Abstract

A novel formula is proposed to determine the index profile of optical fibers or preforms from transverse interferograms. Neither numerical differentiation nor an Abel transformation of the fringe shift is required. Index profiles can be calculated only from simple algebra using the Fourier coefficients of the fringe shift and a matrix independent of fiber parameters.

© 1983 Optical Society of America

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References

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  1. H. M. Presby, D. Marcuse, H. M. Astle, Appl. Opt. 17, 2209 (1978).
    [CrossRef] [PubMed]
  2. B. C. Wonsiewicz, W. G. French, P. D. Lazay, J. R. Simpson, Appl. Opt. 15, 1048 (1976).
    [CrossRef] [PubMed]
  3. H. M. Presby, D. Marcuse, H. W. Astle, L. M. Boggs, Bell Syst. Tech. J. 58, 883 (1979).
  4. A. M. Hunter, P. W. Schreiber, Appl. Opt. 14, 634 (1975).
    [CrossRef]
  5. Y. Kokubun, K. Iga, Trans. IECE Jpn, E60, 184 (1978).
  6. D. Marcuse, H. M. Presby, Proc. IEEE 68, 666 (1980).
    [CrossRef]
  7. G. N. Watson, Theory of Bessel Functions (Cambridge U.P., London, 1952).

1980 (1)

D. Marcuse, H. M. Presby, Proc. IEEE 68, 666 (1980).
[CrossRef]

1979 (1)

H. M. Presby, D. Marcuse, H. W. Astle, L. M. Boggs, Bell Syst. Tech. J. 58, 883 (1979).

1978 (2)

1976 (1)

1975 (1)

Astle, H. M.

Astle, H. W.

H. M. Presby, D. Marcuse, H. W. Astle, L. M. Boggs, Bell Syst. Tech. J. 58, 883 (1979).

Boggs, L. M.

H. M. Presby, D. Marcuse, H. W. Astle, L. M. Boggs, Bell Syst. Tech. J. 58, 883 (1979).

French, W. G.

Hunter, A. M.

Iga, K.

Y. Kokubun, K. Iga, Trans. IECE Jpn, E60, 184 (1978).

Kokubun, Y.

Y. Kokubun, K. Iga, Trans. IECE Jpn, E60, 184 (1978).

Lazay, P. D.

Marcuse, D.

D. Marcuse, H. M. Presby, Proc. IEEE 68, 666 (1980).
[CrossRef]

H. M. Presby, D. Marcuse, H. W. Astle, L. M. Boggs, Bell Syst. Tech. J. 58, 883 (1979).

H. M. Presby, D. Marcuse, H. M. Astle, Appl. Opt. 17, 2209 (1978).
[CrossRef] [PubMed]

Presby, H. M.

D. Marcuse, H. M. Presby, Proc. IEEE 68, 666 (1980).
[CrossRef]

H. M. Presby, D. Marcuse, H. W. Astle, L. M. Boggs, Bell Syst. Tech. J. 58, 883 (1979).

H. M. Presby, D. Marcuse, H. M. Astle, Appl. Opt. 17, 2209 (1978).
[CrossRef] [PubMed]

Schreiber, P. W.

Simpson, J. R.

Watson, G. N.

G. N. Watson, Theory of Bessel Functions (Cambridge U.P., London, 1952).

Wonsiewicz, B. C.

Appl. Opt. (3)

Bell Syst. Tech. J. (1)

H. M. Presby, D. Marcuse, H. W. Astle, L. M. Boggs, Bell Syst. Tech. J. 58, 883 (1979).

Proc. IEEE (1)

D. Marcuse, H. M. Presby, Proc. IEEE 68, 666 (1980).
[CrossRef]

Trans. IECE Jpn (1)

Y. Kokubun, K. Iga, Trans. IECE Jpn, E60, 184 (1978).

Other (1)

G. N. Watson, Theory of Bessel Functions (Cambridge U.P., London, 1952).

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Figures (5)

Fig. 1
Fig. 1

Reconstructed normalized index profile Δn(ρ)/Δn of the parabolic-index profile, where the number N of sampling points of the fringe shift was 21.

Fig. 2
Fig. 2

Numerical error between the reconstructed and actual profiles at the calculated points shown in Fig. 1.

Fig. 3
Fig. 3

Numerical error between the calculated and actual exponents g of the power-law index profile, where N = 21.

Fig. 4
Fig. 4

Reconstructed normalized parabolic profile Δn(ρ)/Δn with a shallow dip (D = 0.5 and W = 1.0), where N = 21.

Fig. 5
Fig. 5

Reconstructed normalized parabolic profile Δn(ρ)/Δn with a sharp dip (D = 1.0 and W = 0.05), where N = 21.

Tables (1)

Tables Icon

Table I Elements of Matrix [Wmn]

Equations (11)

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Δ n ( r ) = λ π D r a d s ( y ) d y d y y 2 r 2 ,
s ( y ) = n = 0 a n cos ( n W s y ) , Δ n ( r ) = m = 0 b m cos ( m W s r ) ,
b m = λ W s π D e m n = 0 W m n a n , m = 0 , 1 , 2 , , W m n 1 m a W s 0 1 cos ( n a W s t ) J l ( m a W s t ) d t ,
Δ n ( ρ ) = Δ n ( 1 ρ g ) ,
Δ n ( ρ ) = Δ n ( 1 ρ 2 ) Δ n D ( 1 1 + ρ 2 / W 2 1 1 + 1 / W 2 ) .
S ( w ) = 2 0 s ( y ) cos ( w y ) d y , Δ N ( w ) = 2 0 Δ n ( r ) cos ( w r ) d r .
S ( w ) = W s π n = S ( n W s ) sin a ( W n W s ) W n W s ,
Δ n ( r ) = λ π D r d s ( y ) d y d y y 2 r 2 = λ 2 π 2 D r w S ( w ) sin ( w y ) y 2 r 2 d w d y = λ 4 π D | w | S ( w ) J 0 ( w r ) d w = λ W s 4 π 2 D n = S ( n W s ) | w | sin a ( w n W s ) w n W s J 0 ( w r ) d w = λ W s 2 π 2 D n = S ( n W s ) [ cos ( n a W s ) a 2 r 2 + n W s r a × sin ( n W s t ) t 2 r 2 d t ] ,
Δ N ( m W s ) = λ W s 2 π D n = W m n S ( n W s ) ,
2 π 0 a cos ( n a W s ) a 2 r 2 cos ( w r ) d r = cos ( n a W s ) J 0 ( a w ) , 2 π 0 a r a n W s sin ( n W s t ) t 2 r 2 cos ( w r ) d t d r = 2 π 0 a d t n W s sin ( n W s t ) 0 t cos ( w r ) t 2 r 2 d r = 0 a n W s sin ( n W s t ) J 0 ( w t ) d t = 1 cos ( n a W s ) J 0 ( a w ) a w 0 1 cos ( n a W s t ) J 1 ( a w t ) d t .
a n = 2 a e n 0 a s ( y ) cos ( n W s y ) d y = 1 a e n S ( n W s ) , b m = 2 a e m 0 a Δ n ( r ) cos ( m W s r ) d r = 1 a e m Δ N ( m W s ) ,

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