Abstract

This paper describes a method for the mapping of spatially-distributed states-of-polarization of light with a simple and compact configuration. A tiny block of polarization-analyzing optics, consisting of four thin birefringent wedge prisms and a sheet analyzer, are incorporated into an imaging polarimeter, such that mesh-like multiple fringes are generated over a CCD image sensor of a video camera. Fourier analysis of the obtained fringes provides information for determining the two-dimensional distribution of the state-of-polarization. No mechanical or active elements for analyzing polarization are used, and all the parameters related to the spatially-dependent monochromatic Stokes parameters corresponding to azimuth and ellipticity angles can be determined from a single frame. The effectiveness of this method is demonstrated by a prototype incorporating calcite wedge prisms.

© 2003 Optical Society of America

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References

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  1. J.F.S.Gomes, �??Photoelasticity�?? in Optical Metrology ed. by O. D. D. Soares, Martinus Nijhoff Publishers, Dordrecht, 1987.
  2. Y.Otani, T.Shimada, T.Yoshizawa, and N.Umeda,�??Two-dimensional Birefringence Measurement using the Phase Shifting Technique,�?? Opt. Eng. 33, 1604�??1609 (1994).
    [CrossRef]
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    [CrossRef]
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  14. K. Oka and T. Kaneko, �??Polarization Mapping Using Birefringent Prism,�?? in Proceedings of the SICE Annual Conference 2002 (Society of Instrument and Control Engineers, Tokyo, 2002), pp. 2581�??2582.
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Appl. Opt. (2)

Exp. Mech. (1)

K. Oka and Y. Ohtsuka, �??Polarimetry for spatiotemporal photoelastic analysis,�?? Exp. Mech. 33, 44�??48 (1993).
[CrossRef]

J. Mod. Opt. (1)

K. Oka, J. Ikeda, and Y. Ohtsuka, �??Novel polarimetric technique exploring spatiotemporal birefringent response of an anti-ferroelectric liquid crystal cell,�?? J. Mod. Opt. 40, 1713�??1723 (1993).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

Y.Otani, T.Shimada, T.Yoshizawa, and N.Umeda,�??Two-dimensional Birefringence Measurement using the Phase Shifting Technique,�?? Opt. Eng. 33, 1604�??1609 (1994).
[CrossRef]

Opt. Lett. (1)

Other (9)

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1988) p 51.

T. Tsuruta, Applied Optics II, Sec.5.1, (Baifukan, Tokyo, 1990).

N. Saito and K. Oka, �??Two-dimensional measurement of polarization using spatial carrier,�?? in Extended Abstracts of the 47th Spring Meeting of the Japan Society of Applied Physics and Related Societies (Japan Society of Applied Physics, Tokyo, 2000), p. 1101 (in Japanese).

N. Saito and K. Oka, �??Spatiotemporal polarimeter using spatial carrier fringes,�?? in Proceedings of the Optics Japan 2000, (Optical Society of Japan, Tokyo, 2000), p. 345�??346 (in Japanese).

T. Kaneko and K. Oka, �??Two-Dimensional Mapping of Polarization Using Birefringent Wedges,�?? in Extended Abstracts of the 49th Spring Meeting of the Japan Society of Applied Physics and Related Societies, (Japan Society of Applied Physics, Tokyo, 2002), p. 977 (in Japanese).

K. Oka and T. Kaneko, �??Polarization Mapping Using Birefringent Prism,�?? in Proceedings of the SICE Annual Conference 2002 (Society of Instrument and Control Engineers, Tokyo, 2002), pp. 2581�??2582.

J.F.S.Gomes, �??Photoelasticity�?? in Optical Metrology ed. by O. D. D. Soares, Martinus Nijhoff Publishers, Dordrecht, 1987.

D. J. Sanchez, S. A. Gregory, S. Storm, T. E. Payne, C. K. Davis, �??Photopolarimetric Measurements of Geosynchronous Satellites,�?? in Multifrequency Electronic/Photonic Devices and Systems for Dual-Use Applications, Proc. SPIE 4490, 221�??236(2001).
[CrossRef]

H. Kikuta, K. Numata, H. Arimitsu, K. Iwata, and N. Kato, �??Imaging polarimetry with an micro-retarder array,�?? in Proceedings of the SICE Annual Conference 2002, (Society of Instrument and Control Engineers, Tokyo, 2002), pp. 2583�??2584.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the imaging polarimeter using birefringent wedge prisms.

Fig. 2.
Fig. 2.

Configuration of the block of the polarimetric devices.

Fig. 3.
Fig. 3.

Photograph of the fabricated imaging polarimeter.

Fig. 4.
Fig. 4.

Intensity pattern with mesh-like fringes.

Fig. 5.
Fig. 5.

Power spectrum of the intensity pattern.

Fig. 6.
Fig. 6.

Spatial distribution of (a) azimuth angle θ(x, y) and (b) ellipticity angle ε(x, y).

Fig. 7.
Fig. 7.

Cross sections of Fig. 6.

Equations (16)

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I ( x , y ) = 1 2 S 0 ( x , y ) + 1 2 S 1 ( x , y ) cos 2 π U x
+ 1 4 S 23 ( x , y ) cos { 2 π U ( x y ) + arg [ S 23 ( x , y ) ] }
1 4 S 23 ( x , y ) cos { 2 π U ( x + y ) arg [ S 23 ( x , y ) ] } ,
S 23 ( x , y ) = S 2 ( x , y ) + i S 3 ( x , y ) ,
U = 2 B λ tan α ,
I ˜ ( f x , f y ) = 1 2 A 0 ( f x , f y ) + 1 4 A 1 ( f x U , f y ) + 1 4 A 1 * ( f x U , f y )
+ 1 8 A 23 ( f x U , f y + U ) + 1 8 A 23 * ( f x U , f y + U )
1 8 A 23 * ( f x U , f y U ) 1 8 A 23 ( f x U , f y U ) ,
A 0 ( f x , f y ) = [ S 0 ( x , y ) ] ,
A 1 ( f x , f y ) = [ S 1 ( x , y ) ] ,
A 23 ( f x , f y ) = [ S 23 ( x , y ) ] .
F 0 ( x , y ) = 1 2 S 0 ( x , y ) ,
F 1 ( x , y ) = 1 4 S 1 ( x , y ) exp [ i 2 π U x ] ,
F 23 ( x , y ) = 1 8 S 23 ( x , y ) exp [ i 2 π U ( x y ) ] .
θ ( x , y ) = 1 2 tan 1 [ S 2 ( x , y ) S 1 ( x , y ) ] ,
ε ( x , y ) = 1 2 tan 1 [ S 3 ( x , y ) S 1 ( x , y ) 2 + S 2 ( x , y ) 2 ] .

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