Abstract

Two ways are described in which dispersion can be used to improve the information transfer through fiber bundles. First, the use of dispersion at the entrance and exit ends of a fiber-optics image-transmitting bundle produces an image with resolution improved by about a factor of two. The individual fiber elements are not seen in the image. Second, it is possible to reduce drastically the number of fibers in the bundle and still transmit a complete image. One way is to arrange a number of rows of fibers parallel to each other but spaced a distance apart. The dispersion is perpendicular to the rows. Each row of fibers carries a chromatic image of the object. At the exit end the different chromatic images from the various rows of fibers are recombined by a dispersion system similar to that at the entrance end. Thus, each image point is reconstructed by a plurality of wavelengths. The image can therefore contain color as well as intensity information. The improvement of information transfer per fiber depends on the number of rows and on the ratio of dispersion distance to fiber diameter. It is shown that with a ratio of 100, a 20-row fiberscope can transfer the same effective information as a conventional fiberscope containing 660 rows. The relationship between dispersion and achromatic field is discussed and a comparison is given of prism and grating dispersion systems.

© 1968 Optical Society of America

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References

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  1. W. P. Siegmund, Light and Heat Sensing (Pergamon Press, Ltd., Oxford, 1963), Ch. 19.
  2. N. S. Kapany, in Concepts of Classical Optics, J. Strong, Ed. (W. H. Freeman and Company, San Francisco, 1958), p. 553.
  3. A. K. Chitayat, U. S. Patent3,217,588, issued 16Nov.1965.
  4. N. E. Lindenblad, U. S. Patent2,443,258 (1948).
  5. A. I. Kartashev, Opt. Spectry. (USSR) 9, 204 (1960).
  6. J. D. Armitage, A. Lohmann, and D. P. Paris, J. Appl. Phys. (Japan) 4, Suppl. 1, 273 (1965).
  7. W. Lukosz, Z. Naturforsch. 18a, 436 (1963); W. Lukosz and M. Marchand, Opt. Acta 10, 241 (1963).
    [Crossref]
  8. M. L. Polanyi, J. Opt. Soc. Am. 56, 1454 (1966).
  9. P. N. Kruythoff and S. L. Boersma, U. S. Patent3,191,487, issued 29June1965.
  10. A. W. Lohmann, U. S. Patent3,264,611, issued 2Aug.1966.
  11. F. L. O. Wadsworth, Astrophys. J. 1, 232 (1895), or R. A. SawyerExperimental Spectroscopy (Prentice Hall, Inc., N. Y., 1951), 2nd ed., p. 79
    [Crossref]
  12. N. S. Kapany, J. A. Eyer, and R. E. Keim, J. Opt. Soc. Am. 47, 423 (1957).
    [Crossref]

1966 (1)

M. L. Polanyi, J. Opt. Soc. Am. 56, 1454 (1966).

1965 (1)

J. D. Armitage, A. Lohmann, and D. P. Paris, J. Appl. Phys. (Japan) 4, Suppl. 1, 273 (1965).

1963 (1)

W. Lukosz, Z. Naturforsch. 18a, 436 (1963); W. Lukosz and M. Marchand, Opt. Acta 10, 241 (1963).
[Crossref]

1960 (1)

A. I. Kartashev, Opt. Spectry. (USSR) 9, 204 (1960).

1957 (1)

1895 (1)

F. L. O. Wadsworth, Astrophys. J. 1, 232 (1895), or R. A. SawyerExperimental Spectroscopy (Prentice Hall, Inc., N. Y., 1951), 2nd ed., p. 79
[Crossref]

Armitage, J. D.

J. D. Armitage, A. Lohmann, and D. P. Paris, J. Appl. Phys. (Japan) 4, Suppl. 1, 273 (1965).

Boersma, S. L.

P. N. Kruythoff and S. L. Boersma, U. S. Patent3,191,487, issued 29June1965.

Chitayat, A. K.

A. K. Chitayat, U. S. Patent3,217,588, issued 16Nov.1965.

Eyer, J. A.

