Abstract

The Fourier transform imaging spectrometer (FTIS) is an important tool for the measurement of spectral information in a scene. Advances in electro-optic crystal systems have led to the advent of the FTIS based on polarization interference filters. The operation of these devices as spectrometers has been well characterized, but the imaging capabilities have yet to be thoroughly explored. We explore the field-of-view limitations that occur when using this particular type of FTIS.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2010

C.-Y. Huang and W.-C. Wang, “Compact liquid crystal based Fourier transform spectrometer system,” Int. J. Optomechatron. 4, 157–176 (2010).
[CrossRef]

2008

T. H. Chao, T. T. Lu, S. R. Davis, S. D. Rommel, G. Farca, B. Luey, A. Martin, and M. H. Anderson, “Compact liquid crystal waveguide based Fourier transform spectrometer for in-situ and remote gas and chemical sensing,” Proc. SPIE 6977, 69770P (2008).
[CrossRef]

2005

T. H. Chao, H. Zhou, X. Xia, and S. Serati, “Near IR electro optic imaging Fourier transform spectrometer,” Proc. SPIE 5816, 163–172 (2005).
[CrossRef]

2004

1998

G. Sharp, P. Wang, S. Serati, and T. Ewing, “Liquid crystal Fourier transform spectrometer,” Proc. SPIE 3384, 161–171(1998).
[CrossRef]

1990

Anderson, M. H.

T. H. Chao, T. T. Lu, S. R. Davis, S. D. Rommel, G. Farca, B. Luey, A. Martin, and M. H. Anderson, “Compact liquid crystal waveguide based Fourier transform spectrometer for in-situ and remote gas and chemical sensing,” Proc. SPIE 6977, 69770P (2008).
[CrossRef]

Boer, G.

Chao, T. H.

T. H. Chao, T. T. Lu, S. R. Davis, S. D. Rommel, G. Farca, B. Luey, A. Martin, and M. H. Anderson, “Compact liquid crystal waveguide based Fourier transform spectrometer for in-situ and remote gas and chemical sensing,” Proc. SPIE 6977, 69770P (2008).
[CrossRef]

T. H. Chao, H. Zhou, X. Xia, and S. Serati, “Near IR electro optic imaging Fourier transform spectrometer,” Proc. SPIE 5816, 163–172 (2005).
[CrossRef]

Dandliker, R.

Davis, S. R.

T. H. Chao, T. T. Lu, S. R. Davis, S. D. Rommel, G. Farca, B. Luey, A. Martin, and M. H. Anderson, “Compact liquid crystal waveguide based Fourier transform spectrometer for in-situ and remote gas and chemical sensing,” Proc. SPIE 6977, 69770P (2008).
[CrossRef]

Ewing, T.

G. Sharp, P. Wang, S. Serati, and T. Ewing, “Liquid crystal Fourier transform spectrometer,” Proc. SPIE 3384, 161–171(1998).
[CrossRef]

Farca, G.

T. H. Chao, T. T. Lu, S. R. Davis, S. D. Rommel, G. Farca, B. Luey, A. Martin, and M. H. Anderson, “Compact liquid crystal waveguide based Fourier transform spectrometer for in-situ and remote gas and chemical sensing,” Proc. SPIE 6977, 69770P (2008).
[CrossRef]

Huang, C.-Y.

C.-Y. Huang and W.-C. Wang, “Compact liquid crystal based Fourier transform spectrometer system,” Int. J. Optomechatron. 4, 157–176 (2010).
[CrossRef]

Liang, Q.-T.

Lu, T. T.

T. H. Chao, T. T. Lu, S. R. Davis, S. D. Rommel, G. Farca, B. Luey, A. Martin, and M. H. Anderson, “Compact liquid crystal waveguide based Fourier transform spectrometer for in-situ and remote gas and chemical sensing,” Proc. SPIE 6977, 69770P (2008).
[CrossRef]

Luey, B.

T. H. Chao, T. T. Lu, S. R. Davis, S. D. Rommel, G. Farca, B. Luey, A. Martin, and M. H. Anderson, “Compact liquid crystal waveguide based Fourier transform spectrometer for in-situ and remote gas and chemical sensing,” Proc. SPIE 6977, 69770P (2008).
[CrossRef]

Martin, A.

T. H. Chao, T. T. Lu, S. R. Davis, S. D. Rommel, G. Farca, B. Luey, A. Martin, and M. H. Anderson, “Compact liquid crystal waveguide based Fourier transform spectrometer for in-situ and remote gas and chemical sensing,” Proc. SPIE 6977, 69770P (2008).
[CrossRef]

Rommel, S. D.

T. H. Chao, T. T. Lu, S. R. Davis, S. D. Rommel, G. Farca, B. Luey, A. Martin, and M. H. Anderson, “Compact liquid crystal waveguide based Fourier transform spectrometer for in-situ and remote gas and chemical sensing,” Proc. SPIE 6977, 69770P (2008).
[CrossRef]

Ruffieux, P.

Scharf, T.

Seitz, P.

Serati, S.

T. H. Chao, H. Zhou, X. Xia, and S. Serati, “Near IR electro optic imaging Fourier transform spectrometer,” Proc. SPIE 5816, 163–172 (2005).
[CrossRef]

G. Sharp, P. Wang, S. Serati, and T. Ewing, “Liquid crystal Fourier transform spectrometer,” Proc. SPIE 3384, 161–171(1998).
[CrossRef]

Sharp, G.

G. Sharp, P. Wang, S. Serati, and T. Ewing, “Liquid crystal Fourier transform spectrometer,” Proc. SPIE 3384, 161–171(1998).
[CrossRef]

Wang, P.

