieval of aerosol properties over the ocean using multispectral and multiangle photopolarimetric measurements from the Research Scanning Polarimeter,�?? Geophys. Research Lett. 28, 243-246 (2001).
    [CrossRef]
  3. M. Mishchenko and L. Travis, �??Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight,�?? Journal of Geophysical Research 102(D14), 16989-17013, 1997.
    [CrossRef]
  4. P. Kebabian, �??Polarimetric spectral intensity modulation spectropolarimeter,�?? US Patent 6,490,043 (2002).
  5. F. J. Iannarilli, S. H. Jones, H. E. Scott, and P. L. Kebabian, �??Polarimetric Spectral Intensity Modulation (P-SIM): Enabling Simultaneous Hyperspectral and Polarimetric Imaging,�?? in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik, eds., Proc. SPIE 3698, 474�??481 (1999).
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    [CrossRef]
  7. M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1965).
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  9. G. H. Golub and C. F. V. Loan, Matrix Computations (The Johns Hopkins University Press, Baltimore, Maryland, 1983).
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    [CrossRef]
  13. R. Manduchi, P. Perona, and D. Shy, �??Efficient Deformable Filter Banks,�?? IEEE Trans. on Signal Processing 46, 1168�??1173 (1998).
    [CrossRef]
  14. F. Iannarilli, �??Spectro-Polarimetric Remote Surface Orientation Measurement,�?? US Patent 6,678,632 (2004).
  15. I. Daubechies, B. Han, A. Ron, and Z. Shen, �??Framelets: MRA-Based Constructions ofWavelet Frames,�?? Applied and Computational Harmonic Analysis 14(1), 1�??46 (2003).
    [CrossRef]
  16. J. D. Howe, �??Two-color infrared full-Stokes imaging polarimeter development,�?? IEEE Aerospace Conference (1999).
  17. J. A. Shaw and M. R. Descour, �??Instrument effects in polarized infrared images,�?? Opt. Eng. 34, 1396-1399 (1995).
    [CrossRef]
  18. G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. W. Jones, �??Micropolarizer array for infrared imaging polarimetry,�?? J. Opt. Soc. Am. A. 16(5) (1999).
  19. J. K. Boger et al., �??An error evaluation template for use with imaging spectro-polarimeters,�?? Proc. of SPIE 5158, 113-124 (2003).
    [CrossRef]
  20. J. Q. Peterson, G. L. Jensen, and J. A. Kristl, �??Imaging polarimetry capabilities and measurement uncertainties in remote sensing applications,�?? Proc. of SPIE 4133, 221-228 (2000).
    [CrossRef]
  21. J. Q. Peterson, G. L. Jensen, J. A. Kristl, and J. A. Shaw, �??Polarimetric imaging using a continuously spinning polarizer element,�?? Proc. of SPIE 4133, 292-300 (2000).
    [CrossRef]

Applied and Computational Harmonic Anal.

I. Daubechies, B. Han, A. Ron, and Z. Shen, �??Framelets: MRA-Based Constructions ofWavelet Frames,�?? Applied and Computational Harmonic Analysis 14(1), 1�??46 (2003).
[CrossRef]

Geophys. Research Lett.

J. Chowdhary, B. Cairns, M. Mishchenko and L. Travis, �??Retrieval of aerosol properties over the ocean using multispectral and multiangle photopolarimetric measurements from the Research Scanning Polarimeter,�?? Geophys. Research Lett. 28, 243-246 (2001).
[CrossRef]

IEEE Aerospace Conference

J. D. Howe, �??Two-color infrared full-Stokes imaging polarimeter development,�?? IEEE Aerospace Conference (1999).

IEEE Trans. on Signal Processing

R. Manduchi, P. Perona, and D. Shy, �??Efficient Deformable Filter Banks,�?? IEEE Trans. on Signal Processing 46, 1168�??1173 (1998).
[CrossRef]

IEEE Trans. Pattern Analysis and Machine

W. T. Freeman and E. H. Adelson, �??The Design and Use of Steerable Filters,�?? IEEE Trans. Pattern Analysis and Machine Intelligence 13, 891�??906 (1991).
[CrossRef]

J. Opt. Soc. Am. A

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. W. Jones, �??Micropolarizer array for infrared imaging polarimetry,�?? J. Opt. Soc. Am. A. 16(5) (1999).

Journal of Geophysical Research

M. Mishchenko and L. Travis, �??Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight,�?? Journal of Geophysical Research 102(D14), 16989-17013, 1997.
[CrossRef]

Opt. Eng.

