Abstract

A novel technique for extending the unambiguous measurement range for differential measurements of angular deflections is presented. The technique utilizes a common-path interferometer that simultaneously probes the out-of-plane displacement of three points on the object surface. The system is based on a single laser diode, and all the optical functions of the system are implemented in a dedicated holographic optical element (HOE). The HOE automatically provides spatially phase-stepped interference signals for real-time phase measurement. It is therefore not necessary to employ any polarizing optics or active elements to introduce the phase stepping. The common-path scheme combined with the HOE provides a system that is inherently stable, since the HOE operates as both transmitter and receiver in the system. The system is compact, is robust, and has the potential for being mass-produced at a low cost and is thus well suited for industrial use, such as in commercial vibrometers. The technique is demonstrated in a system for measuring angular deflections of a plane mirror. The technique, however, is not restricted to this use alone and can easily be configured to probe other types of surface displacements, e.g., the deflection of a diaphragm. In the present configuration, the system can measure angular deflections with a sensitivity of 2.5 × 10-7 rad over a measurement range that is approximately 3.5 × 10-3 rad, i.e., a dynamic range of approximately 1:14,000. Furthermore, the system can easily be reconfigured for a desired angular sensitivity and measurement range.

© 2003 Optical Society of America

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References

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  1. G. Giuliani, S. Donati, M. Passerini, “Angle measurement by injection detection in a laser diode,” Opt. Eng. 40, 95–99 (2001).
    [CrossRef]
  2. 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]
  3. G. D. Chapman, “Interferometric angular measurement,” Appl. Opt. 13, 1646–1651 (1974).
    [CrossRef] [PubMed]
  4. P. Shi, E. Stijns, “New optical method for measuring small-angle rotations,” Appl. Opt. 27, 4642–4344 (1988).
    [CrossRef]
  5. S. G. Hanson, L. R. Lindvold, B. H. Hansen, “Robust optical systems for nondestructive testing based on laser diodes and diffractive optical elements,” Opt. Lasers Eng. 30, 179–189 (1998).
    [CrossRef]
  6. X. Wang, X. Wang, H. Lu, F. Qian, Y. Bu, “Laser diode interferometer for measuring displacements in large range with nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
    [CrossRef]
  7. T. Suzuki, O. Sasaki, T. Maruyama, “Absolute distance measurement using wavelength multiplexed phase-locked laser diode interferometry,” Opt. Eng. 35, 492–497 (1996).
    [CrossRef]
  8. O. Y. Kwon, D. M. Shough, R. A. Williams, “Stroboscopic phase-shifting interferometry,” Opt. Lett. 12, 855–857 (1987).
    [CrossRef] [PubMed]
  9. M. Deininger, L. Wang, K. Gersner, T. Tschudi, “Optical phase step method for absolute interferometry using computer-generated holograms,” Appl. Opt. 34, 5620–5623 (1995).
    [CrossRef] [PubMed]
  10. N. B. E. Sawyer, C. W. See, M. Clarc, M. G. Somekh, J. Y. Goh, “Ultrastable absolute-phase common-path optical profiler based on computer-generated holography,” Appl. Opt. 37, 6716–6720 (1998).
    [CrossRef]
  11. C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
    [CrossRef] [PubMed]
  12. O. Sasaki, H. Sasazaki, T. Suzuki, “Two-wavelength sinusoidal phase/modulating laser-diode interferometer insensitive to external disturbances,” Appl. Opt. 30, 4040–4045 (1991).
    [CrossRef] [PubMed]
  13. P. de Groot, S. Kishner, “Synthetic wavelength stabilization for two-color laser-diode interferometry,” Appl. Opt. 30, 4026–4033 (1991).
    [CrossRef] [PubMed]
  14. D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  15. J. E. Greivenkamp, “Sub-Nyquist interferometry,” Appl. Opt. 26, 5245–5258 (1987).
    [CrossRef] [PubMed]
  16. J. E. Greivenkamp, A. E. Lowman, R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35, 2962–2969 (1996).
    [CrossRef]
  17. S. R. Kitchen, C. Dam-Hansen, S. G. Hanson, “Optical displacement sensor based on common-path interferometry for industrial purposes,” in Proceedings of the Northern Optics 2000 and EOSAM 2000 Conference, K. Biedermann, U. Olin, eds. (Uppsala, Sweden, 2000), p. 134.
  18. M. D. Giovanni, Flat and Corrugated Diaphragm Design Handbook (Marcel Dekker, 1982), pp. 134–135.
  19. J. N. Latta, “Computer-based analysis of hologram imagery and abberations,” Appl. Opt. 10, 609–618 (1971).
    [CrossRef] [PubMed]
  20. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics XXVI, E. Wolf, ed. (Elsevier Science, 1988), pp. 351–391.
  21. P. L. Wizinowich, “Phase shifting interferometry in the presence of vibration: a new algorithm and system,” Appl. Opt. 29, 3271–3279 (1990).
    [CrossRef] [PubMed]
  22. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Topics in Applied Physics, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), Vol. 9, pp. 9–74.

