Abstract

This paper presents a simple displacement sensor for indoor machine calibrations. The sensor, which is placed in the path of a diverging laser beam, consists of two plane mirror pieces laterally displaced with the line joining their centers initially held perpendicular to the optical axis of the beam during the displacement of the sensor with one of the mirrors always traveling along the optical axis of the laser beam. The optical signals from the two mirrors are combined and a simple detector at the interference plane counts the fringes during the sensor displacement. The sensor could be mounted on the moving head of any mechanical machine, e.g., the lathe machine for displacement calibration. The device has been tested over a range of 10 cm beyond a distance of 150 cm from a diverging laser source giving an accuracy of 1.1015 μm. Theoretical modeling, simulation, and experimental results are presented which establish that the proposed sensor can be used as a promising displacement measuring device.

© 2013 Optical Society of America

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References

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2011

2009

2007

H.-J. Yang, S. Nyberg, and K. Riles, “High-precision absolute distance measurement using dual-laser frequency scanned interferometry under realistic conditions,” Nucl. Instrum. Methods Phys. Res. Sect. A 575, 395–401 (2007).
[CrossRef]

2005

2002

1991

Abou-Zeid, A.

Bhattacharya, N.

Cui, M.

Dalhoff, E.

E. Dalhoff, E. Fischer, S. Kreuz, and H. J. Tiziani, “Double heterodyne interferometry for high-precision distance measurements,” Optical 3D Measurement Techniques II, G. Kahmen, ed. (Wichmann, 1993), p. 397.

Dasari, R. R.

Deibel, J.

Deliwala, S.

S. Deliwala, A. Flusberg, and S. D. Swartz, “Method and apparatus for enhanced precision interferometric distance measurement,” U.S. patent 6,573,996 (3June2003).

Falaggis, K.

Feld, M. S.

Fischer, E.

E. Dalhoff, E. Fischer, S. Kreuz, and H. J. Tiziani, “Double heterodyne interferometry for high-precision distance measurements,” Optical 3D Measurement Techniques II, G. Kahmen, ed. (Wichmann, 1993), p. 397.

Flusberg, A.

S. Deliwala, A. Flusberg, and S. D. Swartz, “Method and apparatus for enhanced precision interferometric distance measurement,” U.S. patent 6,573,996 (3June2003).

Huang, H.

Kreuz, S.

E. Dalhoff, E. Fischer, S. Kreuz, and H. J. Tiziani, “Double heterodyne interferometry for high-precision distance measurements,” Optical 3D Measurement Techniques II, G. Kahmen, ed. (Wichmann, 1993), p. 397.

Lin, Y.-J.

Majumdar, A.

Meiners-Hagen, K.

Nyberg, S.

H.-J. Yang, S. Nyberg, and K. Riles, “High-precision absolute distance measurement using dual-laser frequency scanned interferometry under realistic conditions,” Nucl. Instrum. Methods Phys. Res. Sect. A 575, 395–401 (2007).
[CrossRef]

H.-J. Yang, J. Deibel, S. Nyberg, and K. Riles, “High-precision absolute distance and vibration measurement with frequency scanned interferometry,” Appl. Opt. 44, 3937–3944 (2005).
[CrossRef]

Pan, C.-L.

Pollinger, F.

Riles, K.

H.-J. Yang, S. Nyberg, and K. Riles, “High-precision absolute distance measurement using dual-laser frequency scanned interferometry under realistic conditions,” Nucl. Instrum. Methods Phys. Res. Sect. A 575, 395–401 (2007).
[CrossRef]

H.-J. Yang, J. Deibel, S. Nyberg, and K. Riles, “High-precision absolute distance and vibration measurement with frequency scanned interferometry,” Appl. Opt. 44, 3937–3944 (2005).
[CrossRef]

Swartz, S. D.

S. Deliwala, A. Flusberg, and S. D. Swartz, “Method and apparatus for enhanced precision interferometric distance measurement,” U.S. patent 6,573,996 (3June2003).

Tiziani, H. J.

