Abstract

The theoretical and experimental demonstration of a dispersion-compensated polarization Sagnac interferometer (DCPSI) is presented. An application of the system is demonstrated by substituting the uniaxial crystal-based Savart plate (SP) in K. Oka’s original snapshot polarimeter implementation with a DCPSI. The DCPSI enables the generation of an achromatic fringe field in white-light, yielding significantly more radiative throughput than the original quasi-monochromatic SP polarimeter. Additionally, this interferometric approach offers an alternative to the crystal SP, enabling the use of standard reflective or transmissive materials. Advantages are anticipated to be greatest in the thermal infrared, where uniaxial crystals are rare and the at-sensor radiance is often low when compared to the visible spectrum. First, the theoretical operating principles of the Savart plate polarimeter and a standard polarization Sagnac interferometer polarimeter are provided. This is followed by the theoretical and experimental development of the DCPSI, created through the use of two blazed diffraction gratings. Outdoor testing of the DCPSI is also performed, demonstrating the ability to detect either the S 2 and S 3, or the S 1 and S 2 Stokes parameters in white-light.

© 2009 OSA

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  6. M. W. Kudenov, L. Pezzaniti, E. L. Dereniak, and G. R. Gerhart, “Prismatic imaging polarimeter calibration for the infrared spectral region,” Opt. Express 16(18), 13720–13737 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2009 (2)

M. W. Kudenov, J. L. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[CrossRef]

F. Snik, T. Karalidi, and C. U. Keller, “Spectral modulation for full linear polarimetry,” Appl. Opt. 48(7), 1337–1346 (2009).
[CrossRef] [PubMed]

2008 (2)

2006 (2)

2003 (1)

2002 (1)

G. Zhan, K. Oka, T. Ishigaki, and N. Baba, “Static Fourier-transform spectrometer based on Savart polariscope,” Proc. SPIE 4480, 198–203 (2002).
[CrossRef]

1999 (1)

1994 (1)

1975 (1)

Baba, N.

G. Zhan, K. Oka, T. Ishigaki, and N. Baba, “Static Fourier-transform spectrometer based on Savart polariscope,” Proc. SPIE 4480, 198–203 (2002).
[CrossRef]

Chenault, D. B.

DeHoog, E.

Dereniak, E. L.

Gerhart, G. R.

Goldstein, D. L.

Graf, U. U.

Ishigaki, T.

G. Zhan, K. Oka, T. Ishigaki, and N. Baba, “Static Fourier-transform spectrometer based on Savart polariscope,” Proc. SPIE 4480, 198–203 (2002).
[CrossRef]

Jaffe, D. T.

Kaneko, T.

Karalidi, T.

Kato, T.

Keller, C. U.

Kim, E. J.

Kudenov, M.

Kudenov, M. W.

Lacy, J. H.

Ling, H.

Luo, H.

Moore, J. T.

Oka, K.

Pezzaniti, J. L.

M. W. Kudenov, J. L. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[CrossRef]

Pezzaniti, L.

Rebeiz, G.

Saito, N.

K. Oka and N. Saito, “Snapshot complete imaging polarimeter using Savart plates,” Proc. SPIE 6295, 629508 (2006).
[CrossRef]

Schiewgerling, J.

Shaw, J. A.

Snik, F.

Tyo, J. S.

Wyant, J. C.

Zhan, G.

G. Zhan, K. Oka, T. Ishigaki, and N. Baba, “Static Fourier-transform spectrometer based on Savart polariscope,” Proc. SPIE 4480, 198–203 (2002).
[CrossRef]

Appl. Opt. (5)

Opt. Eng. (1)

M. W. Kudenov, J. L. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (2)

K. Oka and N. Saito, “Snapshot complete imaging polarimeter using Savart plates,” Proc. SPIE 6295, 629508 (2006).
[CrossRef]

G. Zhan, K. Oka, T. Ishigaki, and N. Baba, “Static Fourier-transform spectrometer based on Savart polariscope,” Proc. SPIE 4480, 198–203 (2002).
[CrossRef]

Other (6)

R. Suda, N. Saito, and K. Oka, “Imaging Polarimetry by Use of Double Sagnac Interferometers,” in Extended Abstracts of the 69th Autumn Meeting of the Japan Society of Applied Physics (Japan Society of Applied Physics, Tokyo), p. 877 (2008).

M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 1999), p. 831.

R. S. Sirohi, and M. P. Kothiyal, Optical components, Systems, and Measurement Techniques, (Marcel Dekker, 1991), p. 68.

M. W. Kudenov, College of Optical Sciences, The University of Arizona, 1630 E. University Blvd. #94, Tucson, AZ 85721, M. E. L. Jungwirth, E. L. Dereniak, and G. R. Gerhart are preparing a manuscript to be called, “White light Sagnac interferometer for snapshot multispectral imaging.”

D. Malacara, Optical Shop Testing (John Wiley & Sons, Inc., New York, 1992), p. 100.

M. H. Smith, J. B. Woodruff, and J. D. Howe, “Beam wander considerations in imaging polarimetry,” in Proc. SPIE 3754, 50–54 (1999).