J. A. Shaw and M. R. Descour, �??Instrument effects in polarized infrared images,�?? Opt. Eng. 34, 1396-1399 (1995).
[CrossRef]

Opt. Lett.

Proc. of SPIE

J. K. Boger et al., �??An error evaluation template for use with imaging spectro-polarimeters,�?? Proc. of SPIE 5158, 113-124 (2003).
[CrossRef]

J. Q. Peterson, G. L. Jensen, and J. A. Kristl, �??Imaging polarimetry capabilities and measurement uncertainties in remote sensing applications,�?? Proc. of SPIE 4133, 221-228 (2000).
[CrossRef]

J. Q. Peterson, G. L. Jensen, J. A. Kristl, and J. A. Shaw, �??Polarimetric imaging using a continuously spinning polarizer element,�?? Proc. of SPIE 4133, 292-300 (2000).
[CrossRef]

Proc. SPIE

F. J. Iannarilli, S. H. Jones, H. E. Scott, and P. L. Kebabian, �??Polarimetric Spectral Intensity Modulation (P-SIM): Enabling Simultaneous Hyperspectral and Polarimetric Imaging,�?? in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik, eds., Proc. SPIE 3698, 474�??481 (1999).

SIAM Review

S. Chen, D. Donoho, and M. Saunders, �??Atomic Decomposition by Basis Pursuit,�?? SIAM Review 43(1), 129�??59 (2001).
[CrossRef]

Space Science Reviews

J. E. Hansen and L. D. Travis, �??Light scattering in planetary atmospheres,�?? Space Science Reviews 16, 527-610 (1974).
[CrossRef]

Other

P. Kebabian, �??Polarimetric spectral intensity modulation spectropolarimeter,�?? US Patent 6,490,043 (2002).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1965).

E. Collett, Polarized Light (Marcel Dekker, 1993).

G. H. Golub and C. F. V. Loan, Matrix Computations (The Johns Hopkins University Press, Baltimore, Maryland, 1983).

D. L. Donoho and M. Elad, �??Optimally Sparse Representation in General (Non-Orthogonal) Dictionaries Via L1 Minimization,�?? Tech. rep., Stanford University, Department of Statistics (2002).

F. Iannarilli, �??Spectro-Polarimetric Remote Surface Orientation Measurement,�?? US Patent 6,678,632 (2004).

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Figures (6)

Fig. 1.
Fig. 1.

Effect of a PSIM module within a line-imaging slit spectrometer. On the right side are shown four measured focal plane snapshots of PSIM modulated spectra from a simple line-imaging spectrometer. Dispersion is in the horizontal dimension and the vertical dimension is aligned with the spectrometer slit. The light source was viewed through a linear polarizer set at various rotation angles to yield input angles of polarization of 0, 90, 45, and 135 degrees.

Fig. 2.
Fig. 2.

Schematic layout of a PSIM sensor. Collection optic, L1. Relay optics, L2, L3. Waveplates, W1, W2. Polarizer, P. Offner spectrometer mirrors, M1, M2. Convex diffraction grating, G. Detector, D.

Fig. 3.
Fig. 3.

Photograph of the HyperSpectral Polarimeter for Aerosol Retrievals (HySPAR).

Fig. 4.
Fig. 4.

Measurement results on tilted Pyrex plate. (Top) Degree of linear polarization. (Bottom) Difference between measured result and calculation based on Fresnel transmittances.

Fig. 5.
Fig. 5.

Stokes and DoP spectra of transmission through a Pyrex plate tilted at 50 degrees.

Fig. 6.
Fig. 6.

Measurement results using wide field of view HySPAR prototype sensor. The vertical axes represent scattering angle in the solar principle plane. (Left) Spectral radiance in mW/cm2/sr/µm. (Right) Degree of polarization.

Equations (35)

