Abstract

Equations which describe the flux transmitted and the angular distribution of the emergent light from straight cylindrical fibers of circular cross section have been derived and numerically evaluated. Loss of light due to imperfect reflections, bulk absorption, and Fresnel reflections, are included in the formulation. All skew rays in the fiber have been considered in these calculations.

Measurements of the attenuation and angular distribution of the emitted light from plastic scintillating fibers have been made. From the theoretical equations it has been deduced that these fibers are characterized by an internal reflectivity of 0.993±0.002 and an absorption coefficient of 0.015±0.003 cm-1.

Measurements of the light transmitted by single-clad glass fibers indicate that these fibers are characterized by an internal reflectivity of 0.9993±0.0002 and an absorption coefficient of the order of 10-4 cm-1. Some experimental data on glass fiber bundles also are included.

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  1. N. S. Kapany, in Concepts of Classical Optics, edited by John Strong (W. H. Freeman & Company, San Francisco, 1958), Appendix N. See also references contained therein.
  2. R. J. Potter and R. E. Hopkins, Proceedings of the Image Intensifier Symposium (U. S. Army Engineer Research and Development Laboratories, Fort Belvoir, Virginia, 1958), pp. 91–109.
  3. L. Reiffel and N. S. Kapany, Rev. Sci. Instr. 31, 1136 (1960).
  4. The author wishes to thank J. W. Hicks and W. P. Seigmund for private communications concerning the "black band" at the early stages of clad-fiber fabrication.
  5. Robert J. Potter, U. S. Atomic Energy Commission Rept. NYO-9033 (April 1, 1960).
  6. See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., London and New York, 1959), pp. 36–41 for the usual Fresnel equation. They are rewritten here expressing the transmissivity in terms of the axial angle θ.
  7. Because Fresnel reflection losses are considered, zero fiber length is not equivalent to no fiber at all. The attenuation curves represent the relative transmittance of the fiber for various lengths, and not the percentage of incident flux transmitted.
  8. Large scintillation counters used at the University of Rochester 130-in. Cyclotron Laboratory made of the same material as these fibers have shown the same kind of surface crazing. Moreover, other users of the scintillating plastic fibers have observed deterioration similar to that described here.
  9. R. J. Potter, Rev. Sci. Instr. 32, 286 (1961).
  10. Mark Hyman, Jr., Pilot Chemicals, Inc., Watertown, Massachusetts (private communication).
  11. R. J. Potter and R. E. Hopkins, IRE Trans. on Nuclear Sci., NS-7, 150 (1960).
  12. See, for example, the use of a long fiber bundle for nuclear tracking in reference 11.
  13. There are some special cases where a clad fiber might be used in isolation from other fibers, and any fiber action by the cladding's outer surface would increase the transmission and numerical aperture if the surface were clean and optically good. However, this aspect of the performance of fibers is virtually unpredictable, depending on very special conditions and applications.
  14. N. S. Kapany, J. Opt. Soc. Am. 49, 770 (1959).
  15. The computed curve is subject to the assumption of a circular cross section, which is not the case here. However, it appears that the shape of the fiber cross section probably does not affect the attenuation of the fiber very severely.
  16. The points are specified by the fiber numbers listed in Table I. All the fibers had a core index of 1.62 and a cladding index of 1.52.
  17. Note that although these curves are for approximately the same value of α as those used before, the numerical aperture of the illumination was different, which is reflected in a different attenuation curve.
  18. A study has been made of the decollimation properties of fibers. This work is included in reference 5 and has been reported in part at the October 8–10, 1959 meeting of the Optical Society of America; see J. Opt. Soc. Am. 49, 1128 (1959).
  19. The difference between an attenuation curve normalized at zero fiber length and an absolute transmittance also involves a correction for Fresnel reflection at the faces of the fibers.
  20. Note added in proof. In recent months there has been an improvement in commercially available fibers such that these data should now be considered as a conservative estimate of fiber performance.

Born, M.

See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., London and New York, 1959), pp. 36–41 for the usual Fresnel equation. They are rewritten here expressing the transmissivity in terms of the axial angle θ.

Hicks, J. W.

The author wishes to thank J. W. Hicks and W. P. Seigmund for private communications concerning the "black band" at the early stages of clad-fiber fabrication.

Hopkins, R. E.

R. J. Potter and R. E. Hopkins, Proceedings of the Image Intensifier Symposium (U. S. Army Engineer Research and Development Laboratories, Fort Belvoir, Virginia, 1958), pp. 91–109.

