Abstract

We describe a simple heterodyne laser interferometer that has subnanometer periodic errors and is applicable to industrial fields. Two spatially separated beams can reduce the periodic errors, and the use of a right-angle prism makes the optical configuration much simpler than previous interferometers. Moreover, the optical resolution can be enhanced by a factor of 2, because the phase change direction is opposite between reference and measurement signals. Experiments have demonstrated the periodic errors are less than 0.15nm owing to the frequency mixing of the optical source. The improvements for reducing the frequency mixing of the optical system are also discussed.

© 2009 Optical Society of America

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References

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  1. N. Bobroff, Meas. Sci. Technol. 4, 907 (1993).
    [CrossRef]
  2. R. C. Quenelle, Hewlett-Packard J. 34, 10 (1983).
  3. W. Hou and G. Wilkening, Precis. Eng. 14, 91 (1992).
    [CrossRef]
  4. T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, Meas. Sci. Technol. 13, 222 (2002).
    [CrossRef]
  5. S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 26, 448 (2002).
    [CrossRef]
  6. T. L. Schmitz, D. Chu, and L. Hoouck III, Meas. Sci. Technol. 17, 3195 (2006).
    [CrossRef]
  7. C. Wu, J. Lawall, and R. D. Deslattes, Appl. Opt. 38, 4089 (1999).
    [CrossRef]
  8. T. L. Schmitz and J. F. Beckwith, J. Mod. Opt. 49, 2105 (2002).
    [CrossRef]
  9. J. Lawall and E. Kessler, Rev. Sci. Instrum. 71, 2669 (2000).
    [CrossRef]
  10. J. Lawall and J. M. Pedulla, Rev. Sci. Instrum. 72, 2879 (2001).
    [CrossRef]

2006

T. L. Schmitz, D. Chu, and L. Hoouck III, Meas. Sci. Technol. 17, 3195 (2006).
[CrossRef]

2002

T. L. Schmitz and J. F. Beckwith, J. Mod. Opt. 49, 2105 (2002).
[CrossRef]

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, Meas. Sci. Technol. 13, 222 (2002).
[CrossRef]

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 26, 448 (2002).
[CrossRef]

2001

J. Lawall and J. M. Pedulla, Rev. Sci. Instrum. 72, 2879 (2001).
[CrossRef]

2000

J. Lawall and E. Kessler, Rev. Sci. Instrum. 71, 2669 (2000).
[CrossRef]

1999

1993

N. Bobroff, Meas. Sci. Technol. 4, 907 (1993).
[CrossRef]

1992

W. Hou and G. Wilkening, Precis. Eng. 14, 91 (1992).
[CrossRef]

1983

R. C. Quenelle, Hewlett-Packard J. 34, 10 (1983).

Beckwith, J. F.

T. L. Schmitz and J. F. Beckwith, J. Mod. Opt. 49, 2105 (2002).
[CrossRef]

Bobroff, N.

N. Bobroff, Meas. Sci. Technol. 4, 907 (1993).
[CrossRef]

Choi, H.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, Meas. Sci. Technol. 13, 222 (2002).
[CrossRef]

Choi, T.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, Meas. Sci. Technol. 13, 222 (2002).
[CrossRef]

Chu, D.

T. L. Schmitz, D. Chu, and L. Hoouck III, Meas. Sci. Technol. 17, 3195 (2006).
[CrossRef]

Cosijns, S. J. A. G.

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 26, 448 (2002).
[CrossRef]

Deslattes, R. D.

Eom, T.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, Meas. Sci. Technol. 13, 222 (2002).
[CrossRef]

Haitjema, H.

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 26, 448 (2002).
[CrossRef]

Hoouck, L.

T. L. Schmitz, D. Chu, and L. Hoouck III, Meas. Sci. Technol. 17, 3195 (2006).
[CrossRef]

Hou, W.

W. Hou and G. Wilkening, Precis. Eng. 14, 91 (1992).
[CrossRef]

Kessler, E.

J. Lawall and E. Kessler, Rev. Sci. Instrum. 71, 2669 (2000).
[CrossRef]

Lawall, J.

