Abstract

Interference between the LP01 and LP02 modes is used to measure fiber elongation. We present a passive phase-detection technique that uses a mask in the far field of the output beam and spatial filters in the image of the fiber end face, giving a linear response. Experimental results show a precision of about 3% of one period, which corresponds to a 4-μm elongation.

© 1988 Optical Society of America

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References

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  1. M. R. Layton, J. A. Bucaro, Appl. Opt. 18, 666 (1979).
    [Crossref] [PubMed]
  2. R. B. Franks, W. Torruellas, R. C. Youngquist, Proc. Soc. Photo-Opt. Instrum. Eng. 586, 84 (1985).
  3. J. L. McMillan, S. C. Robertson, Electron. Lett. 20, 136 (1984).
    [Crossref]
  4. J. G. Hanse, G. L. Mitchell, Opt. Eng. 23, 309 (1984).
  5. P. L. Frangois, F. Alard, J. F. Bayon, B. Rose, Electron. Lett. 20, 37 (1984).
    [Crossref]
  6. M. Spajer, B. Carquille, H. Maillotte, Opt. Commun. 60, 261 (1986).
    [Crossref]
  7. J. E. Midwinter, Opt. Quantum Electron. 7, 297 (1975).
    [Crossref]
  8. J. L. McMillan, S. C. Robertson, Electron. Lett. 21, 295 (1985).
    [Crossref]
  9. B. Carquille, M. Spajer, J. Monneret, in Opto 85 (E.S.I., Paris, 1985), p. 173.

1986 (1)

M. Spajer, B. Carquille, H. Maillotte, Opt. Commun. 60, 261 (1986).
[Crossref]

1985 (2)

J. L. McMillan, S. C. Robertson, Electron. Lett. 21, 295 (1985).
[Crossref]

R. B. Franks, W. Torruellas, R. C. Youngquist, Proc. Soc. Photo-Opt. Instrum. Eng. 586, 84 (1985).

1984 (3)

J. L. McMillan, S. C. Robertson, Electron. Lett. 20, 136 (1984).
[Crossref]

J. G. Hanse, G. L. Mitchell, Opt. Eng. 23, 309 (1984).

P. L. Frangois, F. Alard, J. F. Bayon, B. Rose, Electron. Lett. 20, 37 (1984).
[Crossref]

1979 (1)

1975 (1)

J. E. Midwinter, Opt. Quantum Electron. 7, 297 (1975).
[Crossref]

Alard, F.

P. L. Frangois, F. Alard, J. F. Bayon, B. Rose, Electron. Lett. 20, 37 (1984).
[Crossref]

Bayon, J. F.

P. L. Frangois, F. Alard, J. F. Bayon, B. Rose, Electron. Lett. 20, 37 (1984).
[Crossref]

Bucaro, J. A.

Carquille, B.

M. Spajer, B. Carquille, H. Maillotte, Opt. Commun. 60, 261 (1986).
[Crossref]

B. Carquille, M. Spajer, J. Monneret, in Opto 85 (E.S.I., Paris, 1985), p. 173.

Frangois, P. L.

P. L. Frangois, F. Alard, J. F. Bayon, B. Rose, Electron. Lett. 20, 37 (1984).
[Crossref]

Franks, R. B.

R. B. Franks, W. Torruellas, R. C. Youngquist, Proc. Soc. Photo-Opt. Instrum. Eng. 586, 84 (1985).

Hanse, J. G.

J. G. Hanse, G. L. Mitchell, Opt. Eng. 23, 309 (1984).

Layton, M. R.

Maillotte, H.

M. Spajer, B. Carquille, H. Maillotte, Opt. Commun. 60, 261 (1986).
[Crossref]

McMillan, J. L.

J. L. McMillan, S. C. Robertson, Electron. Lett. 21, 295 (1985).
[Crossref]

J. L. McMillan, S. C. Robertson, Electron. Lett. 20, 136 (1984).
[Crossref]

Midwinter, J. E.

J. E. Midwinter, Opt. Quantum Electron. 7, 297 (1975).
[Crossref]

Mitchell, G. L.

J. G. Hanse, G. L. Mitchell, Opt. Eng. 23, 309 (1984).

Monneret, J.

B. Carquille, M. Spajer, J. Monneret, in Opto 85 (E.S.I., Paris, 1985), p. 173.

Robertson, S. C.

