Abstract

Exact equations for the analysis of elliptically polarized light with a nonexact quarter-wave compensator are developed. Procedures are described for calibrating a quarter-wave compensator.

© 1960 Optical Society of America

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References

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  1. H. G. Jerrard, J. Opt. Soc. Am. 38, 35 (1948).
    [Crossref]
  2. M. Richartz and Hsien-Yü Hsü, J. Opt. Soc. Am. 39, 136 (1949).
    [Crossref]
  3. J. R. Partington, An Advanced Treatise on Physical Chemistry (Longman’s Green and Company, Inc., New York, 1953), Vol. IV, p. 156.
  4. A. Vasicek, Czechoslav. J. Phys. 4, 204–220 (1954).
    [Crossref]
  5. J. Strong, Procedures in Experimental Physics (Prentice Hall, Inc., Englewood Cliffs, Princeton, New Jersey, 1938).

1954 (1)

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

1949 (1)

1948 (1)

Hsü, Hsien-Yü

Jerrard, H. G.

Partington, J. R.

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

Richartz, M.

Strong, J.

J. Strong, Procedures in Experimental Physics (Prentice Hall, Inc., Englewood Cliffs, Princeton, New Jersey, 1938).

Vasicek, A.

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

Czechoslav. J. Phys. (1)

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

J. Opt. Soc. Am. (2)

Other (2)

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

J. Strong, Procedures in Experimental Physics (Prentice Hall, Inc., Englewood Cliffs, Princeton, New Jersey, 1938).

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram showing (a) the light to be analyzed (b) an equivalent representation which would be compensated by an exact quarter-wave plate at orientation ϕ′, and (c) an equivalent representation which would be compensated with a wave plate of phase retardation Δ.

Fig. 2
Fig. 2

Approximate determination of phase retardation of a quarter-wave compensator.

Fig. 3
Fig. 3

Calculated phase difference between components of elliptically polarized light as determined using a quarter-wave plate of phase retardation 96°20′ with the exact equations and using the approximation for a 90° quarter-wave plate.

Equations (12)

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cos 2 γ = cos 2 ψ cos 2 ϕ
cos δ tan 2 γ = tan 2 ϕ .
A = A ° sin ( ω t + δ ) A = A ° sin ( ω t ) .
cos 2 ψ = cos 2 ψ cos 2 ( ϕ - ϕ )
cos Δ = tan 2 ( ϕ - ϕ ) / tan 2 ψ .
cos 2 γ = cos 2 ψ cos 2 ϕ ( 1 - cos Δ tan 2 ϕ tan 2 ψ )
cos δ = [ cos 2 ψ cos 2 ϕ ( tan 2 ϕ + cos Δ tan 2 ψ ) ] / sin 2 γ
( A ° ) 2 sin 2 Δ = ( A ) 2 + ( A ) 2 - 2 A A cos Δ .
a / b = ( 1 + cos Δ ) / ( 1 - cos Δ ) .
cos Δ = cos 2 ψ ( 1 ) sin 2 ϕ ( 1 ) - cos 2 ψ ( 2 ) sin 2 ϕ ( 2 ) sin 2 ψ ( 2 ) cos 2 ϕ ( 2 ) - sin 2 ψ ( 1 ) cos 2 ϕ ( 1 )
cos Δ = cos 2 ψ ( 1 ) cos 2 ϕ ( 1 ) - cos 2 ψ ( 2 ) cos 2 ϕ ( 2 ) sin 2 ψ ( 1 ) sin 2 ϕ ( 1 ) - sin 2 ψ ( 2 ) sin 2 ϕ ( 2 ) .
t = ( δ / 2 π ) × [ λ / ( n e - n 0 ) ] .