Abstract

The relationship between the characteristics of gradient-index rod lenses obtained by ion exchange and their mother glass compositions is studied. It is observed that Li2O content, R2O (Li2O + Na2O) content, and the Li2O/Na2O ratio are important factors in attaining a high acceptance angle and a small field curvature. Thus the gradient-index lens array is fabricated by the use of a newly developed glass composition and its optical performance; the modulation transfer function, luminous intensity, and chromatic aberration are precisely evaluated. The array is found to have a sufficiently high performance to be applicable for color use.

© 1994 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

1990 (1)

1985 (1)

1983 (1)

1982 (2)

1980 (5)

1971 (1)

H. Kita, I. Kitano, T. Uchida, M. Furukawa, “Light-focusing glass fibers and rods,” J. Am. Ceram. Soc. 54, 321–326 (1971).
[CrossRef]

1970 (1)

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A light-focusing fiber guide prepared by ion-exchange techniques,” Jpn. J. Appl. Phys. Suppl. 39, 63–70 (1970).

Fantone, S. D.

Furukawa, M.

H. Kita, I. Kitano, T. Uchida, M. Furukawa, “Light-focusing glass fibers and rods,” J. Am. Ceram. Soc. 54, 321–326 (1971).
[CrossRef]

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A light-focusing fiber guide prepared by ion-exchange techniques,” Jpn. J. Appl. Phys. Suppl. 39, 63–70 (1970).

Hatate, Y.

K. Komiya, M. Kanzaki, Y. Hatate, T. Yamashita, A4 Size Contact Type Image Sensor, IECE Tech. Rep. IE80-72 (The Institute of Electronics and Communication Engineers of Japan, Tokyo, 1980), pp. 73–82.

Haun, N.

Iga, K.

Ikeda, Y.

K. Tateishi, Y. Ikeda, S. Kotani, LED Printer, IECE Tech. Rep. IE80-71 (The Institute of Electronics and Communication Engineers of Japan, Tokyo, 1980), pp. 65–71.

Kanzaki, M.

K. Komiya, M. Kanzaki, Y. Hatate, T. Yamashita, A4 Size Contact Type Image Sensor, IECE Tech. Rep. IE80-72 (The Institute of Electronics and Communication Engineers of Japan, Tokyo, 1980), pp. 73–82.

Kawazu, M.

Kindred, D. S.

Kita, H.

H. Kita, I. Kitano, T. Uchida, M. Furukawa, “Light-focusing glass fibers and rods,” J. Am. Ceram. Soc. 54, 321–326 (1971).
[CrossRef]

Kitano, I.

H. Kita, I. Kitano, T. Uchida, M. Furukawa, “Light-focusing glass fibers and rods,” J. Am. Ceram. Soc. 54, 321–326 (1971).
[CrossRef]

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A light-focusing fiber guide prepared by ion-exchange techniques,” Jpn. J. Appl. Phys. Suppl. 39, 63–70 (1970).

Koizumi, K.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A light-focusing fiber guide prepared by ion-exchange techniques,” Jpn. J. Appl. Phys. Suppl. 39, 63–70 (1970).

Komiya, K.

K. Komiya, M. Kanzaki, Y. Hatate, T. Yamashita, A4 Size Contact Type Image Sensor, IECE Tech. Rep. IE80-72 (The Institute of Electronics and Communication Engineers of Japan, Tokyo, 1980), pp. 73–82.

Kotani, S.

K. Tateishi, Y. Ikeda, S. Kotani, LED Printer, IECE Tech. Rep. IE80-71 (The Institute of Electronics and Communication Engineers of Japan, Tokyo, 1980), pp. 65–71.

Lama, W.

Matsumura, H.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A light-focusing fiber guide prepared by ion-exchange techniques,” Jpn. J. Appl. Phys. Suppl. 39, 63–70 (1970).

Matsushita, K.

Moore, D. T.

Nishizawa, K.

Ogura, Y.

Rees, J. D.

Ryan-Howard, D. P.

Takami, M.

Tateishi, K.

K. Tateishi, Y. Ikeda, S. Kotani, LED Printer, IECE Tech. Rep. IE80-71 (The Institute of Electronics and Communication Engineers of Japan, Tokyo, 1980), pp. 65–71.

Toyama, M.

Uchida, T.

H. Kita, I. Kitano, T. Uchida, M. Furukawa, “Light-focusing glass fibers and rods,” J. Am. Ceram. Soc. 54, 321–326 (1971).
[CrossRef]

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A light-focusing fiber guide prepared by ion-exchange techniques,” Jpn. J. Appl. Phys. Suppl. 39, 63–70 (1970).

Yamamoto, N.

Yamashita, T.

K. Komiya, M. Kanzaki, Y. Hatate, T. Yamashita, A4 Size Contact Type Image Sensor, IECE Tech. Rep. IE80-72 (The Institute of Electronics and Communication Engineers of Japan, Tokyo, 1980), pp. 73–82.