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M sys = M pol · M crystal 2 · M crystal 1 .
𝓘 ( ν ) = m sys , 1 ( ν ) · s ( ν )
= 1 2 [ I , Q cos ϕ 2 , 1 2 U ( cos Δ ϕ cos Σ ϕ ) , 1 2 V ( sin Σ ϕ sin Δ ϕ ) ]
𝒥 raw ( λ ) = λ R ( λ λ ) K ( λ λ ) m sys , 1 ( λ , Δ n ( λ λ ) ; 1 , 2 ) · s ( λ λ ) d λ + C ( λ ) ,
L ( λ ) = ( 𝒥 raw ( λ ) C ( λ ) ) R ( λ ) = λ K ( λ λ ) m sys , 1 ( λ ; 1 , 2 , Δ n ( λ ) ) · s ( λ λ ) d λ ,
L ( x o , y o ) = 0 s ( λ ) · K ( λ ; x o ) d λ x o 0.5 3 σ x o + 0.5 + 3 σ s ( λ ( p ) ) · K ( p x o ) d p
K ( x ) = 1 2 [ erf ( x 0.5 σ 2 ) erf ( x + 0.5 σ 2 ) ]
d = M 1 ( δ ; x o , y o ) s 1 ( x o , y o )
d = [ L ( x o N , y o ) L ( x o 1 , y o ) L ( x o , y o ) L ( x o + 1 , y o ) L ( x o + N , y o ) ] ,
s ( x x o ) = [ I o + I 1 ( x x o ) Q o + Q 1 ( x x o ) U 0 + U 1 ( x x o ) V 0 + V 1 ( x x o ) ]
s 1 ( x o , y o ) = [ I 0 Q 0 U 0 V 0 I 1 Q 1 U 1 V 1 ] .
M 1 ( δ ; x o , y o ) = [ m 0 ( δ ; x o N , y o ) m 1 ( δ ; x o N , y o ) m 0 ( δ ; x o 1 , y o ) m 1 ( δ ; x o 1 , y o ) m 0 ( δ ; x o , y o ) m 1 ( δ ; x o , y o ) m 0 ( δ ; x o + 1 , y o ) m 1 ( δ ; x o + 1 , y o ) m 0 ( δ ; x o + N , y o ) m 1 ( δ ; x o + N , y o ) ]
m P ( δ ; x o + i , y o ) = [ m Ip ( δ ; x o + i , y o ) m Qp ( δ ; x o + i , y o ) m Up ( δ ; x o + i , y o ) m Vp ( δ ; x o + i , y o ) ]
m I 0 ( δ ; x o + i , y o ) = F I ( x , δ ; x o + i , y o ) d x
m Q 0 ( δ ; x o + i , y o ) = F Q ( x , δ ; x o + i , y o ) d x
m U 0 ( δ ; x o + i , y o ) = F U ( x , δ ; x o + i , y o ) d x
m V 0 ( δ ; x o + i , y o ) = F V ( x , δ ; x o + i , y o ) d x
m I 1 ( δ ; x o + i , y o ) = ( x + i ) F I ( x , δ ; x o + i , y o ) d x
m Q 1 ( δ ; x o + i , y o ) = ( x + i ) F Q ( x , δ ; x o + i , y o ) d x
m U 1 ( δ ; x o + i , y o ) = ( x + i ) F U ( x , δ ; x o + i , y o ) d x
m V 1 ( δ ; x o + i , y o ) = ( x + i ) F V ( x , δ ; x o + i , y o ) d x
F I = ( x , δ ; x o + i , y o ) = 1 2 K ( x )
F Q = ( x , δ ; x o + i , y o ) = 1 2 K ( x ) cos 2 π ( 1 + δ ) Δ n ( x o + i , y o ) 2 λ ( x o + i + x , y o )
F U = ( x , δ ; x o + i , y o ) = 1 2 K ( x ) sin 2 π ( 1 + δ ) Δ n ( x o + i , y o ) 2 λ ( x o + i + x , y o ) sin 2 π ( 1 + δ ) Δ n ( x o + i , y o ) 1 λ ( x o + i + x , y o )
F V = ( x , δ ; x o + i , y o ) = 1 2 K ( x ) sin 2 π ( 1 + δ ) Δ n ( x o + i , y o ) 2 λ ( x o + i + x , y o ) sin 2 π ( 1 + δ ) Δ n ( x o + i , y o ) 1 λ ( x o + i + x , y o )
S ̂ 1 ( x o , y o ) = M 1 + ( δ ; x o , y o ) d .
s ̂ = [ I ̂ 0 Q ̂ 0 U ̂ 0 V ̂ 0 ] ,
δ ̂ ( x o , y o ) = min δ ε T ε
ε = ( M 1 C ( M 1 C ) + I ) d
C = diag [ 1 1 1 1 0 1 1 1 0 ] .
s 1 ( x x o ) = z 1 ( x x o ) s 1 ( x o , y o )
s 1 = [ I 0 Q 0 U 0 V 0 I 1 Q 1 U 1 V 1 ]
z 1 ( x ) = diag [ 1 1 1 1 x x x x ]
m { I , Q , U , V } p ( δ ; x o + i , y o ) = z { I , Q , U , V } p ( x + i ) F { I , Q , U , V } ( x , δ ; x o + i , y o ) dx .
ε = M P s ̂ P d .

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