Kapany, N. S.

N. S. Kapany, J. A. Eyer, and R. E. Keim, J. Opt. Soc. Am. 47, 423 (1957).
[Crossref]

N. S. Kapany, in Concepts of Classical Optics, J. Strong, Ed. (W. H. Freeman and Company, San Francisco, 1958), p. 553.

Kartashev, A. I.

A. I. Kartashev, Opt. Spectry. (USSR) 9, 204 (1960).

Keim, R. E.

Kruythoff, P. N.

P. N. Kruythoff and S. L. Boersma, U. S. Patent3,191,487, issued 29June1965.

Lindenblad, N. E.

N. E. Lindenblad, U. S. Patent2,443,258 (1948).

Lohmann, A.

J. D. Armitage, A. Lohmann, and D. P. Paris, J. Appl. Phys. (Japan) 4, Suppl. 1, 273 (1965).

Lohmann, A. W.

A. W. Lohmann, U. S. Patent3,264,611, issued 2Aug.1966.

Lukosz, W.

W. Lukosz, Z. Naturforsch. 18a, 436 (1963); W. Lukosz and M. Marchand, Opt. Acta 10, 241 (1963).
[Crossref]

Paris, D. P.

J. D. Armitage, A. Lohmann, and D. P. Paris, J. Appl. Phys. (Japan) 4, Suppl. 1, 273 (1965).

Polanyi, M. L.

M. L. Polanyi, J. Opt. Soc. Am. 56, 1454 (1966).

Siegmund, W. P.

W. P. Siegmund, Light and Heat Sensing (Pergamon Press, Ltd., Oxford, 1963), Ch. 19.

Wadsworth, F. L. O.

F. L. O. Wadsworth, Astrophys. J. 1, 232 (1895), or R. A. SawyerExperimental Spectroscopy (Prentice Hall, Inc., N. Y., 1951), 2nd ed., p. 79
[Crossref]

Astrophys. J. (1)

F. L. O. Wadsworth, Astrophys. J. 1, 232 (1895), or R. A. SawyerExperimental Spectroscopy (Prentice Hall, Inc., N. Y., 1951), 2nd ed., p. 79
[Crossref]

J. Appl. Phys. (Japan) (1)

J. D. Armitage, A. Lohmann, and D. P. Paris, J. Appl. Phys. (Japan) 4, Suppl. 1, 273 (1965).

J. Opt. Soc. Am. (2)

Opt. Spectry. (USSR) (1)

A. I. Kartashev, Opt. Spectry. (USSR) 9, 204 (1960).

Z. Naturforsch. (1)

W. Lukosz, Z. Naturforsch. 18a, 436 (1963); W. Lukosz and M. Marchand, Opt. Acta 10, 241 (1963).
[Crossref]

Other (6)

P. N. Kruythoff and S. L. Boersma, U. S. Patent3,191,487, issued 29June1965.

A. W. Lohmann, U. S. Patent3,264,611, issued 2Aug.1966.

W. P. Siegmund, Light and Heat Sensing (Pergamon Press, Ltd., Oxford, 1963), Ch. 19.

N. S. Kapany, in Concepts of Classical Optics, J. Strong, Ed. (W. H. Freeman and Company, San Francisco, 1958), p. 553.

A. K. Chitayat, U. S. Patent3,217,588, issued 16Nov.1965.

N. E. Lindenblad, U. S. Patent2,443,258 (1948).

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Figures (15)

Fig. 1
Fig. 1

Schematic diagram of wavelength-multiplexing system. Blue, yellow, and red rays are indicated by b, y, r, respectively.

Fig. 2
Fig. 2

Schematic diagram of end of fiberscope. The physical width is w. As seen through the dispersing system, the total width is w + d. The achromatic portion has a width wd.

Fig. 3
Fig. 3

Dispersing element between object and lens, finite conjugates. S is a white point source. The distance s is the separation between the virtual sources in C and F light, as seen through the dispersing element. In this case d = ms = mδl1 where m is the magnification of the lens system.