Appl. Opt. (10)

J. Am. Ceram. Soc. (1)

H. Kita, I. Kitano, T. Uchida, M. Furukawa, “Light-focusing glass fibers and rods,” J. Am. Ceram. Soc. 54, 321–326 (1971).
[CrossRef]

Jpn. J. Appl. Phys. Suppl. (1)

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A light-focusing fiber guide prepared by ion-exchange techniques,” Jpn. J. Appl. Phys. Suppl. 39, 63–70 (1970).

Other (3)

K. Komiya, M. Kanzaki, Y. Hatate, T. Yamashita, A4 Size Contact Type Image Sensor, IECE Tech. Rep. IE80-72 (The Institute of Electronics and Communication Engineers of Japan, Tokyo, 1980), pp. 73–82.

K. Tateishi, Y. Ikeda, S. Kotani, LED Printer, IECE Tech. Rep. IE80-71 (The Institute of Electronics and Communication Engineers of Japan, Tokyo, 1980), pp. 65–71.

NSG Catalog, Vol. 4 of SLA Series (Nippon Sheet Glass Company, Tokyo, 1990), pp. 11–12.

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Figures (9)

Fig. 1
Fig. 1

Maximum acceptance angle (θmax) of the GRIN rod lens fabricated by an ion exchange with NaNO3 molten salt versus Li2O contents in their typical mother glasses.

Fig. 2
Fig. 2

Optical setup for measuring the periodic length and the field curvature of the GRIN rod lens. The extent of the field curvature is defined as the quantity of deviation (ΔF) of the image plane from the focal plane on the axis.14

Fig. 3
Fig. 3

Schematic illustration of experimental setup for measuring the luminous intensity and the modulation transfer function of the GRIN lens array. For the former measurement the Ronchi grating chart is removed from the setup, whereas for the latter measurement it is attached to the setup.

Fig. 4
Fig. 4

Maximum acceptance angles of the GRIN rod lenses as functions of R2O content in the SiO2−MgO−BaO−PbO−TiO2−Li2O−Na2O glasses. The Li2O content of the glasses is denoted beside each line. R2O represents an alkaline metal oxide such as Li2O or Na2O. In this figure, R2O means the total amount of alkaline metal oxide in the glass.

Fig. 5
Fig. 5

Maximum acceptance angles of the GRIN rod lenses as functions of the Li2O/N2O ratio in the SiO2−MgO−BaO−PbO−TiO2−Li2O−Na2O glasses.

Fig. 6
Fig. 6

Maximum acceptance angles θmax and grid pattern images of the GRIN rod lenses as a function of the Li2O/Na2O ratio in 56 SiO2−5.5 TiO2−(14 − x)MgO−2BaO−6PbO-11.5 Li2O−(5 + x)Na2O glass (in mole percent): a, x = 6.5; b, x = 4; c, x = 2; d, x = 0.

Fig. 7
Fig. 7

Diagram for combination of Li2O and Na2O in the glass. The darkest portion shows the preferred region, which has a higher θmax (> 14°) and a smaller field curvature (|ΔF| < 50 μm).

Fig. 8
Fig. 8

Luminous intensities of the GRIN lens arrays in which the intensity of the EX(Li) sample is set to 100.

Fig. 9
Fig. 9

MTF values of tho GRIN Ions arrays as functions of spatial frequency W lp/mm.

Tables (5)

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Table 1 Compositions of Typical Mother Glasses that Contain Li+ for the Ion Exchange with NaNO3 Molten Salt and the Resulting Maximum Acceptance Angles (θmax) of the GRIN Rod Lenses

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Table 2 Compositions of Mother Glasses Investigated in the Ion-Exchange Experiment with NaNO3 Molten Salt and the Resulting Optical Properties, θmax and ΔF, of the GRIN Rod Lenses

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Table 3 Parameters or Dimensions for GRIN Lens Arrays at the 570-nm Wavelengtha

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Table 4 F-Numbers and Brightness Ratios of the GRIN Lens Arrays

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Table 5 Periodic Lengths P at Different Wavelengths and Chromatic Aberrations ΔP/P of the GRIN Lens Arraysa

Equations (12)

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n ( r ) = n 0 ( 1 A 2 r 2 ) ,
P = ( 2 π ) / A ,
θ max = sin 1 ( n 0 A r 0 ) = sin 1 ( n 0 2 π P r 0 ) = ( 2 n 0 Δ n ) 1 / 2 ,
Δ P / P = P ( C ) P ( F ) P ( D ) ,
TC = Z 0 + 2 l 0 = Z 0 2 n 0 A tan ( Z 0 p P ) ,
l 0 = 1 n 0 A tan ( Z 0 p P ) .
m = X 0 2 r 0 ,
X 0 = r 0 sec ( Z 0 π P ) .
F = { m 2 π [ 2 ( 3 / 8 ) m 2 ] } 1 / 2 θ .
MTF ( W ) = i ( W ) max i ( W ) min i ( W ) max + i ( W ) min 100 ( % ) ,
brightness ratio = [ F - number of EX ( Li ) ] 2 [ F - number of NEW or EX ( Tl ) ] 2 .
A ( m m 1 )

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