2001 (2)

X. Wang, X. Wang, H. Lu, F. Qian, Y. Bu, “Laser diode interferometer for measuring displacements in large range with nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

G. Giuliani, S. Donati, M. Passerini, “Angle measurement by injection detection in a laser diode,” Opt. Eng. 40, 95–99 (2001).
[CrossRef]

1998 (2)

S. G. Hanson, L. R. Lindvold, B. H. Hansen, “Robust optical systems for nondestructive testing based on laser diodes and diffractive optical elements,” Opt. Lasers Eng. 30, 179–189 (1998).
[CrossRef]

N. B. E. Sawyer, C. W. See, M. Clarc, M. G. Somekh, J. Y. Goh, “Ultrastable absolute-phase common-path optical profiler based on computer-generated holography,” Appl. Opt. 37, 6716–6720 (1998).
[CrossRef]

1996 (2)

T. Suzuki, O. Sasaki, T. Maruyama, “Absolute distance measurement using wavelength multiplexed phase-locked laser diode interferometry,” Opt. Eng. 35, 492–497 (1996).
[CrossRef]

J. E. Greivenkamp, A. E. Lowman, R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35, 2962–2969 (1996).
[CrossRef]

1995 (1)

1992 (1)

1991 (2)

1990 (1)

1988 (1)

P. Shi, E. Stijns, “New optical method for measuring small-angle rotations,” Appl. Opt. 27, 4642–4344 (1988).
[CrossRef]

1987 (2)

1974 (1)

1973 (1)

1971 (1)

Bu, Y.

X. Wang, X. Wang, H. Lu, F. Qian, Y. Bu, “Laser diode interferometer for measuring displacements in large range with nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

Chapman, G. D.

Clarc, M.

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics XXVI, E. Wolf, ed. (Elsevier Science, 1988), pp. 351–391.

Dam-Hansen, C.

S. R. Kitchen, C. Dam-Hansen, S. G. Hanson, “Optical displacement sensor based on common-path interferometry for industrial purposes,” in Proceedings of the Northern Optics 2000 and EOSAM 2000 Conference, K. Biedermann, U. Olin, eds. (Uppsala, Sweden, 2000), p. 134.

de Groot, P.

Deininger, M.

Donati, S.

G. Giuliani, S. Donati, M. Passerini, “Angle measurement by injection detection in a laser diode,” Opt. Eng. 40, 95–99 (2001).
[CrossRef]

Gersner, K.

Ghiglia, D. C.

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Giovanni, M. D.

M. D. Giovanni, Flat and Corrugated Diaphragm Design Handbook (Marcel Dekker, 1982), pp. 134–135.

Giuliani, G.

G. Giuliani, S. Donati, M. Passerini, “Angle measurement by injection detection in a laser diode,” Opt. Eng. 40, 95–99 (2001).
[CrossRef]

Goh, J. Y.

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Topics in Applied Physics, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), Vol. 9, pp. 9–74.

Greivenkamp, J. E.

J. E. Greivenkamp, A. E. Lowman, R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35, 2962–2969 (1996).
[CrossRef]

J. E. Greivenkamp, “Sub-Nyquist interferometry,” Appl. Opt. 26, 5245–5258 (1987).
[CrossRef] [PubMed]

Hansen, B. H.

S. G. Hanson, L. R. Lindvold, B. H. Hansen, “Robust optical systems for nondestructive testing based on laser diodes and diffractive optical elements,” Opt. Lasers Eng. 30, 179–189 (1998).
[CrossRef]

Hanson, S. G.

S. G. Hanson, L. R. Lindvold, B. H. Hansen, “Robust optical systems for nondestructive testing based on laser diodes and diffractive optical elements,” Opt. Lasers Eng. 30, 179–189 (1998).
[CrossRef]

S. R. Kitchen, C. Dam-Hansen, S. G. Hanson, “Optical displacement sensor based on common-path interferometry for industrial purposes,” in Proceedings of the Northern Optics 2000 and EOSAM 2000 Conference, K. Biedermann, U. Olin, eds. (Uppsala, Sweden, 2000), p. 134.

Huang, P. S.

Kamada, O.

