Abstract

In an image transmitting assembly of small diameter fibers, a marked deterioration in image contrast and resolution may occur when there is substantial light leakage between neighboring fibers at the region of the line contact. Expressions have been derived for the magnitude of flux leakage between neighboring fibers due to frustrated total reflections and thereby the point-spread function for an uninsulated fiber assembly is computed. Further, the static and dynamic point-spread functions of fiber bundles have been measured experimentally and the lower limit in fiber diameter for an image transmitting assembly of uninsulated fibers is derived.

© 1959 Optical Society of America

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References

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  1. N. S. Kapany in Concepts of Classical Optics by John Strong (W. H. Freeman and Company, San Francisco, 1958), Appendix N.
  2. N. S. Kapany and W. A. Oberheim, J. Opt. Soc. Am. 48, 870(FB 42) (1958).
  3. G. Quincke, Pogg. Ann. 117, 1117 (1863).
  4. J. Joss, Theoretical Physics (1951), p. 352, Ct., Seg.
  5. W. Weinstein, J. Opt. Soc. Am. 37, 576 (1947).
    [Crossref] [PubMed]
  6. Kapany, Eyer, and Keim, J. Opt. Soc. Am. 47, 423 (1957).
    [Crossref]

1958 (1)

N. S. Kapany and W. A. Oberheim, J. Opt. Soc. Am. 48, 870(FB 42) (1958).

1957 (1)

1951 (1)

J. Joss, Theoretical Physics (1951), p. 352, Ct., Seg.

1947 (1)

1863 (1)

G. Quincke, Pogg. Ann. 117, 1117 (1863).

Eyer,

Joss, J.

J. Joss, Theoretical Physics (1951), p. 352, Ct., Seg.

Kapany,

Kapany, N. S.

N. S. Kapany and W. A. Oberheim, J. Opt. Soc. Am. 48, 870(FB 42) (1958).

N. S. Kapany in Concepts of Classical Optics by John Strong (W. H. Freeman and Company, San Francisco, 1958), Appendix N.

Keim,

Oberheim, W. A.

N. S. Kapany and W. A. Oberheim, J. Opt. Soc. Am. 48, 870(FB 42) (1958).

Quincke, G.

G. Quincke, Pogg. Ann. 117, 1117 (1863).

Weinstein, W.

J. Opt. Soc. Am. (3)

Pogg. Ann. (1)

G. Quincke, Pogg. Ann. 117, 1117 (1863).

Theoretical Physics (1)

J. Joss, Theoretical Physics (1951), p. 352, Ct., Seg.

Other (1)

N. S. Kapany in Concepts of Classical Optics by John Strong (W. H. Freeman and Company, San Francisco, 1958), Appendix N.

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Figures (9)

F. 1
F. 1

Light leakage due to frustrated total reflection. (a) Frustrated total reflection at plane parallel interfaces. (b) Leakage between dielectric cylinders due to frustrated total reflection.

F. 2
F. 2

Light transmission due to frustrated total reflection at plane parallel interfaces when the index of the two bounding media is equal to 1.6 and index of the intermediate medium is equal to 1.0. (a) τ for parallel plane of polarization. (b) τ for perpendicular plane of polarization.

F. 3
F. 3

Light transmission due to frustrated total reflection at plane parallel interfaces when the index of the two bounding media is equal to 1.80 and index of the intermediate medium is equal to 1.50. (a) τ for parallel plane of polarization. (b) τ for perpendicular plane of polarization.

F. 4
F. 4

Light transmission of straight fibers. (a) Percentage transmission as a function of half-angle of incident cone of light with 1% surface absorption. d = 200μ, (b) d = 50 μ. (c) Percentage transmission as a function of length for various diameter fibers.

F. 5
F. 5

Illustrating light losses from the central fiber into the six surrounding fibers. (a) Passage of an axial cone along the central fiber. (b) Illustrating the leakage regions in the reflected light cone. (c) Light leakage at cylindrical interfaces.

F. 6
F. 6

Illustrating flux penetration in the surrounding fibers.

F. 7
F. 7

τ and τ′ for various lengths of 25-μ diam fibers as a function of the f/number of the incident light cone.