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Figures (15)

Fig. 1
Fig. 1

Schematic of the Savart plate polarimeter (SPP). Two Savart plates, SP1 and SP2, reside in front of an objective lens with focal length f obj. The combination of both Savart plates generates four sheared beams, separated by a distance 2 Δ . A depiction of the initial beam, as well as the beams generated after transmission through SP1 and SP2, is also provided in the x, y plane (denoted xp , yp ). A narrow bandpass filter is used to maintain a high fringe visibility.

Fig. 2
Fig. 2

One configuration for a polarization Sagnac interferometer. The distance between the WGBS and mirrors, M1 and M2, is denoted d 1 and d 2, respectively. A shear (SPSI ) is produced when d 1d 2. The case d 1 > d 2 is illustrated, with d 1 = d 2 + α.

Fig. 3
Fig. 3

A simplified SPP with a single Savart plate.

Fig. 4
Fig. 4

OPD generated by a shearing distance, Sshear , for a PSI and simplified SPP.

Fig. 5
Fig. 5

DCPSI with blazed diffraction gratings, G1 and G2, positioned at each output of the WGBS. To remove the achromatic shear, the distance between the WGBS and mirrors, M1 and M2, depicted previously in Fig. 2, is d1 = d2 . Inclusion of the gratings generates a shear that is directly proportional to the wavelength.

Fig. 6
Fig. 6

DCPSI with an unfolded optical layout. Light traveling from left to right was initially transmitted through the WGBS, while light traveling from right to left was initially reflected from the WGBS.

Fig. 7
Fig. 7

Experimental setup for laboratory testing of the DCPSI using white light. The distances a, b, and c are 14.4 mm, 57.2 mm, and 12.9 mm, respectively.

Fig. 8
Fig. 8

(a) Transmission percentages vs. wavelength for the IR blocking filter, crossed linear polarizers (to demonstrate their effective spectral region of operation), and the multiplication of the two curves. (b) Ideal theoretical diffraction efficiencies vs. wavelength for gratings G1 and G2 illustrating the m = 0, 1, and 2 diffraction orders.

Fig. 9
Fig. 9

Monochrometer configuration for sending light into the DCPSI for verification of the fringe frequency. The bandwidth of the light exiting the monochrometer was approximately 8.9 nm using a 2 mm exit slit.

Fig. 10
Fig. 10

Measured carrier frequency vs. wavelength for the DCPSI (solid dark-gray line) and the theoretical carrier frequency for a PSI (dotted light-gray line). The PSI’s carrier frequency was set to equal the DCPSI’s carrier frequency at a wavelength of 600 nm.

Fig. 11
Fig. 11

(a) Reconstructed Stokes parameters for a PG consisting of a LP at 45° followed by a rotating QWR. (b) Reconstructed Stokes parameters for a rotating LP followed by a QWR oriented at 45°, thereby forming an imaging polarimeter capable of full linear polarization measurements.

Fig. 12
Fig. 12

Raw image of several large windows viewing the sky in reflection through the DCPSI. Fringes are observed where polarized light is present. The fringes change in phase and amplitude due to the varying amounts of S 2 and S 3 over the surface of the window.

Fig. 13
Fig. 13

Processed polarization data of the large windows, calculated from the data in Fig. 12. From the image in the first row and first column and moving clockwise: S 0, DOCP, S 2/S 0, and S 3/S 0.

Fig. 14
Fig. 14

Raw image of a moving vehicle. The QWR is inserted in front of the DCPSI to measure S 1 and S 2.

Fig. 15
Fig. 15

Processed polarization data of the vehicle, calculated from the data in Fig. 14. From the image in the first row and first column and moving clockwise: S 0, DOLP, S 2/S 0, and S 1/S 0.

Equations (41)