Fig. 4
Fig. 4

Dispersing element between lens and fiberscope, either finite or infinite conjugates. By inspection, d = δl2.

Fig. 5
Fig. 5

Dispersing element in front of lens, infinite conjugate. By inspection, d = δf, where f is the focal length of the lens system.

Fig. 6
Fig. 6

Limitation imposed by zero order. Δθ01 is the largest angle for which the zero order from the upper portion of the object does not overlap the first-order F line from the lower portion of the object.

Fig. 7
Fig. 7

(a) Image obtained without dispersion. Fiber elements are 10-μm diam in 6 × 6 multifibers, the overall bundle dimensions are 8 × 10 mm. (b) Image obtained with 0.67-mm dispersion distance. Dispersion distance d, is given by Eq. (8), in which the angular separation of the C and F lines was δ = 0.0262 rad. (c) Image obtained with 0.93-mm dispersion.

Fig. 8
Fig. 8

Direction, θ, and magnitude, d, of dispersion on the fiberscope entrance face.

Fig. 9
Fig. 9

Images obtained with higher magnification of fibers. Top. Without dispersion. Bottom. With dispersion distance of 0.48 mm.

Fig. 10
Fig. 10

Abbreviated fiberscope entrance face. Direction and magnitude of dispersion are shown. The rectangle represents the spectrum from an object point.

Fig. 11
Fig. 11

Spectral radiance of an object point. Bars represent the sampling by 5 rows of fibers. (b) Spectrum of object point as sampled by abbreviated fiberscope.

Fig. 12
Fig. 12

Achromatic-field dimension. Line is graph of Eq. (13) made dimensionless by dividing by b, the distance between slits. Points are expersimentally determined. Circles represent wa/b, where wa is the achromatic field dimension. Triangles represent wa/b, where, wa′ is the quasi-achromatic field as defined in the text, and squares represent wt/b, where wt is the total field dimension. For this study the parameter p = 4.4.

Fig. 13
Fig. 13

Image obtained with a simulated seven-row fiberscope. Dispersion is horizontal.

Fig. 14
Fig. 14

Figure of merit, Γ, for an abbreviated fiberscope. Γ is the factor of improvement in resolvable lines per fiber for a multiplexed abbreviated fiberscope compared to a standard fiberscope. For this case the number of rows over which the C-F spectrum is spread is p = 4.4.

Fig. 15
Fig. 15

Abbreviated fiberscopes. (a) Each circle represents either a single fiber or a multifiber. The use of a double row reduces the streaking effect caused by the spaces between fibers. (b) Instead of a single row of single fibers, a triple row of multifibers is used to transmit a chromatic image.

Tables (1)

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Table I Resolution obtained with 10.3-μm element fiberscope, with and without dispersion.

Equations (21)

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d 1 = δ 1 f 1             d 2 = δ 2 f 2 ,
δ 1 f 1 = δ 2 f 2 d .
n = d / b .
w a = w - d .
w a / w = 1 - ( b n / w ) .
w a / w = 0.9.
w t = w + d .
d = s m = m δ l 1 ,
d = δ l 2 ,
d = δ f .
Δ θ 01 = Δ θ F = sin - 1 ( λ F / g ) ,
Δ θ 12 = sin - 1 ( 2 λ F / g ) - sin - 1 ( λ C / g ) .
sin - 1 2 λ F g = 2 λ F g ,
δ = ( λ C - λ F ) / g .
Δ θ 01 = [ λ F / ( λ C - λ F ) ] δ = 2.86 δ
Δ θ 12 = 2 λ F - λ C λ C - λ F δ = 1.86 δ ,
p = d / b = δ l 2 / b .
w a = ( r - 1 ) b - d .
[ ( r - 1 ) b - d ] / a ,
γ ( r - 1 ) b - d r a = d p a r - 1 - p r ,
Γ = γ 0.5 = 2 d p a r - 1 - p r .