Abstract

We present a contactless optical sensor based on the laser-self-mixing effect for real-time measurement of linear and transverse displacements of a moving stage. The sensor is able to measure linear displacements of up to 400mm along the main optical axis while simultaneously estimating straightness and flatness deviations up to 1mm. The sensor exploits two identical coplanar nonparallel self-mixing interferometers and requires only one reference plane. The reduction in the number of optical elements allowed by the self-mixing configuration and the intrinsic stiffness of the adopted geometry result in a compact, low-cost, and easy-to-align setup.

© 2009 Optical Society of America

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References

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  1. K. C. Fan, C. L. Chu, J. L. Liao, and J. I. Mou, “Development of a high-precision straightness measuring system with DVD pick-up head,” Meas. Sci. Technol. 14, 47-54 (2003).
    [CrossRef]
  2. Q. Feng, B. Zhang, and C. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36, 279-283 (2004).
    [CrossRef]
  3. W. Baldwin, “Interferometer system for measuring straightness and roll,” U.S. patent 3,790,284 (5 February 1974).
  4. S. T. Lin, “A laser interferometer for measuring straightness,” Opt. Laser Technol. 33, 195-199 (2001).
    [CrossRef]
  5. J. Zhang and L. Cai, “Interferometric straightness measurement system using triangular prism,” Opt. Eng. 37, 1785-1789 (1998).
    [CrossRef]
  6. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347-355 (1980).
    [CrossRef]
  7. G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163-1169 (1984).
    [CrossRef]
  8. S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31, 113-119 (1995).
    [CrossRef]

2004 (1)

Q. Feng, B. Zhang, and C. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36, 279-283 (2004).
[CrossRef]

2003 (1)

K. C. Fan, C. L. Chu, J. L. Liao, and J. I. Mou, “Development of a high-precision straightness measuring system with DVD pick-up head,” Meas. Sci. Technol. 14, 47-54 (2003).
[CrossRef]

2001 (1)

S. T. Lin, “A laser interferometer for measuring straightness,” Opt. Laser Technol. 33, 195-199 (2001).
[CrossRef]

1998 (1)

J. Zhang and L. Cai, “Interferometric straightness measurement system using triangular prism,” Opt. Eng. 37, 1785-1789 (1998).
[CrossRef]

1995 (1)

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31, 113-119 (1995).
[CrossRef]

1984 (1)

G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163-1169 (1984).
[CrossRef]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

Acket, G. A.

G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163-1169 (1984).
[CrossRef]

Baldwin, W.

W. Baldwin, “Interferometer system for measuring straightness and roll,” U.S. patent 3,790,284 (5 February 1974).

Cai, L.

J. Zhang and L. Cai, “Interferometric straightness measurement system using triangular prism,” Opt. Eng. 37, 1785-1789 (1998).
[CrossRef]

Chu, C. L.

K. C. Fan, C. L. Chu, J. L. Liao, and J. I. Mou, “Development of a high-precision straightness measuring system with DVD pick-up head,” Meas. Sci. Technol. 14, 47-54 (2003).
[CrossRef]

Den Boef, A. J.

G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163-1169 (1984).
[CrossRef]

Donati, S.

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31, 113-119 (1995).
[CrossRef]

Fan, K. C.

K. C. Fan, C. L. Chu, J. L. Liao, and J. I. Mou, “Development of a high-precision straightness measuring system with DVD pick-up head,” Meas. Sci. Technol. 14, 47-54 (2003).
[CrossRef]

Feng, Q.

Q. Feng, B. Zhang, and C. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36, 279-283 (2004).
[CrossRef]

Giuliani, G.

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31, 113-119 (1995).
[CrossRef]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

Kuang, C.

Q. Feng, B. Zhang, and C. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36, 279-283 (2004).
[CrossRef]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

Lenstra, D.

G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163-1169 (1984).
[CrossRef]

Liao, J. L.

K. C. Fan, C. L. Chu, J. L. Liao, and J. I. Mou, “Development of a high-precision straightness measuring system with DVD pick-up head,” Meas. Sci. Technol. 14, 47-54 (2003).
[CrossRef]

Lin, S. T.

S. T. Lin, “A laser interferometer for measuring straightness,” Opt. Laser Technol. 33, 195-199 (2001).
[CrossRef]

Merlo, S.

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31, 113-119 (1995).
[CrossRef]

Mou, J. I.

