Abstract

We describe a double-grating interferometer for the measurement of cylinder diameters. The unique characteristic of this interferometer is that one can freely change the period of the interference fringes by turning the grating, which permits the measurement range of the interferometer also to be changed freely according to the cylinder diameter to be measured. A clear image of the cylinder can be obtained because the aperture diaphragm blocks the beams diffracted from the edge of the cylinder. The outside and inside diameters of the M4 × 0.7 mm hand tap are measured with this double-grating interferometer.

© 2004 Optical Society of America

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References

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  1. T. K. Millard, T. A. Herchenreder, “Automatic diameter measurement: state of the art,” Wire J. Intern. 24, 61–69 (1991).
  2. J. F. Fardeau, “New laser sensors for wire diameter measurement,” Wire J. Intern. 22, 42–51 (1989).
  3. J. Xie, Y. Qiu, H. Ming, C. Li, “Light polarization effect in measurement of thin wire diameter by laser diffraction and its explanation with boundary diffraction wave,” J. Appl. Phys. 69, 6899–6903 (1991).
    [CrossRef]
  4. D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz-Mie theory,” Opt. Eng. 35, 946–950 (1966).
    [CrossRef]
  5. E. Bernabeu, I. Serroukh, L. M. Sanchez-Brea, “Geometrical model for wire optical diffraction selected by experimental analysis,” Opt. Eng. 38, 1319–1325 (1999).
    [CrossRef]
  6. S. Yoshida, “Static mechanics quantity: device of measuring quantity,” in Handbook on Optical Measurements, T. Takou, J. Tsujiuchi, S. Minami, eds. (Asakura, Tokyo, 1981; in Japanese), pp. 585–587.
  7. O. Sasaki, K. Hashimoto, Y. Fujimori, T. Suzuki, “Measurement of cylinder diameter by using sinusoidally vibrating sinusoidal gratings,” in Optical Engineering for Sensing and Nanotechnology, K. Iwata, ed., Proc. SPIE4416, 35–3835(2001).
    [CrossRef]
  8. J. Li, O. Sasaki, T. Suzuki, “Measurement of sectional profile of a cylinder using a sinusoidally vibrating light with sinusoidal intensity,” Opt. Rev. 9, 159–162 (2002).
    [CrossRef]
  9. O. Sasaki, H. Okazaki, “Detection of time-varying intensity distribution with CCD image sensors,” Appl. Opt. 24, 2124–2126 (1985).
    [CrossRef] [PubMed]
  10. O. Sasaki, H. Okazaki, “Analysis of measurement accuracy in sinusoidal phase modulating interferometry,” Appl. Opt. 25, 3152–3158 (1986).
    [CrossRef] [PubMed]

2002 (1)

J. Li, O. Sasaki, T. Suzuki, “Measurement of sectional profile of a cylinder using a sinusoidally vibrating light with sinusoidal intensity,” Opt. Rev. 9, 159–162 (2002).
[CrossRef]

1999 (1)

E. Bernabeu, I. Serroukh, L. M. Sanchez-Brea, “Geometrical model for wire optical diffraction selected by experimental analysis,” Opt. Eng. 38, 1319–1325 (1999).
[CrossRef]

1991 (2)

T. K. Millard, T. A. Herchenreder, “Automatic diameter measurement: state of the art,” Wire J. Intern. 24, 61–69 (1991).

J. Xie, Y. Qiu, H. Ming, C. Li, “Light polarization effect in measurement of thin wire diameter by laser diffraction and its explanation with boundary diffraction wave,” J. Appl. Phys. 69, 6899–6903 (1991).
[CrossRef]

1989 (1)

J. F. Fardeau, “New laser sensors for wire diameter measurement,” Wire J. Intern. 22, 42–51 (1989).

1986 (1)

1985 (1)

1966 (1)

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz-Mie theory,” Opt. Eng. 35, 946–950 (1966).
[CrossRef]

Belaid, S.

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz-Mie theory,” Opt. Eng. 35, 946–950 (1966).
[CrossRef]

Bernabeu, E.

E. Bernabeu, I. Serroukh, L. M. Sanchez-Brea, “Geometrical model for wire optical diffraction selected by experimental analysis,” Opt. Eng. 38, 1319–1325 (1999).
[CrossRef]

Fardeau, J. F.

J. F. Fardeau, “New laser sensors for wire diameter measurement,” Wire J. Intern. 22, 42–51 (1989).

Fujimori, Y.

O. Sasaki, K. Hashimoto, Y. Fujimori, T. Suzuki, “Measurement of cylinder diameter by using sinusoidally vibrating sinusoidal gratings,” in Optical Engineering for Sensing and Nanotechnology, K. Iwata, ed., Proc. SPIE4416, 35–3835(2001).
[CrossRef]

Gréhan, G.

