Abstract

A technique is proposed to measure cylindrically symmetric refractive index profiles of transparent rods. A probe ray is incident to the side of the rod, and its emergent point is observed on an end surface of the rod. A simple relationship between incident and emergent ray positions is used to determine the index profile. The profile of a graded index rod lens was measured with an accuracy to within 1 part in 103. An extension of the method to a more general profile distribution is discussed.

© 1983 Optical Society of America

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References

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  1. D. Marcuse, Appl. Opt. 18, 9 (1979).
    [CrossRef] [PubMed]
  2. I. Sasaki, D. N. Payne, R. J. Mansfield, Appl. Opt. 21, 4256 (1982).
  3. Y. Kokubun, K. Iga, Appl. Opt. 21, 1030 (1982).
    [CrossRef] [PubMed]
  4. W. E. Martin, Appl. Opt. 13, 2112 (1974).
    [CrossRef] [PubMed]
  5. L. S. Watkins, Appl. Opt. 18, 2214 (1979).
    [CrossRef] [PubMed]
  6. D. Gregoris, K. Iizuka, Appl. Opt. 22, 424 (1982).
    [CrossRef]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 122.
  8. E. Marchand, Gradient Index Optics (Academic, New York, 1978), p. 56.
  9. R. M. Allen, Practical Refractometry (R.P. Cargille Laboratories Inc., Cedar Grove, N.J. 070091962).
  10. Nippon Sheet Glass America, Ltd.Clark, N.J.1980).

1982 (3)

1979 (2)

1974 (1)

Allen, R. M.

R. M. Allen, Practical Refractometry (R.P. Cargille Laboratories Inc., Cedar Grove, N.J. 070091962).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 122.

Gregoris, D.

Iga, K.

Iizuka, K.

Kokubun, Y.

Mansfield, R. J.

I. Sasaki, D. N. Payne, R. J. Mansfield, Appl. Opt. 21, 4256 (1982).

Marchand, E.

E. Marchand, Gradient Index Optics (Academic, New York, 1978), p. 56.

Marcuse, D.

Martin, W. E.

Payne, D. N.

I. Sasaki, D. N. Payne, R. J. Mansfield, Appl. Opt. 21, 4256 (1982).

Sasaki, I.

I. Sasaki, D. N. Payne, R. J. Mansfield, Appl. Opt. 21, 4256 (1982).

Watkins, L. S.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 122.

Appl. Opt. (6)

Other (4)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 122.

E. Marchand, Gradient Index Optics (Academic, New York, 1978), p. 56.

R. M. Allen, Practical Refractometry (R.P. Cargille Laboratories Inc., Cedar Grove, N.J. 070091962).

Nippon Sheet Glass America, Ltd.Clark, N.J.1980).

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Figures (7)

Fig. 1
Fig. 1

(a) Geometry of probe ray incident at an angle γ in the meridional plane. (b) Ray trajectory at point P0 is found by axially translating the probe ray.

Fig. 2
Fig. 2

Schematic of the experimental apparatus.

Fig. 3
Fig. 3

Measurements of the ray path in the plastic slab sample.

Fig. 4
Fig. 4

Measurements of the ray path in a Selfoc microlens.

Fig. 5
Fig. 5

Measured refractive index profile of a Selfoc microlens.

Fig. 6
Fig. 6

Geometry of ray path direction.

Fig. 7
Fig. 7

Geometry of a ray in a cylinder with a more general refractive index distribution.

Equations (12)

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d d s ( n s ^ ) = n ,
d z d r = ± l 0 r [ n 2 ( r ) - l 0 2 ] r 2 - c 2 ,
n ( r ) = l 0 [ 1 + ( d z d r ) - 2 ] 1 / 2 ,
l 0 = n l sin γ ,
k ^ · d d s ( n s ^ ) = k ^ · n .
k ^ · ( d n d s ) s ^ + k ^ · n d s ^ d s = 0.
d n ( k ^ · s ) d s = k ^ · ( d n d s ) s ^ + k ^ · n d s ^ d s + n d k ^ d s · s ^ .
d n ( k ^ · s ^ ) d s = 0.
n cos β = l 0 = constant ,
d z d v = cot β .
d z d v = l 0 n 2 ( v ) - l 0 2
n ( v ) = l 0 [ ( d z d v ) - 2 + 1 ] 1 / 2 .

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