G. Sharp, P. Wang, S. Serati, and T. Ewing, “Liquid crystal Fourier transform spectrometer,” Proc. SPIE 3384, 161–171(1998).
[CrossRef]

Wang, W.-C.

C.-Y. Huang and W.-C. Wang, “Compact liquid crystal based Fourier transform spectrometer system,” Int. J. Optomechatron. 4, 157–176 (2010).
[CrossRef]

Wolfe, W. J.

W. J. Wolfe, Introduction to Imaging Spectrometers (SPIE, 1997).
[CrossRef]

Xia, X.

T. H. Chao, H. Zhou, X. Xia, and S. Serati, “Near IR electro optic imaging Fourier transform spectrometer,” Proc. SPIE 5816, 163–172 (2005).
[CrossRef]

Zhou, H.

T. H. Chao, H. Zhou, X. Xia, and S. Serati, “Near IR electro optic imaging Fourier transform spectrometer,” Proc. SPIE 5816, 163–172 (2005).
[CrossRef]

Appl. Opt.

Int. J. Optomechatron.

C.-Y. Huang and W.-C. Wang, “Compact liquid crystal based Fourier transform spectrometer system,” Int. J. Optomechatron. 4, 157–176 (2010).
[CrossRef]

Proc. SPIE

T. H. Chao, T. T. Lu, S. R. Davis, S. D. Rommel, G. Farca, B. Luey, A. Martin, and M. H. Anderson, “Compact liquid crystal waveguide based Fourier transform spectrometer for in-situ and remote gas and chemical sensing,” Proc. SPIE 6977, 69770P (2008).
[CrossRef]

T. H. Chao, H. Zhou, X. Xia, and S. Serati, “Near IR electro optic imaging Fourier transform spectrometer,” Proc. SPIE 5816, 163–172 (2005).
[CrossRef]

G. Sharp, P. Wang, S. Serati, and T. Ewing, “Liquid crystal Fourier transform spectrometer,” Proc. SPIE 3384, 161–171(1998).
[CrossRef]

Other

W. J. Wolfe, Introduction to Imaging Spectrometers (SPIE, 1997).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

FTIS-based principle of polarization interference. The system consists of LPs, HWPs, a QWP, and birefringent phase delays.

Fig. 2
Fig. 2

Optical schematic for a Michelson interferometer. For an on-axis beam, the OPD is a function of the difference between d1 and d2—the length of the sample and reference arm. A tunnel diagram of the same system shows that OPD is also introduced by the difference in path length between an on-axis ray and a ray at some field angle θ.

Fig. 3
Fig. 3

Optical schematic for a four-stage polarization interference FTIS. For an on-axis beam, the OPD is a function of the path difference for the ordinary ray (plates have index n o ) and the extraordinary ray (plates have index n e ). For an extraordinary ray propagation at angle θ, the OPD is also introduced by the difference in path length between an on-axis ray and a ray at some field angle θ due to the effective index of refractive changing a function of the propagation angle.

Fig. 4
Fig. 4

Phase difference between an ordinary and the corresponding extraordinary ray for a 0 ° 20 ° field angle along the x and y axes for a PIFTIS with four to nine stages.

Fig. 5
Fig. 5

Comparison of the interference pattern for the (a)  PIFTIS and (b) conventional FTIS utilizing the Michelson interferometer configuration. Both systems have equivalent optical path lengths (1024 waves at 550 nm ) and simulated for a 6 ° × 6 ° field. Limiting FOV is labeled for both cases.

Fig. 6
Fig. 6

Half-FOV of a PIFTIS as a function of (a) number of stages N and (b) spectral resolution. Results are compared to an equivalent conventional interferometer system with the same 0.25 wave OPD requirement.

Equations (14)

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S ( ω ) = a 0 + m = 1 a m cos ( 2 π m ω Δ ω ) + m = 1 b m sin ( 2 π m ω Δ ω ) ,
a 0 = 1 Δ ω Δ ω 2 Δ ω 2 S ( ω ) d ω ,
a m = 2 Δ ω Δ ω 2 Δ ω 2 S ( ω ) cos ( 2 π m ω Δ ω ) d ω ,
b m = 2 Δ ω Δ ω 2 Δ ω 2 S ( ω ) sin ( 2 π m ω Δ ω ) d ω .
P m a = P m 0 P m π = ω 0 Δ ω 2 ω 0 + Δ ω 2 S ( ω ) cos ( 2 π m ω Δ ω ) d ω ,
P m b = P m π 2 P m π 2 = ω 0 Δ ω 2 ω 0 + Δ ω 2 S ( ω ) sin ( 2 π m ω Δ ω ) d ω ,
P 0 = P m 0 + P m π = P m π 2 + P m π 2 = ω 0 Δ ω 2 ω 0 + Δ ω 2 S ( ω ) d ω .
S ( ω ) = 1 Δ ω [ P 0 + 2 m = 1 P m a cos ( 2 π m ω Δ ω ) + 2 m = 1 P m b sin ( 2 π m ω Δ ω ) ] .
Δ λ = λ o 2 N .
ϕ = 2 π ( n e n o ) t λ o ,
( 1 n ( θ ) ) 2 = ( cos θ n o ) 2 + ( sin θ n e ) 2 .
ϕ = ( n ( θ ) cos θ n ( 0 ) ) t ,
λ 4 = j = 1 N ( n j ( θ ) cos θ n j ( 0 ) ) t j .
t = 2 N λ ( n e n o ) = 60.22 × 2 N μm .

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