R. J. Potter and R. E. Hopkins, IRE Trans. on Nuclear Sci., NS-7, 150 (1960).

Hyman, Jr., Mark

Mark Hyman, Jr., Pilot Chemicals, Inc., Watertown, Massachusetts (private communication).

Kapany, N. S.

L. Reiffel and N. S. Kapany, Rev. Sci. Instr. 31, 1136 (1960).

N. S. Kapany, J. Opt. Soc. Am. 49, 770 (1959).

N. S. Kapany, in Concepts of Classical Optics, edited by John Strong (W. H. Freeman & Company, San Francisco, 1958), Appendix N. See also references contained therein.

Potter, R. J.

R. J. Potter and R. E. Hopkins, Proceedings of the Image Intensifier Symposium (U. S. Army Engineer Research and Development Laboratories, Fort Belvoir, Virginia, 1958), pp. 91–109.

R. J. Potter and R. E. Hopkins, IRE Trans. on Nuclear Sci., NS-7, 150 (1960).

R. J. Potter, Rev. Sci. Instr. 32, 286 (1961).

Potter, Robert J.

Robert J. Potter, U. S. Atomic Energy Commission Rept. NYO-9033 (April 1, 1960).

Reiffel, L.

L. Reiffel and N. S. Kapany, Rev. Sci. Instr. 31, 1136 (1960).

Seigmund, W. P.

The author wishes to thank J. W. Hicks and W. P. Seigmund for private communications concerning the "black band" at the early stages of clad-fiber fabrication.

Wolf, E.

See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., London and New York, 1959), pp. 36–41 for the usual Fresnel equation. They are rewritten here expressing the transmissivity in terms of the axial angle θ.

Other (20)

N. S. Kapany, in Concepts of Classical Optics, edited by John Strong (W. H. Freeman & Company, San Francisco, 1958), Appendix N. See also references contained therein.

R. J. Potter and R. E. Hopkins, Proceedings of the Image Intensifier Symposium (U. S. Army Engineer Research and Development Laboratories, Fort Belvoir, Virginia, 1958), pp. 91–109.

L. Reiffel and N. S. Kapany, Rev. Sci. Instr. 31, 1136 (1960).

The author wishes to thank J. W. Hicks and W. P. Seigmund for private communications concerning the "black band" at the early stages of clad-fiber fabrication.

Robert J. Potter, U. S. Atomic Energy Commission Rept. NYO-9033 (April 1, 1960).

See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., London and New York, 1959), pp. 36–41 for the usual Fresnel equation. They are rewritten here expressing the transmissivity in terms of the axial angle θ.

Because Fresnel reflection losses are considered, zero fiber length is not equivalent to no fiber at all. The attenuation curves represent the relative transmittance of the fiber for various lengths, and not the percentage of incident flux transmitted.

Large scintillation counters used at the University of Rochester 130-in. Cyclotron Laboratory made of the same material as these fibers have shown the same kind of surface crazing. Moreover, other users of the scintillating plastic fibers have observed deterioration similar to that described here.

R. J. Potter, Rev. Sci. Instr. 32, 286 (1961).

Mark Hyman, Jr., Pilot Chemicals, Inc., Watertown, Massachusetts (private communication).

R. J. Potter and R. E. Hopkins, IRE Trans. on Nuclear Sci., NS-7, 150 (1960).

See, for example, the use of a long fiber bundle for nuclear tracking in reference 11.

There are some special cases where a clad fiber might be used in isolation from other fibers, and any fiber action by the cladding's outer surface would increase the transmission and numerical aperture if the surface were clean and optically good. However, this aspect of the performance of fibers is virtually unpredictable, depending on very special conditions and applications.

N. S. Kapany, J. Opt. Soc. Am. 49, 770 (1959).

The computed curve is subject to the assumption of a circular cross section, which is not the case here. However, it appears that the shape of the fiber cross section probably does not affect the attenuation of the fiber very severely.

The points are specified by the fiber numbers listed in Table I. All the fibers had a core index of 1.62 and a cladding index of 1.52.

Note that although these curves are for approximately the same value of α as those used before, the numerical aperture of the illumination was different, which is reflected in a different attenuation curve.

A study has been made of the decollimation properties of fibers. This work is included in reference 5 and has been reported in part at the October 8–10, 1959 meeting of the Optical Society of America; see J. Opt. Soc. Am. 49, 1128 (1959).

The difference between an attenuation curve normalized at zero fiber length and an absolute transmittance also involves a correction for Fresnel reflection at the faces of the fibers.

Note added in proof. In recent months there has been an improvement in commercially available fibers such that these data should now be considered as a conservative estimate of fiber performance.

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