Abstract

A new interferometric device for measuring small angles or rotations with high accuracy is described. This instrument works by counting fringes formed by the rotation of a flat-parallel plate of glass illuminated with a collimated beam from a gas laser. Some possible applications are given.

© 1970 Optical Society of America

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References

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  1. R. D. Geiser, in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic Press, Inc., New York, 1965), Vol. 1, p. 399.
  2. F. W. Twyman, Prism and Lens Making (Hilger and Watts, Ltd., London, 1957) p. 422.
  3. R. Hoffman, L. Gross, J. Opt. Soc. Amer. 59, 507 (1969).
  4. J. Rholin, Appl. Opt. 2, 762 (1963).
    [CrossRef]
  5. M. V. R. K. Murty, Appl. Opt. 3, 531 (1964).
    [CrossRef]
  6. D. Malacara, “Testing of Optical Surfaces,” (Ph.D. Thesis, Univ. of Rochester, 1965) p. 20.
  7. F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill Book Co., Inc., New York, 1957), p. 206.

1969 (1)

R. Hoffman, L. Gross, J. Opt. Soc. Amer. 59, 507 (1969).

1964 (1)

1963 (1)

Geiser, R. D.

R. D. Geiser, in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic Press, Inc., New York, 1965), Vol. 1, p. 399.

Gross, L.

R. Hoffman, L. Gross, J. Opt. Soc. Amer. 59, 507 (1969).

Hoffman, R.

R. Hoffman, L. Gross, J. Opt. Soc. Amer. 59, 507 (1969).

Jenkins, F.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill Book Co., Inc., New York, 1957), p. 206.

Malacara, D.

D. Malacara, “Testing of Optical Surfaces,” (Ph.D. Thesis, Univ. of Rochester, 1965) p. 20.

Murty, M. V. R. K.

Rholin, J.

Twyman, F. W.

F. W. Twyman, Prism and Lens Making (Hilger and Watts, Ltd., London, 1957) p. 422.

White, H.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill Book Co., Inc., New York, 1957), p. 206.

Appl. Opt. (2)

J. Opt. Soc. Amer. (1)

R. Hoffman, L. Gross, J. Opt. Soc. Amer. 59, 507 (1969).

Other (4)

R. D. Geiser, in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic Press, Inc., New York, 1965), Vol. 1, p. 399.

F. W. Twyman, Prism and Lens Making (Hilger and Watts, Ltd., London, 1957) p. 422.

D. Malacara, “Testing of Optical Surfaces,” (Ph.D. Thesis, Univ. of Rochester, 1965) p. 20.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill Book Co., Inc., New York, 1957), p. 206.

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Figures (6)

Fig. 1
Fig. 1

Flat-parallel plate of glass.

Fig. 2
Fig. 2

Angle of rotation vs m/t for e1 = 0.

Fig. 3
Fig. 3

Optimum angle θ1 vs measured angle (θ2θ1).

Fig. 4
Fig. 4

m/t vs angle to be measured (θ2θ1).

Fig. 5
Fig. 5

Sensitivities vs angle to be measured (θ2θ1).

Fig. 6
Fig. 6

Error in the angle to be measured for a given change in the index of refraction (ΔN = 0.001).

Tables (1)

Tables Icon

Table I Maximum Error at Several Angles for a Plate 30 mm Thick

Equations (22)

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OPD = 2 N t cos θ ,
OPD 1 OPD 2 = 2 N t ( cos θ 1 cos θ 2 ) .
OPD 1 OPD 2 = m λ ,
m / t = ( 2 / λ ) [ ( N 2 sin 2 θ 1 ) 1 2 ( N 2 sin 2 θ 2 ) 1 2 ] .
m / t = ( 2 / λ ) [ N ( N 2 sin 2 θ 2 ) 1 2 ] .
( θ 2 θ 1 ) / θ 1 = 0
θ 2 / θ 1 = 1.
sin θ 1 cos θ 1 / ( N 2 sin 2 θ 1 ) 1 2 = sin θ 2 cos θ 2 / ( N 2 sin 2 θ 2 ) 1 2 ;
G ( θ ) = sin θ cos θ / ( N 2 sin 2 θ ) 1 2 ,
sin 2 θ = 1 2 ( 1 + G 2 ) ± [ 1 4 ( 1 + G 2 ) 2 G 2 N 2 ] 1 2 .
| G ( θ ) | N [ N 2 1 ] 1 2 .
sin θ m = [ N 2 N ( N 2 1 ) 1 2 ] 1 2 .
θ 1 = ( 1 θ 2 θ 1 / 90 ° ) sin 1 [ N 2 N ( N 2 1 ) 1 2 ] 1 2 .
m / t = ( 2 / λ ) [ N ( N 2 1 ) 1 2 ] .
m / t = ( 2 / λ ) [ N ( N 2 1 ) 1 2 ] sin ( θ 2 θ 1 ) ,
S / l = ( π / 180 ° ) ( 1 / t ) ( m / θ 2 ) .
S / t = ( π / 90 ° λ ) sin θ 2 cos θ 2 / ( N 2 sin 2 θ 2 ) 1 2 .
( θ 1 θ 2 ) / 2 ( see Fig . 3 ) .
0 = N ( N 2 sin 2 θ 1 ) 1 2 N ( N 2 sin 2 θ 2 ) 1 2 + sin θ 2 cos θ 2 ( N 2 sin 2 ν 2 ) 1 2 θ 2 N
( θ 2 θ 1 ) / N = θ 2 / N = N [ ( sin θ 2 cos θ 2 ) 1 ( sin θ 1 cos θ 1 ) 1 ] .
Δ ( θ 2 θ 1 ) = ( 180 ° N / π ) [ ( sin θ 2 cos θ 2 ) 1 ( sin θ 1 cos ρ 1 ) 1 ] Δ N .
f = m / t = ( s / 60 ) Δ ( θ 2 θ 1 ) / Δ t = s ω ,

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