Abstract

A theoretical study of unevenness of illuminance on the image plane of a gradient-index fiber array is discussed under the first-order approximation.

© 1980 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Aoki, J. Opt. Soc. Am. 56, 1648 (1966).
    [CrossRef]
  2. M. Sakamoto, H. Uejima, M. Furukawa, T. Yamada, M. Toyama, Electrophotogr. Jpn. 12, 12 (1973).
  3. H. Ochi, J. Inst. Image Electron. Eng. Jpn. 4, 13 (1975).
  4. T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
    [CrossRef]

1975 (1)

H. Ochi, J. Inst. Image Electron. Eng. Jpn. 4, 13 (1975).

1973 (1)

M. Sakamoto, H. Uejima, M. Furukawa, T. Yamada, M. Toyama, Electrophotogr. Jpn. 12, 12 (1973).

1970 (1)

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

1966 (1)

Aoki, Y.

Furukawa, M.

M. Sakamoto, H. Uejima, M. Furukawa, T. Yamada, M. Toyama, Electrophotogr. Jpn. 12, 12 (1973).

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Kitano, I.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Koizumi, K.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Matsumura, H.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Ochi, H.

H. Ochi, J. Inst. Image Electron. Eng. Jpn. 4, 13 (1975).

Sakamoto, M.

M. Sakamoto, H. Uejima, M. Furukawa, T. Yamada, M. Toyama, Electrophotogr. Jpn. 12, 12 (1973).

Toyama, M.

M. Sakamoto, H. Uejima, M. Furukawa, T. Yamada, M. Toyama, Electrophotogr. Jpn. 12, 12 (1973).

Uchida, T.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Uejima, H.

M. Sakamoto, H. Uejima, M. Furukawa, T. Yamada, M. Toyama, Electrophotogr. Jpn. 12, 12 (1973).

Yamada, T.

M. Sakamoto, H. Uejima, M. Furukawa, T. Yamada, M. Toyama, Electrophotogr. Jpn. 12, 12 (1973).

Electrophotogr. Jpn. (1)

M. Sakamoto, H. Uejima, M. Furukawa, T. Yamada, M. Toyama, Electrophotogr. Jpn. 12, 12 (1973).

IEEE J. Quantum Electron. (1)

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

J. Inst. Image Electron. Eng. Jpn. (1)

H. Ochi, J. Inst. Image Electron. Eng. Jpn. 4, 13 (1975).

J. Opt. Soc. Am. (1)

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 (14)

Fig. 1
Fig. 1

Principle of the SLA.

Fig. 2
Fig. 2

Cylindrical coordinates and the wave vector in Selfoc.

Fig. 3
Fig. 3

Ray traveling in Selfoc and its projection on the end surface.

Fig. 4
Fig. 4

Incident ray on the end surface of Selfoc.

Fig. 5
Fig. 5

Ray accepted in Selfoc.

Fig. 6
Fig. 6

Diagram for obtaining the luminous intensity at point P on the end surface of Selfoc.

Fig. 7
Fig. 7

Diagram of formation of an image through the lens with unit magnification.

Fig. 8
Fig. 8

Diagram for obtaining the illuminance on the image plane of an elementary lens.

Fig. 9
Fig. 9

Two scanning methods for using the SLA.

Fig. 10
Fig. 10

Illuminance through the lens represented by the x-y coordinates.

Fig. 11
Fig. 11

Illuminance in line scanning: (a) one-row SLA; (b) two-row SLA; (c) three-row SLA.

Fig. 12
Fig. 12

Unevenness of illuminance of the SLA in line scanning.

Fig. 13
Fig. 13

Illuminance in field scanning: (a) one-row SLA; (b) two-row SLA.

Fig. 14
Fig. 14

Unevenness of illuminance of the SLA in field scanning.

Equations (57)

