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References

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  1. O. S. Heavens, Optical Properties of Thin Films (Dover, New York, 1965).
  2. D. A. Holmes, “Exact Theory of Retardation Plates,” J. Opt. Soc. Am 54, 1115 (1964).
    [CrossRef]
  3. W. A. Shurcliff, Polarized Light; Production and Use (Harvard U.P.Cambridge, 1962).
  4. G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. Etzel, “Limits to the Precision of Electro-Optic and Magneto-Optic Sensors,” Natl. Bur. Stand. (U.S.) Tech. Note 1307 (1987); G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. EtzelElectric Power Research Institute Report EL 5431, Vol. 1 (1987).

1987 (1)

G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. Etzel, “Limits to the Precision of Electro-Optic and Magneto-Optic Sensors,” Natl. Bur. Stand. (U.S.) Tech. Note 1307 (1987); G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. EtzelElectric Power Research Institute Report EL 5431, Vol. 1 (1987).

1964 (1)

D. A. Holmes, “Exact Theory of Retardation Plates,” J. Opt. Soc. Am 54, 1115 (1964).
[CrossRef]

Conrad, D.

G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. Etzel, “Limits to the Precision of Electro-Optic and Magneto-Optic Sensors,” Natl. Bur. Stand. (U.S.) Tech. Note 1307 (1987); G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. EtzelElectric Power Research Institute Report EL 5431, Vol. 1 (1987).

Day, G. W.

G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. Etzel, “Limits to the Precision of Electro-Optic and Magneto-Optic Sensors,” Natl. Bur. Stand. (U.S.) Tech. Note 1307 (1987); G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. EtzelElectric Power Research Institute Report EL 5431, Vol. 1 (1987).

Deeter, M.

G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. Etzel, “Limits to the Precision of Electro-Optic and Magneto-Optic Sensors,” Natl. Bur. Stand. (U.S.) Tech. Note 1307 (1987); G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. EtzelElectric Power Research Institute Report EL 5431, Vol. 1 (1987).

Etzel, S.

G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. Etzel, “Limits to the Precision of Electro-Optic and Magneto-Optic Sensors,” Natl. Bur. Stand. (U.S.) Tech. Note 1307 (1987); G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. EtzelElectric Power Research Institute Report EL 5431, Vol. 1 (1987).

Hale, P.

G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. Etzel, “Limits to the Precision of Electro-Optic and Magneto-Optic Sensors,” Natl. Bur. Stand. (U.S.) Tech. Note 1307 (1987); G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. EtzelElectric Power Research Institute Report EL 5431, Vol. 1 (1987).

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Films (Dover, New York, 1965).

Holmes, D. A.

D. A. Holmes, “Exact Theory of Retardation Plates,” J. Opt. Soc. Am 54, 1115 (1964).
[CrossRef]

Milner, T.

G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. Etzel, “Limits to the Precision of Electro-Optic and Magneto-Optic Sensors,” Natl. Bur. Stand. (U.S.) Tech. Note 1307 (1987); G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. EtzelElectric Power Research Institute Report EL 5431, Vol. 1 (1987).

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light; Production and Use (Harvard U.P.Cambridge, 1962).

J. Opt. Soc. Am (1)

D. A. Holmes, “Exact Theory of Retardation Plates,” J. Opt. Soc. Am 54, 1115 (1964).
[CrossRef]

Natl. Bur. Stand. (U.S.) Tech. Note (1)

G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. Etzel, “Limits to the Precision of Electro-Optic and Magneto-Optic Sensors,” Natl. Bur. Stand. (U.S.) Tech. Note 1307 (1987); G. W. Day, P. Hale, M. Deeter, T. Milner, D. Conrad, S. EtzelElectric Power Research Institute Report EL 5431, Vol. 1 (1987).

Other (2)

O. S. Heavens, Optical Properties of Thin Films (Dover, New York, 1965).

W. A. Shurcliff, Polarized Light; Production and Use (Harvard U.P.Cambridge, 1962).

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Figures (3)

Fig. 1
Fig. 1

Configurations for analysis of (a) an electrooptic sensor and (b) a magnetooptic sensor.