Kishner, S.

Kitchen, S. R.

S. R. Kitchen, C. Dam-Hansen, S. G. Hanson, “Optical displacement sensor based on common-path interferometry for industrial purposes,” in Proceedings of the Northern Optics 2000 and EOSAM 2000 Conference, K. Biedermann, U. Olin, eds. (Uppsala, Sweden, 2000), p. 134.

Kiyono, S.

Kwon, O. Y.

Latta, J. N.

Lindvold, L. R.

S. G. Hanson, L. R. Lindvold, B. H. Hansen, “Robust optical systems for nondestructive testing based on laser diodes and diffractive optical elements,” Opt. Lasers Eng. 30, 179–189 (1998).
[CrossRef]

Lowman, A. E.

J. E. Greivenkamp, A. E. Lowman, R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35, 2962–2969 (1996).
[CrossRef]

Lu, H.

X. Wang, X. Wang, H. Lu, F. Qian, Y. Bu, “Laser diode interferometer for measuring displacements in large range with nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

Maruyama, T.

T. Suzuki, O. Sasaki, T. Maruyama, “Absolute distance measurement using wavelength multiplexed phase-locked laser diode interferometry,” Opt. Eng. 35, 492–497 (1996).
[CrossRef]

Palum, R. J.

J. E. Greivenkamp, A. E. Lowman, R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35, 2962–2969 (1996).
[CrossRef]

Passerini, M.

G. Giuliani, S. Donati, M. Passerini, “Angle measurement by injection detection in a laser diode,” Opt. Eng. 40, 95–99 (2001).
[CrossRef]

Polhemus, C.

Pritt, M. D.

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Qian, F.

X. Wang, X. Wang, H. Lu, F. Qian, Y. Bu, “Laser diode interferometer for measuring displacements in large range with nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

Sasaki, O.

T. Suzuki, O. Sasaki, T. Maruyama, “Absolute distance measurement using wavelength multiplexed phase-locked laser diode interferometry,” Opt. Eng. 35, 492–497 (1996).
[CrossRef]

O. Sasaki, H. Sasazaki, T. Suzuki, “Two-wavelength sinusoidal phase/modulating laser-diode interferometer insensitive to external disturbances,” Appl. Opt. 30, 4040–4045 (1991).
[CrossRef] [PubMed]

Sasazaki, H.

Sawyer, N. B. E.

See, C. W.

Shi, P.

P. Shi, E. Stijns, “New optical method for measuring small-angle rotations,” Appl. Opt. 27, 4642–4344 (1988).
[CrossRef]

Shough, D. M.

Somekh, M. G.

Stijns, E.

P. Shi, E. Stijns, “New optical method for measuring small-angle rotations,” Appl. Opt. 27, 4642–4344 (1988).
[CrossRef]

Suzuki, T.

T. Suzuki, O. Sasaki, T. Maruyama, “Absolute distance measurement using wavelength multiplexed phase-locked laser diode interferometry,” Opt. Eng. 35, 492–497 (1996).
[CrossRef]

O. Sasaki, H. Sasazaki, T. Suzuki, “Two-wavelength sinusoidal phase/modulating laser-diode interferometer insensitive to external disturbances,” Appl. Opt. 30, 4040–4045 (1991).
[CrossRef] [PubMed]

Tschudi, T.

Wang, L.

Wang, X.

X. Wang, X. Wang, H. Lu, F. Qian, Y. Bu, “Laser diode interferometer for measuring displacements in large range with nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

X. Wang, X. Wang, H. Lu, F. Qian, Y. Bu, “Laser diode interferometer for measuring displacements in large range with nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

Williams, R. A.

Wizinowich, P. L.

Appl. Opt. (11)

P. Shi, E. Stijns, “New optical method for measuring small-angle rotations,” Appl. Opt. 27, 4642–4344 (1988).
[CrossRef]

J. N. Latta, “Computer-based analysis of hologram imagery and abberations,” Appl. Opt. 10, 609–618 (1971).
[CrossRef] [PubMed]

G. D. Chapman, “Interferometric angular measurement,” Appl. Opt. 13, 1646–1651 (1974).
[CrossRef] [PubMed]

J. E. Greivenkamp, “Sub-Nyquist interferometry,” Appl. Opt. 26, 5245–5258 (1987).
[CrossRef] [PubMed]

P. L. Wizinowich, “Phase shifting interferometry in the presence of vibration: a new algorithm and system,” Appl. Opt. 29, 3271–3279 (1990).
[CrossRef] [PubMed]