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz-Mie theory,” Opt. Eng. 35, 946–950 (1966).
[CrossRef]

Hashimoto, K.

O. Sasaki, K. Hashimoto, Y. Fujimori, T. Suzuki, “Measurement of cylinder diameter by using sinusoidally vibrating sinusoidal gratings,” in Optical Engineering for Sensing and Nanotechnology, K. Iwata, ed., Proc. SPIE4416, 35–3835(2001).
[CrossRef]

Herchenreder, T. A.

T. K. Millard, T. A. Herchenreder, “Automatic diameter measurement: state of the art,” Wire J. Intern. 24, 61–69 (1991).

Lebrun, D.

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz-Mie theory,” Opt. Eng. 35, 946–950 (1966).
[CrossRef]

Li, C.

J. Xie, Y. Qiu, H. Ming, C. Li, “Light polarization effect in measurement of thin wire diameter by laser diffraction and its explanation with boundary diffraction wave,” J. Appl. Phys. 69, 6899–6903 (1991).
[CrossRef]

Li, J.

J. Li, O. Sasaki, T. Suzuki, “Measurement of sectional profile of a cylinder using a sinusoidally vibrating light with sinusoidal intensity,” Opt. Rev. 9, 159–162 (2002).
[CrossRef]

Millard, T. K.

T. K. Millard, T. A. Herchenreder, “Automatic diameter measurement: state of the art,” Wire J. Intern. 24, 61–69 (1991).

Ming, H.

J. Xie, Y. Qiu, H. Ming, C. Li, “Light polarization effect in measurement of thin wire diameter by laser diffraction and its explanation with boundary diffraction wave,” J. Appl. Phys. 69, 6899–6903 (1991).
[CrossRef]

Okazaki, H.

Özkul, C.

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz-Mie theory,” Opt. Eng. 35, 946–950 (1966).
[CrossRef]

Qiu, Y.

J. Xie, Y. Qiu, H. Ming, C. Li, “Light polarization effect in measurement of thin wire diameter by laser diffraction and its explanation with boundary diffraction wave,” J. Appl. Phys. 69, 6899–6903 (1991).
[CrossRef]

Ren, K. F.

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz-Mie theory,” Opt. Eng. 35, 946–950 (1966).
[CrossRef]

Sanchez-Brea, L. M.

E. Bernabeu, I. Serroukh, L. M. Sanchez-Brea, “Geometrical model for wire optical diffraction selected by experimental analysis,” Opt. Eng. 38, 1319–1325 (1999).
[CrossRef]

Sasaki, O.

J. Li, O. Sasaki, T. Suzuki, “Measurement of sectional profile of a cylinder using a sinusoidally vibrating light with sinusoidal intensity,” Opt. Rev. 9, 159–162 (2002).
[CrossRef]

O. Sasaki, H. Okazaki, “Analysis of measurement accuracy in sinusoidal phase modulating interferometry,” Appl. Opt. 25, 3152–3158 (1986).
[CrossRef] [PubMed]

O. Sasaki, H. Okazaki, “Detection of time-varying intensity distribution with CCD image sensors,” Appl. Opt. 24, 2124–2126 (1985).
[CrossRef] [PubMed]

O. Sasaki, K. Hashimoto, Y. Fujimori, T. Suzuki, “Measurement of cylinder diameter by using sinusoidally vibrating sinusoidal gratings,” in Optical Engineering for Sensing and Nanotechnology, K. Iwata, ed., Proc. SPIE4416, 35–3835(2001).
[CrossRef]

Serroukh, I.

E. Bernabeu, I. Serroukh, L. M. Sanchez-Brea, “Geometrical model for wire optical diffraction selected by experimental analysis,” Opt. Eng. 38, 1319–1325 (1999).
[CrossRef]

Suzuki, T.

J. Li, O. Sasaki, T. Suzuki, “Measurement of sectional profile of a cylinder using a sinusoidally vibrating light with sinusoidal intensity,” Opt. Rev. 9, 159–162 (2002).
[CrossRef]

O. Sasaki, K. Hashimoto, Y. Fujimori, T. Suzuki, “Measurement of cylinder diameter by using sinusoidally vibrating sinusoidal gratings,” in Optical Engineering for Sensing and Nanotechnology, K. Iwata, ed., Proc. SPIE4416, 35–3835(2001).
[CrossRef]

Xie, J.

