Abstract

We present a new class of interferometer system that is capable of simultaneous measurement of absolute position and rotation in all six degrees of freedom (DOF) with nanometer precision. This novel capability is due to the employment of a system of interference fringes that is not periodic. One of the key strengths offered by this new approach is that the absolute position of the system can be determined with a single measurement, rather than by counting fringes during displacement from a known location. The availability of a simultaneous measurement of all six DOF eliminates many problems associated with conventional interferometry.

© 2012 Optical Society of America

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References

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  1. T. Young, Phil. Trans. R. Soc. Lond. 94, 1 (1804).
    [CrossRef]
  2. D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).
    [CrossRef]
  3. R. Penrose, “Set of tiles for covering a surface,” UK patent GB1548164 (July4, 1979).
  4. H. Xue and R. Yang, IEE Proc. Gen. Transm. Distrib. 150, 583 (2003).
    [CrossRef]
  5. N. Yoshimizu, A. Lal, and C. R. Pollock, Opt. Express, 18, 20827 (2010).
    [CrossRef]
  6. G. L. Turin, IRE Trans. Inf. Theor. 6, 311 (1960).
    [CrossRef]
  7. International Technology Roadmap for Semiconductors, http://www.itrs.net .

2010

2003

H. Xue and R. Yang, IEE Proc. Gen. Transm. Distrib. 150, 583 (2003).
[CrossRef]

1984

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).
[CrossRef]

1960

G. L. Turin, IRE Trans. Inf. Theor. 6, 311 (1960).
[CrossRef]

1804

T. Young, Phil. Trans. R. Soc. Lond. 94, 1 (1804).
[CrossRef]

Blech, I.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).
[CrossRef]

Cahn, J. W.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).
[CrossRef]

Gratias, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).
[CrossRef]

Lal, A.

Penrose, R.

R. Penrose, “Set of tiles for covering a surface,” UK patent GB1548164 (July4, 1979).

Pollock, C. R.

Shechtman, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).
[CrossRef]

Turin, G. L.

G. L. Turin, IRE Trans. Inf. Theor. 6, 311 (1960).
[CrossRef]

Xue, H.

H. Xue and R. Yang, IEE Proc. Gen. Transm. Distrib. 150, 583 (2003).
[CrossRef]

Yang, R.

H. Xue and R. Yang, IEE Proc. Gen. Transm. Distrib. 150, 583 (2003).
[CrossRef]

Yoshimizu, N.

Young, T.

T. Young, Phil. Trans. R. Soc. Lond. 94, 1 (1804).
[CrossRef]

IEE Proc. Gen. Transm. Distrib.

H. Xue and R. Yang, IEE Proc. Gen. Transm. Distrib. 150, 583 (2003).
[CrossRef]

IRE Trans. Inf. Theor.

G. L. Turin, IRE Trans. Inf. Theor. 6, 311 (1960).
[CrossRef]

Opt. Express

Phil. Trans. R. Soc. Lond.

T. Young, Phil. Trans. R. Soc. Lond. 94, 1 (1804).
[CrossRef]

Phys. Rev. Lett.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).
[CrossRef]

Other

R. Penrose, “Set of tiles for covering a surface,” UK patent GB1548164 (July4, 1979).

International Technology Roadmap for Semiconductors, http://www.itrs.net .

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Figures (3)

Fig. 1.
Fig. 1.

Principle system components (laser, optic, camera) and simulated diffraction patterns showing the distortion of the interference field at different distances from the optic.

Fig. 2.
Fig. 2.

(a) Experimental and (b) simulated regions of the diffraction pattern produced by coherent illumination of five 1 µm diameter pinholes arranged as a regular pentagon on a 411.159(±0.01)μm radius. Absolute laser wavelength 778.8(±0.1)nm, pixel spacing 5.2 µm square. Approximate optic–camera separation in mm: x=1.66, y=-1.3, z=28.2, and all angles <1°. Simulated interference patterns exaggerate distortions in the detected interference pattern brought about by changes in the relative pinhole–camera position. The white cross indicates the motion of the center of the interference field.

Fig. 3.
Fig. 3.

Residual error plots. Plots were obtained at the following positions (x, y, z, θx, θy, θz): (a) (11.77.8mm, 1.5 mm, 37 mm, 1°, 2°, 0.1°), (b) (2 to 1mm, 1.9 to 1.33mm, 42.3 to 17.3 mm, 1°, 2°, 0.3°), (c) (-0.6 to 0 mm, -0.2mm, 22.5 mm, 1°, -10° to 10°, 0.5°), (d) (-0.1mm, -0.2mm, 17.8 mm, 0° to 1.5°, 0° to 1.2°, -60° to 40°).

Tables (1)

Tables Icon

Table 1. Measured Precision (One Standard Deviation) and Accuracya

Metrics