Abstract

A new technique capable of obtaining quantitative values of the rotation angle of the polarization vector by using holography is presented. This is a two-stage holographic process; during the recording stage a hologram of the object of interest is obtained. The reference beam is composed of two beams that form a small angle between them and keep their polarization states at right angles to each other. In the reconstruction stage of the hologram, two images from the hologram are obtained along two different angles. As a result of the interference between these two images, a set of parallel fringes is formed at the image plane. The fringe contrast on the reconstruction is related to the angle of the polarization vector of the light at each position on the image plane. Measurements of the rotation of the polarization angle of a fraction of a degree were obtained. The main application of this technique is in the study of transient phenomena, where single-shot measurements are the only means of obtaining reliable data.

© 2008 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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2001 (1)

R. J. Wijngaarden, K. Heeck, M. Welling, R. Limburg, M. Pannetier, K. van Zetten, V. L. G. Roorda, and A. R. Voorwinden, “Fast imaging polarimeter for magneto-optical investigations”, Rev. Sci. Instrum. 72, 2661-2664 (2001).
[CrossRef]

1990 (1)

1984 (1)

1976 (1)

H. Kubo and R. Nagata, “Further consideration of photoelasticity using polarization holography,” J. Mod. Opt. 23, 519-528 (1976).

1975 (1)

K. Gasvik, “Holographic reconstruction of the state of polarization,” J. Mod. Opt. 22, 189-206 (1975).

1971 (1)

D. Garvanska, “Polarization holography applied to detection of shape deviations of metal surfaces,” J. Opt. 12, 201-206 (1971).
[CrossRef]

1965 (1)

Appl. Opt. (3)

J. Mod. Opt. (1)

H. Kubo and R. Nagata, “Further consideration of photoelasticity using polarization holography,” J. Mod. Opt. 23, 519-528 (1976).

J. Opt. (1)

D. Garvanska, “Polarization holography applied to detection of shape deviations of metal surfaces,” J. Opt. 12, 201-206 (1971).
[CrossRef]

Rev. Sci. Instrum. (1)

R. J. Wijngaarden, K. Heeck, M. Welling, R. Limburg, M. Pannetier, K. van Zetten, V. L. G. Roorda, and A. R. Voorwinden, “Fast imaging polarimeter for magneto-optical investigations”, Rev. Sci. Instrum. 72, 2661-2664 (2001).
[CrossRef]

Other (3)

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970).

W. T. Welford, Optics, Vol. 14 of Oxford Physics Series (Oxford University Press, 1976).

K. Gasvik, “Holographic reconstruction of the state of polarization,” J. Mod. Opt. 22, 189-206 (1975).

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. M, mirror; BS, beam splitter; NF, neutral filter; L, lens; λ / 4 , quarter-wave plate; P, polarizer; SF, spatial filter; O, object; PW, polarizing wedge; H, holographic plate.

Fig. 2
Fig. 2

Image of the reconstruction of a hologram. The reconstruction is divided into two zones; the right-hand side has a bias of 10 ° .

Fig. 3
Fig. 3

Typical line profile obtained from the image in Fig. 2.

Fig. 4
Fig. 4

Polarization rotation along the length of the cell in which a solution with a gradient concentration of tartaric acid was established.

Fig. 5
Fig. 5

Comparison of normalized measured values for a typical case against the theoretical curve.

Tables (2)

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Table 1 Tested Emulsions and Corresponding Typical Normalizing Factors Obtained

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Table 2 Rotation Values for Solutions ( 41 g Solute, 100 g Solution)

Equations (16)

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R + 45 ° = 1 2 ( 1 0 ) ,
J PW = ( e - i ω x 0 0 e - i ω x ) ,
R r = J PW R + 45 ° ˙ = 1 2 ( e - i ω x e - i ω x ) ,
J O = ( e - i ϕ ( x , y ) / 2 0 0 e i ϕ ( x , y ) / 2 ) .
I o = ( e - i α e i α ) ,
O = J O I o = ( e - i ϕ ( x , y ) / 2 - i α e i ϕ ( x , y ) / 2 + i α ) .
A H = O + R ref = 1 2 ( e - i ω x + e - i ϕ ( x , y ) / 2 - i α e - i ω x + e i ϕ ( x , y ) / 2 + i α ) .
I H = 1 2 ( e i ω x + e i ϕ ( x , y ) / 2 + i α e i ω x + e - i ϕ ( x , y ) / 2 - i α ) ( e - i ω x + e - i ϕ ( x , y ) / 2 - i α e - i ω x + e i ϕ ( x , y ) / 2 + i α ) = 2 + 1 2 [ e i ϕ ( x , y ) / 2 + α ( e - i ω x + e - i ω x ) + e - i ϕ ( x , y ) - i α ( e i ω x + e i ω x ) ] .
t ( x , y ) = t 0 + β τ I H ,
r t ( x , y ) = r t 0 + r β τ I H = r e - i ω x ( t 0 + 4 ) + r e i ϕ ( x , y ) + 2 i α ( e - i 2 ω x + e - i ( ω + ω ) x ) + r e - i ϕ ( x , y ) - i 2 α ( 1 + e i ( ω - ω ) x ) .
A = A sin θ ,
A = A cos θ ,
I = A 2 sin 2 θ ,
I = A 2 cos 2 θ .
V = I max - I min I max + I min = 2 sin 2 θ cos 2 θ .
7.4 °

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