K. C. Fan, C. L. Chu, J. L. Liao, and J. I. Mou, “Development of a high-precision straightness measuring system with DVD pick-up head,” Meas. Sci. Technol. 14, 47-54 (2003).
[CrossRef]

Verbeek, B. H.

G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163-1169 (1984).
[CrossRef]

Zhang, B.

Q. Feng, B. Zhang, and C. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36, 279-283 (2004).
[CrossRef]

Zhang, J.

J. Zhang and L. Cai, “Interferometric straightness measurement system using triangular prism,” Opt. Eng. 37, 1785-1789 (1998).
[CrossRef]

IEEE J. Quantum Electron. (3)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163-1169 (1984).
[CrossRef]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31, 113-119 (1995).
[CrossRef]

Meas. Sci. Technol. (1)

K. C. Fan, C. L. Chu, J. L. Liao, and J. I. Mou, “Development of a high-precision straightness measuring system with DVD pick-up head,” Meas. Sci. Technol. 14, 47-54 (2003).
[CrossRef]

Opt. Eng. (1)

J. Zhang and L. Cai, “Interferometric straightness measurement system using triangular prism,” Opt. Eng. 37, 1785-1789 (1998).
[CrossRef]

Opt. Laser Technol. (2)

S. T. Lin, “A laser interferometer for measuring straightness,” Opt. Laser Technol. 33, 195-199 (2001).
[CrossRef]

Q. Feng, B. Zhang, and C. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36, 279-283 (2004).
[CrossRef]

Other (1)

W. Baldwin, “Interferometer system for measuring straightness and roll,” U.S. patent 3,790,284 (5 February 1974).

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Figures (6)

Fig. 1
Fig. 1

Schematic geometry of the self-mixing interferometers ( SMI i ) for the (a) straightness and (b) flatness measurements. Each interferometer is made by a laser diode L i , a converging lens F i , and a plane mirror M i as target. The monitor photodiode, placed at the rear facet of each laser inside the laser package, is not shown.

Fig. 2
Fig. 2

(a) Ray-tracing analysis of the SMI with a divergent laser beam, where the peripheral rays are reflected outside of the laser whereas the rays orthogonal to the target reenter the laser. (b) Linear displacement Δ x measured by two lasers: L tilt tilted by an angle φ and L aligned well aligned to the x axis; the orthogonal beam is the same in both the cases. (c) Misalignment ϑ of the target with respect to the optical axis; only the incident rays orthogonal to the target reenter into the laser. (d) Misalignment δ of the axis of the translation motion with respect to the x axis.

Fig. 3
Fig. 3

Schematics of the setup for a linear/transverse measuring system.

Fig. 4
Fig. 4

(a) Target displacement Δ x measured by the linear stage interferometer SMI 1 ; (b) and (c) transverse target displacement Δ y ( Δ z ) along the y and z axes, measured at two distances from the laser sources, 20 (squares) and 120 cm (crosses), as a function of the reference displacements. The error bars are always smaller than the symbol size.

Fig. 5
Fig. 5

Experimental (circles) and theoretical (solid curve) straightness resolution versus the tilt angle of SMI 2 .

Fig. 6
Fig. 6

Simultaneous measurement of two degrees of freedom as a function of the reference displacement Δ x ref : (a) linear displacement Δ x (black squares) and straightness Δ y (open circles), (b) linear displacement Δ x (black squares) and flatness Δ z (open circles). The error bars correspond to the calculated accuracy for a dis placement Δ y , Δ z = 0.5 mm .

Equations (4)

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{ Δ x = Δ l 2 / cos ( α ) = N 2 · λ 2 2 / cos ( α ) if Δ Y = 0 , Δ y = Δ l 2 / sen ( α ) = N 2 · λ 2 2 / sen ( α ) if Δ X = 0.
{ Δ x = Δ l 1 , Δ y = Δ l 2 / sin ( α ) Δ x / tan ( α )
{ Δ x = N 1 · λ 1 2 , Δ y = N 2 · λ 2 2 · sin ( α ) N 1 · λ 1 2 · tan ( α ) .
{ σ Δ x = ( Δ l i ( N , λ ) N ) 2 σ N 2 = λ 2 σ N , σ Δ y = ( Δ y ( N , λ , α ) N ) 2 σ N 2 + ( Δ y ( N , λ , α ) α ) 2 σ α 2 1 2 ( λ α ) 2 σ N 2 + ( Δ y α ) 2 σ α 2 ,

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