Abstract

We describe an improved interferometer for angle measurement based on the internal reflection effect. The improvement is achieved by eliminating the influence of wave-plate rotation on the measurement. In the proposed angle interferometer the wave plate is fixed and placed between a rhomb assembly and a retroreflector. This scheme not only allows the angle interferometer to keep the optical configuration compact but also doubles the resolution and can measure the pitch and yaw of moving objects. Both a theoretical analysis and an experimental verification have been conducted on the interferometer. The results indicate that the performance of the modified angle interferometer is greatly improved, especially when the rotation angle is large. The nonlinearity error of the measurement equation is also addressed.

© 1999 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).
    [CrossRef] [PubMed]
  2. P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect and the use of right-angle prisms,” Appl. Opt. 34, 4976–4981 (1995).
    [CrossRef] [PubMed]
  3. P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect using elongated critical-angle prisms,” Appl. Opt. 35, 2239–2241 (1996).
    [CrossRef] [PubMed]
  4. M.-H. Chiu, D.-C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
    [CrossRef]
  5. M.-H. Chiu, D.-C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36, 7104–7106 (1997).
    [CrossRef]
  6. W. Zhou, L. Cai, “Interferometer for small-angle measurement based on total internal reflection,” Appl. Opt. 37, 5957–5963 (1998).
    [CrossRef]
  7. Newport Corporation, Optics, (Newport Corporation, Irvine, Calif., 1997).
  8. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 47–50.
  9. R. S. Longhurst, Geometrical and Physical Optics, 2nd ed. (Wiley, New York, 1967).

1998 (1)

1997 (2)

M.-H. Chiu, D.-C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
[CrossRef]

M.-H. Chiu, D.-C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36, 7104–7106 (1997).
[CrossRef]

1996 (1)

1995 (1)

1992 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 47–50.

Cai, L.

Chiu, M.-H.

M.-H. Chiu, D.-C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36, 7104–7106 (1997).
[CrossRef]

M.-H. Chiu, D.-C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
[CrossRef]

Huang, P. S.

Kamada, O.

Kiyono, S.

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics, 2nd ed. (Wiley, New York, 1967).

Ni, J.

Su, D.-C.

M.-H. Chiu, D.-C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
[CrossRef]

M.-H. Chiu, D.-C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36, 7104–7106 (1997).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 47–50.

Zhou, W.

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Figures (13)

Fig. 1
Fig. 1

Prism assembly.

Fig. 2
Fig. 2

Retardance deviation caused by rotation of the wave plate.

Fig. 3
Fig. 3

Improved angle interferometer.

Fig. 4
Fig. 4

Rhomb assembly.

Fig. 5
Fig. 5

Curve of sensitivity k versus rhombic angle α.

Fig. 6
Fig. 6

Curve of sensitivity k versus refractive-index ratio (n/n′).

Fig. 7
Fig. 7

Measurement range θmax versus rhombic angle α.

Fig. 8
Fig. 8

Measurement range θmax versus refractive-index ratio (n/n′).

Fig. 9
Fig. 9

Nonlinearity error versus rotation angle θ.

Fig. 10
Fig. 10

Schematic diagram of the experimental arrangement.

Fig. 11
Fig. 11

Photo of the experimental arrangement.

Fig. 12
Fig. 12

Experimental curve of φ versus θ.

Fig. 13
Fig. 13

Calibration results.

Equations (17)

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θi1=α+sin-1sin θn/n,
θi2=α-sin-1sin θn/n,
φ=φ0+4 tan-1cos θi1n/n2 sin2 θi1-11/2n/nsin2 θi1-4 tan-1cos θi2n/n2 sin2 θi2-11/2n/nsin2 θi2+Δφ,
Δφ=n/n2-cos θn/n2-sin2 θ1/2-sin2 θn/n2-sin2 θ1/2-n-nnt Δff2πλ,
φ=φ0+4 tan-1cos θi1n/n2 sin2 θi1-11/2n/nsin2 θi1-4 tan-1cos θi2n/n2 sin2 θi2-11/2n/nsin2 θi2+n/n2-cos θn/n2-sin2 θ1/2-sin2 θn/n2-sin2 θ1/2-n-nnt Δff2πλ.
Δφθ=Δφ0+Δφ0θ+12! Δφ0θ2+13! Δφ0θ3+,
Δφ0=0,  Δφ0=0,  Δφ0=Δff2πλ t n/n-1n/n,  Δφ0=0.
Δφ=Δff2πλ t n/n-1n/nθ22.
Δφ0.000356θ2.
φ=φ0+4 tan-1cos θi1n/n2 sin2 θi1-11/2n/nsin2 θi1-4 tan-1cos θi2n/n2 sin2 θi2-11/2n/nsin2 θi2.
φθ=φ0+φ0+φ0θ+12! φ0θ2+13! φ0θ3+,
φ0=0,  φ0=-8 sin α2-n/n2+1sin2 α1-n/n2+1sin2 αn/n2 sin2 α-11/2,  φ0=0.
φθφ0+-8 sin α2-n/n2+1sin2 α1-n/n2+1sin2 αn/n2 sin2 α-11/2,  =φ0+kθ,
k=-8 sin α2-n/n2+1sin2 α1-n/n2+1sin2 αn/n2 sin2 α-11/2.
θmax=sin-1n/nsinα-sin-11n/n.
δ=φ0θ33!=-4 n/n12-10n/n10+48n/n8-54n/n6-65n/n4+48n/n2+963n/n2-25/2n/n2-1n/n2 θ3.
δ294θ3.

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