Abstract

A Michelson interferometer based on an optical set-up allowing multiple reflection between two plane mirrors performs the multiplication of the optical path by a factor N, proportionally increasing the resolution of the measurement. A multiplication factor of almost two orders of magnitude has been demonstrated with a simple set-up. The technique can be applied to any interferometric measurement where the classical interferometer limits due to fringe nonlinearities and quantum noise are an issue. Applications in precision engineering, vibration analysis, nanometrology, and spectroscopy are foreseen.

© 2008 Optical Society of America

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References

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  1. A. A. Michelson and E. W. Morley, "On the Relative Motion of the Earth and the Luminiferous Ether," Am. J. Sci. 34, 333-335 (1887).
  2. M. Tanaka, T. Yamagami, and K. Nakayama, "Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels," IEEE Trans. Instrum. Meas. 38, 552-554 (1989).
    [CrossRef]
  3. P. L. M. Heydemann, "Determination and correction of quadrature fringe measurement errors in interferometers," Appl. Opt. 20, 3382-3384 (1981).
    [CrossRef] [PubMed]
  4. W. How and G. Wilkening, "Investigation and compensation of the nonlinearity of heterodyne interferometers," Prec. Eng. 14,91-98 (1992).
    [CrossRef]
  5. EMRP T3.J1.4.NANOTRACE "New traceability routes for nanometrology," www.emrponline.eu.
  6. M. Pisani and M. Astrua, "Angle apmplification for nanoradian measurements," Appl. Opt. 45, 1725-1729 (2006).
    [CrossRef] [PubMed]

2006 (1)

1992 (1)

W. How and G. Wilkening, "Investigation and compensation of the nonlinearity of heterodyne interferometers," Prec. Eng. 14,91-98 (1992).
[CrossRef]

1989 (1)

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

1981 (1)

1887 (1)

A. A. Michelson and E. W. Morley, "On the Relative Motion of the Earth and the Luminiferous Ether," Am. J. Sci. 34, 333-335 (1887).

Astrua, M.

Heydemann, P. L. M.

How, W.

W. How and G. Wilkening, "Investigation and compensation of the nonlinearity of heterodyne interferometers," Prec. Eng. 14,91-98 (1992).
[CrossRef]

Michelson, A. A.

A. A. Michelson and E. W. Morley, "On the Relative Motion of the Earth and the Luminiferous Ether," Am. J. Sci. 34, 333-335 (1887).

Morley, E. W.

A. A. Michelson and E. W. Morley, "On the Relative Motion of the Earth and the Luminiferous Ether," Am. J. Sci. 34, 333-335 (1887).

Nakayama, K.

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

Pisani, M.

Tanaka, M.

M. Tanaka, T. Yamagami, and 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. How and G. Wilkening, "Investigation and compensation of the nonlinearity of heterodyne interferometers," Prec. Eng. 14,91-98 (1992).
[CrossRef]

Yamagami, T.

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

Am. J. Sci. (1)

A. A. Michelson and E. W. Morley, "On the Relative Motion of the Earth and the Luminiferous Ether," Am. J. Sci. 34, 333-335 (1887).

Appl. Opt. (2)

IEEE Trans. Instrum. Meas. (1)

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

Prec. Eng. (1)

W. How and G. Wilkening, "Investigation and compensation of the nonlinearity of heterodyne interferometers," Prec. Eng. 14,91-98 (1992).
[CrossRef]

Other (1)

EMRP T3.J1.4.NANOTRACE "New traceability routes for nanometrology," www.emrponline.eu.

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Figures (6)

Fig. 1.
Fig. 1.

Simplified schematic of the multireflection heterodyne interferometer (see text for details).

Fig. 2.
Fig. 2.

Picture of the experimental apparatus. In the larger picture mirror A is visible (mounted on the translation stage piled up the rotary table), facing mirror B. The λ/4 plate, the lens and the back of the fixed mirror are visible on the right. The beam is coming from the top right corner. In the frame, a detail of the multireflection pattern is seen from the opposite side.

Fig. 3.
Fig. 3.

Blue squares: gain of the interferometer (ratio between the measured displacement and the true mirror displacement) plotted versus N; red diamonds: ratio between measured gain and theoretical gain (N+1) plotted versus N.

Fig. 4.
Fig. 4.

Evaluation of the errors due to the incidence angle. In the example N=α/β=5. Mirror A is moved in the position A’ with a displacement d. The optical path changes from the black to the red pattern. The optical path increment can be seen as the added parts below initial mirror position, which is larger than d×(N+1) because a 1/cos correction (e.g. the length of the blue segment on the right is d/cos α). To this, because of a shift of the pattern to the left, the green segments must be subtracted. The net effect, that can be calculated and corrected, is a gain G slightly less than N+1.

Fig. 5.
Fig. 5.

Noise spectral density in the acoustic band of the multiple reflection interferometer with G=60 (black) compared with the noise in the G=1 (red) configuration. The reduction of the noise floor is consistent with the gain ratio. See text for the 8 kHz peak.

Fig. 6.
Fig. 6.

Response of the phase-meter to a sinusoidal vibration at 5kHz with 1 nm p.p amplitude. The signal is sampled at 100 ksamples/s, high pass filtered at 1 kHz and lowpass filtered at 50 kHz, without averaging (one shot).

Equations (1)

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Δ φ = Δ l 4 π λ

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