Abstract

With the use of concepts of elementary physical optics it is shown under what conditions the application of inexact compensators to the analysis of elliptically polarized light is justified. The validity of a procedure used by Vasicek, which has been questioned, is examined in detail.

© 1963 Optical Society of America

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References

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  1. J. R. Partington, An Advanced Treatise on Physical Chemistry (Longman’s Green and Company, Inc., New York, 1953), Vol. IV, pp. 156 et seq.
  2. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), pp. 24 et seq.
  3. Reference 2, p. 689.
  4. A. Vasicek, Czech. J. Phys. 4, 204–220 (1954).
    [Crossref]
  5. Robert C. Plumb, J. Opt. Soc. Am. 50, 892 (1960).
    [Crossref]

1960 (1)

1954 (1)

A. Vasicek, Czech. J. Phys. 4, 204–220 (1954).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), pp. 24 et seq.

Partington, J. R.

J. R. Partington, An Advanced Treatise on Physical Chemistry (Longman’s Green and Company, Inc., New York, 1953), Vol. IV, pp. 156 et seq.

Plumb, Robert C.

Vasicek, A.

A. Vasicek, Czech. J. Phys. 4, 204–220 (1954).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), pp. 24 et seq.

Czech. J. Phys. (1)

A. Vasicek, Czech. J. Phys. 4, 204–220 (1954).
[Crossref]

J. Opt. Soc. Am. (1)

Other (3)

J. R. Partington, An Advanced Treatise on Physical Chemistry (Longman’s Green and Company, Inc., New York, 1953), Vol. IV, pp. 156 et seq.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), pp. 24 et seq.

Reference 2, p. 689.

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Figures (2)

Fig. 1
Fig. 1

An elliptical vibration, Ex = 2 cos(τ + 25°), Ey = 3 cos(τ + 10°).

Fig. 2
Fig. 2

Δ vs ψ for the elliptical vibration of Fig. 1, incident on a birefringent plate.

Equations (26)

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sin 2 ϕ = ± sin 2 γ sin δ ,
tan 2 ψ = tan 2 γ cos δ ,
cos 2 γ = cos 2 ϕ cos 2 ψ ,
tan 2 ϕ = ± sin 2 ψ tan δ .
E x = a 1 cos ( τ + δ 1 ) , E y = a 2 cos ( τ + δ 2 ) .
E f = E x cos ψ + E y sin ψ , E s = E x sin ψ + E y cos ψ .
A = a 1 sin ψ , A = a 2 cos ψ , B = a 1 cos ψ ,
B = a 2 sin ψ ,
E f = B cos ( τ + δ )
E s = A cos ( τ + δ ) ;
B 2 = B 2 + B 2 + 2 B B cos ( δ 1 δ 2 ) , A 2 = A 2 + A 2 2 A A cos ( δ 1 δ 2 ) ,
tan δ = ( B sin δ 1 + B sin δ 2 ) / ( B cos δ 1 + B cos δ 2 ) ,
tan δ = ( A sin δ 2 A sin δ 1 ) / ( A cos δ 2 A cos δ 1 ) .
tan Δ = ( A B + A B ) sin ( δ 2 δ 1 ) / [ A B A B ( A B A B ) cos ( δ 2 δ 1 ) ] .
tan Δ = sin δ / ( cos 2 ψ cos δ cot 2 γ sin 2 ψ ) .
tan 2 ψ = cot 2 γ / cos δ .
cos 2 ψ = [ cos δ sin δ ± ( K tan Δ sin 2 δ ) 1 2 ] / K , sin 2 ψ = [ sin δ cot 2 γ ± ( K tan Δ sin 2 δ ) 1 2 ] / K , ( K = tan Δ cos 2 δ + tan Δ cot 2 2 γ ) ,
tan 2 ψ = tan 2 γ cos δ ,
cot 2 γ sin 2 ψ = cos δ cos 2 ψ .
cos 2 ψ cos δ sin δ sin 2 ψ sin δ cot 2 γ = cos 2 ψ cos δ sin δ + sin 2 ψ sin δ cot 2 γ .
cos 2 ψ cot 2 γ ( K tan Δ sin 2 δ ) 1 2
sin 2 ψ cos δ ( K tan Δ sin 2 δ ) 1 2
cos 2 ψ cos 2 ψ + sin 2 ψ sin 2 ψ = cos 2 ψ cos 2 ψ sin 2 ψ sin 2 ψ = cos 2 ψ ( cos 2 ψ cos 180 sin 2 ψ sin 180 ) + sin 2 ψ ( sin 2 ψ cos 180 ° + cos 2 ψ sin 180 ) = cos 2 ψ cos ( 2 ψ + 180 ) + sin 2 ψ sin ( 2 ψ + 180 ° ) .
cos ( 2 ψ 2 ψ ) = cos [ 2 ψ ( 2 ψ + 180 ° ) ] ,
ψ = ( ψ + ψ 90 ) / 2 .
sin 2 ϕ = sin 2 ϕ sin Δ .