Abstract

The method of measuring birefringence properties using a quarterwave plate and an analyzer is examined, and explicit equations are derived for the case of a linear retarder and for a retarder–rotator system. These equations have been tested empirically by characterizing some previously known birefringent elements. In the case of a pure retarder agreement is generally better than 1°, while for retarder–rotator systems errors were typically 2° for retardation and between 1° and 2° for rotation. Possible sources of these errors are discussed.

© 1983 Optical Society of America

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References

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  1. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
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1966 (1)

1965 (1)

1964 (1)

1942 (1)

1941 (2)

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Figures (1)

Fig. 1
Fig. 1

Schematic diagram of apparatus.

Equations (27)

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E = ( cos θ sin θ ) ,
E 0 = ( E x E y ) ,
( cos θ sin θ ) = J ( ω , λ / 4 ) ( E x E y ) ,
J ( ω , λ / 4 ) = ( A B B A * ) ,
A = exp ( i π / 4 ) cos 2 ω + exp ( - i π / 4 ) sin 2 ω , B = 2 i sin ω cos ω .
( E x E y ) = J - 1 ( ω , λ / 4 ) ( cos θ sin θ ) ,
J - 1 ( ω , λ / 4 ) = ( A * - B - B A )
k = ( A * cos θ - B sin θ ) / ( A sin θ - B cos θ ) .
k = [ cos 2 ( ω - θ ) sin 2 ω + i sin 2 ( ω - θ ) ] / [ 1 - cos 2 ( ω - θ ) cos 2 ω ] .
M = ( m 11 m 12 m 12 m 11 * ) ,
m 11 = exp ( i δ / 2 ) cos 2 β + exp ( - i δ / 2 ) sin 2 β , m 12 = 2 i sin ( δ / 2 ) sin β cos β ,
( E x E y ) = ( m 11 m 12 m 12 m 11 * ) ( 1 0 ) = ( m 11 m 12 ) .
M = i ( k 2 + 1 ) - 1 / 2 ( k 1 1 - k * ) ,
J = ( 1 0 ) ,
k = [ cos 2 ( ω - θ ) sin 2 ( ω - α ) + i sin 2 ( ω - θ ) ] / [ 1 - cos 2 ( ω - θ ) cos 2 ( ω - α ) ] ,
M α = R ( - α ) MR ( α ) ,
R ( α ) = ( cos α - sin α sin α cos α )
λ 1 = exp ( i ϕ 1 ) , λ 2 = exp ( i ϕ 2 ) ,
δ = ϕ 1 - ϕ 2 .
( cos β sin β )             and             ( - sin β cos β ) .
δ = 2 cos - 1 [ - Im ( k ) / ( k 2 + 1 ) 1 / 2 ] .
β = tan - 1 ( - Re ( k ) + { [ Re ( k ) ] 2 + 1 } 1 / 2 ) .
δ = 2 cos - 1 [ Im ( k ) / ( k 2 + 1 ) 1 / 2 ] ,
β = tan - 1 ( - Re ( k ) + { [ Re ( k ) ] 2 + 1 } 1 / 2 )
k = [ cos 2 ( ω - θ ) sin 2 ( ω - α - ϕ ) + i sin 2 ( ω - θ ) ] / [ 1 - cos 2 ( ω - θ ) cos 2 ( ω - α - θ ) ] ,
k = ( P * - Q sin η ) / ( P - Q cos η ) ,
η = θ - α - ϕ , P = exp ( i γ / 2 ) cos 2 ξ , Q = 2 i sin ( γ / 2 ) sin ξ cos ξ , ξ = ω - α - ϕ .

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