Abstract

A high resolution heterodyne laser interferometer without periodic nonlinearity for linear displacement measurements is described. It uses two spatially separated beams with an offset frequency and an interferometer configuration which has no mixed states to prevent polarization mixing. In this research, a simple interferometer configuration for both retroreflector and plane mirror targets which are both applicable to industrial applications was developed. Experimental results show there is no detectable periodic nonlinearity for both of the retro-reflector interferometer and plane mirror interferometer to the noise level of 20 pm. Additionally, the optical configuration has the benefit of doubling the measurement resolution when compared to its respective traditional counterparts. Because of non-symmetry in the plane mirror interferometer, a differential plane mirror interferometer to reduce the thermal error is also discussed.

© 2010 OSA

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  1. W. T. Estler, “High-accuracy displacement interferometry in air,” Appl. Opt. 24(6), 808–815 (1985).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
    [CrossRef]
  4. F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
    [CrossRef]
  5. R. C. Quenelle, “Nonlinearity in interferometer measurements,” Hewlett Packard J. 34, 10 (1983).
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    [CrossRef]
  7. S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng. 26(4), 448–455 (2002).
    [CrossRef]
  8. V. G. Badami and S. R. Patterson, “A frequency domain method for the measurement of nonlinearity in heterodyne interferometry,” Precis. Eng. 24(1), 41–49 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instrum. 71(7), 2669–2676 (2000).
    [CrossRef]
  16. T. L. Schmitz and J. F. Beckwith, “Acousto-optic displacement-measuring interferometer: a new heterodyne interferometer with Anstrom-level periodic error,” J. Mod. Opt. 49(13), 2105–2114 (2002).
    [CrossRef]
  17. K.-N. Joo, J. D. Ellis, J. W. Spronck, P. J. M. van Kan, and R. H. M. Schmidt, “Simple heterodyne laser interferometer with subnanometer periodic errors,” Opt. Lett. 34(3), 386–388 (2009).
    [CrossRef] [PubMed]

2009

2006

T. L. Schmitz, D. Chu, and L. Houck, “First-order periodic error correction: validation for constant and non-constant velocities with variable error magnitudes,” Meas. Sci. Technol. 17(12), 3195–3203 (2006).
[CrossRef]

2005

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005).
[CrossRef]

2003

H. Haitjema, S. J. A. G. Cosijns, N. J. J. Roset, M. J. Jansen, and P. H. J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE , 347–354 (2003).
[CrossRef]

2002

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13(2), 222–225 (2002).
[CrossRef]

T. L. Schmitz and J. F. Beckwith, “Acousto-optic displacement-measuring interferometer: a new heterodyne interferometer with Anstrom-level periodic error,” J. Mod. Opt. 49(13), 2105–2114 (2002).
[CrossRef]

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng. 26(4), 448–455 (2002).
[CrossRef]

2000

V. G. Badami and S. R. Patterson, “A frequency domain method for the measurement of nonlinearity in heterodyne interferometry,” Precis. Eng. 24(1), 41–49 (2000).
[CrossRef]

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instrum. 71(7), 2669–2676 (2000).
[CrossRef]

1999

1998

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
[CrossRef]

1993

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[CrossRef]

1992

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91–98 (1992).
[CrossRef]

1989

M. Tanaka, T. Yamagami, and K. Nakayama, “Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels (dimension measurement),” IEEE Trans. Instrum. Meas. 38(2), 552–554 (1989).
[CrossRef]

1985

1983

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

Badami, V. G.

V. G. Badami and S. R. Patterson, “A frequency domain method for the measurement of nonlinearity in heterodyne interferometry,” Precis. Eng. 24(1), 41–49 (2000).
[CrossRef]

Beckwith, J. F.

T. L. Schmitz and J. F. Beckwith, “Acousto-optic displacement-measuring interferometer: a new heterodyne interferometer with Anstrom-level periodic error,” J. Mod. Opt. 49(13), 2105–2114 (2002).
[CrossRef]

Bobroff, N.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[CrossRef]

Bosse, H.

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005).
[CrossRef]

Choi, H.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13(2), 222–225 (2002).
[CrossRef]

Choi, T.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13(2), 222–225 (2002).
[CrossRef]

Chu, D.