J. L. McMillan, S. C. Robertson, Electron. Lett. 21, 295 (1985).
[Crossref]

J. L. McMillan, S. C. Robertson, Electron. Lett. 20, 136 (1984).
[Crossref]

Rose, B.

P. L. Frangois, F. Alard, J. F. Bayon, B. Rose, Electron. Lett. 20, 37 (1984).
[Crossref]

Spajer, M.

M. Spajer, B. Carquille, H. Maillotte, Opt. Commun. 60, 261 (1986).
[Crossref]

B. Carquille, M. Spajer, J. Monneret, in Opto 85 (E.S.I., Paris, 1985), p. 173.

Torruellas, W.

R. B. Franks, W. Torruellas, R. C. Youngquist, Proc. Soc. Photo-Opt. Instrum. Eng. 586, 84 (1985).

Youngquist, R. C.

R. B. Franks, W. Torruellas, R. C. Youngquist, Proc. Soc. Photo-Opt. Instrum. Eng. 586, 84 (1985).

Appl. Opt. (1)

Electron. Lett. (3)

J. L. McMillan, S. C. Robertson, Electron. Lett. 20, 136 (1984).
[Crossref]

P. L. Frangois, F. Alard, J. F. Bayon, B. Rose, Electron. Lett. 20, 37 (1984).
[Crossref]

J. L. McMillan, S. C. Robertson, Electron. Lett. 21, 295 (1985).
[Crossref]

Opt. Commun. (1)

M. Spajer, B. Carquille, H. Maillotte, Opt. Commun. 60, 261 (1986).
[Crossref]

Opt. Eng. (1)

J. G. Hanse, G. L. Mitchell, Opt. Eng. 23, 309 (1984).

Opt. Quantum Electron. (1)

J. E. Midwinter, Opt. Quantum Electron. 7, 297 (1975).
[Crossref]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

R. B. Franks, W. Torruellas, R. C. Youngquist, Proc. Soc. Photo-Opt. Instrum. Eng. 586, 84 (1985).

Other (1)

B. Carquille, M. Spajer, J. Monneret, in Opto 85 (E.S.I., Paris, 1985), p. 173.

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Figures (4)

Fig. 1
Fig. 1

Far-field amplitude Alm(r) of the four propagating LP modes. Shaded zones correspond to the ring-shaped (R) and disk-shaped (D) parts of the mask.

Fig. 2
Fig. 2

Amplitudes a lm D and a lm R diffracted in the Fourier plane of the mask by its two zones ( a 11 D and a 21 D are omitted).

Fig. 3
Fig. 3

Experimental setup matched to LP02/LP01 interference.

Fig. 4
Fig. 4

Oscillations of (IDkIR) and (I+I) recorded during fiber elongation and the result of the phase calculation.

Equations (11)

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I D = D ( | A 01 | 2 + | A 02 | 2 + 2 A 01 A 02 cos φ 02 + | A 11 | 2 + | A 21 | 2 ) d S
D | A 01 | 2 d S / R | A 01 | 2 d S = D | A 02 | 2 d S / R | A 02 | 2 d S = k .
I D k I R = ( D k ) ( 2 A 01 A 02 cos φ 02 + | A 11 | 2 + | A 21 | 2 ) d S .
I D k I R = F [ 2 ( a 01 D a 02 D ka 01 R a 02 R ) cos φ 02 + | a 11 D | 2 k | a 11 R | 2 + | a 21 D | 2 k | a 21 R | 2 ]
F | a 01 D | 2 d s / F | a 01 R | 2 d s = F | a 02 D 2 d s / F | a 02 R | 2 d s = k .
φ m + = φ m 0 + δ φ m , φ m = φ m 0 + δ φ m
a ± = l , m [ a lm D + a lm R exp ( m ± ) ] exp ( i φ lm ) .
I + I = 4 φ m 0 [ sin δ φ m F l , m ( a lm D a lm R * d s + sin φ 02 cos δ φ m F ( a 01 R a 02 D a 01 D a 02 R ) d s cos φ 02 sin δ φ m F ( a 01 R a 02 D a 01 D a 02 R ) d s ] .
F ( a 01 D a 01 R + a 02 D a 02 R ) d s ,
tan ( Δ φ ) = [ F ( a 01 R a 02 D + a 01 D a 02 R d s ] sin δ φ m [ F ( a 01 R a 02 D a 01 D a 02 R ) d s ] cos δ φ m .
φ 02 = arctan [ k ( I D k I R ) / ( I + I ) ] ,

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