Abstract

To demonstrate the principle for detecting a phase of equidistant and straight fringes, experimental results for measuring a displacement of a piezoelectric transducer device using a new polarizing Michelson interferometer are presented. A simple birefringent wedge of a uniaxial crystal is used to form an equidistant and straight fringe pattern. The shift of the fringe pattern is calculated from an arctangent of Fourier cosine and sine integrals of the fringe intensity. The minimum detectable phase change is approximately a 470th of the wavelength of the laser light, including external disturbances in the interferometer. Applications of the phase detection include use in highly sensitive optical sensors for pressure and temperature.

© 1988 Optical Society of America

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References

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  1. S. Nakadate, “Phase detection of equidistant fringes for highly sensitive optical sensings. I. Principle and error analyses,” J. Opt. Soc. Am. A 5, 1258–1264 (1988).
    [CrossRef]
  2. S. Nakadate, “Highly sensitive optical sensings using a phase detection of Young’s fringes,” in Optics and the Information Age, H. H. Arsenault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.813, 523–524 (1987).
    [CrossRef]
  3. M. Françon, S. Mallick, Polarization Interferometers: Application in Microscopy and Macroscopy (Wiley, London, 1971).
  4. M. Haruna, H. Nakajima, H. Nishihara, “Optical π-arc waveguide interferometer in proton-exchanged LiNbO3for temperature sensing,” Appl. Opt. 24, 2483–2484 (1985).
    [CrossRef] [PubMed]
  5. T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. QE-18, 626–664 (1982).
    [CrossRef]

1988 (1)

1985 (1)

1982 (1)

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. QE-18, 626–664 (1982).
[CrossRef]

Bucaro, J. A.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. QE-18, 626–664 (1982).
[CrossRef]

Cole, J. H.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. QE-18, 626–664 (1982).
[CrossRef]

Dandridge, A.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. QE-18, 626–664 (1982).
[CrossRef]

Françon, M.

M. Françon, S. Mallick, Polarization Interferometers: Application in Microscopy and Macroscopy (Wiley, London, 1971).

Giallorenzi, T. G.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. QE-18, 626–664 (1982).
[CrossRef]

Haruna, M.

Mallick, S.

M. Françon, S. Mallick, Polarization Interferometers: Application in Microscopy and Macroscopy (Wiley, London, 1971).

Nakadate, S.

S. Nakadate, “Phase detection of equidistant fringes for highly sensitive optical sensings. I. Principle and error analyses,” J. Opt. Soc. Am. A 5, 1258–1264 (1988).
[CrossRef]

S. Nakadate, “Highly sensitive optical sensings using a phase detection of Young’s fringes,” in Optics and the Information Age, H. H. Arsenault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.813, 523–524 (1987).
[CrossRef]

Nakajima, H.

Nishihara, H.

Priest, R. G.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. QE-18, 626–664 (1982).
[CrossRef]

Rashleigh, S. C.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. QE-18, 626–664 (1982).
[CrossRef]

Sigel, G. H.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. QE-18, 626–664 (1982).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. QE-18, 626–664 (1982).
[CrossRef]

J. Opt. Soc. Am. A (1)

Other (2)

S. Nakadate, “Highly sensitive optical sensings using a phase detection of Young’s fringes,” in Optics and the Information Age, H. H. Arsenault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.813, 523–524 (1987).
[CrossRef]

M. Françon, S. Mallick, Polarization Interferometers: Application in Microscopy and Macroscopy (Wiley, London, 1971).

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of a polarizing Michelson interferometer. PBS, polarizing beam splitter; QWP, quarter-wave plates; M’s, mirrors.

Fig. 2
Fig. 2

Illustration of a birefringent wedge made with a uniaxial crystal.

Fig. 3
Fig. 3

(a) Photograph of equidistant and straight fringes obtained in the polarizing Michelson interferometer. (b) Output voltage from the image sensor.

Fig. 4
Fig. 4

(a) Bias component, R + O, of the interferogram shown in Fig. 3. (b) Ratio of the modulation and bias components of the interferogram, 2 R O / ( R + O ), which is equal to the fringe contrast. (c) Fringe profile corrected with the bias and modulation components.

Fig. 5
Fig. 5

Phase-shifted fringe profiles of Young’s fringes: (a) the original and (b) the corrected data with the bias and modulation components. The rows and columns represent the spatial coordinate on the image sensor and the voltage applied to the PZT device, respectively.

Fig. 6
Fig. 6

Displacement of the PZT calculated from the corrected data shown in Fig. 5(b). Displacements for gradual increase and decrease of the voltage applied to the PZT are shown by lines a and b, respectively.

Fig. 7
Fig. 7

Difference between phases calculated from the original and the corrected data using the Hanning window.

Fig. 8
Fig. 8

Normalized power spectrum of the bias component, R + O, shown in Fig. 4(a), which is obtained by a digital Fourier transform.

Fig. 9
Fig. 9

(a) Phase change in the stable state of the polarizing interferometer during 34.5 sec. (b) Phase difference between the original data of (a) and the data average over five sample points.

Fig. 10
Fig. 10

Schematic diagram of a pressure sensor using the phase detection of Young’s fringes.

Equations (3)

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θ i = α sin 1 ( n i sin α ) ( i = o , e )
I ( x ) = 1 + cos [ 4 π λ cos ( β θ o + θ e 2 ) sin ( θ e θ o 2 ) x ] ,
I ( x ) = R + O + 2 R O cos ( 2 π f o ϕ ) .

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