T. L. Schmitz, D. Chu, and L. Houck, “First-order periodic error correction: validation for constant and non-constant velocities with variable error magnitudes,” Meas. Sci. Technol. 17(12), 3195–3203 (2006).
[CrossRef]

Cosijns, S. J. A. G.

H. Haitjema, S. J. A. G. Cosijns, N. J. J. Roset, M. J. Jansen, and P. H. J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE , 347–354 (2003).
[CrossRef]

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng. 26(4), 448–455 (2002).
[CrossRef]

Demarest, F. C.

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
[CrossRef]

Deslattes, R. D.

Ellis, J. D.

Eom, T.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13(2), 222–225 (2002).
[CrossRef]

Estler, W. T.

Haitjema, H.

H. Haitjema, S. J. A. G. Cosijns, N. J. J. Roset, M. J. Jansen, and P. H. J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE , 347–354 (2003).
[CrossRef]

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng. 26(4), 448–455 (2002).
[CrossRef]

Hou, W.

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91–98 (1992).
[CrossRef]

Houck, L.

T. L. Schmitz, D. Chu, and L. Houck, “First-order periodic error correction: validation for constant and non-constant velocities with variable error magnitudes,” Meas. Sci. Technol. 17(12), 3195–3203 (2006).
[CrossRef]

Jansen, M. J.

H. Haitjema, S. J. A. G. Cosijns, N. J. J. Roset, M. J. Jansen, and P. H. J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE , 347–354 (2003).
[CrossRef]

Joo, K.-N.

Kessler, E.

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instrum. 71(7), 2669–2676 (2000).
[CrossRef]

Lawall, J.

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instrum. 71(7), 2669–2676 (2000).
[CrossRef]

C. M. Wu, J. Lawall, and R. D. Deslattes, “Heterodyne interferometer with subatomic periodic nonlinearity,” Appl. Opt. 38(19), 4089–4094 (1999).
[CrossRef]

Lee, K.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13(2), 222–225 (2002).
[CrossRef]

Lee, S.

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13(2), 222–225 (2002).
[CrossRef]

Nakayama, K.

M. Tanaka, T. Yamagami, and K. Nakayama, “Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels (dimension measurement),” IEEE Trans. Instrum. Meas. 38(2), 552–554 (1989).
[CrossRef]

Patterson, S. R.

V. G. Badami and S. R. Patterson, “A frequency domain method for the measurement of nonlinearity in heterodyne interferometry,” Precis. Eng. 24(1), 41–49 (2000).
[CrossRef]

Quenelle, R. C.

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

Roset, N. J. J.

H. Haitjema, S. J. A. G. Cosijns, N. J. J. Roset, M. J. Jansen, and P. H. J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE , 347–354 (2003).
[CrossRef]

Schellekens, P. H. J.

H. Haitjema, S. J. A. G. Cosijns, N. J. J. Roset, M. J. Jansen, and P. H. J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE , 347–354 (2003).
[CrossRef]

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng. 26(4), 448–455 (2002).
[CrossRef]

Schmidt, R. H. M.

Schmitz, T. L.

T. L. Schmitz, D. Chu, and L. Houck, “First-order periodic error correction: validation for constant and non-constant velocities with variable error magnitudes,” Meas. Sci. Technol. 17(12), 3195–3203 (2006).
[CrossRef]

T. L. Schmitz and J. F. Beckwith, “Acousto-optic displacement-measuring interferometer: a new heterodyne interferometer with Anstrom-level periodic error,” J. Mod. Opt. 49(13), 2105–2114 (2002).
[CrossRef]

Spronck, J. W.

Tanaka, M.

M. Tanaka, T. Yamagami, and K. Nakayama, “Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels (dimension measurement),” IEEE Trans. Instrum. Meas. 38(2), 552–554 (1989).
[CrossRef]

van Kan, P. J. M.

Wilkening, G.

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005).
[CrossRef]

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91–98 (1992).
[CrossRef]

Wu, C. M.

Yamagami, T.

M. Tanaka, T. Yamagami, and K. Nakayama, “Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels (dimension measurement),” IEEE Trans. Instrum. Meas. 38(2), 552–554 (1989).
[CrossRef]

Appl. Opt.

Hewlett Packard J.

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

IEEE Trans. Instrum. Meas.