P. de Groot, S. Kishner, “Synthetic wavelength stabilization for two-color laser-diode interferometry,” Appl. Opt. 30, 4026–4033 (1991).
[CrossRef] [PubMed]

O. Sasaki, H. Sasazaki, T. Suzuki, “Two-wavelength sinusoidal phase/modulating laser-diode interferometer insensitive to external disturbances,” Appl. Opt. 30, 4040–4045 (1991).
[CrossRef] [PubMed]

N. B. E. Sawyer, C. W. See, M. Clarc, M. G. Somekh, J. Y. Goh, “Ultrastable absolute-phase common-path optical profiler based on computer-generated holography,” Appl. Opt. 37, 6716–6720 (1998).
[CrossRef]

M. Deininger, L. Wang, K. Gersner, T. Tschudi, “Optical phase step method for absolute interferometry using computer-generated holograms,” Appl. Opt. 34, 5620–5623 (1995).
[CrossRef] [PubMed]

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]

C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
[CrossRef] [PubMed]

Opt. Eng. (3)

T. Suzuki, O. Sasaki, T. Maruyama, “Absolute distance measurement using wavelength multiplexed phase-locked laser diode interferometry,” Opt. Eng. 35, 492–497 (1996).
[CrossRef]

G. Giuliani, S. Donati, M. Passerini, “Angle measurement by injection detection in a laser diode,” Opt. Eng. 40, 95–99 (2001).
[CrossRef]

J. E. Greivenkamp, A. E. Lowman, R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35, 2962–2969 (1996).
[CrossRef]

Opt. Laser Technol. (1)

X. Wang, X. Wang, H. Lu, F. Qian, Y. Bu, “Laser diode interferometer for measuring displacements in large range with nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

Opt. Lasers Eng. (1)

S. G. Hanson, L. R. Lindvold, B. H. Hansen, “Robust optical systems for nondestructive testing based on laser diodes and diffractive optical elements,” Opt. Lasers Eng. 30, 179–189 (1998).
[CrossRef]

Opt. Lett. (1)

Other (5)

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

S. R. Kitchen, C. Dam-Hansen, S. G. Hanson, “Optical displacement sensor based on common-path interferometry for industrial purposes,” in Proceedings of the Northern Optics 2000 and EOSAM 2000 Conference, K. Biedermann, U. Olin, eds. (Uppsala, Sweden, 2000), p. 134.

M. D. Giovanni, Flat and Corrugated Diaphragm Design Handbook (Marcel Dekker, 1982), pp. 134–135.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics XXVI, E. Wolf, ed. (Elsevier Science, 1988), pp. 351–391.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Topics in Applied Physics, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), Vol. 9, pp. 9–74.

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Figures (8)

Fig. 1
Fig. 1

Common-path interferometer implemented to probe the angular displacement of mirrorlike surfaces.

Fig. 2
Fig. 2

Technique applied to probe the deflection of a circular diaphragm.

Fig. 3
Fig. 3

Setup for the common-path interferometer showing (a) the HOE operating as a transmitter in the system and (b) the HOE operating as a receiver in the system.

Fig. 4
Fig. 4

Measurements showing the mean detector output value of the three interference areas that are obtained when the two beams separated by distance d 1 as a function of the object angle are mixed.

Fig. 5
Fig. 5

Interference signals after the effect of the calibration routine.

Fig. 6
Fig. 6

Calculated phase difference between the two interference signals, corresponding to the two interfocal distances d 1 and d 2.

Fig. 7
Fig. 7

Calculated fringe numbers having the desired staircase shape as a function of the object angle.

Fig. 8
Fig. 8

Measured differential tilt angle of the object compared with the angle of the gimbal mirror mount. The gray-tinted inset shows a magnification of a part of the plot.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

S1  cos2πλ z1+ϕk2,
S2  cos2πλ z2+ϕk1,
M=z2z1.
ϕd=2πλ |z2-z1|=2πλ |M-1|z1,
2πΛeff z1=2πλ |M-1|z1,  Λeff=1|M-1| λ.
Λeff=d1|d1-d2| λ.
Λeff=λ1λ2|λ1-λ2|
z=z01-ra22,
z1=z0,
z2=z0-z01-d2d122.
Λeff=11-d2d122 λ
IG1=I01+γ cos ϕ1, IG3=I01+γ cosϕ1+π/2, IG5=I01+γ cosϕ1-π/2,
ϕ1=arctanIG1-IG3IG1+IG3-2I0,
m1=ϕd+2π/N/4mod 2π2π/Nfor 0ϕ1<πϕd-2π/N/4mod 2π2π/Nfor πϕ1<2π,
Δz1=m1+ϕ12πλ2,

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