Abstract

We propose and discuss an optical heterodyne technique to measure the phase retardation of a wave plate. The accuracy of this measurement technique in determining the optical path difference of a quarter-wave plate is of the order of 0.1 nm, thus exceeding the accuracy of other measurement techniques.

© 1988 Optical Society of America

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References

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  1. C. M. McIntyre, S. E. Harris, J. Opt. Soc. Am. 58, 1575 (1968).
    [CrossRef]
  2. H. G. Jerrard, J. Opt. Soc. Am. 44, 634 (1954).
    [CrossRef]
  3. H. G. Berry, G. Gabrielse, A. E. Livingston, Appl. Opt. 16, 3200 (1977).
    [CrossRef] [PubMed]
  4. B. R. Grunstra, H. B. Perkins, Appl. Opt. 5, 585 (1966).
    [CrossRef] [PubMed]
  5. L. Quanting, Optics (Mechanical Industry, China, 1980), p. 217.
  6. H. Yuefeng, Opt. Tech. (China) 2, 2 (1984).

1984

H. Yuefeng, Opt. Tech. (China) 2, 2 (1984).

1977

1968

1966

1954

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the principle of the experiment. Z, Zeeman split He–Ne laser; W, wave plate; P, polarizer, R, photodetector; A, rapid axis; O, oscilloscope, D, direction of the polarizer orientation.

Fig. 2
Fig. 2

Optical heterodyne wave when the angle between the rapid axis of the quarter-wave plate and the X direction is 45°.

Fig. 3
Fig. 3

Optical heterodyne wave when the angle between the rapid axis of the quarter-wave plate and the X direction is 90°.

Fig. 4
Fig. 4

Measurement of the phase retardation of the measured wave plate along the diameter in the X direction.

Fig. 5
Fig. 5

Measurement of the phase retardation of the measured wave plate along the diameter in the Y direction.

Fig. 6
Fig. 6

Comparison of the experimental and theoretical results of the Ic amplitude.

Equations (12)

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E + = 1 2 [ 1 - i ] A exp [ - i ( ω + t + φ 0 + ) ] ,
E - = 1 2 [ 1 i ] A exp [ - i ( ω - t + φ 0 - ) ] ,
P = [ 0 0 0 1 ] .
M ( δ , θ ) = [ cos δ 2 + i sin δ 2 cos 2 θ - i sin δ 2 sin 2 θ - i sin δ 2 sin 2 θ cos δ 2 - i sin δ 2 cos 2 θ ] .
E + ( f + ) = P M ( δ , θ ) E + = ( - i sin δ 2 sin 2 θ - i cos δ 2 - sin δ 2 cos 2 θ ) × 1 2 A exp [ - i ( ω + t + φ 0 + ) ] ,
E - ( f - = P M ( δ , θ ) E - = ( - i sin δ 2 sin 2 θ + i cos δ 2 + sin δ 2 cos 2 θ ) × 1 2 A exp [ - i ( ω - t + φ 0 - ) ] ,
I = E + ( f + ) + E - ( f - ) 2 = A 2 - A 2 sin 2 δ 2 cos ( Δ ω t - 4 θ + φ 0 ) - A 2 cos 2 δ 2 cos ( Δ ω t + φ 0 ) ,
I c = A 2 sin 2 δ 2 cos ( Δ ω t - 4 θ + φ 0 ) - A 2 cos 2 δ 2 cos ( Δ ω t + φ 0 ) .
I c amplitude = d I c d δ | θ = π 4 ( 2 m + 1 ) amplitude · Δ δ = A 2 Δ δ .
Δ δ = Δ I c θ = π 4 ( 2 m + 1 ) amplitude / I c × maximum amplitude .
Δ δ 2 π λ < λ 6000 ,
Δ δ 2 π 360 ° < 0.06 ° .

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