Abstract

Absolute and angular transmission measurements were made on a single sheathed fiber 0.15 mm in diameter and 2.1 m long, and an optical angular transfer function was defined and calculated. The effective transmission of the source brightness was calculated as a function of the f numbers of the entrance and output optics of the fiber, and these results were used to choose a suitable optical system for illumination of a spectrometer.

© 1971 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Optics Technology, Inc., 901 California Ave., Palo Alto, California 94304.
  2. N. S. Kapany, Fiber Optics (Academic, New York, 1967).
  3. B. G. Phillips, Proceedings of a Seminar on Fiber Optics, Baltimore, 29–30 April 1968 (SPIE Seminar Proceedings, 1968), Vol. 14, p. 69.
  4. B. G. Phillips, private communication.
  5. P. Jacquinot, Rept. Prog. Phys. 23, 267 (1960).
    [CrossRef]

1960 (1)

P. Jacquinot, Rept. Prog. Phys. 23, 267 (1960).
[CrossRef]

Jacquinot, P.

P. Jacquinot, Rept. Prog. Phys. 23, 267 (1960).
[CrossRef]

Kapany, N. S.

N. S. Kapany, Fiber Optics (Academic, New York, 1967).

Phillips, B. G.

B. G. Phillips, Proceedings of a Seminar on Fiber Optics, Baltimore, 29–30 April 1968 (SPIE Seminar Proceedings, 1968), Vol. 14, p. 69.

B. G. Phillips, private communication.

Rept. Prog. Phys. (1)

P. Jacquinot, Rept. Prog. Phys. 23, 267 (1960).
[CrossRef]

Other (4)

Optics Technology, Inc., 901 California Ave., Palo Alto, California 94304.

N. S. Kapany, Fiber Optics (Academic, New York, 1967).

B. G. Phillips, Proceedings of a Seminar on Fiber Optics, Baltimore, 29–30 April 1968 (SPIE Seminar Proceedings, 1968), Vol. 14, p. 69.

B. G. Phillips, private communication.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic diagram of angular distribution measurements. a, Photoflood lamp; b, f/1.8 50-mm focal length camera lens; c, optical fiber, 0.15-mm diameter, 2.1 m long; d, photomultiplier.

Fig. 2
Fig. 2

Angular distribution of light intensity Ir(θ2, θe), normalized to unity at θ2 = 0. θe is the half-angle corresponding to the entrance f number, and this relation is indicated on the abscissa.

Fig. 3
Fig. 3

Light intensity Ia(θe) at θ2 = 0, normalized to unity at f/1.8 (θe = 15.5°). The normalized output brightness is given by the product of Figs. 2 and 3, B2′(θ2,θe) = Ir(θ2,θe) × Ia(θe).

Fig. 4
Fig. 4

Angular optical transfer function g(θ1,θ2) plotted as a function of θ1.

Fig. 5
Fig. 5

Angular optical transfer function g(θ1,θ2) plotted as a function of θ2.

Fig. 6
Fig. 6

The effective transmission T ¯ (θe,θ0) plotted as a function of θ0 (the half-angle corresponding to the output f number) with θe (the half-angle corresponding to the entrance f number) as a parameter. The f number correspondence is indicated on the abscissa, and T ¯ (θe,θ0) is normalized to unity for θe = 90°, θ0 → 0.

Fig. 7
Fig. 7

The total transmission T(θ) of a ray entering the fiber at angle θ.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

S = A Ω ,
B 2 ( θ 2 ) = 0 π / 2 B 1 ( θ 1 ) g ( θ 1 , θ 2 ) cos θ 1 2 π θ 1 d θ 1 .
B 2 ( θ 2 , θ e ) = B 0 cos θ 2 0 θ e g ( θ 1 , θ 2 ) cos θ 1 2 π θ 1 d θ 1
B eff = T ¯ ( θ e , θ 0 ) B 0 ,
B 2 ( θ 2 ) = 0 π / 2 B 1 ( θ 1 ) g ( θ 1 , θ 2 ) cos θ 1 2 π θ 1 d θ 1 .
g ( θ 1 , θ 2 ) = δ ( θ 1 - θ 2 ) / cos θ 1 2 π θ 1 ,
B 2 ( θ 2 , θ e ) = B 0 cos θ 2 0 θ e g ( θ 1 , θ 2 ) cos θ 1 2 π θ 1 d θ 1 .
g ( θ e , θ 2 ) = ( B 0 2 π θ e cos θ e cos θ 2 ) - 1 d B ( θ e , θ 2 ) / d θ e .
P 0 ( θ 1 ) = B 1 ( θ 1 ) cos θ 1 2 π θ 1 δ θ 1 0 π / 2 g ( θ 1 , θ 2 ) cos θ 2 2 π θ 2 d θ 2 .
T ( θ 1 ) = 0 π / 2 g ( θ 1 , θ 2 ) cos θ 2 2 π θ 2 d θ 2 .
P 2 ( θ e , θ 0 ) = B 0 0 θ e cos θ 1 2 π θ 1 d θ 1 0 θ 0 g ( θ 1 , θ 2 ) cos θ 2 2 π θ 2 d θ 2 ,
P 2 ( max ) = B 0 0 θ 0 cos θ 2 2 π θ 2 d θ 2 ,
T ¯ ( θ e , θ 0 ) = P 2 ( θ e , θ 0 ) / P 2 ( max ) .
P 2 ( θ e , θ 0 ) = 0 θ 0 B 2 ( θ 2 , θ e ) 2 π θ 2 d θ 2 .
P 1 ( θ e ) = B 0 0 θ 0 cos θ 1 2 π θ 1 d θ 1 ,
f = P 2 ( θ e , θ 0 ) / P 1 ( θ e ) .

Metrics