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

n = n 0 ( 1 A 2 r 2 ) ,
Z = r C 1 [ k 2 C 1 2 ( C 2 r ) 2 ] 1 / 2 d r φ = r C 2 r 2 [ k 2 C 1 2 ( C 2 r ) 2 ] 1 / 2 d r } ,
C 1 = k z , C 2 = r k φ ,
k 2 = K 0 2 n 0 2 ( 1 A r 2 ) ,
r 2 sin [ 2 ( φ φ 0 ) ] = ( Q 2 r 2 2 C 0 2 ) ( Q 4 4 M 2 C 0 2 ) 1 / 2 ,
C 0 = C 2 / C 1 , M = ( k 0 n 0 / C 1 ) A , Q 2 = ( k 0 n 0 / C 1 ) 2 1 .
φ 0 = ( ½ ) sin 1 [ h 2 ( Q 2 h 2 2 C 0 2 ) ( Q 4 4 M 2 C 0 2 ) 1 / 2 ] .
Q 2 ( X 2 + Y 2 ) 2 ( Q 4 4 M 2 C 0 2 ) 1 / 2 ( X Y ) 2 C 0 2 = 0 ,
( x / R x ) 2 + ( y / R y ) 2 = 1 ,
R x 2 = 2 C 0 2 / [ Q 2 ( Q 4 4 M 2 C 0 2 ) 1 / 2 ] ,
R y 2 = 2 C 0 2 / [ Q 2 + ( Q 4 4 M 2 C 0 2 ) 1 / 2 ] .
sin ( I ) = n sin ( γ ) .
k x = k cos ( α ) , k y = k cos ( β ) , k z = k cos ( γ ) ,
C 1 = k [ 1 n 2 sin 2 ( I ) ] 1 / 2 ,
C 2 = k r sin ( I ) sin ( ϕ ) / n .
r 0 R x ,
C 2 2 + C 1 2 r 0 2 K 0 2 n 0 2 r 0 2 ( 1 A r 0 2 )
sin 2 ( I ) A n 0 2 r 0 2 ( 1 R 2 ) / [ 1 R 2 sin 2 ( ϕ ) ] ,
R = r / r 0 ,
sin 2 ( θ ) = A n 0 2 r 0 2 ( 1 R 2 ) / [ 1 R 2 sin 2 ( ϕ ) ] .
U ̂ x = sin ( θ ) cos ( ϕ ) , U ̂ y = sin ( θ ) sin ( ϕ ) ,
( U ̂ x / θ m ) 2 + ( U ̂ y / θ t ) 2 = 1 ,
θ m 2 = θ 0 2 ( 1 R 2 ) ,
θ t 2 = θ 0 2 = A n 0 2 r 0 2 ,
d e = B cos ( φ ) × d ω = B cos ( φ ) d S / ρ 2 = B × d S / ρ 2 ,
e = B S / ρ 2 .
S = π θ m × θ t ,
ρ = 1 .
e = e 0 [ 1 ( r / r 0 ) 2 ] 1 / 2 ,
e 0 = B π θ 0 2 .
l 0 = r 0 tan ( Z 0 ) / θ 0 ,
Z 0 = A Z 0 / 2
π / 2 < Z 0 < π .
f = r 0 sec ( Z 0 ) × csc ( Z 0 ) / ( 2 θ 0 ) .
x 0 = r 0 sec ( Z 0 ) ,
α = θ 0 cos ( Z 0 ) , β = θ 0 sin ( Z 0 ) x α = r 0 sin ( Z 0 ) , x β = r 0 cos ( Z 0 ) } .
E = E 0 [ 1 ( x / x 0 ) 2 ] 1 / 2 ,
η = ( 2 π / 3 ) r 0 2 e 0 = ( 2 π / 3 ) x 0 2 E 0 ,
E 0 = e 0 ( r 0 / x 0 ) 2 = B π θ 0 2 cos 2 ( Z 0 )
E 0 = B π α 2 .
Δ I = ( I max I min ) / I min ,
E L ( x , y ) = E 0 [ 1 ( x 2 + y 2 ) / x 0 2 ] 1 / 2 ,
E F ( y ) = ( π / 2 ) E 0 x 0 [ 1 ( y / x 0 ) 2 ] .
m = ( ½ ) × ( x 0 / r 0 ) = x 0 / D ,
E L ( x , y ) = [ 1 ( x 2 + y 2 ) / m 2 ] 1 / 2 ,
E F ( y ) = 1 y 2 / m 2 ,
I = E L ( y ) + j = 1 n [ E L ( y ) j + E L ( y ) j ] ,
I = E L ( y ) + j = 1 n [ E L ( y ) j + E L ( y ) j + E L ( y ) j 1 / 2 + E L ( y ) j + 1 / 2 ] ,
I = E L ( y ) + j = 1 n [ E L ( y ) j + E L ( y ) j ] + 2 j = 1 n [ E L ( y ) j 1 / 2 + E L ( y ) j + 1 / 2 ] .
E L ( y ) = E ( 0 , y ) = [ 1 ( y / m ) 2 ] 1 / 2 ,
E L ( y ) = E ( ¾ , y ) = [ 1 ( 3 / 16 + y 2 ) / m 2 ] 1 / 2 ,
E L ( y ) = E ( 3 / 2 , y ) = [ 1 ¾ + y 2 ) / m 2 ] 1 / 2 .
I = E F ( y ) + j = 1 n [ E F ( y ) j + E F ( y ) j ] ,
I = E F ( y ) + j = 1 n [ E F ( y ) j / 2 + E F ( y ) j / 2 ] ,
E F ( y ) = 1 ( y / m ) 2 .
E F ( y ) = 1 [ y / ( 2 m ) ] 2 ,
I = E F ( y ) + j = 1 n [ E F ( y ) j + E ( y ) j ] ,

Metrics