Abstract

By magnifying the high-quality image produced by a rigid miniature endoscope onto a large flexible multifiber, an instrument has been developed which provides both high resolution and flexibility. It is shown theoretically, and verified experimentally, that the MTF of a system of coupled multifibers is the product of the individual MTFs. Measurements show that the coupled instruments outperform state-of-the-art all-flexible systems. The technique should greatly facilitate observation, display, and photography in percutaneous endoscopy and in a variety of industrial applications.

© 1978 Optical Society of America

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References

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  1. H. H. Hopkins, in Endoscopy, G. Berci, Ed. (Appleton-Century-Crofts, New York, 1976), p. 39.
  2. M. Epstein, Opt. Eng. 13, 139 (1974).
    [CrossRef]
  3. M. E. Marhic, S. E. Schacham, M. Epstein, Appl. Opt. 17, 3503 (1978).
    [CrossRef] [PubMed]
  4. As in Ref. 3, we omit some constant factors in the rest of the analysis.
  5. Up to this point f has denoted the spatial frequency in the output plane of the system. To compare systems with different magnifications, however, as well as to speak easily in terms of resolution, it is advantageous to deal with spatial frequencies in the input plane. From now on, then, f refers to the spatial frequency at the input of the systems being compared.

1978 (1)

1974 (1)

M. Epstein, Opt. Eng. 13, 139 (1974).
[CrossRef]

Epstein, M.

Hopkins, H. H.

H. H. Hopkins, in Endoscopy, G. Berci, Ed. (Appleton-Century-Crofts, New York, 1976), p. 39.

Marhic, M. E.

Schacham, S. E.

Appl. Opt. (1)

Opt. Eng. (1)

M. Epstein, Opt. Eng. 13, 139 (1974).
[CrossRef]

Other (3)

H. H. Hopkins, in Endoscopy, G. Berci, Ed. (Appleton-Century-Crofts, New York, 1976), p. 39.

As in Ref. 3, we omit some constant factors in the rest of the analysis.

Up to this point f has denoted the spatial frequency in the output plane of the system. To compare systems with different magnifications, however, as well as to speak easily in terms of resolution, it is advantageous to deal with spatial frequencies in the input plane. From now on, then, f refers to the spatial frequency at the input of the systems being compared.

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Figures (5)

Fig. 1
Fig. 1

Representative fibers and coordinate systems for the calculation of the MTF of two coupled multifibers.

Fig. 2
Fig. 2

Enlarged view of fused multifiber cross section.

Fig. 3
Fig. 3

MTF of coupled and all-flexible fiberscopes.

Fig. 4
Fig. 4

Computed and measured MTFs of coupled multifibers.

Fig. 5
Fig. 5

View of the rigid multifiber through the flexible bundle.

Equations (12)

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I ( x , y ) = i = 1 N 1 e 1 ( x x 1 i , y y 1 i ) × I ( x , y ) e 1 ( x x 1 i , y y 1 i ) d x d y , I ( x , y ) = j = 1 N 2 e 2 ( x x 2 j , y y 2 j ) × I ( x , y ) e 2 ( x x 2 j , y y 2 j ) d x d y = i = 1 N 1 j = 1 N 2 .. I ( x , y ) e 1 ( x x 1 i , y y 1 i ) e 1 ( x x 1 i , y y 1 i ) × e 2 ( x x 2 j , y y 2 j ) e 2 ( x x 2 j , y y 2 j ) d x d y d x d y .
I ( x , y ) = i = 1 N 1 j = 1 N 2 e 1 ( x x 1 i , y y 1 i ) / g 1 ( x 0 x 1 i ) × e 2 ( x x 2 j , y y 2 j ) e 2 ( x x 2 j , y y 2 j ) d x d y .
L ( x , x 0 ) = I ( x , y ) d y = i = 1 N 1 j = 1 N 2 e 1 ( x x 1 i , y y 1 i ) g 1 ( x 0 x 1 i ) × g 2 ( x x 2 j ) e 2 ( x x 2 j , y y 2 j ) d x d y ,
L ( x , x 0 ) = i = 1 N 1 j = 1 N 2 g 1 ( x 0 x 1 i ) × h 12 ( x 2 j x 1 i , y 2 j y 1 i ) g 2 ( x x 2 j ) ,
L ( x , x 0 ) = .. g 1 ( x 0 x 1 ) ρ 1 Δ ( x 1 x 1 ) h 12 ( x 2 x 1 , Δ y ) × ρ 2 Δ ( x 2 x 2 ) g 2 ( x x 2 ) d x 1 d x 1 d x 2 d x 2 d ( Δ y ) ,
L ( x , x 0 ) = .. g 1 ( x 0 x 1 ) ρ 1 Δ ( x 1 x 1 ) h 12 ( x 2 x 1 , y 2 y 1 ) × ρ 2 Δ ( x 2 x 2 ) g 2 ( x x 2 ) d x 1 d x 1 d x 2 d x 2 d y 1 d y 2 = .. g 1 ( x 0 x 1 ) ρ 1 Δ ( x 1 x 1 ) e 1 ( x x 1 , y y 1 ) × e 2 ( x x 2 , y y 2 ) ρ 2 Δ ( x 2 x 2 ) × g 2 ( x x 2 ) d x 1 d x 1 d x 2 d x 2 d y 1 d y 2 d x d y = .. g 1 ( x 0 x 1 ) ρ 1 Δ ( x 1 x 1 ) g 1 ( x x 1 ) g 2 ( x x 2 ) × ρ 2 Δ ( x x 2 ) g 2 ( x x 2 ) d x 1 d x 1 d x 2 d x 2 d x d y = g 2 ( x ) * ρ 2 Δ ( x ) * g 2 ( x ) * g 1 ( x ) * ρ 1 Δ ( x ) × * g 1 ( x 0 x ) .
H 12 ( f ) = H 1 ( f ) H 2 ( f ) ,
H 1 ( f ) = G 1 ( f ) G 1 * ( f ) | P 1 ( f ) | , H 2 ( f ) = G 2 ( f ) G 2 * ( f ) | P 2 ( f ) | ,
H 12 M ( f ) = m = 1 M H m ( f ) ,
H 12 M , 12 K ( f ) = m = 1 M H m ( f ) k = 1 K H k a ( k ) .
H c ( f ) = [ 2 J 1 ( π f d 2 ) π f d 2 ] 2 · | P 2 ( f ) | ,
H c ( f ) = [ 2 J 1 ( π f d 2 ) π f d 2 ] 2 · [ 2 J 1 ( π f d 1 ) π f d 1 ] 2 · | P 2 ( f ) | ,

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