M. Tanaka, T. Yamagami, and K. Nakayama, “Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels (dimension measurement),” IEEE Trans. Instrum. Meas. 38(2), 552–554 (1989).
[CrossRef]

J. Mod. Opt.

T. L. Schmitz and J. F. Beckwith, “Acousto-optic displacement-measuring interferometer: a new heterodyne interferometer with Anstrom-level periodic error,” J. Mod. Opt. 49(13), 2105–2114 (2002).
[CrossRef]

Meas. Sci. Technol.

T. L. Schmitz, D. Chu, and L. Houck, “First-order periodic error correction: validation for constant and non-constant velocities with variable error magnitudes,” Meas. Sci. Technol. 17(12), 3195–3203 (2006).
[CrossRef]

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, “A simple method for the compensation of the nonlinearity in the heterodyne interferometer,” Meas. Sci. Technol. 13(2), 222–225 (2002).
[CrossRef]

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005).
[CrossRef]

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[CrossRef]

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
[CrossRef]

Opt. Lett.

Precis. Eng.

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91–98 (1992).
[CrossRef]

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng. 26(4), 448–455 (2002).
[CrossRef]

V. G. Badami and S. R. Patterson, “A frequency domain method for the measurement of nonlinearity in heterodyne interferometry,” Precis. Eng. 24(1), 41–49 (2000).
[CrossRef]

Proc. SPIE

H. Haitjema, S. J. A. G. Cosijns, N. J. J. Roset, M. J. Jansen, and P. H. J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE , 347–354 (2003).
[CrossRef]

Rev. Sci. Instrum.

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instrum. 71(7), 2669–2676 (2000).
[CrossRef]

Other

D. Chu, and A. Ray, “Nonlinearity measurement and correction of metrology data from an interferometer system,” Proc. of 4th euspen Int. Conf., 300–301 (2004).

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Figures (6)

Fig. 1
Fig. 1

The optical configuration of a high resolution heterodyne laser interferometer with no detectable periodic nonlinearity; BS1, BS2, beams splitters; AOFS1, AOFS2, acousto-optic frequency shifters; PH, pinhole; M1, M2, M3, adjustable mirrors; RR, retro-reflector; RAP, right angle prism; B, beam blocker; PDR, PDM, reference and measurement photodetectors, respectively. The dotted line is used to indicate that the beam is at the bottom. ΔfD is the Doppler shift from the stage motion (ΔL).

Fig. 2
Fig. 2

Measured wrapped phase of the interferometer depicted in Fig. 1 (Linear RR, grey line) and a typical interferometer (Zeeman RR, black line). In both interferometer configurations a retro-reflector is used as a measurement target. The inset means the phase change of our interferometer is twice as faster as that of the typical one.

Fig. 3
Fig. 3

(a) FFT analysis of the difference between measured displacements and the fitted one in our interferometer (Linear RR, grey line) and the typical interferometer (Zeeman RR, black line), (b) enlargement of the FFT results in the proposed interferometer. The periodic nonlinearity of approximately 7 nm was detected in the typical interferometer while there was no observable periodic nonlinearity in the proposed interferometer except for peaks caused by vibrations.

Fig. 4
Fig. 4

The schematic of plane mirror interferometer with two spatially separated beams and right angle prism; BS, beams splitter; PBS, polarizing beam splitter; QWP, quarter-wave plate; RR, retro-reflector; RAP, right angle prism; M, target mirror; PDR, PDM, reference and measurement photodetectors, respectively.

Fig. 5
Fig. 5

(a) FFT analysis of the difference between measured displacements and the fitted one in the proposed interferometer (Linear PMI, grey line) and the commercial interferometer (Agilent PMI, black line), (b) indicating several peaks caused by stage vibrations in both of the results. The peaks of the commercial interferometer were matched with the peaks of our interferometer considering the optical resolution.

Fig. 6
Fig. 6

The differential plane mirror interferometer configuration; DBS, displacement beams splitter; PBS, polarizing beam splitter; QWP, quarter-wave plate; RR, retro-reflector; RAP, right angle prism; MR, MM, reference and measurement mirrors; PDR, PDM, reference and measurement photodetectors, respectively. The dotted line is used to indicate that the beam is at the bottom.

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