E. Dalhoff, E. Fischer, S. Kreuz, and H. J. Tiziani, “Double heterodyne interferometry for high-precision distance measurements,” Optical 3D Measurement Techniques II, G. Kahmen, ed. (Wichmann, 1993), p. 397.

Towers, C. E.

Towers, D. P.

Urbach, H. P.

van den Berg, S. A.

Wax, A.

Wedde, M.

Yang, C.

Yang, H.-J.

H.-J. Yang, S. Nyberg, and K. Riles, “High-precision absolute distance measurement using dual-laser frequency scanned interferometry under realistic conditions,” Nucl. Instrum. Methods Phys. Res. Sect. A 575, 395–401 (2007).
[CrossRef]

H.-J. Yang, J. Deibel, S. Nyberg, and K. Riles, “High-precision absolute distance and vibration measurement with frequency scanned interferometry,” Appl. Opt. 44, 3937–3944 (2005).
[CrossRef]

Zeitouny, M. G.

Appl. Opt.

Nucl. Instrum. Methods Phys. Res. Sect. A

H.-J. Yang, S. Nyberg, and K. Riles, “High-precision absolute distance measurement using dual-laser frequency scanned interferometry under realistic conditions,” Nucl. Instrum. Methods Phys. Res. Sect. A 575, 395–401 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Other

S. Deliwala, A. Flusberg, and S. D. Swartz, “Method and apparatus for enhanced precision interferometric distance measurement,” U.S. patent 6,573,996 (3June2003).

E. Dalhoff, E. Fischer, S. Kreuz, and H. J. Tiziani, “Double heterodyne interferometry for high-precision distance measurements,” Optical 3D Measurement Techniques II, G. Kahmen, ed. (Wichmann, 1993), p. 397.

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Figures (7)

Fig. 1.
Fig. 1.

Geometry for path length calculations of two beams generated from a diverging beam.

Fig. 2.
Fig. 2.

Schematic diagram of interferometry-based displacement sensor.

Fig. 3.
Fig. 3.

Plots of intensities from mirrors M1 and M2 received at the detector plane.

Fig. 4.
Fig. 4.

Plot of fringe visibility versus the sensor displacement.

Fig. 5.
Fig. 5.

Computer-simulated plots of intensities from mirrors M1 and M2 received at the detector plane as a function of the separation between the two mirrors.

Fig. 6.
Fig. 6.

Computer-simulated plots of path length differences versus the sensor displacement for different separations of the mirror M2 from mirror M1.

Fig. 7.
Fig. 7.

Computer-simulated plots of visibilities versus the sensor displacement for different separations of the mirror M2 from mirror M1.

Equations (12)

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path1=OA¯+AE¯+EF¯=d+L+d.tan[θ].cos[β],
path2=OB¯+BC¯+CF¯=d+d.tan[θ]sin[β]+(Ld.tan[θ].cos2[β]sin[β])=dcos[θ]+L+d.tan[θ]sin[β](1cos2[β])=dcos[θ]+L+d.tan[θ].sin[β].
pathdiff1=path2path1=d(1cos[θ]1)+d.tan[θ](sin[β]cos[β]).
path2path2±δd.cos[2θN2]cos[θN2]sin[α1+θ2]dd±δddd±δdcos[θ].
pathdiff2=(d+δd)(1cos[θ]1)+(d+δd).tan[θ](sin[β]cos[β])±δdcos[2θN2]cos[θN2]sin[α1+θ2]=pathdiff1+δd.(1cos[θ]1)+δd.tan[θ](sin[β]cos[β])±δdcos[2θN2]cos[θN2]sin[α1+θ2].
pathdiff2pathdiff1=δd.(1cos[θ]1)±δdcos[2θN2]cos[θN2]sin[α1+θ2]pathdiff=δd{C(θ)±cos[2θN2]cos[θN2]sin[α1+θ2]},
fringes=2(1+cos[k.pathdiff])=2(1+cos[k.δd.{C(θ)±cos[2θN2]cos[θN2]sin(α1+θ2)}]).
θN1=β2,
θN2=θN1+θ2,
α1=12(π+β),
α2=α1+12θ.
radiusofM2=Lotan[θ](sin[α2]+|cos[α2]|).

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