J. Xie, Y. Qiu, H. Ming, C. Li, “Light polarization effect in measurement of thin wire diameter by laser diffraction and its explanation with boundary diffraction wave,” J. Appl. Phys. 69, 6899–6903 (1991).
[CrossRef]

Yoshida, S.

S. Yoshida, “Static mechanics quantity: device of measuring quantity,” in Handbook on Optical Measurements, T. Takou, J. Tsujiuchi, S. Minami, eds. (Asakura, Tokyo, 1981; in Japanese), pp. 585–587.

Appl. Opt. (2)

J. Appl. Phys. (1)

J. Xie, Y. Qiu, H. Ming, C. Li, “Light polarization effect in measurement of thin wire diameter by laser diffraction and its explanation with boundary diffraction wave,” J. Appl. Phys. 69, 6899–6903 (1991).
[CrossRef]

Opt. Eng. (2)

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz-Mie theory,” Opt. Eng. 35, 946–950 (1966).
[CrossRef]

E. Bernabeu, I. Serroukh, L. M. Sanchez-Brea, “Geometrical model for wire optical diffraction selected by experimental analysis,” Opt. Eng. 38, 1319–1325 (1999).
[CrossRef]

Opt. Rev. (1)

J. Li, O. Sasaki, T. Suzuki, “Measurement of sectional profile of a cylinder using a sinusoidally vibrating light with sinusoidal intensity,” Opt. Rev. 9, 159–162 (2002).
[CrossRef]

Wire J. Intern. (2)

T. K. Millard, T. A. Herchenreder, “Automatic diameter measurement: state of the art,” Wire J. Intern. 24, 61–69 (1991).

J. F. Fardeau, “New laser sensors for wire diameter measurement,” Wire J. Intern. 22, 42–51 (1989).

Other (2)

S. Yoshida, “Static mechanics quantity: device of measuring quantity,” in Handbook on Optical Measurements, T. Takou, J. Tsujiuchi, S. Minami, eds. (Asakura, Tokyo, 1981; in Japanese), pp. 585–587.

O. Sasaki, K. Hashimoto, Y. Fujimori, T. Suzuki, “Measurement of cylinder diameter by using sinusoidally vibrating sinusoidal gratings,” in Optical Engineering for Sensing and Nanotechnology, K. Iwata, ed., Proc. SPIE4416, 35–3835(2001).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic of the double-grating interferometer.

Fig. 2
Fig. 2

Interference patterns for various values of φ.

Fig. 3
Fig. 3

Schematic of measurement of the diameter of a cylinder.

Fig. 4
Fig. 4

Double-grating interferometer for the measurement of a cylinder’s diameter. LD, Laser diode.

Fig. 5
Fig. 5

Interference pattern for φ = 9.5°. The object measured is a M4 × 0.7 mm hand tap.

Fig. 6
Fig. 6

Interference patterns of the vibration of the half-period of grating G2. t 0 = 2π/ω0 is the vibration period of grating G2.

Fig. 7
Fig. 7

Phase distribution of the interference pattern in Fig. 5.

Tables (1)

Tables Icon

Table 1 Results of Measuring α, D1, and D2 a

Equations (16)

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g1x=n gn expi2πnx/P cos φ,
g2x=n gn expi2πnx/P,
U+1,0x, z=Ag+1g0 expikx sin θ+1,0+z cos θ+1,0,
U0,+1x, z=Ag0g+1 expikx sin θ0,+1+z cos θ0,+1,
Ix, z=C1+cos2πTX x+2πTZ z,
TX=P cos φ1-cos φ,
TZ=2P2 cos2 φλ1-cos2 φλ  P,
D=TD cosθ+1,0+θ0,+1/2=|αA-αB|2πP cos φ1-cos φcosθ+1,0+θ0,+1/2.
It, x=C1+cosu cosω0t+θ+αx,
Fω=2πCδω+Aωcos α+Bωsin α,
Aω=J0uδω+m=1 J2mu-1mAm,Bω=m=1 J2m-1u-1mBm,Am=expi2mθδω-2mω0+exp-i2mθδω+2mω0,Bm=expi2m-1θδω-2m-1ω0+exp-i2m-1θδω+2m-1ω0.
Fω0=-2πC sin αJ1uexpjθ,F2ω0=-2πC cos αJ2uexpj2θ,F3ω0=2πC sin αJ3uexpj3θ,
F3ω0Fω0=J3uJ1u,
Arg-Fω0=Arg2πC sin αJ1uexpjθ, =θα0θ+πα<0,
α=tan-1 ×|Fω0/J1u|sgn-ReFω0/cos θ|F2ω0/J2u|sgn-ReF2ω0/cos 2θ,
sgnx=1x0-1x<0.

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