Abstract

To measure small-angle rotations, the two mirrors of a Michelson interferometer are replaced by right-angle prisms. Rotation of the latter shifts the interference pattern. Measurement of that shift gives, after calibration, the rotation. The experimental setup is insensitive to vibrations, provides good linearity between +5° and −5°, and has a resolution of 10−4 deg.

© 1988 Optical Society of America

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References

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  1. G. D. Chapman, “Interferometric Angular Measurement,” Appl. Opt. 13, 1646 (1974).
    [CrossRef] [PubMed]
  2. Hewlett-Packard laser measurement system 5526A.
  3. G. D. Chapman, National Research Council of Canada; private communications.
  4. E. Stijns, “Measuring Small Rotation Rates with a Modified Michelson Interferometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 264 (1986).

1986

E. Stijns, “Measuring Small Rotation Rates with a Modified Michelson Interferometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 264 (1986).

1974

Chapman, G. D.

G. D. Chapman, “Interferometric Angular Measurement,” Appl. Opt. 13, 1646 (1974).
[CrossRef] [PubMed]

G. D. Chapman, National Research Council of Canada; private communications.

Stijns, E.

E. Stijns, “Measuring Small Rotation Rates with a Modified Michelson Interferometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 264 (1986).

Appl. Opt.

Proc. Soc. Photo-Opt. Instrum. Eng.

E. Stijns, “Measuring Small Rotation Rates with a Modified Michelson Interferometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 264 (1986).

Other

Hewlett-Packard laser measurement system 5526A.

G. D. Chapman, National Research Council of Canada; private communications.

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Figures (6)

Fig. 1
Fig. 1

Experimental setup with a single prism.

Fig. 2
Fig. 2

Path of the light ray before and after rotation of the prism; the light ray enters the prism at the axis of rotation.

Fig. 3
Fig. 3

Path of the light ray before and after rotation of the prism; the axis of rotation is displaced in the x direction.

Fig. 4
Fig. 4

Path of the light ray before and after rotation of the prism; the axis of rotation is displaced in the x and y directions.

Fig. 5
Fig. 5

Basic setup with two prisms.

Fig. 6
Fig. 6

Experimental points compared to the theoretical curve.

Equations (9)

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P = [ n ( D o E + E F + F G ) + G M ] ,
P ( θ ) = 2 a n cos α + G M ,
n sin α = sin θ ,
G M = G o M o + sin θ ( 2 a + 2 a tan α - 2 δ ) .
Δ P = P ( θ ) - P ( 0 ) = 2 a n ( cos α - 1 ) + ( 2 a - 2 δ ) sin θ .
Δ P = 2 a n ( cos α - 1 ) + ( 2 a - 2 δ + 2 y tan θ 2 ) sin θ
Δ P ( 2 a - 2 δ ) θ + ( y - a 2 n ) θ 2 .
y = a 2 n .
Δ P = 2 ( 2 a + l ) sin θ .

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