Abstract

A generalized laser interferometer system based on three design principles, i.e., heterodyne frequency, prevention of mixing, and perfect symmetry, is described. These design principles give rise to an interferometer in a highly stable system with no periodic nonlinearity. A novel straightness sensor, consisting of a straightness prism and a straightness reflector, is incorporated into the generalized system to form a straightness interferometer. A Hewlett-Packard commercial linear interferometer was used to validate the interferometer’s parameters. Based on the present design, the interferometer has a gain of 0.348, a periodic nonlinearity of less than 40 pm, and a displacement noise of 12 pm/Hz at a bandwidth of 7.8 kHz. This system is useful for precision straightness measurements.

© 2004 Optical Society of America

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References

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  1. R. R. Baldwin, “Interferometer system for measuring straightness and roll,” U.S. patent3,790,284 (5February1974).
  2. G. E. Sommargren, P. S. Yang, “Straightness of travel interferometer,” U.S. patent4,787,747 (29November1988).
  3. W. Hou, G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14, 91–98 (1992).
    [CrossRef]
  4. C. M. Wu, C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
    [CrossRef]
  5. C. M. Wu, R. D. Deslattes, “Analytical modeling of the periodic nonlinearity in heterodyne interferometry,” Appl. Opt. 37, 6696–6700 (1998).
    [CrossRef]
  6. C. M. Wu, “Periodic nonlinearity resulting from ghost reflections in heterodyne interferometry,” Opt. Commun. 215, 17–23 (2003).
    [CrossRef]
  7. Y. Gursel, “Laser metrology gauges for OSI,” in Spaceborne Interferometry, R. D. Reasenberg, ed., Proc. SPIE1947, 188–197 (1993).
    [CrossRef]
  8. M. Tanaka, T. Yamagami, K. Nakayama, “Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels,” IEEE Trans. Instrum. Meas. 38, 552–554 (1989).
    [CrossRef]
  9. C. M. Wu, S. T. Lin, J. Fu, “Heterodyne interferometer with two spatial-separated polarization beams for nanometrology,” Opt. Quantum Electron. 34, 1267–1276 (2002).
    [CrossRef]
  10. R. C. Quenelle, “Nonlinearity in interferometer measurements,” Hewlett Packard J. 34, 10–10 (1983).
  11. C. M. Sutton, “Nonlinearity in length measurements using heterodyne laser Michelson interferometry,” J. Phys. E 20, 1290–1292 (1987).
    [CrossRef]

2003 (1)

C. M. Wu, “Periodic nonlinearity resulting from ghost reflections in heterodyne interferometry,” Opt. Commun. 215, 17–23 (2003).
[CrossRef]

2002 (1)

C. M. Wu, S. T. Lin, J. Fu, “Heterodyne interferometer with two spatial-separated polarization beams for nanometrology,” Opt. Quantum Electron. 34, 1267–1276 (2002).
[CrossRef]

1998 (1)

1996 (1)

C. M. Wu, C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
[CrossRef]

1992 (1)

W. Hou, G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14, 91–98 (1992).
[CrossRef]

1989 (1)

M. Tanaka, T. Yamagami, K. Nakayama, “Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels,” IEEE Trans. Instrum. Meas. 38, 552–554 (1989).
[CrossRef]

1987 (1)

C. M. Sutton, “Nonlinearity in length measurements using heterodyne laser Michelson interferometry,” J. Phys. E 20, 1290–1292 (1987).
[CrossRef]

1983 (1)

R. C. Quenelle, “Nonlinearity in interferometer measurements,” Hewlett Packard J. 34, 10–10 (1983).

Baldwin, R. R.

R. R. Baldwin, “Interferometer system for measuring straightness and roll,” U.S. patent3,790,284 (5February1974).

Deslattes, R. D.

Fu, J.

C. M. Wu, S. T. Lin, J. Fu, “Heterodyne interferometer with two spatial-separated polarization beams for nanometrology,” Opt. Quantum Electron. 34, 1267–1276 (2002).
[CrossRef]

Gursel, Y.

Y. Gursel, “Laser metrology gauges for OSI,” in Spaceborne Interferometry, R. D. Reasenberg, ed., Proc. SPIE1947, 188–197 (1993).
[CrossRef]

Hou, W.

W. Hou, G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14, 91–98 (1992).
[CrossRef]

Lin, S. T.

C. M. Wu, S. T. Lin, J. Fu, “Heterodyne interferometer with two spatial-separated polarization beams for nanometrology,” Opt. Quantum Electron. 34, 1267–1276 (2002).
[CrossRef]

Nakayama, K.

M. Tanaka, T. Yamagami, K. Nakayama, “Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels,” IEEE Trans. Instrum. Meas. 38, 552–554 (1989).
[CrossRef]

Quenelle, R. C.

R. C. Quenelle, “Nonlinearity in interferometer measurements,” Hewlett Packard J. 34, 10–10 (1983).

Sommargren, G. E.

G. E. Sommargren, P. S. Yang, “Straightness of travel interferometer,” U.S. patent4,787,747 (29November1988).

Su, C. S.

C. M. Wu, C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
[CrossRef]

Sutton, C. M.