F. 8
F. 8

τ and τ′ for various lengths of 50-μ diam fibers as a function of the f/number of the incident light cone.

F. 9
F. 9

The point-spread function of a 50-μ diam uninsulated fiber bundle. (a) Static point-spread function showing streaks of light leakage at the region of contact. (b) Dynamic point-spread function for the same fiber bundle.

Tables (1)

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Table I

Equations (24)

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E 1 + + E 1 = E 0 E 1 + E 1 = U 0 U 1 E 0 E 2 + + E 2 = E 1 + exp ( i υ 1 t 1 ) + E 1 exp ( i υ 1 t 1 ) E 2 + E 2 = U 1 U 2 E 1 + exp ( i υ 1 t 1 ) E 1 exp ( i υ 1 t 1 ) } ,
V 1 = 2 π λ N 1 cos ϕ 1
U 1 = N 1 / cos ϕ 1
U 1 = N 1 · cos ϕ 1
cos ϕ 1 = i [ ( N 0 N 1 ) 2 sin 2 ϕ 0 1 ] 1 2 = i ω
| E 2 + | 2 = cosh 2 [ 2 π t N 1 ω λ ] + sinh 2 [ 2 π t · N 1 ω λ ] [ N 1 2 cos 2 ϕ 0 N 0 2 ω 2 2 N 0 N 1 ω cos ϕ 0 ] 2
| E 2 + | 2 = cosh 2 [ 2 π t N 1 ω λ ] + sinh 2 [ 2 π t · N 1 ω λ ] [ N 1 2 ω 2 N 0 2 cos 2 ϕ 0 2 N 0 N 1 ω cos ϕ 0 ] 2 .
[ T ] ; [ T ] = N 2 cos ϕ 2 N 0 cos ϕ 0 | E 2 + E 0 + | 2 .
[ T ] ; [ T ] = | E 2 + E 0 + | 2 .
λ / 4 r ( θ / 2 ) 2
θ = ( λ / r ) 1 2 .
σ = ( 3 / π ) ( λ / r ) 1 2 .
d E ( I ) in = 2 π F ( I ) sin IdI .
R ( I ) = 1 2 { [ cos I ( N 2 sin 2 I ) 1 2 cos I + ( N 2 sin 2 I ) 1 2 ] 2 + [ N 2 cos I ( N 2 sin 2 I ) 1 2 N 2 cos I + ( N 2 sin 2 I ) 1 2 ] 2 } .
1 exp { A L / [ 1 ( sin I / N ) 2 ] 1 2 }
τ = 2 π · K 0 α F ( I ) [ 1 R ( I ) ] 2 · [ 1 Ā ( I ) ] η · exp ( A L sec I ) sin I d I ,
θ = 2 cos 1 [ ( r λ ) / r ] .
τ 1 = K 1 0 α [ 1 R ( I ) ] 2 · exp ( A L sec I ) sin I d I ,
τ 2 = C 1 K 2 α α [ 1 R ( I ) ] 2 × exp ( A L sec I ) sin I d I ,
τ 3 = C 2 K 2 2 λ α α 0 2 λ [ 1 R ( I ) ] 2 [ 1 ( t , ϕ 0 ) ] η × exp ( A L sec I ) sin I dtd I ,
( t , ϕ 0 ) = 1 2 [ T ( N 0 , N 1 , ϕ 0 , t , λ ) + T ( N 0 , N 1 , ϕ 0 , t , λ ) ] C 2 = 3 θ / π η = L tan I / D is the number of reflections .
τ = K 3 [ τ 1 K 1 + τ 2 K 2 + τ 3 K 2 ]
τ ( α ) = ( t , ϕ 0 ) · exp ( A L sec I ) { [ 1 ( t , ϕ 0 ) ] + [ 1 ( t , ϕ 0 ) ] 2 + [ 1 ( t , ϕ 0 ) ] η } = [ 1 ( t , ϕ 0 ) ] · { 1 [ 1 ( t , ϕ 0 ) ] η } · exp ( A L sec I ) .
τ = K 3 · C 3 2 λ 0 α 0 2 λ [ 1 ( t , ϕ 0 ) ] { 1 [ 1 ( t , ϕ 0 ) ] η } × exp ( A L sec I ) sin I dtd I