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S ( x , y ) = [ S 0 ( x , y ) S 1 ( x , y ) S 2 ( x , y ) S 3 ( x , y ) ] = [ I 0 ( x , y ) + I 90 ( x , y ) I 0 ( x , y ) I 90 ( x , y ) I 45 ( x , y ) I 135 ( x , y ) I R ( x , y ) I L ( x , y ) ]
I ( x , y ) = 1 2 S 0 + 1 2 S 1 cos [ 2 π Ω 2 y ] + 1 4 | S 23 | cos [ 2 π ( Ω 1 + Ω 2 ) x arg ( S 23 ) ] 1 4 | S 23 | cos [ 2 π ( Ω 1 + Ω 2 ) y + arg ( S 23 ) ]
S 23 = S 2 + j S 3 ,
Ω 1 = Δ 1 λ f and Ω 2 = Δ 2 λ f ,
S S P = 2 Δ = 2 n e 2 n o 2 n e 2 + n o 2 t ,
B = 0.6 λ 2 O P D max ,
S P S I = 2 α
O P D = S s h e a r sin ( θ ) S s h e a r θ ,
I S P P ( x i , y i ) = | 1 2 E x ( x i , y i , t ) e j ϕ 1 + 1 2 E y ( x i , y i , t ) e j ϕ 2 | 2 ,
I S P P ( x i , y i ) = 1 2 { ( E x E x * + E x E y * ) + ( E x E y * + E x * E y ) cos ( ϕ 1 ϕ 2 ) + j ( E x E y * + E x * E y ) sin ( ϕ 1 ϕ 2 ) } ,
ϕ 1 = 2 π Δ λ f o b j x i and ϕ 2 = 2 π Δ λ f o b j y i .
[ S 0 S 1 S 2 S 3 ] = [ E x E x * + E y E y * E x E x * E y E y * E x E y * + E x * E y j ( E x E y * E x * E y ) ] .
I S P P ( x i , y i ) = 1 2 [ S 0 + S 2 cos ( 2 π λ f o b j Δ ( x i y i ) ) S 3 sin ( 2 π λ f o b j Δ ( x i y i ) ) ] .
U S P P = 2 Δ λ f o b j .
ϕ 1 = 2 π λ f o b j α 2 x i and ϕ 2 = 2 π λ f o b j α 2 x i .
I P S I ( x i , y i ) = 1 2 [ S 0 + S 2 cos ( 2 π λ f o b j 2 α x i ) S 3 sin ( 2 π λ f o b j 2 α x i ) ] .
U P S I = 2 α λ f o b j .
sin ( θ ) = m λ d ,
S D C P S I = 2 m λ d ( a + b + c )
ϕ 1 = 2 π f o b j m d ( a + b + c ) x i and ϕ 2 = 2 π f o b j m d ( a + b + c ) x i .
I D C P S I ( x i , y i ) = 1 2 m = 0 d / λ 1 S 0 ' ( m ) + 1 2 m = 1 d / λ 1 [ S 2 ' ( m ) cos ( 2 π f o b j 2 m d ( a + b + c ) x i ) S 3 ' ( m ) sin ( 2 π f o b j 2 m d ( a + b + c ) x i ) ]
S 0 ' ( m ) = λ 1 λ 2 D E 2 ( λ , m ) S 0 ( λ ) d λ
S 2 ' ( m ) = λ 1 λ 2 D E 2 ( λ , m ) S 2 ( λ ) d λ
S 3 ' ( m ) = λ 1 λ 2 D E 2 ( λ , m ) S 3 ( λ ) d λ
U D C P S I = 2 m d f o b j ( a + b + c ) .
I ( x i , y i ) = A + B cos ( ω x i + ϕ ) , { x min x i x max y i = y 0 }
F [ I D C P S I ( x i , y i ) ] = S 0 ' ( 1 ) 2 δ ( ξ , η ) + 1 4 ( S 2 ' ( 1 ) + j S 3 ' ( 1 ) ) δ ( ξ U D C P S I , η ) 1 4 ( S 2 ' ( 1 ) j S 3 ' ( 1 ) ) δ ( ξ + U D C P S I , η ) ,
F 1 [ C 0 ] = S 0 ' ( 1 ) 2
F 1 [ C 1 ] = 1 4 ( S 2 ' ( 1 ) + j S 3 ' ( 1 ) ) exp ( j 2 π U D C P S I x i )
S 0 , s a m p l e ( x i , y i ) = | F ( C 0 , s a m p l e ) |
S 2 , s a m p l e ( x i , y i ) = [ F ( C 2 , s a m p l e ) F ( C 2 , r e f e r e n c e , 45 ° ) | F ( C 0 , r e f e r e n c e , 45 ° ) | S 0 , s a m p l e ]
S 3 , s a m p l e ( x i , y i ) = [ ( C 2 , s a m p l e ) F ( C 2 , r e f e r e n c e , 45 ° ) | F ( C 0 , r e f e r e n c e , 45 ° ) | S 0 , s a m p l e ] ,
ε R M S , S i = 1 N n = 1 N ( S i , M e a s ( n ) S i , P G ( n ) ) 2 ,
M Q W R , 45 ° = [ 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 ]
S o u t = M Q W R , 45 ° [ S 0 S 1 S 2 S 3 ] T = [ S 0 S 3 S 2 S 1 ] T .
I D C P S I ( x i , y i ) = 1 2 m = 0 d / λ 1 S 0 ' ( m ) + 1 2 m = 1 d / λ 1 [ S 2 ' ( m ) cos ( 2 π f o b j 2 m d ( a + b + c ) x i ) S 1 ' ( m ) sin ( 2 π f o b j 2 m d ( a + b + c ) x i ) ] ,
S 1 ' ( m ) = λ 1 λ 2 D E 2 ( λ , m ) S 1 ( λ ) d λ .
F 1 [ C 0 ] = S 0 ' ( 1 ) 2
F 1 [ C 1 ] = 1 4 ( S 2 ' ( 1 ) + j S 1 ' ( 1 ) ) exp ( j 2 π U D C P S I x i ) ,
D O L P = S 1 2 + S 2 2 S 0
ϕ = 1 2 a tan ( S 2 S 1 ) .

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