Fig. 2
Fig. 2

Response functions for either an electrooptic sensor [Rpe as a function of ϕ, Eq. (5a)] or a magnetooptic sensor [Rpm as a function of 2θ, Eq. (11)] for R = 0.1 and three values of 2βh. The curves for 2βh = 2 and (2n + 1)π are limiting cases, representing the maximum and minimum sensitivity, respectively, of the sensor.

Fig. 3
Fig. 3

Computed imprecision resulting from multiple reflections as a function of the reflectance of the surfaces. The relative imprecision is defined as the largest slope near ϕ or 2θ = 0 (i.e., for 2βh = 2) minus the smallest slope [2βh = (2n + 1)π] divided by the sum of the slopes. The lower line shows the improvement obtained by normalizing the slopes to the mean value of the response function.

Equations (18)

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E x 2 E x 1 = t x 2 exp ( - i β x h ) [ 1 + r x 2 exp ( - 2 i β x h ) + r x 4 exp ( - 4 i β x h ) + ] ,
E x 2 E x 1 = t x 2 exp ( i β x h ) - r x 2 exp ( - i β x h ) A x exp ( - i ϕ x ) ,
A x = t x 2 ( 1 + r x 4 - 2 r x 2 cos 2 β x h ) 1 / 2 ,
ϕ x = tan - 1 ( 1 + r x 2 1 - r x 2 tan β x h ) .
E y 2 E y 1 = t y 2 exp ( i β y h ) - r y 2 exp ( - i β y h ) A y exp ( - i ϕ y ) ,
A y = t y 2 ( 1 + r y 4 - 2 r y 2 cos 2 β y h ) 1 / 2 ,
ϕ y = tan - 1 ( 1 + r y 2 1 - r y 2 tan β y h ) .
| E x 3 0 | = 1 / 2 | 1 - 1 - 1 1 | | exp ( + i π / 4 ) 0 0 exp ( - i π / 4 ) | | A x exp ( - i ϕ x ) 0 0 A y exp ( - i ϕ y ) | | E 1 / 2 E 1 / 2 | .
R p c P 2 c P 1 c = E x 3 E x 3 * + E y 3 E y 3 * E 1 2 = ( T 2 / 2 ) [ ( 1 - sin ϕ ) + R 2 ( 1 + sin ϕ ) - 2 R cos 2 β h cos ϕ ] 1 + R 4 + 2 R 2 cos 4 β h - 4 R ( 1 + R 2 ) cos ϕ cos 2 β h + 4 R 2 cos 2 ϕ ,
ϕ = ( β x - β y ) h ,
β = ( β x + β y ) / 2 ,
R p e = ( T 2 / 2 ) ( 1 - sin ϕ - 2 R cos 2 β h cos ϕ ) ( 1 - 4 R cos ϕ cos 2 β h ) .
E x 2 = T [ E x 1 n = 0 r 2 n cos ( 2 n + 1 ) θ exp ( - 2 n i β h ) - E y 1 n = 0 r 2 n sin ( 2 n + 1 ) θ exp ( - 2 n i β h ) ] ,
E x 2 = T [ exp ( 2 i β h ) - R ] cos θ E x 1 - [ exp ( 2 i β h ) + R ] sin θ E y 1 [ exp ( 2 i β h ) + R 2 exp ( - 2 i β h ) - 2 R cos 2 θ ] A M E x 1 + B M E y 1 .
E y 2 = T [ exp ( 2 i β h ) + R ] sin θ E x 1 - [ exp ( 2 i β h ) + R ] cos θ E y 1 [ exp ( 2 i β h ) + R 2 exp ( - 2 i β h ) - 2 R cos 2 θ ] C M E x 1 + D M E y 1 .
| E x 3 E y 3 | = 1 / 2 | 1 1 1 1 | | A M B M C M D M | | 0 E y 1 | ,
R p m ( P 2 m P 1 m ) = E x 3 E x 3 * + E y 3 E y 3 * E y 1 E y 1 * = ( T 2 / 2 ) [ 1 - sin 2 θ + R 2 ( 1 + sin 2 θ ) - 2 R cos 2 β h cos 2 θ ] 1 + R 4 + 2 R 2 cos 4 β h - 4 R ( 1 + R 2 ) cos 2 θ cos 2 β h + 4 R 2 cos 2 2 θ .
R p m = ( T 2 / 2 ) [ 1 - sin 2 θ - 2 R cos 2 β h cos 2 θ ] 1 - 4 R cos 2 θ cos 2 β h .

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