Abstract

A statistical approach is used to characterize image transmission through misaligned multifibers, i.e., differently arranged at the input and output faces, leading to a spatially invariant line spread function. The resulting MTF is the product of the MTF for the aligned system and a function characterizing stochastic departures from alignment. The case of circular fibers with Gaussian misalignment is treated theoretically and is found to account satisfactorily for experimentally observed results.

© 1978 Optical Society of America

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References

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  1. N. S. Kapany, J. Opt. Soc. Am. 49, 779 (1959).
    [CrossRef]
  2. H. Ohzu, T. Sawatari, K. Sayanagi, J. Appl. Phys. (Jpn.) 4, Suppl. 1, 323 (1965).
  3. R. Drougard, J. Opt. Soc. Am. 54, 907 (1964).
    [CrossRef]
  4. N. S. Kapany, J. A. Eyer, R. E. Klein, J. Opt. Soc. Am. 47, 423 (1957).
    [CrossRef]
  5. P. G. Roetling, W. P. Ganley, J. Opt. Soc. Am. 52, 99 (1962).
    [CrossRef]
  6. Since the final result is eventually normalized, we have omitted proportionality constants in the rest of the analysis.

1965 (1)

H. Ohzu, T. Sawatari, K. Sayanagi, J. Appl. Phys. (Jpn.) 4, Suppl. 1, 323 (1965).

1964 (1)

1962 (1)

1959 (1)

1957 (1)

Drougard, R.

Eyer, J. A.

Ganley, W. P.

Kapany, N. S.

Klein, R. E.

Ohzu, H.

H. Ohzu, T. Sawatari, K. Sayanagi, J. Appl. Phys. (Jpn.) 4, Suppl. 1, 323 (1965).

Roetling, P. G.

Sawatari, T.

H. Ohzu, T. Sawatari, K. Sayanagi, J. Appl. Phys. (Jpn.) 4, Suppl. 1, 323 (1965).

Sayanagi, K.

H. Ohzu, T. Sawatari, K. Sayanagi, J. Appl. Phys. (Jpn.) 4, Suppl. 1, 323 (1965).

J. Appl. Phys. (Jpn.) (1)

H. Ohzu, T. Sawatari, K. Sayanagi, J. Appl. Phys. (Jpn.) 4, Suppl. 1, 323 (1965).

J. Opt. Soc. Am. (4)

Other (1)

Since the final result is eventually normalized, we have omitted proportionality constants in the rest of the analysis.

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Figures (4)

Fig. 1
Fig. 1

Coordinate systems in the input and output planes.

Fig. 2
Fig. 2

The chord function g(x0xi) is the length of segment AB.

Fig. 3
Fig. 3

Schematic outline of the measurement of MTF.

Fig. 4
Fig. 4

MTF of flexible and fused imaging multifibers.

Equations (22)

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e ( x , y ) = 1 for ( x , y ) on the cross section of a fiber core centered at ( 0,0 ) , = 0 otherwise .
I ( x , y ) = i = 1 N e ( x x i , y y i ) × I ( x , y ) e ( x x i , y y i ) d x d y ,
I ( x , y ) = δ ( x x 0 ) ,
I ( x , y ) = i e ( x x i , y y i ) e ( x 0 x i , y y i ) d y = i e ( x x i , y y i ) g ( x 0 x i ) ,
g ( x 0 x i ) = e ( x 0 x i , y y i ) d y ,
L ( x , x 0 ) = i g ( x 0 x i ) g ( x x i ) .
L ( x , x 0 ) = x 1 = x 1 = g ( x 0 x 1 ) × g ( x x 1 ) ρ j ( x 1 ; x 1 ) d x 1 d x 1 ,
ρ j ( x 1 ; x 1 ) = ρ ( x 1 ) ρ c ( x 1 | x 1 ) ,
L ( x , x 0 ) = g ( x 0 x 1 ) g ( x x 1 ) ρ ( x 1 ) ρ c ( x 1 | x 1 ) d x 1 d x 1 .
ρ c ( x 1 | x 1 ) = ρ Δ ( x 1 x 1 ) .
L ( x , x 0 ) = g ( x 0 x 1 ) ρ Δ ( x 1 x 1 ) g ( x x 1 ) d x 1 d x 1
= g ( x 1 ) ρ Δ ( x 1 x 1 ) g ( x x 0 x 1 ) d x 1 d x 1 = g ( u ) ρ Δ ( υ ) g ( x x 0 u υ ) d u d υ = g ( x ) * ρ Δ ( x ) * g ( x x 0 ) ,
H ( f ) = exp ( i 2 π f x ) L ( x , x 0 ) d x = G ( f ) G ( f ) P ( f ) exp ( i 2 π f x 0 ) = G * ( f ) G ( f ) P ( f ) exp ( i 2 π f x 0 ) ,
H ( f ) = | H ( f ) | = G ( f ) G * ( f ) | P ( f ) | .
g c ( x ) = ( d 2 4 x 2 ) 1 / 2 for x 2 < d 2 4
= 0 otherwise .
G c ( f ) = 2 0 d / 2 ( d 2 4 x 2 ) 1 / 2 cos ( 2 π f x ) d x .
0 1 cos ( a ξ ) ( 1 ξ 2 ) 1 / 2 d ξ = π 2 a J 1 ( a ) ,
G c ( f ) = [ 2 J 1 ( π f d ) ] / ( π f d ) ,
H c ( f ) = { [ 2 J 1 ( π f d ) ] / ( π f d ) } 2
ρ g ( x 1 x 1 ) = 1 ( 2 π ) 1 / 2 σ exp [ 1 2 ( x 1 x 1 ) 2 σ 2 ] ,
H c ( f ) = [ 2 J 1 ( π f d ) π f d ] 2 exp ( 2 π 2 f 2 σ 2 ) .

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