J. Lawall and J. M. Pedulla, Rev. Sci. Instrum. 72, 2879 (2001).
[CrossRef]

J. Lawall and E. Kessler, Rev. Sci. Instrum. 71, 2669 (2000).
[CrossRef]

C. Wu, J. Lawall, and R. D. Deslattes, Appl. Opt. 38, 4089 (1999).
[CrossRef]

Lee, K.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, Meas. Sci. Technol. 13, 222 (2002).
[CrossRef]

Lee, S.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, Meas. Sci. Technol. 13, 222 (2002).
[CrossRef]

Pedulla, J. M.

J. Lawall and J. M. Pedulla, Rev. Sci. Instrum. 72, 2879 (2001).
[CrossRef]

Quenelle, R. C.

R. C. Quenelle, Hewlett-Packard J. 34, 10 (1983).

Schellekens, P. H. J.

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 26, 448 (2002).
[CrossRef]

Schmitz, T. L.

T. L. Schmitz, D. Chu, and L. Hoouck III, Meas. Sci. Technol. 17, 3195 (2006).
[CrossRef]

T. L. Schmitz and J. F. Beckwith, J. Mod. Opt. 49, 2105 (2002).
[CrossRef]

Wilkening, G.

W. Hou and G. Wilkening, Precis. Eng. 14, 91 (1992).
[CrossRef]

Wu, C.

Appl. Opt.

Hewlett-Packard J.

R. C. Quenelle, Hewlett-Packard J. 34, 10 (1983).

J. Mod. Opt.

T. L. Schmitz and J. F. Beckwith, J. Mod. Opt. 49, 2105 (2002).
[CrossRef]

Meas. Sci. Technol.

N. Bobroff, Meas. Sci. Technol. 4, 907 (1993).
[CrossRef]

T. L. Schmitz, D. Chu, and L. Hoouck III, Meas. Sci. Technol. 17, 3195 (2006).
[CrossRef]

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, Meas. Sci. Technol. 13, 222 (2002).
[CrossRef]

Precis. Eng.

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 26, 448 (2002).
[CrossRef]

W. Hou and G. Wilkening, Precis. Eng. 14, 91 (1992).
[CrossRef]

Rev. Sci. Instrum.

J. Lawall and E. Kessler, Rev. Sci. Instrum. 71, 2669 (2000).
[CrossRef]

J. Lawall and J. M. Pedulla, Rev. Sci. Instrum. 72, 2879 (2001).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Proposed optical configuration of a heterodyne laser interferometer to reduce the periodic errors. NPBS, nonpolarizing beam splitter; PD 1 , PD 2 , photodetectors.

Fig. 2
Fig. 2

Experimental setup. AOFS, acousto-optic frequency shifter; M 0 , M 1 , M 2 , M 3 , angle-adjusted mirrors; NPBS, nonpolarizing beam splitter; RAP, right-angle prism; RR, retroreflector; PD R , PD M , reference and measurement photodetectors; PBS, polarizing beam splitter; P, polarizer. The inlet is the configuration of the optical source with two spatially separated beams on the side view. Note that the solid line is the spatially upper beam, and the dotted line is the lower beam.

Fig. 3
Fig. 3

Experimental result of the periodic error from the phase quadrature measurement method and (b) Fourier transformed result of the periodic errors (a). The main error is caused by the frequency mixing of the optical source and other noises are from ghost reflections and electronics.

Fig. 4
Fig. 4

Proposed optical source to obtain a frequency-stabilized laser with two parallel beams to reduce frequency mixing. PBS, polarizing beam splitter; AOFS, acousto-optic frequency shifter; QWP, quarter-wave plate; M, mirror; AFC, angled fiber coupler; PD, photodetector.

Equations (4)

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E 1 = exp [ j ( 2 π f 2 t ) ] + ε 1 exp [ j ( 2 π f 1 t ) ] ,
E 2 = exp [ j ( 2 π ( f 1 + δ f ) t ) ] + ε 1 exp [ j ( 2 π ( f 2 + δ f ) t ) ] + ε 2 exp [ j ( 2 π f 1 t ) ] + ε 1 ε 2 exp [ j ( 2 π f 2 t ) ] ,
d ϕ = 2 ε 1 ε 2 sin ( 2 k Δ L ) ,
d R R = 2 ε 1 ε 2 cos ( 2 k Δ L ) .

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