C. M. Sutton, “Nonlinearity in length measurements using heterodyne laser Michelson interferometry,” J. Phys. E 20, 1290–1292 (1987).
[CrossRef]

Tanaka, M.

M. Tanaka, T. Yamagami, K. Nakayama, “Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels,” IEEE Trans. Instrum. Meas. 38, 552–554 (1989).
[CrossRef]

Wilkening, G.

W. Hou, G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14, 91–98 (1992).
[CrossRef]

Wu, C. M.

C. M. Wu, “Periodic nonlinearity resulting from ghost reflections in heterodyne interferometry,” Opt. Commun. 215, 17–23 (2003).
[CrossRef]

C. M. Wu, S. T. Lin, J. Fu, “Heterodyne interferometer with two spatial-separated polarization beams for nanometrology,” Opt. Quantum Electron. 34, 1267–1276 (2002).
[CrossRef]

C. M. Wu, R. D. Deslattes, “Analytical modeling of the periodic nonlinearity in heterodyne interferometry,” Appl. Opt. 37, 6696–6700 (1998).
[CrossRef]

C. M. Wu, C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
[CrossRef]

Yamagami, T.

M. Tanaka, T. Yamagami, K. Nakayama, “Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels,” IEEE Trans. Instrum. Meas. 38, 552–554 (1989).
[CrossRef]

Yang, P. S.

G. E. Sommargren, P. S. Yang, “Straightness of travel interferometer,” U.S. patent4,787,747 (29November1988).

Appl. Opt. (1)

Hewlett Packard J. (1)

R. C. Quenelle, “Nonlinearity in interferometer measurements,” Hewlett Packard J. 34, 10–10 (1983).

IEEE Trans. Instrum. Meas. (1)

M. Tanaka, T. Yamagami, K. Nakayama, “Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels,” IEEE Trans. Instrum. Meas. 38, 552–554 (1989).
[CrossRef]

J. Phys. E (1)

C. M. Sutton, “Nonlinearity in length measurements using heterodyne laser Michelson interferometry,” J. Phys. E 20, 1290–1292 (1987).
[CrossRef]

Meas. Sci. Technol. (1)

C. M. Wu, C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
[CrossRef]

Opt. Commun. (1)

C. M. Wu, “Periodic nonlinearity resulting from ghost reflections in heterodyne interferometry,” Opt. Commun. 215, 17–23 (2003).
[CrossRef]

Opt. Quantum Electron. (1)

C. M. Wu, S. T. Lin, J. Fu, “Heterodyne interferometer with two spatial-separated polarization beams for nanometrology,” Opt. Quantum Electron. 34, 1267–1276 (2002).
[CrossRef]

Precis. Eng. (1)

W. Hou, G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14, 91–98 (1992).
[CrossRef]

Other (3)

Y. Gursel, “Laser metrology gauges for OSI,” in Spaceborne Interferometry, R. D. Reasenberg, ed., Proc. SPIE1947, 188–197 (1993).
[CrossRef]

R. R. Baldwin, “Interferometer system for measuring straightness and roll,” U.S. patent3,790,284 (5February1974).

G. E. Sommargren, P. S. Yang, “Straightness of travel interferometer,” U.S. patent4,787,747 (29November1988).

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Figures (6)

Fig. 1
Fig. 1

Generalized configuration for interferometers based on three design principles: heterodyne frequency, avoidance of frequency and polarization mixing, and the design of perfect symmetry: He–Ne, stabilized He–Ne laser; FSU, frequency shift unit; f 1, measurement beam with TM polarization at frequency f 1; f2, reference beam with TE polarization at frequency f 2; BDs, beam dividers; BS, beam splitter; PBS, polarizing beam splitter; QWP, quarter-wave plate; PhDs, photodetectors; PM, phasemeter.

Fig. 2
Fig. 2

Straightness sensor and paths of the submeasurement beams.

Fig. 3
Fig. 3

Gain of the straightness sensor. The optical path-length difference between the straightness prism and the straightness reflector for one submeasurement beam illustrated as a straightness prism with straightness Δx. The gain was obtained by division of the optical path-length difference by the straightness.

Fig. 4
Fig. 4

Experimental setup for verifying the validity of the straightness interferometer. A moving stage upon which a straightness prism is clamped driven by a piezoelectric element (not shown) with a maximum stroke of 15 μm in the x axis, is used to simulate the transverse displacement for the straightness interferometer, which is simultaneously measured by a commercial linear interferometer (HP 5528). The two measurement axes, one for each interferometer, are orthogonal, such that the transverse displacement for the straightness interferometer becomes the linear displacement for the linear interferometer: BS, beam splitter; PBS, polarizing beam splitter; PhDs, photodetectors; QWP, quarter-wave plate.

Fig. 5
Fig. 5

Results of the experiments shown in Fig. 4. Gain G is obtained by division of the transverse displacement measured by the straightness interferometer by the linear displacement measured by the linear interferometer.

Fig. 6
Fig. 6

Typical straightness error of a moving stage measured by the developed straightness interferometer.

Equations (5)

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

n2b-n1d,
b=Δx tan θ,
d=b cos α=Δx tan θ cos α.
G=n2b-n1dΔx=tan θ(n2-n1 cos α).
|ds|=λ4πdRR.

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