Abstract

Elongated critical-angle prisms that provide multiple reflections have been used to increase measurement sensitivity while retaining excellent linearity in the recently developed angle-measurement method, angle measurement based on the internal-reflection effect.

© 1996 Optical Society of America

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References

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  1. P. S. Huang, S. Kiyono, O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt. 31, 6047–6055 (1992).
  2. P. S. Huang, “Laser optical measurement systems and their application to the on-line error compensation of coordinate measuring machines,” Ph.D. dissertation (The University of Michigan, Ann Arbor, Mich., 1993), pp. 131–135.

1992

Appl. Opt.

Other

P. S. Huang, “Laser optical measurement systems and their application to the on-line error compensation of coordinate measuring machines,” Ph.D. dissertation (The University of Michigan, Ann Arbor, Mich., 1993), pp. 131–135.

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Figures (4)

Fig. 1
Fig. 1

Principle of AMIRE with elongated critical-angle prisms.

Fig. 2
Fig. 2

Nonlinearity error versus the initial angle of incidence for p-polarized light; m is the number of reflections.

Fig. 3
Fig. 3

Linearized reflectance versus the angular displacement for p-polarized light. The initial angles of incidence are at the optimal angles.

Fig. 4
Fig. 4

Calibration result of the prototype sensor.

Equations (7)

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R m = R m .
R l ( Δθ ) = R m ( Δθ ) R m ( Δθ ) R m ( Δθ ) + R m ( Δθ ) = b 1 Δθ + b 3 Δθ 3 + ,
b 1 s = 4 m tan θ t ,
b 1 p = 4 m tan θ t cos ( θ 0 θ t ) cos ( θ 0 + θ t ) ,
θ t = sin 1 ( n i sin θ 0 / n t )
R m ( Δθ ) = R ( Δθ ) R ( Δθ α 1 ) L R [ Δθ ( m 1 ) α 1 ] ,
R m ( Δθ ) = R ( Δθ ) R ( Δθ α 2 ) L R [ Δθ ( m 1 ) α 2 ] ,

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